%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW383+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n017.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 12:26:05 EDT 2023

% Result   : Theorem 1.69s 2.48s
% Output   : Proof 1.69s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW383+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 21:44:00 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 1.69/2.48  
% 1.69/2.48  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 1.69/2.48  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.69/2.48  %-----------------------------------------------------
% 1.69/2.48  ncf(matrix, plain, [(51848 ^ _782652) ^ [] : [hBOOL(hAPP(c_Com_OWT, v_y))], (2 ^ _782652) ^ [_782682] : [-(_782682 = _782682)], (4 ^ _782652) ^ [_782705, _782707] : [_782707 = _782705, -(_782705 = _782707)], (10 ^ _782652) ^ [_782778, _782780, _782782] : [-(_782782 = _782778), _782782 = _782780, _782780 = _782778], (20 ^ _782652) ^ [_782915, _782917, _782919, _782921, _782923, _782925, _782927, _782929, _782931, _782933, _782935, _782937] : [-(c_Finite__Set_Ofolding__image__simple__idem(_782935, _782931, _782927, _782923, _782919, _782915)), c_Finite__Set_Ofolding__image__simple__idem(_782937, _782933, _782929, _782925, _782921, _782917), _782937 = _782935, _782933 = _782931, _782929 = _782927, _782925 = _782923, _782921 = _782919, _782917 = _782915], (50 ^ _782652) ^ [_783460, _783462, _783464, _783466, _783468, _783470, _783472, _783474, _783476, _783478, _783480, _783482] : [-(c_Nitpick_Ofold__graph_H(_783480, _783476, _783472, _783468, _783464, _783460)), c_Nitpick_Ofold__graph_H(_783482, _783478, _783474, _783470, _783466, _783462), _783482 = _783480, _783478 = _783476, _783474 = _783472, _783470 = _783468, _783466 = _783464, _783462 = _783460], (80 ^ _782652) ^ [_784005, _784007, _784009, _784011] : [-(c_Option_Ois__none(_784009, _784005)), c_Option_Ois__none(_784011, _784007), _784011 = _784009, _784007 = _784005], (94 ^ _782652) ^ [_784198, _784200, _784202, _784204, _784206, _784208, _784210, _784212, _784214, _784216, _784218, _784220] : [-(c_Finite__Set_Ofolding__image__simple(_784218, _784214, _784210, _784206, _784202, _784198)), c_Finite__Set_Ofolding__image__simple(_784220, _784216, _784212, _784208, _784204, _784200), _784220 = _784218, _784216 = _784214, _784212 = _784210, _784208 = _784206, _784204 = _784202, _784200 = _784198], (124 ^ _782652) ^ [_784743, _784745, _784747, _784749, _784751, _784753, _784755, _784757, _784759, _784761] : [-(c_Big__Operators_Ocomm__monoid__big(_784759, _784755, _784751, _784747, _784743)), c_Big__Operators_Ocomm__monoid__big(_784761, _784757, _784753, _784749, _784745), _784761 = _784759, _784757 = _784755, _784753 = _784751, _784749 = _784747, _784745 = _784743], (150 ^ _782652) ^ [_785188, _785190, _785192, _785194, _785196, _785198] : [-(c_Big__Operators_Osemilattice__big(_785196, _785192, _785188)), c_Big__Operators_Osemilattice__big(_785198, _785194, _785190), _785198 = _785196, _785194 = _785192, _785190 = _785188], (168 ^ _782652) ^ [_785457, _785459] : [-(class_Rings_Odivision__ring__inverse__zero(_785457)), _785459 = _785457, class_Rings_Odivision__ring__inverse__zero(_785459)], (178 ^ _782652) ^ [_785582, _785584] : [-(class_Rings_Odivision__ring(_785582)), _785584 = _785582, class_Rings_Odivision__ring(_785584)], (188 ^ _782652) ^ [_785707, _785709] : [-(class_Fields_Olinordered__field(_785707)), _785709 = _785707, class_Fields_Olinordered__field(_785709)], (198 ^ _782652) ^ [_785832, _785834] : [-(class_Fields_Ofield(_785832)), _785834 = _785832, class_Fields_Ofield(_785834)], (208 ^ _782652) ^ [_785957, _785959] : [-(c_Nat__Transfer_Ois__nat(_785957)), _785959 = _785957, c_Nat__Transfer_Ois__nat(_785959)], (218 ^ _782652) ^ [_786082, _786084] : [-(class_Fields_Olinordered__field__inverse__zero(_786082)), _786084 = _786082, class_Fields_Olinordered__field__inverse__zero(_786084)], (228 ^ _782652) ^ [_786207, _786209, _786211, _786213] : [-(c_Int_Oiszero(_786211, _786207)), c_Int_Oiszero(_786213, _786209), _786213 = _786211, _786209 = _786207], (242 ^ _782652) ^ [_786400, _786402] : [-(class_Fields_Ofield__inverse__zero(_786400)), _786402 = _786400, class_Fields_Ofield__inverse__zero(_786402)], (252 ^ _782652) ^ [_786525, _786527, _786529, _786531, _786533, _786535, _786537, _786539, _786541, _786543, _786545, _786547] : [-(c_Equiv__Relations_Ocongruent2(_786545, _786541, _786537, _786533, _786529, _786525)), c_Equiv__Relations_Ocongruent2(_786547, _786543, _786539, _786535, _786531, _786527), _786547 = _786545, _786543 = _786541, _786539 = _786537, _786535 = _786533, _786531 = _786529, _786527 = _786525], (282 ^ _782652) ^ [_787070, _787072, _787074, _787076] : [-(c_Nitpick_Orefl_H(_787074, _787070)), c_Nitpick_Orefl_H(_787076, _787072), _787076 = _787074, _787072 = _787070], (296 ^ _782652) ^ [_787263, _787265, _787267, _787269] : [-(c_Equiv__Relations_Oequivp(_787267, _787263)), c_Equiv__Relations_Oequivp(_787269, _787265), _787269 = _787267, _787265 = _787263], (310 ^ _782652) ^ [_787456, _787458, _787460, _787462, _787464, _787466, _787468, _787470] : [-(c_Wellfounded_Omax__extp(_787468, _787464, _787460, _787456)), c_Wellfounded_Omax__extp(_787470, _787466, _787462, _787458), _787470 = _787468, _787466 = _787464, _787462 = _787460, _787458 = _787456], (332 ^ _782652) ^ [_787809, _787811, _787813, _787815] : [-(c_FunDef_Oreduction__pair(_787813, _787809)), c_FunDef_Oreduction__pair(_787815, _787811), _787815 = _787813, _787811 = _787809], (346 ^ _782652) ^ [_788002, _788004, _788006, _788008] : [-(c_Predicate_Oreflp(_788006, _788002)), c_Predicate_Oreflp(_788008, _788004), _788008 = _788006, _788004 = _788002], (360 ^ _782652) ^ [_788195, _788197, _788199, _788201] : [-(c_Nitpick_Owf_H(_788199, _788195)), c_Nitpick_Owf_H(_788201, _788197), _788201 = _788199, _788197 = _788195], (374 ^ _782652) ^ [_788388, _788390] : [-(c_Nitpick_Ounknown(_788388)), _788390 = _788388, c_Nitpick_Ounknown(_788390)], (384 ^ _782652) ^ [_788513, _788515, _788517, _788519, _788521, _788523, _788525, _788527] : [-(c_Equiv__Relations_Ocongruent(_788525, _788521, _788517, _788513)), c_Equiv__Relations_Ocongruent(_788527, _788523, _788519, _788515), _788527 = _788525, _788523 = _788521, _788519 = _788517, _788515 = _788513], (406 ^ _782652) ^ [_788866, _788868, _788870, _788872] : [-(c_Wellfounded_OwfP(_788870, _788866)), c_Wellfounded_OwfP(_788872, _788868), _788872 = _788870, _788868 = _788866], (420 ^ _782652) ^ [_789059, _789061, _789063, _789065, _789067, _789069] : [-(c_Hoare__Mirabelle_Otriple__valid(_789067, _789063, _789059)), c_Hoare__Mirabelle_Otriple__valid(_789069, _789065, _789061), _789069 = _789067, _789065 = _789063, _789061 = _789059], (438 ^ _782652) ^ [_789328, _789330, _789332, _789334, _789336, _789338] : [-(c_Hoare__Mirabelle_Ohoare__valids(_789336, _789332, _789328)), c_Hoare__Mirabelle_Ohoare__valids(_789338, _789334, _789330), _789338 = _789336, _789334 = _789332, _789330 = _789328], (456 ^ _782652) ^ [_789597, _789599, _789601, _789603, _789605, _789607, _789609, _789611, _789613, _789615] : [-(c_Finite__Set_Ofolding__image(_789613, _789609, _789605, _789601, _789597)), c_Finite__Set_Ofolding__image(_789615, _789611, _789607, _789603, _789599), _789615 = _789613, _789611 = _789609, _789607 = _789605, _789603 = _789601, _789599 = _789597], (482 ^ _782652) ^ [_790042, _790044, _790046, _790048, _790050, _790052, _790054, _790056] : [-(c_Finite__Set_Ofolding__idem(_790054, _790050, _790046, _790042)), c_Finite__Set_Ofolding__idem(_790056, _790052, _790048, _790044), _790056 = _790054, _790052 = _790050, _790048 = _790046, _790044 = _790042], (504 ^ _782652) ^ [_790395, _790397, _790399, _790401] : [-(c_Relation_Oirrefl(_790399, _790395)), c_Relation_Oirrefl(_790401, _790397), _790401 = _790399, _790397 = _790395], (518 ^ _782652) ^ [_790588, _790590, _790592, _790594, _790596, _790598] : [-(c_Relation_Ototal__on(_790596, _790592, _790588)), c_Relation_Ototal__on(_790598, _790594, _790590), _790598 = _790596, _790594 = _790592, _790590 = _790588], (536 ^ _782652) ^ [_790857, _790859, _790861, _790863, _790865, _790867, _790869, _790871] : [-(c_Finite__Set_Ofolding(_790869, _790865, _790861, _790857)), c_Finite__Set_Ofolding(_790871, _790867, _790863, _790859), _790871 = _790869, _790867 = _790865, _790863 = _790861, _790859 = _790857], (558 ^ _782652) ^ [_791210, _791212, _791214, _791216, _791218, _791220] : [-(c_Finite__Set_Ofolding__one__idem(_791218, _791214, _791210)), c_Finite__Set_Ofolding__one__idem(_791220, _791216, _791212), _791220 = _791218, _791216 = _791214, _791212 = _791210], (576 ^ _782652) ^ [_791479, _791481, _791483, _791485, _791487, _791489] : [-(c_Finite__Set_Ofolding__one(_791487, _791483, _791479)), c_Finite__Set_Ofolding__one(_791489, _791485, _791481), _791489 = _791487, _791485 = _791483, _791481 = _791479], (594 ^ _782652) ^ [_791748, _791750, _791752, _791754, _791756, _791758] : [-(c_Relation_Osingle__valued(_791756, _791752, _791748)), c_Relation_Osingle__valued(_791758, _791754, _791750), _791758 = _791756, _791754 = _791752, _791750 = _791748], (612 ^ _782652) ^ [_792017, _792019] : [-(class_Rings_Oinverse(_792017)), _792019 = _792017, class_Rings_Oinverse(_792019)], (622 ^ _782652) ^ [_792142, _792144, _792146, _792148, _792150, _792152] : [-(c_Nitpick_Oless__frac(_792150, _792146, _792142)), c_Nitpick_Oless__frac(_792152, _792148, _792144), _792152 = _792150, _792148 = _792146, _792144 = _792142], (640 ^ _782652) ^ [_792411, _792413, _792415, _792417, _792419, _792421] : [-(c_Nitpick_Oless__eq__frac(_792419, _792415, _792411)), c_Nitpick_Oless__eq__frac(_792421, _792417, _792413), _792421 = _792419, _792417 = _792415, _792413 = _792411], (658 ^ _782652) ^ [_792680, _792682] : [-(c_Nat__Transfer_Onat__set(_792680)), _792682 = _792680, c_Nat__Transfer_Onat__set(_792682)], (668 ^ _782652) ^ [_792805, _792807, _792809, _792811, _792813, _792815, _792817, _792819, _792821, _792823] : [-(c_Typedef_Otype__definition(_792821, _792817, _792813, _792809, _792805)), c_Typedef_Otype__definition(_792823, _792819, _792815, _792811, _792807), _792823 = _792821, _792819 = _792817, _792815 = _792813, _792811 = _792809, _792807 = _792805], (694 ^ _782652) ^ [_793250, _793252, _793254, _793256, _793258, _793260, _793262, _793264] : [-(c_List_Olistrelp(_793262, _793258, _793254, _793250)), c_List_Olistrelp(_793264, _793260, _793256, _793252), _793264 = _793262, _793260 = _793258, _793256 = _793254, _793252 = _793250], (716 ^ _782652) ^ [_793603, _793605] : [-(class_Lattices_Oab__semigroup__idem__mult(_793603)), _793605 = _793603, class_Lattices_Oab__semigroup__idem__mult(_793605)], (726 ^ _782652) ^ [_793728, _793730, _793732, _793734, _793736, _793738] : [-(c_Finite__Set_Ofun__left__comm__idem(_793736, _793732, _793728)), c_Finite__Set_Ofun__left__comm__idem(_793738, _793734, _793730), _793738 = _793736, _793734 = _793732, _793730 = _793728], (744 ^ _782652) ^ [_793997, _793999, _794001, _794003, _794005, _794007] : [-(c_Equiv__Relations_Oequiv(_794005, _794001, _793997)), c_Equiv__Relations_Oequiv(_794007, _794003, _793999), _794007 = _794005, _794003 = _794001, _793999 = _793997], (762 ^ _782652) ^ [_794266, _794268, _794270, _794272, _794274, _794276] : [-(c_Relation_Orefl__on(_794274, _794270, _794266)), c_Relation_Orefl__on(_794276, _794272, _794268), _794276 = _794274, _794272 = _794270, _794268 = _794266], (780 ^ _782652) ^ [_794535, _794537] : [-(c_List_Onat__list(_794535)), _794537 = _794535, c_List_Onat__list(_794537)], (790 ^ _782652) ^ [_794660, _794662, _794664, _794666, _794668, _794670] : [-(c_Finite__Set_Ofun__left__comm(_794668, _794664, _794660)), c_Finite__Set_Ofun__left__comm(_794670, _794666, _794662), _794670 = _794668, _794666 = _794664, _794662 = _794660], (808 ^ _782652) ^ [_794929, _794931, _794933, _794935, _794937, _794939] : [-(c_Enum_Oall__n__lists(_794937, _794933, _794929)), c_Enum_Oall__n__lists(_794939, _794935, _794931), _794939 = _794937, _794935 = _794933, _794931 = _794929], (826 ^ _782652) ^ [_795198, _795200, _795202, _795204, _795206, _795208] : [-(c_Enum_Oex__n__lists(_795206, _795202, _795198)), c_Enum_Oex__n__lists(_795208, _795204, _795200), _795208 = _795206, _795204 = _795202, _795200 = _795198], (844 ^ _782652) ^ [_795467, _795469, _795471, _795473, _795475, _795477, _795479, _795481] : [-(c_Fun_Oinj__on(_795479, _795475, _795471, _795467)), c_Fun_Oinj__on(_795481, _795477, _795473, _795469), _795481 = _795479, _795477 = _795475, _795473 = _795471, _795469 = _795467], (866 ^ _782652) ^ [_795820, _795822, _795824, _795826] : [-(c_Wellfounded_Owf(_795824, _795820)), c_Wellfounded_Owf(_795826, _795822), _795826 = _795824, _795822 = _795820], (880 ^ _782652) ^ [_796013, _796015, _796017, _796019, _796021, _796023, _796025, _796027, _796029, _796031] : [-(c_List_Olist__all2(_796029, _796025, _796021, _796017, _796013)), c_List_Olist__all2(_796031, _796027, _796023, _796019, _796015), _796031 = _796029, _796027 = _796025, _796023 = _796021, _796019 = _796017, _796015 = _796013], (906 ^ _782652) ^ [_796458, _796460, _796462, _796464] : [-(c_List_Olinorder__class_Osorted(_796462, _796458)), c_List_Olinorder__class_Osorted(_796464, _796460), _796464 = _796462, _796460 = _796458], (920 ^ _782652) ^ [_796651, _796653, _796655, _796657, _796659, _796661] : [-(c_List_Olist__ex(_796659, _796655, _796651)), c_List_Olist__ex(_796661, _796657, _796653), _796661 = _796659, _796657 = _796655, _796653 = _796651], (938 ^ _782652) ^ [_796920, _796922, _796924, _796926, _796928, _796930] : [-(c_List_Olist__all(_796928, _796924, _796920)), c_List_Olist__all(_796930, _796926, _796922), _796930 = _796928, _796926 = _796924, _796922 = _796920], (956 ^ _782652) ^ [_797189, _797191, _797193, _797195, _797197, _797199] : [-(c_List_Olist__ex1(_797197, _797193, _797189)), c_List_Olist__ex1(_797199, _797195, _797191), _797199 = _797197, _797195 = _797193, _797191 = _797189], (974 ^ _782652) ^ [_797458, _797460, _797462, _797464] : [-(c_FunDef_Ois__measure(_797462, _797458)), c_FunDef_Ois__measure(_797464, _797460), _797464 = _797462, _797460 = _797458], (988 ^ _782652) ^ [_797651, _797653, _797655, _797657, _797659, _797661, _797663, _797665] : [-(c_Nat__Transfer_Otransfer__morphism(_797663, _797659, _797655, _797651)), c_Nat__Transfer_Otransfer__morphism(_797665, _797661, _797657, _797653), _797665 = _797663, _797661 = _797659, _797657 = _797655, _797653 = _797651], (1010 ^ _782652) ^ [_798004, _798006, _798008, _798010] : [-(c_Wellfounded_Oacyclic(_798008, _798004)), c_Wellfounded_Oacyclic(_798010, _798006), _798010 = _798008, _798006 = _798004], (1024 ^ _782652) ^ [_798197, _798199] : [-(class_Lattices_Obounded__lattice(_798197)), _798199 = _798197, class_Lattices_Obounded__lattice(_798199)], (1034 ^ _782652) ^ [_798322, _798324] : [-(class_Rings_Olinordered__semiring__1__strict(_798322)), _798324 = _798322, class_Rings_Olinordered__semiring__1__strict(_798324)], (1044 ^ _782652) ^ [_798447, _798449] : [-(class_Groups_Oordered__ab__group__add__abs(_798447)), _798449 = _798447, class_Groups_Oordered__ab__group__add__abs(_798449)], (1054 ^ _782652) ^ [_798572, _798574] : [-(class_Groups_Olinordered__ab__group__add(_798572)), _798574 = _798572, class_Groups_Olinordered__ab__group__add(_798574)], (1064 ^ _782652) ^ [_798697, _798699] : [-(class_Rings_Oring__1__no__zero__divisors(_798697)), _798699 = _798697, class_Rings_Oring__1__no__zero__divisors(_798699)], (1074 ^ _782652) ^ [_798822, _798824] : [-(class_Rings_Olinordered__ring__strict(_798822)), _798824 = _798822, class_Rings_Olinordered__ring__strict(_798824)], (1084 ^ _782652) ^ [_798947, _798949] : [-(class_Rings_Oring__no__zero__divisors(_798947)), _798949 = _798947, class_Rings_Oring__no__zero__divisors(_798949)], (1094 ^ _782652) ^ [_799072, _799074] : [-(class_Rings_Olinordered__semiring__1(_799072)), _799074 = _799072, class_Rings_Olinordered__semiring__1(_799074)], (1104 ^ _782652) ^ [_799197, _799199] : [-(class_Groups_Oordered__ab__group__add(_799197)), _799199 = _799197, class_Groups_Oordered__ab__group__add(_799199)], (1114 ^ _782652) ^ [_799322, _799324] : [-(class_Rings_Oordered__ring__abs(_799322)), _799324 = _799322, class_Rings_Oordered__ring__abs(_799324)], (1124 ^ _782652) ^ [_799447, _799449] : [-(class_Rings_Olinordered__ring(_799447)), _799449 = _799447, class_Rings_Olinordered__ring(_799449)], (1134 ^ _782652) ^ [_799572, _799574] : [-(class_Rings_Olinordered__idom(_799572)), _799574 = _799572, class_Rings_Olinordered__idom(_799574)], (1144 ^ _782652) ^ [_799697, _799699] : [-(class_Groups_Oab__group__add(_799697)), _799699 = _799697, class_Groups_Oab__group__add(_799699)], (1154 ^ _782652) ^ [_799822, _799824] : [-(class_Rings_Oordered__ring(_799822)), _799824 = _799822, class_Rings_Oordered__ring(_799824)], (1164 ^ _782652) ^ [_799947, _799949] : [-(class_Rings_Ocomm__ring__1(_799947)), _799949 = _799947, class_Rings_Ocomm__ring__1(_799949)], (1174 ^ _782652) ^ [_800072, _800074] : [-(class_Groups_Ogroup__add(_800072)), _800074 = _800072, class_Groups_Ogroup__add(_800074)], (1184 ^ _782652) ^ [_800197, _800199] : [-(class_Divides_Oring__div(_800197)), _800199 = _800197, class_Divides_Oring__div(_800199)], (1194 ^ _782652) ^ [_800322, _800324] : [-(class_Int_Oring__char__0(_800322)), _800324 = _800322, class_Int_Oring__char__0(_800324)], (1204 ^ _782652) ^ [_800447, _800449] : [-(class_Int_Onumber__ring(_800447)), _800449 = _800447, class_Int_Onumber__ring(_800449)], (1214 ^ _782652) ^ [_800572, _800574] : [-(class_Groups_Osgn__if(_800572)), _800574 = _800572, class_Groups_Osgn__if(_800574)], (1224 ^ _782652) ^ [_800697, _800699] : [-(class_Groups_Oabs__if(_800697)), _800699 = _800697, class_Groups_Oabs__if(_800699)], (1234 ^ _782652) ^ [_800822, _800824] : [-(class_Rings_Oring__1(_800822)), _800824 = _800822, class_Rings_Oring__1(_800824)], (1244 ^ _782652) ^ [_800947, _800949] : [-(class_Rings_Oring(_800947)), _800949 = _800947, class_Rings_Oring(_800949)], (1254 ^ _782652) ^ [_801072, _801074] : [-(class_Rings_Oidom(_801072)), _801074 = _801072, class_Rings_Oidom(_801074)], (1264 ^ _782652) ^ [_801197, _801199] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_801197)), _801199 = _801197, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_801199)], (1274 ^ _782652) ^ [_801322, _801324] : [-(class_Orderings_Owellorder(_801322)), _801324 = _801322, class_Orderings_Owellorder(_801324)], (1284 ^ _782652) ^ [_801447, _801449] : [-(class_Complete__Lattice_Ocomplete__lattice(_801447)), _801449 = _801447, class_Complete__Lattice_Ocomplete__lattice(_801449)], (1294 ^ _782652) ^ [_801572, _801574] : [-(class_Lattices_Obounded__lattice__top(_801572)), _801574 = _801572, class_Lattices_Obounded__lattice__top(_801574)], (1304 ^ _782652) ^ [_801697, _801699] : [-(class_Lattices_Obounded__lattice__bot(_801697)), _801699 = _801697, class_Lattices_Obounded__lattice__bot(_801699)], (1314 ^ _782652) ^ [_801822, _801824] : [-(class_Lattices_Osemilattice__sup(_801822)), _801824 = _801822, class_Lattices_Osemilattice__sup(_801824)], (1324 ^ _782652) ^ [_801947, _801949] : [-(class_Lattices_Osemilattice__inf(_801947)), _801949 = _801947, class_Lattices_Osemilattice__inf(_801949)], (1334 ^ _782652) ^ [_802072, _802074] : [-(class_Lattices_Odistrib__lattice(_802072)), _802074 = _802072, class_Lattices_Odistrib__lattice(_802074)], (1344 ^ _782652) ^ [_802197, _802199] : [-(class_Lattices_Oboolean__algebra(_802197)), _802199 = _802197, class_Lattices_Oboolean__algebra(_802199)], (1354 ^ _782652) ^ [_802322, _802324] : [-(class_Lattices_Olattice(_802322)), _802324 = _802322, class_Lattices_Olattice(_802324)], (1364 ^ _782652) ^ [_802447, _802449] : [-(class_Orderings_Otop(_802447)), _802449 = _802447, class_Orderings_Otop(_802449)], (1374 ^ _782652) ^ [_802572, _802574] : [-(class_Orderings_Obot(_802572)), _802574 = _802572, class_Orderings_Obot(_802574)], (1384 ^ _782652) ^ [_802697, _802699] : [-(class_Groups_Ouminus(_802697)), _802699 = _802697, class_Groups_Ouminus(_802699)], (1394 ^ _782652) ^ [_802822, _802824] : [-(class_Lazy__Sequence_Osmall__lazy(_802822)), _802824 = _802822, class_Lazy__Sequence_Osmall__lazy(_802824)], (1404 ^ _782652) ^ [_802947, _802949] : [-(class_Finite__Set_Ofinite(_802947)), _802949 = _802947, class_Finite__Set_Ofinite(_802949)], (1414 ^ _782652) ^ [_803072, _803074] : [-(class_Smallcheck_Osmall(_803072)), _803074 = _803072, class_Smallcheck_Osmall(_803074)], (1424 ^ _782652) ^ [_803197, _803199] : [-(class_Enum_Oenum(_803197)), _803199 = _803197, class_Enum_Oenum(_803199)], (1434 ^ _782652) ^ [_803322, _803324] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_803322)), _803324 = _803322, class_Groups_Oordered__cancel__ab__semigroup__add(_803324)], (1444 ^ _782652) ^ [_803447, _803449] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_803447)), _803449 = _803447, class_Groups_Oordered__ab__semigroup__add__imp__le(_803449)], (1454 ^ _782652) ^ [_803572, _803574] : [-(class_Rings_Olinordered__comm__semiring__strict(_803572)), _803574 = _803572, class_Rings_Olinordered__comm__semiring__strict(_803574)], (1464 ^ _782652) ^ [_803697, _803699] : [-(class_Groups_Olinordered__ab__semigroup__add(_803697)), _803699 = _803697, class_Groups_Olinordered__ab__semigroup__add(_803699)], (1474 ^ _782652) ^ [_803822, _803824] : [-(class_Rings_Olinordered__semiring__strict(_803822)), _803824 = _803822, class_Rings_Olinordered__semiring__strict(_803824)], (1484 ^ _782652) ^ [_803947, _803949] : [-(class_Groups_Oordered__ab__semigroup__add(_803947)), _803949 = _803947, class_Groups_Oordered__ab__semigroup__add(_803949)], (1494 ^ _782652) ^ [_804072, _804074] : [-(class_Groups_Oordered__comm__monoid__add(_804072)), _804074 = _804072, class_Groups_Oordered__comm__monoid__add(_804074)], (1504 ^ _782652) ^ [_804197, _804199] : [-(class_Groups_Ocancel__ab__semigroup__add(_804197)), _804199 = _804197, class_Groups_Ocancel__ab__semigroup__add(_804199)], (1514 ^ _782652) ^ [_804322, _804324] : [-(class_Rings_Oordered__cancel__semiring(_804322)), _804324 = _804322, class_Rings_Oordered__cancel__semiring(_804324)], (1524 ^ _782652) ^ [_804447, _804449] : [-(class_Rings_Oordered__comm__semiring(_804447)), _804449 = _804447, class_Rings_Oordered__comm__semiring(_804449)], (1534 ^ _782652) ^ [_804572, _804574] : [-(class_Groups_Ocancel__semigroup__add(_804572)), _804574 = _804572, class_Groups_Ocancel__semigroup__add(_804574)], (1544 ^ _782652) ^ [_804697, _804699] : [-(class_Rings_Olinordered__semiring(_804697)), _804699 = _804697, class_Rings_Olinordered__semiring(_804699)], (1554 ^ _782652) ^ [_804822, _804824] : [-(class_Rings_Olinordered__semidom(_804822)), _804824 = _804822, class_Rings_Olinordered__semidom(_804824)], (1564 ^ _782652) ^ [_804947, _804949] : [-(class_Groups_Oab__semigroup__mult(_804947)), _804949 = _804947, class_Groups_Oab__semigroup__mult(_804949)], (1574 ^ _782652) ^ [_805072, _805074] : [-(class_Groups_Ocomm__monoid__mult(_805072)), _805074 = _805072, class_Groups_Ocomm__monoid__mult(_805074)], (1584 ^ _782652) ^ [_805197, _805199] : [-(class_Groups_Oab__semigroup__add(_805197)), _805199 = _805197, class_Groups_Oab__semigroup__add(_805199)], (1594 ^ _782652) ^ [_805322, _805324] : [-(class_Rings_Oordered__semiring(_805322)), _805324 = _805322, class_Rings_Oordered__semiring(_805324)], (1604 ^ _782652) ^ [_805447, _805449] : [-(class_Rings_Ono__zero__divisors(_805447)), _805449 = _805447, class_Rings_Ono__zero__divisors(_805449)], (1614 ^ _782652) ^ [_805572, _805574] : [-(class_Groups_Ocomm__monoid__add(_805572)), _805574 = _805572, class_Groups_Ocomm__monoid__add(_805574)], (1624 ^ _782652) ^ [_805697, _805699] : [-(class_Rings_Ocomm__semiring__1(_805697)), _805699 = _805697, class_Rings_Ocomm__semiring__1(_805699)], (1634 ^ _782652) ^ [_805822, _805824] : [-(class_Groups_Osemigroup__add(_805822)), _805824 = _805822, class_Groups_Osemigroup__add(_805824)], (1644 ^ _782652) ^ [_805947, _805949] : [-(class_Divides_Osemiring__div(_805947)), _805949 = _805947, class_Divides_Osemiring__div(_805949)], (1654 ^ _782652) ^ [_806072, _806074] : [-(class_Rings_Ocomm__semiring(_806072)), _806074 = _806072, class_Rings_Ocomm__semiring(_806074)], (1664 ^ _782652) ^ [_806197, _806199] : [-(class_Nat_Osemiring__char__0(_806197)), _806199 = _806197, class_Nat_Osemiring__char__0(_806199)], (1674 ^ _782652) ^ [_806322, _806324] : [-(class_Rings_Ozero__neq__one(_806322)), _806324 = _806322, class_Rings_Ozero__neq__one(_806324)], (1684 ^ _782652) ^ [_806447, _806449] : [-(class_Orderings_Opreorder(_806447)), _806449 = _806447, class_Orderings_Opreorder(_806449)], (1694 ^ _782652) ^ [_806572, _806574] : [-(class_Orderings_Olinorder(_806572)), _806574 = _806572, class_Orderings_Olinorder(_806574)], (1704 ^ _782652) ^ [_806697, _806699] : [-(class_Groups_Omonoid__mult(_806697)), _806699 = _806697, class_Groups_Omonoid__mult(_806699)], (1714 ^ _782652) ^ [_806822, _806824] : [-(class_Groups_Omonoid__add(_806822)), _806824 = _806822, class_Groups_Omonoid__add(_806824)], (1724 ^ _782652) ^ [_806947, _806949] : [-(class_Rings_Osemiring__1(_806947)), _806949 = _806947, class_Rings_Osemiring__1(_806949)], (1734 ^ _782652) ^ [_807072, _807074] : [-(class_Rings_Osemiring__0(_807072)), _807074 = _807072, class_Rings_Osemiring__0(_807074)], (1744 ^ _782652) ^ [_807197, _807199] : [-(class_Rings_Omult__zero(_807197)), _807199 = _807197, class_Rings_Omult__zero(_807199)], (1754 ^ _782652) ^ [_807322, _807324] : [-(class_Orderings_Oorder(_807322)), _807324 = _807322, class_Orderings_Oorder(_807324)], (1764 ^ _782652) ^ [_807447, _807449] : [-(class_Rings_Osemiring(_807447)), _807449 = _807447, class_Rings_Osemiring(_807449)], (1774 ^ _782652) ^ [_807572, _807574] : [-(class_Orderings_Oord(_807572)), _807574 = _807572, class_Orderings_Oord(_807574)], (1784 ^ _782652) ^ [_807697, _807699] : [-(class_Groups_Ominus(_807697)), _807699 = _807697, class_Groups_Ominus(_807699)], (1794 ^ _782652) ^ [_807822, _807824] : [-(class_Power_Opower(_807822)), _807824 = _807822, class_Power_Opower(_807824)], (1804 ^ _782652) ^ [_807947, _807949] : [-(class_Groups_Ozero(_807947)), _807949 = _807947, class_Groups_Ozero(_807949)], (1814 ^ _782652) ^ [_808072, _808074] : [-(class_Int_Onumber(_808072)), _808074 = _808072, class_Int_Onumber(_808074)], (1824 ^ _782652) ^ [_808197, _808199] : [-(class_Groups_Oone(_808197)), _808199 = _808197, class_Groups_Oone(_808199)], (1834 ^ _782652) ^ [_808322, _808324] : [-(class_HOL_Oequal(_808322)), _808324 = _808322, class_HOL_Oequal(_808324)], (1844 ^ _782652) ^ [_808447, _808449] : [-(class_Nat_Osize(_808447)), _808449 = _808447, class_Nat_Osize(_808449)], (1872 ^ _782652) ^ [_808837, _808839] : [-(hBOOL(_808837)), _808839 = _808837, hBOOL(_808839)], (1854 ^ _782652) ^ [_808572, _808574, _808576, _808578, _808580, _808582] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_808580, _808576, _808572)), c_Hoare__Mirabelle_Ohoare__derivs(_808582, _808578, _808574), _808582 = _808580, _808578 = _808576, _808574 = _808572], (1882 ^ _782652) ^ [_809711, _809713, _809715, _809717, _809719, _809721, _809723, _809725] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_809725, _809721, _809717, _809713) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_809723, _809719, _809715, _809711)), _809725 = _809723, _809721 = _809719, _809717 = _809715, _809713 = _809711], (1900 ^ _782652) ^ [_810012, _810014, _810016, _810018, _810020, _810022] : [-(c_Partial__Function_Oflat__lub(_810022, _810018, _810014) = c_Partial__Function_Oflat__lub(_810020, _810016, _810012)), _810022 = _810020, _810018 = _810016, _810014 = _810012], (1914 ^ _782652) ^ [_810233, _810235, _810237, _810239, _810241, _810243, _810245, _810247, _810249, _810251] : [-(c_Fun_Ooverride__on(_810251, _810247, _810243, _810239, _810235) = c_Fun_Ooverride__on(_810249, _810245, _810241, _810237, _810233)), _810251 = _810249, _810247 = _810245, _810243 = _810241, _810239 = _810237, _810235 = _810233], (1936 ^ _782652) ^ [_810622, _810624, _810626, _810628, _810630, _810632, _810634, _810636, _810638, _810640] : [-(c_Option_Ooption_Ooption__rec(_810640, _810636, _810632, _810628, _810624) = c_Option_Ooption_Ooption__rec(_810638, _810634, _810630, _810626, _810622)), _810640 = _810638, _810636 = _810634, _810632 = _810630, _810628 = _810626, _810624 = _810622], (1958 ^ _782652) ^ [_811011, _811013, _811015, _811017] : [-(c_Option_Oset(_811017, _811013) = c_Option_Oset(_811015, _811011)), _811017 = _811015, _811013 = _811011], (1968 ^ _782652) ^ [_811160, _811162, _811164, _811166, _811168, _811170, _811172, _811174, _811176, _811178] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_811178, _811174, _811170, _811166, _811162) = c_SetInterval_Oord_OgreaterThanAtMost(_811176, _811172, _811168, _811164, _811160)), _811178 = _811176, _811174 = _811172, _811170 = _811168, _811166 = _811164, _811162 = _811160], (1990 ^ _782652) ^ [_811549, _811551, _811553, _811555, _811557, _811559, _811561, _811563, _811565, _811567] : [-(c_SetInterval_Oord_OatLeastLessThan(_811567, _811563, _811559, _811555, _811551) = c_SetInterval_Oord_OatLeastLessThan(_811565, _811561, _811557, _811553, _811549)), _811567 = _811565, _811563 = _811561, _811559 = _811557, _811555 = _811553, _811551 = _811549], (2012 ^ _782652) ^ [_811938, _811940, _811942, _811944, _811946, _811948, _811950, _811952] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_811952, _811948, _811944, _811940) = c_SetInterval_Oord_OgreaterThanLessThan(_811950, _811946, _811942, _811938)), _811952 = _811950, _811948 = _811946, _811944 = _811942, _811940 = _811938], (2030 ^ _782652) ^ [_812239, _812241, _812243, _812245, _812247, _812249, _812251, _812253] : [-(c_SetInterval_Oord_OatLeastAtMost(_812253, _812249, _812245, _812241) = c_SetInterval_Oord_OatLeastAtMost(_812251, _812247, _812243, _812239)), _812253 = _812251, _812249 = _812247, _812245 = _812243, _812241 = _812239], (2048 ^ _782652) ^ [_812540, _812542, _812544, _812546, _812548, _812550] : [-(c_SetInterval_Oord_OgreaterThan(_812550, _812546, _812542) = c_SetInterval_Oord_OgreaterThan(_812548, _812544, _812540)), _812550 = _812548, _812546 = _812544, _812542 = _812540], (2062 ^ _782652) ^ [_812761, _812763, _812765, _812767, _812769, _812771] : [-(c_SetInterval_Oord_OlessThan(_812771, _812767, _812763) = c_SetInterval_Oord_OlessThan(_812769, _812765, _812761)), _812771 = _812769, _812767 = _812765, _812763 = _812761], (2076 ^ _782652) ^ [_812982, _812984, _812986, _812988, _812990, _812992] : [-(c_SetInterval_Oord_OatLeast(_812992, _812988, _812984) = c_SetInterval_Oord_OatLeast(_812990, _812986, _812982)), _812992 = _812990, _812988 = _812986, _812984 = _812982], (2090 ^ _782652) ^ [_813203, _813205, _813207, _813209, _813211, _813213] : [-(c_SetInterval_Oord_OatMost(_813213, _813209, _813205) = c_SetInterval_Oord_OatMost(_813211, _813207, _813203)), _813213 = _813211, _813209 = _813207, _813205 = _813203], (2104 ^ _782652) ^ [_813424, _813426, _813428, _813430, _813432, _813434] : [-(c_Finite__Set_Ofold1Set(_813434, _813430, _813426) = c_Finite__Set_Ofold1Set(_813432, _813428, _813424)), _813434 = _813432, _813430 = _813428, _813426 = _813424], (2118 ^ _782652) ^ [_813645, _813647, _813649, _813651, _813653, _813655, _813657, _813659] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_813659, _813655, _813651, _813647) = c_Hoare__Mirabelle_Otriple_Otriple__case(_813657, _813653, _813649, _813645)), _813659 = _813657, _813655 = _813653, _813651 = _813649, _813647 = _813645], (2136 ^ _782652) ^ [_813946, _813948, _813950, _813952] : [-(c_Orderings_Oord_Omax(_813952, _813948) = c_Orderings_Oord_Omax(_813950, _813946)), _813952 = _813950, _813948 = _813946], (2146 ^ _782652) ^ [_814095, _814097, _814099, _814101] : [-(c_Orderings_Oord_Omin(_814101, _814097) = c_Orderings_Oord_Omin(_814099, _814095)), _814101 = _814099, _814097 = _814095], (2156 ^ _782652) ^ [_814244, _814246, _814248, _814250, _814252, _814254] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_814254, _814250, _814246) = c_Hoare__Mirabelle_Otriple_Otriple__size(_814252, _814248, _814244)), _814254 = _814252, _814250 = _814248, _814246 = _814244], (2170 ^ _782652) ^ [_814465, _814467, _814469, _814471, _814473, _814475] : [-(c_Option_Ooption_Ooption__size(_814475, _814471, _814467) = c_Option_Ooption_Ooption__size(_814473, _814469, _814465)), _814475 = _814473, _814471 = _814469, _814467 = _814465], (2184 ^ _782652) ^ [_814686, _814688, _814690, _814692, _814694, _814696, _814698, _814700] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_814700, _814696, _814692, _814688) = c_Nat_Osemiring__1__class_Oof__nat__aux(_814698, _814694, _814690, _814686)), _814700 = _814698, _814696 = _814694, _814692 = _814690, _814688 = _814686], (2202 ^ _782652) ^ [_814987, _814989] : [_814989 = _814987, -(c_Nat_Onat_Onat__size(_814989) = c_Nat_Onat_Onat__size(_814987))], (2208 ^ _782652) ^ [_815072, _815074, _815076, _815078, _815080, _815082, _815084, _815086] : [-(c_Sum__Type_OPlus(_815086, _815082, _815078, _815074) = c_Sum__Type_OPlus(_815084, _815080, _815076, _815072)), _815086 = _815084, _815082 = _815080, _815078 = _815076, _815074 = _815072], (2226 ^ _782652) ^ [_815373, _815375, _815377, _815379] : [-(c_Int_Onat__aux(_815379, _815375) = c_Int_Onat__aux(_815377, _815373)), _815379 = _815377, _815375 = _815373], (2236 ^ _782652) ^ [_815522, _815524, _815526, _815528] : [-(c_Nat__Transfer_Otsub(_815528, _815524) = c_Nat__Transfer_Otsub(_815526, _815522)), _815528 = _815526, _815524 = _815522], (2246 ^ _782652) ^ [_815671, _815673] : [_815673 = _815671, -(c_SetInterval_Oord__class_OatLeast(_815673) = c_SetInterval_Oord__class_OatLeast(_815671))], (2252 ^ _782652) ^ [_815756, _815758] : [_815758 = _815756, -(c_Natural_Oevalc(_815758) = c_Natural_Oevalc(_815756))], (2258 ^ _782652) ^ [_815841, _815843, _815845, _815847, _815849, _815851] : [-(c_Power_Opower_Opower(_815851, _815847, _815843) = c_Power_Opower_Opower(_815849, _815845, _815841)), _815851 = _815849, _815847 = _815845, _815843 = _815841], (2272 ^ _782652) ^ [_816062, _816064, _816066, _816068] : [-(c_SMT_Oz3div(_816068, _816064) = c_SMT_Oz3div(_816066, _816062)), _816068 = _816066, _816064 = _816062], (2282 ^ _782652) ^ [_816211, _816213, _816215, _816217] : [-(c_Nitpick_Onat__lcm(_816217, _816213) = c_Nitpick_Onat__lcm(_816215, _816211)), _816217 = _816215, _816213 = _816211], (2292 ^ _782652) ^ [_816360, _816362, _816364, _816366] : [-(c_SMT_Oz3mod(_816366, _816362) = c_SMT_Oz3mod(_816364, _816360)), _816366 = _816364, _816362 = _816360], (2302 ^ _782652) ^ [_816509, _816511] : [_816511 = _816509, -(c_Int_Oring__1__class_OInts(_816511) = c_Int_Oring__1__class_OInts(_816509))], (2308 ^ _782652) ^ [_816594, _816596, _816598, _816600, _816602, _816604] : [-(c_Nat_Onat_Onat__rec(_816604, _816600, _816596) = c_Nat_Onat_Onat__rec(_816602, _816598, _816594)), _816604 = _816602, _816600 = _816598, _816596 = _816594], (2322 ^ _782652) ^ [_816815, _816817] : [_816817 = _816815, -(c_Int_Opred(_816817) = c_Int_Opred(_816815))], (2328 ^ _782652) ^ [_816900, _816902] : [_816902 = _816900, -(c_Int_Osucc(_816902) = c_Int_Osucc(_816900))], (2334 ^ _782652) ^ [_816985, _816987, _816989, _816991, _816993, _816995, _816997, _816999] : [-(c_Nitpick_Oprod(_816999, _816995, _816991, _816987) = c_Nitpick_Oprod(_816997, _816993, _816989, _816985)), _816999 = _816997, _816995 = _816993, _816991 = _816989, _816987 = _816985], (2352 ^ _782652) ^ [_817286, _817288, _817290, _817292] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_817292, _817288) = c_Code__Numeral_Odiv__mod__code__numeral(_817290, _817286)), _817292 = _817290, _817288 = _817286], (2362 ^ _782652) ^ [_817435, _817437, _817439, _817441] : [-(c_Divides_Odivmod__int__rel(_817441, _817437) = c_Divides_Odivmod__int__rel(_817439, _817435)), _817441 = _817439, _817437 = _817435], (2372 ^ _782652) ^ [_817584, _817586, _817588, _817590] : [-(c_Groups_Osgn__class_Osgn(_817590, _817586) = c_Groups_Osgn__class_Osgn(_817588, _817584)), _817590 = _817588, _817586 = _817584], (2382 ^ _782652) ^ [_817733, _817735, _817737, _817739] : [-(c_Divides_Opdivmod(_817739, _817735) = c_Divides_Opdivmod(_817737, _817733)), _817739 = _817737, _817735 = _817733], (2392 ^ _782652) ^ [_817882, _817884] : [_817884 = _817882, -(c_Divides_Oadjust(_817884) = c_Divides_Oadjust(_817882))], (2398 ^ _782652) ^ [_817967, _817969, _817971, _817973] : [-(c_Nitpick_Onat__gcd(_817973, _817969) = c_Nitpick_Onat__gcd(_817971, _817967)), _817973 = _817971, _817969 = _817967], (2408 ^ _782652) ^ [_818116, _818118, _818120, _818122] : [-(c_Set_Othe__elem(_818122, _818118) = c_Set_Othe__elem(_818120, _818116)), _818122 = _818120, _818118 = _818116], (2418 ^ _782652) ^ [_818265, _818267, _818269, _818271] : [-(c_Divides_Odivmod__int(_818271, _818267) = c_Divides_Odivmod__int(_818269, _818265)), _818271 = _818269, _818267 = _818265], (2428 ^ _782652) ^ [_818414, _818416, _818418, _818420] : [-(c_Divides_OnegDivAlg(_818420, _818416) = c_Divides_OnegDivAlg(_818418, _818414)), _818420 = _818418, _818416 = _818414], (2438 ^ _782652) ^ [_818563, _818565, _818567, _818569] : [-(c_Divides_OposDivAlg(_818569, _818565) = c_Divides_OposDivAlg(_818567, _818563)), _818569 = _818567, _818565 = _818563], (2448 ^ _782652) ^ [_818712, _818714, _818716, _818718, _818720, _818722, _818724, _818726, _818728, _818730] : [-(c_Product__Type_Oprod_Oprod__size(_818730, _818726, _818722, _818718, _818714) = c_Product__Type_Oprod_Oprod__size(_818728, _818724, _818720, _818716, _818712)), _818730 = _818728, _818726 = _818724, _818722 = _818720, _818718 = _818716, _818714 = _818712], (2470 ^ _782652) ^ [_819101, _819103, _819105, _819107] : [-(c_Divides_Odivmod__nat(_819107, _819103) = c_Divides_Odivmod__nat(_819105, _819101)), _819107 = _819105, _819103 = _819101], (2480 ^ _782652) ^ [_819250, _819252, _819254, _819256] : [-(c_Divides_Odivmod__nat__rel(_819256, _819252) = c_Divides_Odivmod__nat__rel(_819254, _819250)), _819256 = _819254, _819252 = _819250], (2490 ^ _782652) ^ [_819399, _819401] : [_819401 = _819399, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_819401) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_819399))], (2496 ^ _782652) ^ [_819484, _819486, _819488, _819490, _819492, _819494, _819496, _819498, _819500, _819502] : [-(c_Product__Type_Oprod_Oprod__rec(_819502, _819498, _819494, _819490, _819486) = c_Product__Type_Oprod_Oprod__rec(_819500, _819496, _819492, _819488, _819484)), _819502 = _819500, _819498 = _819496, _819494 = _819492, _819490 = _819488, _819486 = _819484], (2518 ^ _782652) ^ [_819873, _819875] : [_819875 = _819873, -(c_Nat_Osemiring__1__class_ONats(_819875) = c_Nat_Osemiring__1__class_ONats(_819873))], (2524 ^ _782652) ^ [_819958, _819960, _819962, _819964] : [-(c_FunDef_Orp__inv__image(_819964, _819960) = c_FunDef_Orp__inv__image(_819962, _819958)), _819964 = _819962, _819960 = _819958], (2534 ^ _782652) ^ [_820107, _820109, _820111, _820113, _820115, _820117, _820119, _820121] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_820121, _820117, _820113, _820109) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_820119, _820115, _820111, _820107)), _820121 = _820119, _820117 = _820115, _820113 = _820111, _820109 = _820107], (2552 ^ _782652) ^ [_820408, _820410] : [_820410 = _820408, -(c_Wellfounded_Omeasure(_820410) = c_Wellfounded_Omeasure(_820408))], (2558 ^ _782652) ^ [_820493, _820495, _820497, _820499] : [-(c_Wellfounded_Omin__ext(_820499, _820495) = c_Wellfounded_Omin__ext(_820497, _820493)), _820499 = _820497, _820495 = _820493], (2568 ^ _782652) ^ [_820642, _820644] : [_820644 = _820642, -(c_Wellfounded_Ofinite__psubset(_820644) = c_Wellfounded_Ofinite__psubset(_820642))], (2574 ^ _782652) ^ [_820727, _820729, _820731, _820733, _820735, _820737] : [-(c_Wellfounded_Omlex__prod(_820737, _820733, _820729) = c_Wellfounded_Omlex__prod(_820735, _820731, _820727)), _820737 = _820735, _820733 = _820731, _820729 = _820727], (2588 ^ _782652) ^ [_820948, _820950] : [_820950 = _820948, -(c_Int_Oint__ge__less__than2(_820950) = c_Int_Oint__ge__less__than2(_820948))], (2594 ^ _782652) ^ [_821033, _821035] : [_821035 = _821033, -(c_Int_Oint__ge__less__than(_821035) = c_Int_Oint__ge__less__than(_821033))], (2600 ^ _782652) ^ [_821118, _821120, _821122, _821124, _821126, _821128, _821130, _821132] : [-(c_Recdef_Osame__fst(_821132, _821128, _821124, _821120) = c_Recdef_Osame__fst(_821130, _821126, _821122, _821118)), _821132 = _821130, _821128 = _821126, _821124 = _821122, _821120 = _821118], (2618 ^ _782652) ^ [_821419, _821421] : [_821421 = _821419, -(c_Nitpick_Ozero__frac(_821421) = c_Nitpick_Ozero__frac(_821419))], (2624 ^ _782652) ^ [_821504, _821506] : [_821506 = _821504, -(c_Nitpick_Oone__frac(_821506) = c_Nitpick_Oone__frac(_821504))], (2630 ^ _782652) ^ [_821589, _821591, _821593, _821595] : [-(c_Nitpick_Onumber__of__frac(_821595, _821591) = c_Nitpick_Onumber__of__frac(_821593, _821589)), _821595 = _821593, _821591 = _821589], (2640 ^ _782652) ^ [_821738, _821740, _821742, _821744] : [-(c_Nitpick_Onorm__frac(_821744, _821740) = c_Nitpick_Onorm__frac(_821742, _821738)), _821744 = _821742, _821740 = _821738], (2650 ^ _782652) ^ [_821887, _821889, _821891, _821893, _821895, _821897] : [-(c_FunDef_Oin__rel(_821897, _821893, _821889) = c_FunDef_Oin__rel(_821895, _821891, _821887)), _821897 = _821895, _821893 = _821891, _821889 = _821887], (2664 ^ _782652) ^ [_822108, _822110, _822112, _822114] : [-(c_Predicate_OPowp(_822114, _822110) = c_Predicate_OPowp(_822112, _822108)), _822114 = _822112, _822110 = _822108], (2674 ^ _782652) ^ [_822257, _822259, _822261, _822263, _822265, _822267] : [-(c_Predicate_ODomainP(_822267, _822263, _822259) = c_Predicate_ODomainP(_822265, _822261, _822257)), _822267 = _822265, _822263 = _822261, _822259 = _822257], (2688 ^ _782652) ^ [_822478, _822480, _822482, _822484, _822486, _822488] : [-(c_Predicate_ORangeP(_822488, _822484, _822480) = c_Predicate_ORangeP(_822486, _822482, _822478)), _822488 = _822486, _822484 = _822482, _822480 = _822478], (2702 ^ _782652) ^ [_822699, _822701, _822703, _822705, _822707, _822709, _822711, _822713] : [-(c_Product__Type_Oapsnd(_822713, _822709, _822705, _822701) = c_Product__Type_Oapsnd(_822711, _822707, _822703, _822699)), _822713 = _822711, _822709 = _822707, _822705 = _822703, _822701 = _822699], (2720 ^ _782652) ^ [_823000, _823002, _823004, _823006, _823008, _823010, _823012, _823014] : [-(c_Product__Type_Oapfst(_823014, _823010, _823006, _823002) = c_Product__Type_Oapfst(_823012, _823008, _823004, _823000)), _823014 = _823012, _823010 = _823008, _823006 = _823004, _823002 = _823000], (2738 ^ _782652) ^ [_823301, _823303, _823305, _823307, _823309, _823311, _823313, _823315] : [-(c_Fun_Othe__inv__into(_823315, _823311, _823307, _823303) = c_Fun_Othe__inv__into(_823313, _823309, _823305, _823301)), _823315 = _823313, _823311 = _823309, _823307 = _823305, _823303 = _823301], (2756 ^ _782652) ^ [_823602, _823604] : [_823604 = _823602, -(c_Hoare__Mirabelle_Otriple_Otriple(_823604) = c_Hoare__Mirabelle_Otriple_Otriple(_823602))], (2762 ^ _782652) ^ [_823687, _823689, _823691, _823693, _823695, _823697, _823699, _823701] : [-(c_Hilbert__Choice_OLeastM(_823701, _823697, _823693, _823689) = c_Hilbert__Choice_OLeastM(_823699, _823695, _823691, _823687)), _823701 = _823699, _823697 = _823695, _823693 = _823691, _823689 = _823687], (2780 ^ _782652) ^ [_823988, _823990, _823992, _823994, _823996, _823998] : [-(c_Hoare__Mirabelle_Opeek__and(_823998, _823994, _823990) = c_Hoare__Mirabelle_Opeek__and(_823996, _823992, _823988)), _823998 = _823996, _823994 = _823992, _823990 = _823988], (2794 ^ _782652) ^ [_824209, _824211] : [_824211 = _824209, -(c_Hilbert__Choice_OGreatest(_824211) = c_Hilbert__Choice_OGreatest(_824209))], (2800 ^ _782652) ^ [_824294, _824296, _824298, _824300, _824302, _824304] : [-(c_Hilbert__Choice_OGreatestM(_824304, _824300, _824296) = c_Hilbert__Choice_OGreatestM(_824302, _824298, _824294)), _824304 = _824302, _824300 = _824298, _824296 = _824294], (2814 ^ _782652) ^ [_824515, _824517, _824519, _824521] : [-(c_Wellfounded_Omax__ext(_824521, _824517) = c_Wellfounded_Omax__ext(_824519, _824515)), _824521 = _824519, _824517 = _824515], (2824 ^ _782652) ^ [_824664, _824666] : [_824666 = _824664, -(c_Com_Ocom_Ocom__size(_824666) = c_Com_Ocom_Ocom__size(_824664))], (2830 ^ _782652) ^ [_824749, _824751, _824753, _824755, _824757, _824759] : [-(c_Com_Ocom_OCond(_824759, _824755, _824751) = c_Com_Ocom_OCond(_824757, _824753, _824749)), _824759 = _824757, _824755 = _824753, _824751 = _824749], (2844 ^ _782652) ^ [_824970, _824972, _824974, _824976] : [-(c_Com_Ocom_OWhile(_824976, _824972) = c_Com_Ocom_OWhile(_824974, _824970)), _824976 = _824974, _824972 = _824970], (2854 ^ _782652) ^ [_825119, _825121, _825123, _825125, _825127, _825129] : [-(c_Com_Ocom_OLocal(_825129, _825125, _825121) = c_Com_Ocom_OLocal(_825127, _825123, _825119)), _825129 = _825127, _825125 = _825123, _825121 = _825119], (2868 ^ _782652) ^ [_825340, _825342, _825344, _825346] : [-(c_Com_Ocom_OSemi(_825346, _825342) = c_Com_Ocom_OSemi(_825344, _825340)), _825346 = _825344, _825342 = _825340], (2878 ^ _782652) ^ [_825489, _825491, _825493, _825495, _825497, _825499, _825501, _825503] : [-(c_Random_Oiterate(_825503, _825499, _825495, _825491) = c_Random_Oiterate(_825501, _825497, _825493, _825489)), _825503 = _825501, _825499 = _825497, _825495 = _825493, _825491 = _825489], (2896 ^ _782652) ^ [_825790, _825792, _825794, _825796] : [-(c_Random_Olog(_825796, _825792) = c_Random_Olog(_825794, _825790)), _825796 = _825794, _825792 = _825790], (2906 ^ _782652) ^ [_825939, _825941, _825943, _825945, _825947, _825949] : [-(c_Random_Ominus__shift(_825949, _825945, _825941) = c_Random_Ominus__shift(_825947, _825943, _825939)), _825949 = _825947, _825945 = _825943, _825941 = _825939], (2920 ^ _782652) ^ [_826160, _826162, _826164, _826166] : [-(c_Random_Oinc__shift(_826166, _826162) = c_Random_Oinc__shift(_826164, _826160)), _826166 = _826164, _826162 = _826160], (2930 ^ _782652) ^ [_826309, _826311] : [_826311 = _826309, -(c_Nat_Ofunpow(_826311) = c_Nat_Ofunpow(_826309))], (2936 ^ _782652) ^ [_826394, _826396, _826398, _826400] : [-(c_Relation_OId__on(_826400, _826396) = c_Relation_OId__on(_826398, _826394)), _826400 = _826398, _826396 = _826394], (2946 ^ _782652) ^ [_826543, _826545, _826547, _826549] : [-(c_Transitive__Closure_Otrancl(_826549, _826545) = c_Transitive__Closure_Otrancl(_826547, _826543)), _826549 = _826547, _826545 = _826543], (2956 ^ _782652) ^ [_826692, _826694] : [_826694 = _826692, -(c_Relation_OId(_826694) = c_Relation_OId(_826692))], (2962 ^ _782652) ^ [_826777, _826779, _826781, _826783, _826785, _826787] : [-(c_Finite__Set_Ofold__image(_826787, _826783, _826779) = c_Finite__Set_Ofold__image(_826785, _826781, _826777)), _826787 = _826785, _826783 = _826781, _826779 = _826777], (2976 ^ _782652) ^ [_826998, _827000] : [_827000 = _826998, -(c_Set_OBall(_827000) = c_Set_OBall(_826998))], (2982 ^ _782652) ^ [_827083, _827085] : [_827085 = _827083, -(c_SetInterval_Oord__class_OgreaterThan(_827085) = c_SetInterval_Oord__class_OgreaterThan(_827083))], (2988 ^ _782652) ^ [_827168, _827170, _827172, _827174] : [-(c_Relation_ODomain(_827174, _827170) = c_Relation_ODomain(_827172, _827168)), _827174 = _827172, _827170 = _827168], (2998 ^ _782652) ^ [_827317, _827319, _827321, _827323] : [-(c_Relation_ORange(_827323, _827319) = c_Relation_ORange(_827321, _827317)), _827323 = _827321, _827319 = _827317], (3008 ^ _782652) ^ [_827466, _827468, _827470, _827472, _827474, _827476] : [-(c_Set_Ovimage(_827476, _827472, _827468) = c_Set_Ovimage(_827474, _827470, _827466)), _827476 = _827474, _827472 = _827470, _827468 = _827466], (3022 ^ _782652) ^ [_827687, _827689] : [_827689 = _827687, -(c_Relation_OField(_827689) = c_Relation_OField(_827687))], (3028 ^ _782652) ^ [_827772, _827774] : [_827774 = _827772, -(c_Equiv__Relations_Oquotient(_827774) = c_Equiv__Relations_Oquotient(_827772))], (3034 ^ _782652) ^ [_827857, _827859] : [_827859 = _827857, -(c_HOL_OAll(_827859) = c_HOL_OAll(_827857))], (3040 ^ _782652) ^ [_827942, _827944, _827946, _827948, _827950, _827952, _827954, _827956, _827958, _827960] : [-(c_Finite__Set_Ofold__graph(_827960, _827956, _827952, _827948, _827944) = c_Finite__Set_Ofold__graph(_827958, _827954, _827950, _827946, _827942)), _827960 = _827958, _827956 = _827954, _827952 = _827950, _827948 = _827946, _827944 = _827942], (3062 ^ _782652) ^ [_828331, _828333, _828335, _828337, _828339, _828341] : [-(c_Relation_Orel__comp(_828341, _828337, _828333) = c_Relation_Orel__comp(_828339, _828335, _828331)), _828341 = _828339, _828337 = _828335, _828333 = _828331], (3076 ^ _782652) ^ [_828552, _828554, _828556, _828558] : [-(c_Nitpick_Oint__lcm(_828558, _828554) = c_Nitpick_Oint__lcm(_828556, _828552)), _828558 = _828556, _828554 = _828552], (3086 ^ _782652) ^ [_828701, _828703, _828705, _828707, _828709, _828711] : [-(c_Nitpick_Otimes__frac(_828711, _828707, _828703) = c_Nitpick_Otimes__frac(_828709, _828705, _828701)), _828711 = _828709, _828707 = _828705, _828703 = _828701], (3100 ^ _782652) ^ [_828922, _828924, _828926, _828928, _828930, _828932] : [-(c_Nitpick_Oof__frac(_828932, _828928, _828924) = c_Nitpick_Oof__frac(_828930, _828926, _828922)), _828932 = _828930, _828928 = _828926, _828924 = _828922], (3114 ^ _782652) ^ [_829143, _829145] : [_829145 = _829143, -(c_Rings_Oinverse__class_Odivide(_829145) = c_Rings_Oinverse__class_Odivide(_829143))], (3120 ^ _782652) ^ [_829228, _829230] : [_829230 = _829228, -(c_Int_Oring__1__class_Oof__int(_829230) = c_Int_Oring__1__class_Oof__int(_829228))], (3126 ^ _782652) ^ [_829313, _829315, _829317, _829319] : [-(c_Nitpick_Oinverse__frac(_829319, _829315) = c_Nitpick_Oinverse__frac(_829317, _829313)), _829319 = _829317, _829315 = _829313], (3136 ^ _782652) ^ [_829462, _829464] : [_829464 = _829462, -(c_Nitpick_Ofrac(_829464) = c_Nitpick_Ofrac(_829462))], (3142 ^ _782652) ^ [_829547, _829549, _829551, _829553] : [-(c_Nitpick_OAbs__Frac(_829553, _829549) = c_Nitpick_OAbs__Frac(_829551, _829547)), _829553 = _829551, _829549 = _829547], (3152 ^ _782652) ^ [_829696, _829698, _829700, _829702, _829704, _829706] : [-(c_Nitpick_Oplus__frac(_829706, _829702, _829698) = c_Nitpick_Oplus__frac(_829704, _829700, _829696)), _829706 = _829704, _829702 = _829700, _829698 = _829696], (3166 ^ _782652) ^ [_829917, _829919, _829921, _829923] : [-(c_Nitpick_Ouminus__frac(_829923, _829919) = c_Nitpick_Ouminus__frac(_829921, _829917)), _829923 = _829921, _829919 = _829917], (3176 ^ _782652) ^ [_830066, _830068] : [_830068 = _830066, -(c_Nitpick_Odenom(_830068) = c_Nitpick_Odenom(_830066))], (3182 ^ _782652) ^ [_830151, _830153] : [_830153 = _830151, -(c_Nitpick_Onum(_830153) = c_Nitpick_Onum(_830151))], (3188 ^ _782652) ^ [_830236, _830238] : [_830238 = _830236, -(c_Nitpick_ORep__Frac(_830238) = c_Nitpick_ORep__Frac(_830236))], (3194 ^ _782652) ^ [_830321, _830323, _830325, _830327, _830329, _830331] : [-(c_Smallcheck_Oorelse(_830331, _830327, _830323) = c_Smallcheck_Oorelse(_830329, _830325, _830321)), _830331 = _830329, _830327 = _830325, _830323 = _830321], (3208 ^ _782652) ^ [_830542, _830544, _830546, _830548, _830550, _830552, _830554, _830556, _830558, _830560, _830562, _830564] : [-(c_Map_Omap__comp(_830564, _830560, _830556, _830552, _830548, _830544) = c_Map_Omap__comp(_830562, _830558, _830554, _830550, _830546, _830542)), _830564 = _830562, _830560 = _830558, _830556 = _830554, _830552 = _830550, _830548 = _830546, _830544 = _830542], (3234 ^ _782652) ^ [_831027, _831029, _831031, _831033, _831035, _831037] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_831037, _831033, _831029) = c_Smallcheck_Ofull__small__class_Ofull__small(_831035, _831031, _831027)), _831037 = _831035, _831033 = _831031, _831029 = _831027], (3248 ^ _782652) ^ [_831248, _831250, _831252, _831254, _831256, _831258] : [-(c_Smallcheck_Ofull__small_H(_831258, _831254, _831250) = c_Smallcheck_Ofull__small_H(_831256, _831252, _831248)), _831258 = _831256, _831254 = _831252, _831250 = _831248], (3262 ^ _782652) ^ [_831469, _831471, _831473, _831475, _831477, _831479] : [-(c_Smallcheck_Osmall_H(_831479, _831475, _831471) = c_Smallcheck_Osmall_H(_831477, _831473, _831469)), _831479 = _831477, _831475 = _831473, _831471 = _831469], (3276 ^ _782652) ^ [_831690, _831692] : [_831692 = _831690, -(c_Smallcheck_Osmall__class_Osmall(_831692) = c_Smallcheck_Osmall__class_Osmall(_831690))], (3282 ^ _782652) ^ [_831775, _831777, _831779, _831781, _831783, _831785] : [-(c_Map_Oran(_831785, _831781, _831777) = c_Map_Oran(_831783, _831779, _831775)), _831785 = _831783, _831781 = _831779, _831777 = _831775], (3296 ^ _782652) ^ [_831996, _831998, _832000, _832002] : [-(c_List_Olenlex(_832002, _831998) = c_List_Olenlex(_832000, _831996)), _832002 = _832000, _831998 = _831996], (3306 ^ _782652) ^ [_832145, _832147, _832149, _832151] : [-(c_Nitpick_Ocard_H(_832151, _832147) = c_Nitpick_Ocard_H(_832149, _832145)), _832151 = _832149, _832147 = _832145], (3316 ^ _782652) ^ [_832294, _832296, _832298, _832300, _832302, _832304, _832306, _832308, _832310, _832312, _832314, _832316] : [-(c_Product__Type_Omap__pair(_832316, _832312, _832308, _832304, _832300, _832296) = c_Product__Type_Omap__pair(_832314, _832310, _832306, _832302, _832298, _832294)), _832316 = _832314, _832312 = _832310, _832308 = _832306, _832304 = _832302, _832300 = _832298, _832296 = _832294], (3342 ^ _782652) ^ [_832779, _832781, _832783, _832785, _832787, _832789, _832791, _832793] : [-(c_Wellfounded_Olex__prod(_832793, _832789, _832785, _832781) = c_Wellfounded_Olex__prod(_832791, _832787, _832783, _832779)), _832793 = _832791, _832789 = _832787, _832785 = _832783, _832781 = _832779], (3360 ^ _782652) ^ [_833080, _833082, _833084, _833086] : [-(c_List_Olexn(_833086, _833082) = c_List_Olexn(_833084, _833080)), _833086 = _833084, _833082 = _833080], (3370 ^ _782652) ^ [_833229, _833231, _833233, _833235] : [-(c_Hilbert__Choice_OEps(_833235, _833231) = c_Hilbert__Choice_OEps(_833233, _833229)), _833235 = _833233, _833231 = _833229], (3380 ^ _782652) ^ [_833378, _833380, _833382, _833384, _833386, _833388, _833390, _833392] : [-(c_Nitpick_Osetsum_H(_833392, _833388, _833384, _833380) = c_Nitpick_Osetsum_H(_833390, _833386, _833382, _833378)), _833392 = _833390, _833388 = _833386, _833384 = _833382, _833380 = _833378], (3398 ^ _782652) ^ [_833679, _833681] : [_833681 = _833679, -(c_HOL_OEx(_833681) = c_HOL_OEx(_833679))], (3404 ^ _782652) ^ [_833764, _833766, _833768, _833770, _833772, _833774, _833776, _833778] : [-(c_Product__Type_Oscomp(_833778, _833774, _833770, _833766) = c_Product__Type_Oscomp(_833776, _833772, _833768, _833764)), _833778 = _833776, _833774 = _833772, _833770 = _833768, _833766 = _833764], (3422 ^ _782652) ^ [_834065, _834067] : [_834067 = _834065, -(c_Random_Orange(_834067) = c_Random_Orange(_834065))], (3428 ^ _782652) ^ [_834150, _834152, _834154, _834156] : [-(c_Code__Numeral_Onat__of__aux(_834156, _834152) = c_Code__Numeral_Onat__of__aux(_834154, _834150)), _834156 = _834154, _834152 = _834150], (3438 ^ _782652) ^ [_834299, _834301] : [_834301 = _834299, -(c_Code__Numeral_OSuc__code__numeral(_834301) = c_Code__Numeral_OSuc__code__numeral(_834299))], (3444 ^ _782652) ^ [_834384, _834386] : [_834386 = _834384, -(c_Divides_Odiv__class_Odiv(_834386) = c_Divides_Odiv__class_Odiv(_834384))], (3450 ^ _782652) ^ [_834469, _834471, _834473, _834475, _834477, _834479, _834481, _834483] : [-(c_Map_Orestrict__map(_834483, _834479, _834475, _834471) = c_Map_Orestrict__map(_834481, _834477, _834473, _834469)), _834483 = _834481, _834479 = _834477, _834475 = _834473, _834471 = _834469], (3468 ^ _782652) ^ [_834770, _834772, _834774, _834776] : [-(c_Random_Oselect(_834776, _834772) = c_Random_Oselect(_834774, _834770)), _834776 = _834774, _834772 = _834770], (3478 ^ _782652) ^ [_834919, _834921, _834923, _834925, _834927, _834929] : [-(c_Relation_OImage(_834929, _834925, _834921) = c_Relation_OImage(_834927, _834923, _834919)), _834929 = _834927, _834925 = _834923, _834921 = _834919], (3492 ^ _782652) ^ [_835140, _835142, _835144, _835146, _835148, _835150] : [-(c_List_Oset__Cons(_835150, _835146, _835142) = c_List_Oset__Cons(_835148, _835144, _835140)), _835150 = _835148, _835146 = _835144, _835142 = _835140], (3506 ^ _782652) ^ [_835361, _835363, _835365, _835367] : [-(c_List_Olistset(_835367, _835363) = c_List_Olistset(_835365, _835361)), _835367 = _835365, _835363 = _835361], (3516 ^ _782652) ^ [_835510, _835512, _835514, _835516] : [-(c_Relation_Oconverse(_835516, _835512) = c_Relation_Oconverse(_835514, _835510)), _835516 = _835514, _835512 = _835510], (3526 ^ _782652) ^ [_835659, _835661, _835663, _835665] : [-(c_Transitive__Closure_Ortrancl(_835665, _835661) = c_Transitive__Closure_Ortrancl(_835663, _835659)), _835665 = _835663, _835661 = _835659], (3536 ^ _782652) ^ [_835808, _835810, _835812, _835814, _835816, _835818, _835820, _835822] : [-(c_Nat_Onat_Onat__case(_835822, _835818, _835814, _835810) = c_Nat_Onat_Onat__case(_835820, _835816, _835812, _835808)), _835822 = _835820, _835818 = _835816, _835814 = _835812, _835810 = _835808], (3554 ^ _782652) ^ [_836109, _836111, _836113, _836115] : [-(c_Nat_Ocompow(_836115, _836111) = c_Nat_Ocompow(_836113, _836109)), _836115 = _836113, _836111 = _836109], (3564 ^ _782652) ^ [_836258, _836260] : [_836260 = _836258, -(c_List_Orotate1(_836260) = c_List_Orotate1(_836258))], (3570 ^ _782652) ^ [_836343, _836345] : [_836345 = _836343, -(c_Fun_Oid(_836345) = c_Fun_Oid(_836343))], (3576 ^ _782652) ^ [_836428, _836430, _836432, _836434] : [-(c_Finite__Set_Ofold1(_836434, _836430) = c_Finite__Set_Ofold1(_836432, _836428)), _836434 = _836432, _836430 = _836428], (3586 ^ _782652) ^ [_836577, _836579, _836581, _836583] : [-(c_Complete__Lattice_OSup__class_OSup(_836583, _836579) = c_Complete__Lattice_OSup__class_OSup(_836581, _836577)), _836583 = _836581, _836579 = _836577], (3596 ^ _782652) ^ [_836726, _836728, _836730, _836732] : [-(c_Complete__Lattice_OInf__class_OInf(_836732, _836728) = c_Complete__Lattice_OInf__class_OInf(_836730, _836726)), _836732 = _836730, _836728 = _836726], (3606 ^ _782652) ^ [_836875, _836877, _836879, _836881] : [-(c_Big__Operators_Olattice__class_OSup__fin(_836881, _836877) = c_Big__Operators_Olattice__class_OSup__fin(_836879, _836875)), _836881 = _836879, _836877 = _836875], (3616 ^ _782652) ^ [_837024, _837026, _837028, _837030] : [-(c_Big__Operators_Olattice__class_OInf__fin(_837030, _837026) = c_Big__Operators_Olattice__class_OInf__fin(_837028, _837024)), _837030 = _837028, _837026 = _837024], (3626 ^ _782652) ^ [_837173, _837175, _837177, _837179] : [-(c_Big__Operators_Olinorder__class_OMin(_837179, _837175) = c_Big__Operators_Olinorder__class_OMin(_837177, _837173)), _837179 = _837177, _837175 = _837173], (3636 ^ _782652) ^ [_837322, _837324, _837326, _837328] : [-(c_Big__Operators_Olinorder__class_OMax(_837328, _837324) = c_Big__Operators_Olinorder__class_OMax(_837326, _837322)), _837328 = _837326, _837324 = _837322], (3646 ^ _782652) ^ [_837471, _837473, _837475, _837477, _837479, _837481] : [-(c_Big__Operators_Olattice_OInf__fin(_837481, _837477, _837473) = c_Big__Operators_Olattice_OInf__fin(_837479, _837475, _837471)), _837481 = _837479, _837477 = _837475, _837473 = _837471], (3660 ^ _782652) ^ [_837692, _837694, _837696, _837698, _837700, _837702] : [-(c_Big__Operators_Olattice_OSup__fin(_837702, _837698, _837694) = c_Big__Operators_Olattice_OSup__fin(_837700, _837696, _837692)), _837702 = _837700, _837698 = _837696, _837694 = _837692], (3674 ^ _782652) ^ [_837913, _837915, _837917, _837919] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_837919, _837915) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_837917, _837913)), _837919 = _837917, _837915 = _837913], (3684 ^ _782652) ^ [_838062, _838064, _838066, _838068] : [-(c_Fun_Ofun__upd(_838068, _838064) = c_Fun_Ofun__upd(_838066, _838062)), _838068 = _838066, _838064 = _838062], (3694 ^ _782652) ^ [_838211, _838213, _838215, _838217] : [-(c_List_Olistrel(_838217, _838213) = c_List_Olistrel(_838215, _838211)), _838217 = _838215, _838213 = _838211], (3704 ^ _782652) ^ [_838360, _838362, _838364, _838366] : [-(c_Wellfounded_Oacc(_838366, _838362) = c_Wellfounded_Oacc(_838364, _838360)), _838366 = _838364, _838362 = _838360], (3714 ^ _782652) ^ [_838509, _838511, _838513, _838515] : [-(c_List_Olistrel1(_838515, _838511) = c_List_Olistrel1(_838513, _838509)), _838515 = _838513, _838511 = _838509], (3724 ^ _782652) ^ [_838658, _838660] : [_838660 = _838658, -(c_Lazy__Sequence_Ohb__not__seq(_838660) = c_Lazy__Sequence_Ohb__not__seq(_838658))], (3730 ^ _782652) ^ [_838743, _838745] : [_838745 = _838743, -(c_Groups_Otimes__class_Otimes(_838745) = c_Groups_Otimes__class_Otimes(_838743))], (3736 ^ _782652) ^ [_838828, _838830, _838832, _838834] : [-(c_List_Olexord(_838834, _838830) = c_List_Olexord(_838832, _838828)), _838834 = _838832, _838830 = _838828], (3746 ^ _782652) ^ [_838977, _838979, _838981, _838983, _838985, _838987] : [-(c_List_Olist_Olist__size(_838987, _838983, _838979) = c_List_Olist_Olist__size(_838985, _838981, _838977)), _838987 = _838985, _838983 = _838981, _838979 = _838977], (3760 ^ _782652) ^ [_839198, _839200, _839202, _839204] : [-(c_Random_Opick(_839204, _839200) = c_Random_Opick(_839202, _839198)), _839204 = _839202, _839200 = _839198], (3770 ^ _782652) ^ [_839347, _839349, _839351, _839353] : [-(c_Random_Oselect__weight(_839353, _839349) = c_Random_Oselect__weight(_839351, _839347)), _839353 = _839351, _839349 = _839347], (3780 ^ _782652) ^ [_839496, _839498, _839500, _839502, _839504, _839506, _839508, _839510] : [-(c_List_Omap__filter(_839510, _839506, _839502, _839498) = c_List_Omap__filter(_839508, _839504, _839500, _839496)), _839510 = _839508, _839506 = _839504, _839502 = _839500, _839498 = _839496], (3798 ^ _782652) ^ [_839797, _839799, _839801, _839803, _839805, _839807] : [-(c_List_Osublist(_839807, _839803, _839799) = c_List_Osublist(_839805, _839801, _839797)), _839807 = _839805, _839803 = _839801, _839799 = _839797], (3812 ^ _782652) ^ [_840018, _840020, _840022, _840024] : [-(c_List_Oupto(_840024, _840020) = c_List_Oupto(_840022, _840018)), _840024 = _840022, _840020 = _840018], (3822 ^ _782652) ^ [_840167, _840169, _840171, _840173] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_840173, _840169) = c_SetInterval_Oord__class_OatLeastLessThan(_840171, _840167)), _840173 = _840171, _840169 = _840167], (3832 ^ _782652) ^ [_840316, _840318, _840320, _840322, _840324, _840326, _840328, _840330, _840332, _840334] : [-(c_List_Olinorder__class_Oinsort__insert__key(_840334, _840330, _840326, _840322, _840318) = c_List_Olinorder__class_Oinsort__insert__key(_840332, _840328, _840324, _840320, _840316)), _840334 = _840332, _840330 = _840328, _840326 = _840324, _840322 = _840320, _840318 = _840316], (3854 ^ _782652) ^ [_840705, _840707, _840709, _840711, _840713, _840715] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_840715, _840711, _840707) = c_SetInterval_Oord__class_OatLeastAtMost(_840713, _840709, _840705)), _840715 = _840713, _840711 = _840709, _840707 = _840705], (3868 ^ _782652) ^ [_840926, _840928] : [_840928 = _840926, -(c_SetInterval_Oord__class_OlessThan(_840928) = c_SetInterval_Oord__class_OlessThan(_840926))], (3874 ^ _782652) ^ [_841011, _841013, _841015, _841017] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_841017, _841013) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_841015, _841011)), _841017 = _841015, _841013 = _841011], (3884 ^ _782652) ^ [_841160, _841162, _841164, _841166, _841168, _841170] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_841170, _841166, _841162) = c_SetInterval_Oord__class_OgreaterThanAtMost(_841168, _841164, _841160)), _841170 = _841168, _841166 = _841164, _841162 = _841160], (3898 ^ _782652) ^ [_841381, _841383, _841385, _841387, _841389, _841391] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_841391, _841387, _841383) = c_SetInterval_Oord__class_OgreaterThanLessThan(_841389, _841385, _841381)), _841391 = _841389, _841387 = _841385, _841383 = _841381], (3912 ^ _782652) ^ [_841602, _841604] : [_841604 = _841602, -(c_SetInterval_Oord__class_OatMost(_841604) = c_SetInterval_Oord__class_OatMost(_841602))], (3918 ^ _782652) ^ [_841687, _841689, _841691, _841693] : [-(c_List_Oupt(_841693, _841689) = c_List_Oupt(_841691, _841687)), _841693 = _841691, _841689 = _841687], (3928 ^ _782652) ^ [_841836, _841838, _841840, _841842] : [-(c_List_Orotate(_841842, _841838) = c_List_Orotate(_841840, _841836)), _841842 = _841840, _841838 = _841836], (3938 ^ _782652) ^ [_841985, _841987, _841989, _841991, _841993, _841995] : [-(c_Divides_Odiv__class_Omod(_841995, _841991, _841987) = c_Divides_Odiv__class_Omod(_841993, _841989, _841985)), _841995 = _841993, _841991 = _841989, _841987 = _841985], (3952 ^ _782652) ^ [_842206, _842208, _842210, _842212, _842214, _842216, _842218, _842220, _842222, _842224] : [-(c_List_Ofoldr(_842224, _842220, _842216, _842212, _842208) = c_List_Ofoldr(_842222, _842218, _842214, _842210, _842206)), _842224 = _842222, _842220 = _842218, _842216 = _842214, _842212 = _842210, _842208 = _842206], (3974 ^ _782652) ^ [_842595, _842597] : [_842597 = _842595, -(c_Orderings_Oord__class_Omax(_842597) = c_Orderings_Oord__class_Omax(_842595))], (3980 ^ _782652) ^ [_842680, _842682] : [_842682 = _842680, -(c_List_Otranspose__rel(_842682) = c_List_Otranspose__rel(_842680))], (3986 ^ _782652) ^ [_842765, _842767, _842769, _842771, _842773, _842775, _842777, _842779] : [-(c_List_Olist_Olist__case(_842779, _842775, _842771, _842767) = c_List_Olist_Olist__case(_842777, _842773, _842769, _842765)), _842779 = _842777, _842775 = _842773, _842771 = _842769, _842767 = _842765], (4004 ^ _782652) ^ [_843066, _843068, _843070, _843072] : [-(c_List_Otranspose(_843072, _843068) = c_List_Otranspose(_843070, _843066)), _843072 = _843070, _843068 = _843066], (4014 ^ _782652) ^ [_843215, _843217, _843219, _843221, _843223, _843225, _843227, _843229, _843231, _843233] : [-(c_Map_Omap__upds(_843233, _843229, _843225, _843221, _843217) = c_Map_Omap__upds(_843231, _843227, _843223, _843219, _843215)), _843233 = _843231, _843229 = _843227, _843225 = _843223, _843221 = _843219, _843217 = _843215], (4036 ^ _782652) ^ [_843604, _843606, _843608, _843610, _843612, _843614, _843616, _843618] : [-(c_Map_Omap__add(_843618, _843614, _843610, _843606) = c_Map_Omap__add(_843616, _843612, _843608, _843604)), _843618 = _843616, _843614 = _843612, _843610 = _843608, _843606 = _843604], (4054 ^ _782652) ^ [_843905, _843907, _843909, _843911] : [-(c_List_Olast(_843911, _843907) = c_List_Olast(_843909, _843905)), _843911 = _843909, _843907 = _843905], (4064 ^ _782652) ^ [_844054, _844056, _844058, _844060] : [-(c_List_Obutlast(_844060, _844056) = c_List_Obutlast(_844058, _844054)), _844060 = _844058, _844056 = _844054], (4074 ^ _782652) ^ [_844203, _844205, _844207, _844209] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_844209, _844205) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_844207, _844203)), _844209 = _844207, _844205 = _844203], (4084 ^ _782652) ^ [_844352, _844354] : [_844354 = _844352, -(c_Finite__Set_Ocard(_844354) = c_Finite__Set_Ocard(_844352))], (4090 ^ _782652) ^ [_844437, _844439, _844441, _844443, _844445, _844447] : [-(c_Finite__Set_Ofold(_844447, _844443, _844439) = c_Finite__Set_Ofold(_844445, _844441, _844437)), _844447 = _844445, _844443 = _844441, _844439 = _844437], (4104 ^ _782652) ^ [_844658, _844660] : [_844660 = _844658, -(c_List_Oreturn__list(_844660) = c_List_Oreturn__list(_844658))], (4110 ^ _782652) ^ [_844743, _844745] : [_844745 = _844743, -(c_List_Oembed__list(_844745) = c_List_Oembed__list(_844743))], (4116 ^ _782652) ^ [_844828, _844830] : [_844830 = _844828, -(c_List_Otl(_844830) = c_List_Otl(_844828))], (4122 ^ _782652) ^ [_844913, _844915] : [_844915 = _844913, -(c_List_Ohd(_844915) = c_List_Ohd(_844913))], (4128 ^ _782652) ^ [_844998, _845000] : [_845000 = _844998, -(c_List_Omonoid__add__class_Olistsum(_845000) = c_List_Omonoid__add__class_Olistsum(_844998))], (4134 ^ _782652) ^ [_845083, _845085, _845087, _845089, _845091, _845093] : [-(c_List_Opartition(_845093, _845089, _845085) = c_List_Opartition(_845091, _845087, _845083)), _845093 = _845091, _845089 = _845087, _845085 = _845083], (4148 ^ _782652) ^ [_845304, _845306] : [_845306 = _845304, -(c_Set_OPow(_845306) = c_Set_OPow(_845304))], (4154 ^ _782652) ^ [_845389, _845391] : [_845391 = _845389, -(c_Power_Opower__class_Opower(_845391) = c_Power_Opower__class_Opower(_845389))], (4160 ^ _782652) ^ [_845474, _845476, _845478, _845480] : [-(c_HOL_OLet(_845480, _845476) = c_HOL_OLet(_845478, _845474)), _845480 = _845478, _845476 = _845474], (4170 ^ _782652) ^ [_845623, _845625, _845627, _845629] : [-(c_Enum_Osublists(_845629, _845625) = c_Enum_Osublists(_845627, _845623)), _845629 = _845627, _845625 = _845623], (4180 ^ _782652) ^ [_845772, _845774, _845776, _845778] : [-(c_Enum_Oenum__the(_845778, _845774) = c_Enum_Oenum__the(_845776, _845772)), _845778 = _845776, _845774 = _845772], (4190 ^ _782652) ^ [_845921, _845923, _845925, _845927] : [-(c_HOL_OThe(_845927, _845923) = c_HOL_OThe(_845925, _845921)), _845927 = _845925, _845923 = _845921], (4200 ^ _782652) ^ [_846070, _846072, _846074, _846076] : [-(c_Product__Type_OSigma(_846076, _846072) = c_Product__Type_OSigma(_846074, _846070)), _846076 = _846074, _846072 = _846070], (4210 ^ _782652) ^ [_846219, _846221, _846223, _846225, _846227, _846229, _846231, _846233] : [-(c_Enum_Oproduct(_846233, _846229, _846225, _846221) = c_Enum_Oproduct(_846231, _846227, _846223, _846219)), _846233 = _846231, _846229 = _846227, _846225 = _846223, _846221 = _846219], (4228 ^ _782652) ^ [_846520, _846522, _846524, _846526] : [-(c_List_Olinorder__class_Osorted__list__of__set(_846526, _846522) = c_List_Olinorder__class_Osorted__list__of__set(_846524, _846520)), _846526 = _846524, _846522 = _846520], (4238 ^ _782652) ^ [_846669, _846671, _846673, _846675, _846677, _846679, _846681, _846683] : [-(c_List_Olinorder__class_Osort__key(_846683, _846679, _846675, _846671) = c_List_Olinorder__class_Osort__key(_846681, _846677, _846673, _846669)), _846683 = _846681, _846679 = _846677, _846675 = _846673, _846671 = _846669], (4256 ^ _782652) ^ [_846970, _846972, _846974, _846976, _846978, _846980] : [-(c_Enum_On__lists(_846980, _846976, _846972) = c_Enum_On__lists(_846978, _846974, _846970)), _846980 = _846978, _846976 = _846974, _846972 = _846970], (4270 ^ _782652) ^ [_847191, _847193] : [_847193 = _847191, -(c_Option_Ooption_ONone(_847193) = c_Option_Ooption_ONone(_847191))], (4276 ^ _782652) ^ [_847276, _847278] : [_847278 = _847276, -(c_Enum_Oenum__class_Oenum__all(_847278) = c_Enum_Oenum__class_Oenum__all(_847276))], (4282 ^ _782652) ^ [_847361, _847363] : [_847363 = _847361, -(c_Enum_Oenum__class_Oenum__ex(_847363) = c_Enum_Oenum__class_Oenum__ex(_847361))], (4288 ^ _782652) ^ [_847446, _847448, _847450, _847452] : [-(c_List_Olistsp(_847452, _847448) = c_List_Olistsp(_847450, _847446)), _847452 = _847450, _847448 = _847446], (4298 ^ _782652) ^ [_847595, _847597, _847599, _847601] : [-(c_List_Olists(_847601, _847597) = c_List_Olists(_847599, _847595)), _847601 = _847599, _847597 = _847595], (4308 ^ _782652) ^ [_847744, _847746] : [_847746 = _847744, -(c_List_Odrop(_847746) = c_List_Odrop(_847744))], (4314 ^ _782652) ^ [_847829, _847831, _847833, _847835] : [-(c_List_Olist__update(_847835, _847831) = c_List_Olist__update(_847833, _847829)), _847835 = _847833, _847831 = _847829], (4324 ^ _782652) ^ [_847978, _847980, _847982, _847984] : [-(c_List_Oremdups(_847984, _847980) = c_List_Oremdups(_847982, _847978)), _847984 = _847982, _847980 = _847978], (4334 ^ _782652) ^ [_848127, _848129, _848131, _848133, _848135, _848137] : [-(c_List_Oremove1(_848137, _848133, _848129) = c_List_Oremove1(_848135, _848131, _848127)), _848137 = _848135, _848133 = _848131, _848129 = _848127], (4348 ^ _782652) ^ [_848348, _848350] : [_848350 = _848348, -(c_Orderings_Otop__class_Otop(_848350) = c_Orderings_Otop__class_Otop(_848348))], (4354 ^ _782652) ^ [_848433, _848435, _848437, _848439] : [-(c_List_OremoveAll(_848439, _848435) = c_List_OremoveAll(_848437, _848433)), _848439 = _848437, _848435 = _848433], (4364 ^ _782652) ^ [_848582, _848584] : [_848584 = _848582, -(c_Set_Oinsert(_848584) = c_Set_Oinsert(_848582))], (4370 ^ _782652) ^ [_848667, _848669, _848671, _848673, _848675, _848677] : [-(c_List_Oinsert(_848677, _848673, _848669) = c_List_Oinsert(_848675, _848671, _848667)), _848677 = _848675, _848673 = _848671, _848669 = _848667], (4384 ^ _782652) ^ [_848888, _848890, _848892, _848894, _848896, _848898, _848900, _848902] : [-(c_List_Omaps(_848902, _848898, _848894, _848890) = c_List_Omaps(_848900, _848896, _848892, _848888)), _848902 = _848900, _848898 = _848896, _848894 = _848892, _848890 = _848888], (4402 ^ _782652) ^ [_849189, _849191] : [_849191 = _849189, -(c_Lattices_Osemilattice__inf__class_Oinf(_849191) = c_Lattices_Osemilattice__inf__class_Oinf(_849189))], (4408 ^ _782652) ^ [_849274, _849276] : [_849276 = _849274, -(c_Orderings_Obot__class_Obot(_849276) = c_Orderings_Obot__class_Obot(_849274))], (4414 ^ _782652) ^ [_849359, _849361, _849363, _849365] : [-(c_List_Oconcat(_849365, _849361) = c_List_Oconcat(_849363, _849359)), _849365 = _849363, _849361 = _849359], (4424 ^ _782652) ^ [_849508, _849510, _849512, _849514] : [-(c_Relation_Oinv__image(_849514, _849510) = c_Relation_Oinv__image(_849512, _849508)), _849514 = _849512, _849510 = _849508], (4434 ^ _782652) ^ [_849657, _849659, _849661, _849663] : [-(c_List_Olex(_849663, _849659) = c_List_Olex(_849661, _849657)), _849663 = _849661, _849659 = _849657], (4444 ^ _782652) ^ [_849806, _849808, _849810, _849812] : [-(c_List_Omeasures(_849812, _849808) = c_List_Omeasures(_849810, _849806)), _849812 = _849810, _849808 = _849806], (4454 ^ _782652) ^ [_849955, _849957, _849959, _849961, _849963, _849965, _849967, _849969] : [-(c_List_Ofoldl(_849969, _849965, _849961, _849957) = c_List_Ofoldl(_849967, _849963, _849959, _849955)), _849969 = _849967, _849965 = _849963, _849961 = _849959, _849957 = _849955], (4472 ^ _782652) ^ [_850256, _850258] : [_850258 = _850256, -(c_List_Otake(_850258) = c_List_Otake(_850256))], (4478 ^ _782652) ^ [_850341, _850343] : [_850343 = _850341, -(c_Orderings_Oord__class_Omin(_850343) = c_Orderings_Oord__class_Omin(_850341))], (4484 ^ _782652) ^ [_850426, _850428, _850430, _850432] : [-(c_List_Ozip(_850432, _850428) = c_List_Ozip(_850430, _850426)), _850432 = _850430, _850428 = _850426], (4494 ^ _782652) ^ [_850575, _850577, _850579, _850581] : [-(c_List_Omap(_850581, _850577) = c_List_Omap(_850579, _850575)), _850581 = _850579, _850577 = _850575], (4504 ^ _782652) ^ [_850724, _850726, _850728, _850730] : [-(c_Map_Omap__of(_850730, _850726) = c_Map_Omap__of(_850728, _850724)), _850730 = _850728, _850726 = _850724], (4514 ^ _782652) ^ [_850873, _850875, _850877, _850879, _850881, _850883, _850885, _850887] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_850887, _850883, _850879, _850875) = c_New__Random__Sequence_Opos__not__random__dseq(_850885, _850881, _850877, _850873)), _850887 = _850885, _850883 = _850881, _850879 = _850877, _850875 = _850873], (4532 ^ _782652) ^ [_851174, _851176] : [_851176 = _851174, -(c_New__DSequence_Opos__not__seq(_851176) = c_New__DSequence_Opos__not__seq(_851174))], (4538 ^ _782652) ^ [_851259, _851261, _851263, _851265, _851267, _851269] : [-(c_List_OdropWhile(_851269, _851265, _851261) = c_List_OdropWhile(_851267, _851263, _851259)), _851269 = _851267, _851265 = _851263, _851261 = _851259], (4552 ^ _782652) ^ [_851480, _851482] : [_851482 = _851480, -(c_List_Odistinct(_851482) = c_List_Odistinct(_851480))], (4558 ^ _782652) ^ [_851565, _851567, _851569, _851571, _851573, _851575] : [-(c_List_OtakeWhile(_851575, _851571, _851567) = c_List_OtakeWhile(_851573, _851569, _851565)), _851575 = _851573, _851571 = _851569, _851567 = _851565], (4572 ^ _782652) ^ [_851786, _851788, _851790, _851792, _851794, _851796] : [-(c_List_Olinorder__class_Oinsort__key(_851796, _851792, _851788) = c_List_Olinorder__class_Oinsort__key(_851794, _851790, _851786)), _851796 = _851794, _851792 = _851790, _851788 = _851786], (4586 ^ _782652) ^ [_852007, _852009, _852011, _852013] : [-(c_List_Ofilter(_852013, _852009) = c_List_Ofilter(_852011, _852007)), _852013 = _852011, _852009 = _852007], (4596 ^ _782652) ^ [_852156, _852158] : [_852158 = _852156, -(c_List_Onth(_852158) = c_List_Onth(_852156))], (4602 ^ _782652) ^ [_852241, _852243] : [_852243 = _852241, -(c_List_Orev(_852243) = c_List_Orev(_852241))], (4608 ^ _782652) ^ [_852326, _852328] : [_852328 = _852326, -(c_List_Oappend(_852328) = c_List_Oappend(_852326))], (4614 ^ _782652) ^ [_852411, _852413, _852415, _852417, _852419, _852421] : [-(c_Product__Type_Ointernal__split(_852421, _852417, _852413) = c_Product__Type_Ointernal__split(_852419, _852415, _852411)), _852421 = _852419, _852417 = _852415, _852413 = _852411], (4628 ^ _782652) ^ [_852632, _852634, _852636, _852638] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_852638, _852634) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_852636, _852632)), _852638 = _852636, _852634 = _852632], (4638 ^ _782652) ^ [_852781, _852783] : [_852783 = _852781, -(c_HOL_Obool_Obool__size(_852783) = c_HOL_Obool_Obool__size(_852781))], (4644 ^ _782652) ^ [_852866, _852868] : [_852868 = _852866, -(c_Groups_Oabs__class_Oabs(_852868) = c_Groups_Oabs__class_Oabs(_852866))], (4650 ^ _782652) ^ [_852951, _852953, _852955, _852957] : [-(c_Product__Type_Ofst(_852957, _852953) = c_Product__Type_Ofst(_852955, _852951)), _852957 = _852955, _852953 = _852951], (4660 ^ _782652) ^ [_853100, _853102, _853104, _853106] : [-(c_Product__Type_Osnd(_853106, _853102) = c_Product__Type_Osnd(_853104, _853100)), _853106 = _853104, _853102 = _853100], (4670 ^ _782652) ^ [_853249, _853251] : [_853251 = _853249, -(c_List_Oset(_853251) = c_List_Oset(_853249))], (4676 ^ _782652) ^ [_853334, _853336] : [_853336 = _853334, -(c_Enum_Oenum__class_Oenum(_853336) = c_Enum_Oenum__class_Oenum(_853334))], (4682 ^ _782652) ^ [_853419, _853421] : [_853421 = _853419, -(c_Nat_Osemiring__1__class_Oof__nat(_853421) = c_Nat_Osemiring__1__class_Oof__nat(_853419))], (4688 ^ _782652) ^ [_853504, _853506] : [_853506 = _853504, -(c_Int_Onumber__class_Onumber__of(_853506) = c_Int_Onumber__class_Onumber__of(_853504))], (4694 ^ _782652) ^ [_853589, _853591] : [_853591 = _853589, -(c_Int_OBit1(_853591) = c_Int_OBit1(_853589))], (4700 ^ _782652) ^ [_853674, _853676] : [_853676 = _853674, -(c_Int_OBit0(_853676) = c_Int_OBit0(_853674))], (4706 ^ _782652) ^ [_853759, _853761, _853763, _853765, _853767, _853769, _853771, _853773, _853775, _853777, _853779, _853781, _853783, _853785] : [-(c_New__Random__Sequence_Opos__decr__bind(_853785, _853781, _853777, _853773, _853769, _853765, _853761) = c_New__Random__Sequence_Opos__decr__bind(_853783, _853779, _853775, _853771, _853767, _853763, _853759)), _853785 = _853783, _853781 = _853779, _853777 = _853775, _853773 = _853771, _853769 = _853767, _853765 = _853763, _853761 = _853759], (4736 ^ _782652) ^ [_854348, _854350, _854352, _854354, _854356, _854358, _854360, _854362] : [-(c_New__DSequence_Opos__decr__bind(_854362, _854358, _854354, _854350) = c_New__DSequence_Opos__decr__bind(_854360, _854356, _854352, _854348)), _854362 = _854360, _854358 = _854356, _854354 = _854352, _854350 = _854348], (4754 ^ _782652) ^ [_854649, _854651] : [_854651 = _854649, -(c_HOL_Oequal__class_Oequal(_854651) = c_HOL_Oequal__class_Oequal(_854649))], (4760 ^ _782652) ^ [_854734, _854736] : [_854736 = _854734, -(c_Lazy__Sequence_Oyieldn(_854736) = c_Lazy__Sequence_Oyieldn(_854734))], (4766 ^ _782652) ^ [_854819, _854821, _854823, _854825, _854827, _854829] : [-(c_Lazy__Sequence_Oanamorph(_854829, _854825, _854821) = c_Lazy__Sequence_Oanamorph(_854827, _854823, _854819)), _854829 = _854827, _854825 = _854823, _854821 = _854819], (4780 ^ _782652) ^ [_855040, _855042, _855044, _855046, _855048, _855050, _855052, _855054] : [-(c_New__Random__Sequence_Opos__empty(_855054, _855050, _855046, _855042) = c_New__Random__Sequence_Opos__empty(_855052, _855048, _855044, _855040)), _855054 = _855052, _855050 = _855048, _855046 = _855044, _855042 = _855040], (4798 ^ _782652) ^ [_855341, _855343] : [_855343 = _855341, -(c_New__DSequence_Opos__empty(_855343) = c_New__DSequence_Opos__empty(_855341))], (4804 ^ _782652) ^ [_855426, _855428, _855430, _855432, _855434, _855436, _855438, _855440] : [-(c_New__DSequence_Opos__bind(_855440, _855436, _855432, _855428) = c_New__DSequence_Opos__bind(_855438, _855434, _855430, _855426)), _855440 = _855438, _855436 = _855434, _855432 = _855430, _855428 = _855426], (4822 ^ _782652) ^ [_855727, _855729, _855731, _855733] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_855733, _855729) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_855731, _855727)), _855733 = _855731, _855729 = _855727], (4832 ^ _782652) ^ [_855876, _855878, _855880, _855882, _855884, _855886, _855888, _855890, _855892, _855894] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_855894, _855890, _855886, _855882, _855878) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_855892, _855888, _855884, _855880, _855876)), _855894 = _855892, _855890 = _855888, _855886 = _855884, _855882 = _855880, _855878 = _855876], (4854 ^ _782652) ^ [_856265, _856267] : [_856267 = _856265, -(c_Lazy__Sequence_Oyield(_856267) = c_Lazy__Sequence_Oyield(_856265))], (4860 ^ _782652) ^ [_856350, _856352, _856354, _856356, _856358, _856360, _856362, _856364] : [-(c_New__Random__Sequence_Opos__map(_856364, _856360, _856356, _856352) = c_New__Random__Sequence_Opos__map(_856362, _856358, _856354, _856350)), _856364 = _856362, _856360 = _856358, _856356 = _856354, _856352 = _856350], (4878 ^ _782652) ^ [_856651, _856653, _856655, _856657, _856659, _856661, _856663, _856665] : [-(c_New__Random__Sequence_Opos__bind(_856665, _856661, _856657, _856653) = c_New__Random__Sequence_Opos__bind(_856663, _856659, _856655, _856651)), _856665 = _856663, _856661 = _856659, _856657 = _856655, _856653 = _856651], (4896 ^ _782652) ^ [_856952, _856954, _856956, _856958, _856960, _856962, _856964, _856966, _856968, _856970, _856972, _856974, _856976, _856978] : [-(c_New__Random__Sequence_Oneg__decr__bind(_856978, _856974, _856970, _856966, _856962, _856958, _856954) = c_New__Random__Sequence_Oneg__decr__bind(_856976, _856972, _856968, _856964, _856960, _856956, _856952)), _856978 = _856976, _856974 = _856972, _856970 = _856968, _856966 = _856964, _856962 = _856960, _856958 = _856956, _856954 = _856952], (4926 ^ _782652) ^ [_857541, _857543, _857545, _857547, _857549, _857551, _857553, _857555] : [-(c_New__DSequence_Oneg__decr__bind(_857555, _857551, _857547, _857543) = c_New__DSequence_Oneg__decr__bind(_857553, _857549, _857545, _857541)), _857555 = _857553, _857551 = _857549, _857547 = _857545, _857543 = _857541], (4944 ^ _782652) ^ [_857842, _857844] : [_857844 = _857842, -(c_New__Random__Sequence_Opos__single(_857844) = c_New__Random__Sequence_Opos__single(_857842))], (4950 ^ _782652) ^ [_857927, _857929, _857931, _857933] : [-(c_New__DSequence_Opos__single(_857933, _857929) = c_New__DSequence_Opos__single(_857931, _857927)), _857933 = _857931, _857929 = _857927], (4960 ^ _782652) ^ [_858076, _858078, _858080, _858082, _858084, _858086, _858088, _858090] : [-(c_New__DSequence_Oneg__bind(_858090, _858086, _858082, _858078) = c_New__DSequence_Oneg__bind(_858088, _858084, _858080, _858076)), _858090 = _858088, _858086 = _858084, _858082 = _858080, _858078 = _858076], (4978 ^ _782652) ^ [_858377, _858379, _858381, _858383, _858385, _858387, _858389, _858391] : [-(c_New__Random__Sequence_Oneg__map(_858391, _858387, _858383, _858379) = c_New__Random__Sequence_Oneg__map(_858389, _858385, _858381, _858377)), _858391 = _858389, _858387 = _858385, _858383 = _858381, _858379 = _858377], (4996 ^ _782652) ^ [_858678, _858680, _858682, _858684, _858686, _858688, _858690, _858692] : [-(c_New__Random__Sequence_Oneg__bind(_858692, _858688, _858684, _858680) = c_New__Random__Sequence_Oneg__bind(_858690, _858686, _858682, _858678)), _858692 = _858690, _858688 = _858686, _858684 = _858682, _858680 = _858678], (5014 ^ _782652) ^ [_858979, _858981, _858983, _858985, _858987, _858989, _858991, _858993] : [-(c_Fun_Ocomp(_858993, _858989, _858985, _858981) = c_Fun_Ocomp(_858991, _858987, _858983, _858979)), _858993 = _858991, _858989 = _858987, _858985 = _858983, _858981 = _858979], (5032 ^ _782652) ^ [_859280, _859282] : [_859282 = _859280, -(c_List_Olist_ONil(_859282) = c_List_Olist_ONil(_859280))], (5038 ^ _782652) ^ [_859365, _859367] : [_859367 = _859365, -(c_If(_859367) = c_If(_859365))], (5044 ^ _782652) ^ [_859450, _859452] : [_859452 = _859450, -(c_Groups_Ozero__class_Ozero(_859452) = c_Groups_Ozero__class_Ozero(_859450))], (5050 ^ _782652) ^ [_859535, _859537, _859539, _859541, _859543, _859545] : [-(c_Lazy__Sequence_Obind(_859545, _859541, _859537) = c_Lazy__Sequence_Obind(_859543, _859539, _859535)), _859545 = _859543, _859541 = _859539, _859537 = _859535], (5064 ^ _782652) ^ [_859756, _859758] : [_859758 = _859756, -(c_Groups_Ominus__class_Ominus(_859758) = c_Groups_Ominus__class_Ominus(_859756))], (5070 ^ _782652) ^ [_859841, _859843, _859845, _859847, _859849, _859851, _859853, _859855] : [-(c_Lazy__Sequence_Oproduct(_859855, _859851, _859847, _859843) = c_Lazy__Sequence_Oproduct(_859853, _859849, _859845, _859841)), _859855 = _859853, _859851 = _859849, _859847 = _859845, _859843 = _859841], (5088 ^ _782652) ^ [_860142, _860144] : [_860144 = _860142, -(c_New__Random__Sequence_Oneg__single(_860144) = c_New__Random__Sequence_Oneg__single(_860142))], (5094 ^ _782652) ^ [_860227, _860229, _860231, _860233] : [-(c_New__DSequence_Oneg__single(_860233, _860229) = c_New__DSequence_Oneg__single(_860231, _860227)), _860233 = _860231, _860229 = _860227], (5104 ^ _782652) ^ [_860376, _860378, _860380, _860382] : [-(c_Lazy__Sequence_Ohb__single(_860382, _860378) = c_Lazy__Sequence_Ohb__single(_860380, _860376)), _860382 = _860380, _860378 = _860376], (5114 ^ _782652) ^ [_860525, _860527, _860529, _860531, _860533, _860535, _860537, _860539, _860541, _860543, _860545, _860547] : [-(c_New__Random__Sequence_Opos__union(_860547, _860543, _860539, _860535, _860531, _860527) = c_New__Random__Sequence_Opos__union(_860545, _860541, _860537, _860533, _860529, _860525)), _860547 = _860545, _860543 = _860541, _860539 = _860537, _860535 = _860533, _860531 = _860529, _860527 = _860525], (5140 ^ _782652) ^ [_861010, _861012, _861014, _861016, _861018, _861020] : [-(c_New__DSequence_Opos__union(_861020, _861016, _861012) = c_New__DSequence_Opos__union(_861018, _861014, _861010)), _861020 = _861018, _861016 = _861014, _861012 = _861010], (5154 ^ _782652) ^ [_861231, _861233] : [_861233 = _861231, -(c_Lazy__Sequence_Oempty(_861233) = c_Lazy__Sequence_Oempty(_861231))], (5160 ^ _782652) ^ [_861316, _861318] : [_861318 = _861316, -(c_Lazy__Sequence_Osingle(_861318) = c_Lazy__Sequence_Osingle(_861316))], (5166 ^ _782652) ^ [_861401, _861403, _861405, _861407] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_861407, _861403) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_861405, _861401)), _861407 = _861405, _861403 = _861401], (5176 ^ _782652) ^ [_861550, _861552, _861554, _861556] : [-(c_Lazy__Sequence_Osmall__lazy_H(_861556, _861552) = c_Lazy__Sequence_Osmall__lazy_H(_861554, _861550)), _861556 = _861554, _861552 = _861550], (5186 ^ _782652) ^ [_861699, _861701] : [_861701 = _861699, -(c_Groups_Ouminus__class_Ouminus(_861701) = c_Groups_Ouminus__class_Ouminus(_861699))], (5192 ^ _782652) ^ [_861784, _861786, _861788, _861790] : [-(c_Wellfounded_Oaccp(_861790, _861786) = c_Wellfounded_Oaccp(_861788, _861784)), _861790 = _861788, _861786 = _861784], (5202 ^ _782652) ^ [_861933, _861935, _861937, _861939] : [-(c_Product__Type_OPair(_861939, _861935) = c_Product__Type_OPair(_861937, _861933)), _861939 = _861937, _861935 = _861933], (5212 ^ _782652) ^ [_862082, _862084] : [_862084 = _862082, -(c_Orderings_Oord__class_Oless(_862084) = c_Orderings_Oord__class_Oless(_862082))], (5218 ^ _782652) ^ [_862167, _862169] : [_862169 = _862167, -(c_Groups_Oone__class_Oone(_862169) = c_Groups_Oone__class_Oone(_862167))], (5224 ^ _782652) ^ [_862252, _862254, _862256, _862258, _862260, _862262, _862264, _862266] : [-(c_Option_Ooption_Ooption__case(_862266, _862262, _862258, _862254) = c_Option_Ooption_Ooption__case(_862264, _862260, _862256, _862252)), _862266 = _862264, _862262 = _862260, _862258 = _862256, _862254 = _862252], (5242 ^ _782652) ^ [_862553, _862555] : [_862555 = _862553, -(c_Lazy__Sequence_Ohit__bound(_862555) = c_Lazy__Sequence_Ohit__bound(_862553))], (5248 ^ _782652) ^ [_862638, _862640, _862642, _862644, _862646, _862648] : [-(c_Lazy__Sequence_Oappend(_862648, _862644, _862640) = c_Lazy__Sequence_Oappend(_862646, _862642, _862638)), _862648 = _862646, _862644 = _862642, _862640 = _862638], (5262 ^ _782652) ^ [_862859, _862861, _862863, _862865, _862867, _862869, _862871, _862873] : [-(c_Lazy__Sequence_Ohb__bind(_862873, _862869, _862865, _862861) = c_Lazy__Sequence_Ohb__bind(_862871, _862867, _862863, _862859)), _862873 = _862871, _862869 = _862867, _862865 = _862863, _862861 = _862859], (5280 ^ _782652) ^ [_863160, _863162, _863164, _863166] : [-(c_Lazy__Sequence_Ohb__flat(_863166, _863162) = c_Lazy__Sequence_Ohb__flat(_863164, _863160)), _863166 = _863164, _863162 = _863160], (5290 ^ _782652) ^ [_863309, _863311, _863313, _863315, _863317, _863319] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_863319, _863315, _863311) = c_Lazy__Sequence_Olazy__sequence_OInsert(_863317, _863313, _863309)), _863319 = _863317, _863315 = _863313, _863311 = _863309], (5304 ^ _782652) ^ [_863530, _863532, _863534, _863536] : [-(c_Option_Omap(_863536, _863532) = c_Option_Omap(_863534, _863530)), _863536 = _863534, _863532 = _863530], (5314 ^ _782652) ^ [_863679, _863681, _863683, _863685, _863687, _863689, _863691, _863693, _863695, _863697, _863699, _863701] : [-(c_New__Random__Sequence_Oneg__union(_863701, _863697, _863693, _863689, _863685, _863681) = c_New__Random__Sequence_Oneg__union(_863699, _863695, _863691, _863687, _863683, _863679)), _863701 = _863699, _863697 = _863695, _863693 = _863691, _863689 = _863687, _863685 = _863683, _863681 = _863679], (5340 ^ _782652) ^ [_864164, _864166, _864168, _864170, _864172, _864174] : [-(c_New__DSequence_Oneg__union(_864174, _864170, _864166) = c_New__DSequence_Oneg__union(_864172, _864168, _864164)), _864174 = _864172, _864170 = _864168, _864166 = _864164], (5354 ^ _782652) ^ [_864385, _864387, _864389, _864391, _864393, _864395, _864397, _864399, _864401, _864403] : [-(c_New__DSequence_Oneg__map(_864403, _864399, _864395, _864391, _864387) = c_New__DSequence_Oneg__map(_864401, _864397, _864393, _864389, _864385)), _864403 = _864401, _864399 = _864397, _864395 = _864393, _864391 = _864389, _864387 = _864385], (5376 ^ _782652) ^ [_864774, _864776, _864778, _864780, _864782, _864784, _864786, _864788] : [-(c_Lazy__Sequence_Ohb__map(_864788, _864784, _864780, _864776) = c_Lazy__Sequence_Ohb__map(_864786, _864782, _864778, _864774)), _864788 = _864786, _864784 = _864782, _864780 = _864778, _864776 = _864774], (5394 ^ _782652) ^ [_865075, _865077] : [_865077 = _865075, -(c_Groups_Oplus__class_Oplus(_865077) = c_Groups_Oplus__class_Oplus(_865075))], (5400 ^ _782652) ^ [_865160, _865162] : [_865162 = _865160, -(c_Nat_Osize__class_Osize(_865162) = c_Nat_Osize__class_Osize(_865160))], (5406 ^ _782652) ^ [_865245, _865247] : [_865247 = _865245, -(c_Set_OCollect(_865247) = c_Set_OCollect(_865245))], (5412 ^ _782652) ^ [_865330, _865332, _865334, _865336, _865338, _865340] : [-(c_Product__Type_Oprod_Oprod__case(_865340, _865336, _865332) = c_Product__Type_Oprod_Oprod__case(_865338, _865334, _865330)), _865340 = _865338, _865336 = _865334, _865332 = _865330], (5426 ^ _782652) ^ [_865551, _865553] : [_865553 = _865551, -(c_List_Olist_OCons(_865553) = c_List_Olist_OCons(_865551))], (5432 ^ _782652) ^ [_865636, _865638, _865640, _865642, _865644, _865646] : [-(c_List_Osplice(_865646, _865642, _865638) = c_List_Osplice(_865644, _865640, _865636)), _865646 = _865644, _865642 = _865640, _865638 = _865636], (5446 ^ _782652) ^ [_865857, _865859] : [_865859 = _865857, -(c_Lattices_Osemilattice__sup__class_Osup(_865859) = c_Lattices_Osemilattice__sup__class_Osup(_865857))], (5452 ^ _782652) ^ [_865942, _865944, _865946, _865948, _865950, _865952, _865954, _865956, _865958, _865960] : [-(c_Predicate_Opred__comp(_865960, _865956, _865952, _865948, _865944) = c_Predicate_Opred__comp(_865958, _865954, _865950, _865946, _865942)), _865960 = _865958, _865956 = _865954, _865952 = _865950, _865948 = _865946, _865944 = _865942], (5474 ^ _782652) ^ [_866331, _866333, _866335, _866337, _866339, _866341] : [-(c_Predicate_Oconversep(_866341, _866337, _866333) = c_Predicate_Oconversep(_866339, _866335, _866331)), _866341 = _866339, _866337 = _866335, _866333 = _866331], (5488 ^ _782652) ^ [_866552, _866554] : [_866554 = _866552, -(tc_List_Olist(_866554) = tc_List_Olist(_866552))], (5494 ^ _782652) ^ [_866637, _866639, _866641, _866643] : [-(tc_sum(_866643, _866639) = tc_sum(_866641, _866637)), _866643 = _866641, _866639 = _866637], (5504 ^ _782652) ^ [_866786, _866788, _866790, _866792] : [-(tc_prod(_866792, _866788) = tc_prod(_866790, _866786)), _866792 = _866790, _866788 = _866786], (5514 ^ _782652) ^ [_866935, _866937] : [_866937 = _866935, -(tc_Lazy__Sequence_Olazy__sequence(_866937) = tc_Lazy__Sequence_Olazy__sequence(_866935))], (5520 ^ _782652) ^ [_867020, _867022] : [_867022 = _867020, -(c_COMBI(_867022) = c_COMBI(_867020))], (5526 ^ _782652) ^ [_867105, _867107, _867109, _867111] : [-(c_COMBK(_867111, _867107) = c_COMBK(_867109, _867105)), _867111 = _867109, _867107 = _867105], (5536 ^ _782652) ^ [_867254, _867256, _867258, _867260, _867262, _867264] : [-(c_COMBC(_867264, _867260, _867256) = c_COMBC(_867262, _867258, _867254)), _867264 = _867262, _867260 = _867258, _867256 = _867254], (5550 ^ _782652) ^ [_867475, _867477, _867479, _867481, _867483, _867485] : [-(c_COMBS(_867485, _867481, _867477) = c_COMBS(_867483, _867479, _867475)), _867485 = _867483, _867481 = _867479, _867477 = _867475], (5564 ^ _782652) ^ [_867696, _867698] : [_867698 = _867696, -(c_Finite__Set_Ofinite(_867698) = c_Finite__Set_Ofinite(_867696))], (5570 ^ _782652) ^ [_867781, _867783] : [_867783 = _867781, -(c_member(_867783) = c_member(_867781))], (5576 ^ _782652) ^ [_867866, _867868] : [_867868 = _867866, -(c_Orderings_Oord__class_Oless__eq(_867868) = c_Orderings_Oord__class_Oless__eq(_867866))], (5582 ^ _782652) ^ [_867951, _867953, _867955, _867957] : [-(tc_fun(_867957, _867953) = tc_fun(_867955, _867951)), _867957 = _867955, _867953 = _867951], (5592 ^ _782652) ^ [_868100, _868102] : [_868102 = _868100, -(tc_Option_Ooption(_868102) = tc_Option_Ooption(_868100))], (5598 ^ _782652) ^ [_868185, _868187] : [_868187 = _868185, -(c_Option_Othe(_868187) = c_Option_Othe(_868185))], (5604 ^ _782652) ^ [_868270, _868272] : [_868272 = _868270, -(c_Option_Ooption_OSome(_868272) = c_Option_Ooption_OSome(_868270))], (5610 ^ _782652) ^ [_868355, _868357, _868359, _868361, _868363, _868365] : [-(c_Set_Oimage(_868365, _868361, _868357) = c_Set_Oimage(_868363, _868359, _868355)), _868365 = _868363, _868361 = _868359, _868357 = _868355], (5624 ^ _782652) ^ [_868576, _868578, _868580, _868582, _868584, _868586] : [-(c_COMBB(_868586, _868582, _868578) = c_COMBB(_868584, _868580, _868576)), _868586 = _868584, _868582 = _868580, _868578 = _868576], (5638 ^ _782652) ^ [_868797, _868799] : [_868799 = _868797, -(tc_Hoare__Mirabelle_Otriple(_868799) = tc_Hoare__Mirabelle_Otriple(_868797))], (5658 ^ _782652) ^ [_869099, _869101, _869103, _869105] : [-(hAPP(_869105, _869101) = hAPP(_869103, _869099)), _869105 = _869103, _869101 = _869099], (5644 ^ _782652) ^ [_868882, _868884, _868886, _868888, _868890, _868892] : [-(c_Map_Odom(_868892, _868888, _868884) = c_Map_Odom(_868890, _868886, _868882)), _868892 = _868890, _868888 = _868886, _868884 = _868882], (5668 ^ _782652) ^ [_872118, _872120] : [hAPP(_872118, 5669 ^ [_872118, _872120]) = hAPP(_872120, 5669 ^ [_872118, _872120]), -(_872118 = _872120)], (5675 ^ _782652) ^ [_872244, _872246, _872248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_872244), tc_HOL_Obool)), _872246), _872248)), -(c_Hoare__Mirabelle_Ohoare__derivs(_872244, _872248, _872246))], (5681 ^ _782652) ^ [_872349, _872351, _872353, _872355] : [c_Hoare__Mirabelle_Ohoare__derivs(_872349, _872351, _872353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_872349), tc_HOL_Obool)), _872355), _872353)), -(c_Hoare__Mirabelle_Ohoare__derivs(_872349, _872351, _872355))], (5691 ^ _782652) ^ [_872514, _872516, _872518, _872520] : [c_Hoare__Mirabelle_Ohoare__derivs(_872514, _872516, _872518), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_872514), tc_HOL_Obool)), _872516), _872520)), -(c_Hoare__Mirabelle_Ohoare__derivs(_872514, _872520, _872518))], (5701 ^ _782652) ^ [_872679, _872681, _872683, _872685] : [c_Hoare__Mirabelle_Ohoare__derivs(_872679, _872681, _872683), c_Hoare__Mirabelle_Ohoare__derivs(_872679, _872685, _872681), -(c_Hoare__Mirabelle_Ohoare__derivs(_872679, _872685, _872683))], (5711 ^ _782652) ^ [_872822, _872824] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _872822) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _872824), -(hBOOL(hAPP(c_Com_OWT, _872824)))], (5721 ^ _782652) ^ [_872973] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _872973))), -(hAPP(c_Com_Obody, _872973) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 5724 ^ [_872973]))], (5728 ^ _782652) ^ [_873076] : [5729 ^ _782652 : [(5730 ^ _782652) ^ [_873124] : [hAPP(c_Com_Obody, _873076) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _873124)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _873076))))], (5734 ^ _782652) ^ [_873188, _873190, _873192, _873194] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_873188), _873190)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_873192), hAPP(c_Set_Oimage(_873188, _873192, _873194), _873190))))], (5740 ^ _782652) ^ [_873299, _873301, _873303, _873305, _873307, _873309] : [_873299 = hAPP(_873301, _873303), hBOOL(hAPP(hAPP(c_member(_873305), _873303), _873307)), -(hBOOL(hAPP(hAPP(c_member(_873309), _873299), hAPP(c_Set_Oimage(_873305, _873309, _873301), _873307))))], (5750 ^ _782652) ^ [_873492, _873494, _873496, _873498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873492, tc_HOL_Obool)), _873494), _873496)), hBOOL(hAPP(hAPP(c_member(_873492), _873498), _873494)), -(hBOOL(hAPP(hAPP(c_member(_873492), _873498), _873496)))], (5760 ^ _782652) ^ [_873677, _873679, _873681, _873683, _873685] : [hAPP(_873677, _873679) = hAPP(c_Option_Ooption_OSome(_873681), _873683), -(hBOOL(hAPP(hAPP(c_member(_873685), _873679), c_Map_Odom(_873685, _873681, _873677))))], (5766 ^ _782652) ^ [_873798, _873800, _873802, _873804, _873806] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_873798), _873800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873802, tc_HOL_Obool)), _873804), hAPP(c_Set_Oimage(_873798, _873802, _873806), _873800))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_873802), _873804)))], (5776 ^ _782652) ^ [_873989, _873991, _873993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873989, tc_HOL_Obool)), _873991), _873993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873989, tc_HOL_Obool)), _873993), _873991)), -(_873991 = _873993)], (5786 ^ _782652) ^ [_874162, _874164, _874166, _874168] : [_874162 = _874164, 5791 ^ _782652 : [(5792 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_874166), _874168), _874162)))], (5794 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_874166), _874168), _874164)))]], 5795 ^ _782652 : [(5796 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874166), _874168), _874162))], (5798 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874166), _874168), _874164))]]], (5800 ^ _782652) ^ [_874425, _874427] : [class_Orderings_Opreorder(_874425), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874425), _874427), _874427)))], (5806 ^ _782652) ^ [_874532, _874534, _874536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874532, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_874532, tc_fun(_874532, tc_HOL_Obool), tc_HOL_Obool), c_member(_874532)), _874534)), hAPP(hAPP(c_COMBC(_874532, tc_fun(_874532, tc_HOL_Obool), tc_HOL_Obool), c_member(_874532)), _874536))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874532, tc_HOL_Obool)), _874534), _874536)))], (5812 ^ _782652) ^ [_874707, _874709, _874711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874707, tc_HOL_Obool)), _874709), _874711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874707, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_874707, tc_fun(_874707, tc_HOL_Obool), tc_HOL_Obool), c_member(_874707)), _874709)), hAPP(hAPP(c_COMBC(_874707, tc_fun(_874707, tc_HOL_Obool), tc_HOL_Obool), c_member(_874707)), _874711))))], (5818 ^ _782652) ^ [_874888, _874890] : [-(hAPP(c_Option_Othe(_874888), hAPP(c_Option_Ooption_OSome(_874888), _874890)) = _874890)], (5820 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (5822 ^ _782652) ^ [_874941, _874943, _874945] : [class_Orderings_Olinorder(_874941), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874941), _874943), _874945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874941), _874945), _874943)))], (5832 ^ _782652) ^ [_875061, _875063, _875065, _875067] : [class_Orderings_Oorder(_875061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875061), _875063), _875065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875061), _875067), _875063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875061), _875067), _875065)))], (5846 ^ _782652) ^ [_875294, _875296, _875298] : [class_Orderings_Oorder(_875294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875294), _875296), _875298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875294), _875298), _875296)), -(_875298 = _875296)], (5860 ^ _782652) ^ [_875507, _875509, _875511, _875513] : [class_Orderings_Opreorder(_875507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875507), _875509), _875511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875507), _875511), _875513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875507), _875509), _875513)))], (5874 ^ _782652) ^ [_875740, _875742, _875744] : [class_Orderings_Oorder(_875740), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875740), _875742), _875744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875740), _875744), _875742)), -(_875742 = _875744)], (5888 ^ _782652) ^ [_875953, _875955, _875957, _875959] : [class_Orderings_Oorder(_875953), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875953), _875955), _875957)), _875955 = _875959, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875953), _875959), _875957)))], (5902 ^ _782652) ^ [_876172, _876174, _876176, _876178] : [class_Orderings_Oord(_876172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876172), _876174), _876176)), _876176 = _876178, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876172), _876174), _876178)))], (5916 ^ _782652) ^ [_876391, _876393, _876395, _876397] : [class_Orderings_Oorder(_876391), _876393 = _876395, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876391), _876397), _876395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876391), _876397), _876393)))], (5930 ^ _782652) ^ [_876610, _876612, _876614, _876616] : [class_Orderings_Oord(_876610), _876612 = _876614, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876610), _876614), _876616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876610), _876612), _876616)))], (5944 ^ _782652) ^ [_876829, _876831, _876833] : [class_Orderings_Oorder(_876829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876829), _876831), _876833)), 5951 ^ _782652 : [(5952 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876829), _876833), _876831)), -(_876833 = _876831)], (5958 ^ _782652) ^ [] : [_876833 = _876831, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876829), _876833), _876831)))]]], (5964 ^ _782652) ^ [_877129, _877131, _877133] : [class_Orderings_Opreorder(_877129), _877131 = _877133, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877129), _877131), _877133)))], (5974 ^ _782652) ^ [_877274, _877276, _877278] : [class_Orderings_Oorder(_877274), 5977 ^ _782652 : [(5978 ^ _782652) ^ [] : [_877276 = _877278, 5981 ^ _782652 : [(5982 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877274), _877276), _877278)))], (5984 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877274), _877278), _877276)))]]], (5986 ^ _782652) ^ [] : [-(_877276 = _877278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877274), _877276), _877278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877274), _877278), _877276))]]], (5996 ^ _782652) ^ [_877601, _877603, _877605] : [class_Orderings_Olinorder(_877601), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877601), _877603), _877605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877601), _877605), _877603)))], (6006 ^ _782652) ^ [_877719, _877721, _877723, _877725] : [_877719 = _877721, hBOOL(hAPP(hAPP(c_member(_877723), _877721), _877725)), -(hBOOL(hAPP(hAPP(c_member(_877723), _877719), _877725)))], (6016 ^ _782652) ^ [_877884, _877886, _877888, _877890] : [_877884 = _877886, 6019 ^ _782652 : [(6020 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_877888), _877884), _877890)), -(hBOOL(hAPP(hAPP(c_member(_877888), _877886), _877890)))], (6026 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_877888), _877886), _877890)), -(hBOOL(hAPP(hAPP(c_member(_877888), _877884), _877890)))]]], (6032 ^ _782652) ^ [_878145, _878147, _878149, _878151] : [_878145 = _878147, 6035 ^ _782652 : [(6036 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_878149), _878151), _878145)), -(hBOOL(hAPP(hAPP(c_member(_878149), _878151), _878147)))], (6042 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_878149), _878151), _878147)), -(hBOOL(hAPP(hAPP(c_member(_878149), _878151), _878145)))]]], (6048 ^ _782652) ^ [_878424, _878426, _878428] : [hBOOL(hAPP(hAPP(c_member(_878424), _878426), hAPP(c_fequal, _878428))), -(_878426 = _878428)], (6054 ^ _782652) ^ [_878519, _878521, _878523] : [_878521 = _878523, -(hBOOL(hAPP(hAPP(c_member(_878519), _878521), hAPP(c_fequal, _878523))))], (6060 ^ _782652) ^ [_878638, _878640, _878642] : [hBOOL(hAPP(hAPP(c_member(_878638), _878640), _878642)), -(hBOOL(hAPP(_878642, _878640)))], (6066 ^ _782652) ^ [_878731, _878733, _878735] : [hBOOL(hAPP(_878735, _878733)), -(hBOOL(hAPP(hAPP(c_member(_878731), _878733), _878735)))], (6072 ^ _782652) ^ [_878830, _878832] : [class_Finite__Set_Ofinite(_878830), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_878830), _878832)))], (6078 ^ _782652) ^ [_878913, _878915] : [class_Finite__Set_Ofinite(_878913), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_878913), _878915)))], (6084 ^ _782652) ^ [_878996, _878998, _879000] : [_878996 = _878998, 6087 ^ _782652 : [(6088 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879000, tc_HOL_Obool)), _878996), _878998)))], (6090 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879000, tc_HOL_Obool)), _878998), _878996)))]]], (6092 ^ _782652) ^ [_879145, _879147, _879149, _879151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879145, tc_HOL_Obool)), _879147), _879149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879145, tc_HOL_Obool)), _879149), _879151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879145, tc_HOL_Obool)), _879147), _879151)))], (6102 ^ _782652) ^ [_879342, _879344, _879346, _879348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879342, tc_HOL_Obool)), _879344), _879346)), hBOOL(hAPP(_879344, _879348)), -(hBOOL(hAPP(_879346, _879348)))], (6112 ^ _782652) ^ [_879507, _879509, _879511] : [_879507 = _879509, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879511, tc_HOL_Obool)), _879509), _879507)))], (6118 ^ _782652) ^ [_879606, _879608, _879610] : [_879606 = _879608, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879610, tc_HOL_Obool)), _879606), _879608)))], (6124 ^ _782652) ^ [_879705, _879707, _879709, _879711] : [hBOOL(hAPP(_879705, _879707)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879709, tc_HOL_Obool)), _879705), _879711)), -(hBOOL(hAPP(_879711, _879707)))], (6134 ^ _782652) ^ [_879888, _879890, _879892] : [_879888 = _879890, 6137 ^ _782652 : [(6138 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879892, tc_HOL_Obool)), _879888), _879890)))], (6140 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879892, tc_HOL_Obool)), _879890), _879888)))]]], (6142 ^ _782652) ^ [_880029, _880031, _880033] : [-(_880029 = _880031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880033, tc_HOL_Obool)), _880029), _880031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880033, tc_HOL_Obool)), _880031), _880029))], (6152 ^ _782652) ^ [_880204, _880206] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880204, tc_HOL_Obool)), _880206), _880206)))], (6154 ^ _782652) ^ [_880257, _880259, _880261] : [hAPP(c_Option_Ooption_OSome(_880257), _880259) = hAPP(c_Option_Ooption_OSome(_880257), _880261), -(_880259 = _880261)], (6160 ^ _782652) ^ [_880352, _880354, _880356] : [_880354 = _880356, -(hAPP(c_Option_Ooption_OSome(_880352), _880354) = hAPP(c_Option_Ooption_OSome(_880352), _880356))], (6166 ^ _782652) ^ [_880468, _880470] : [hAPP(c_Com_Ocom_OBODY, _880468) = hAPP(c_Com_Ocom_OBODY, _880470), -(_880468 = _880470)], (6172 ^ _782652) ^ [_880553, _880555] : [_880553 = _880555, -(hAPP(c_Com_Ocom_OBODY, _880553) = hAPP(c_Com_Ocom_OBODY, _880555))], (6178 ^ _782652) ^ [_880662, _880664, _880666] : [hAPP(hAPP(c_COMBC(_880662, tc_fun(_880662, tc_HOL_Obool), tc_HOL_Obool), c_member(_880662)), _880664) = hAPP(hAPP(c_COMBC(_880662, tc_fun(_880662, tc_HOL_Obool), tc_HOL_Obool), c_member(_880662)), _880666), -(_880664 = _880666)], (6184 ^ _782652) ^ [_880797, _880799, _880801] : [_880799 = _880801, -(hAPP(hAPP(c_COMBC(_880797, tc_fun(_880797, tc_HOL_Obool), tc_HOL_Obool), c_member(_880797)), _880799) = hAPP(hAPP(c_COMBC(_880797, tc_fun(_880797, tc_HOL_Obool), tc_HOL_Obool), c_member(_880797)), _880801))], (6190 ^ _782652) ^ [_880938, _880940, _880942, _880944, _880946, _880948] : [-(hAPP(c_Set_Oimage(_880938, _880940, _880942), hAPP(c_Set_Oimage(_880944, _880938, _880946), _880948)) = hAPP(c_Set_Oimage(_880944, _880940, hAPP(hAPP(c_COMBB(_880938, _880940, _880944), _880942), _880946)), _880948))], (6192 ^ _782652) ^ [_881002, _881004, _881006, _881008, _881010] : [class_Orderings_Oord(_881002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881004, _881002)), _881006), _881008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881002), hAPP(_881006, _881010)), hAPP(_881008, _881010))))], (6202 ^ _782652) ^ [_881187, _881189, _881191, _881193, _881195] : [class_Orderings_Oord(_881187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881189, _881187)), _881191), _881193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881187), hAPP(_881191, _881195)), hAPP(_881193, _881195))))], (6212 ^ _782652) ^ [_881372, _881374, _881376, _881378] : [class_Orderings_Oord(_881372), 6215 ^ _782652 : [(6216 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881374, _881372)), _881376), _881378)), 6219 ^ _782652 : [(6220 ^ _782652) ^ [_881529] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881372), hAPP(_881376, _881529)), hAPP(_881378, _881529))))]]], (6222 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881372), hAPP(_881376, 6223 ^ [_881372, _881374, _881376, _881378])), hAPP(_881378, 6223 ^ [_881372, _881374, _881376, _881378]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881374, _881372)), _881376), _881378)))]]], (6229 ^ _782652) ^ [_881718, _881720, _881722, _881724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881718, tc_HOL_Obool)), _881720), _881722)), hBOOL(hAPP(hAPP(c_member(_881718), _881724), _881720)), -(hBOOL(hAPP(hAPP(c_member(_881718), _881724), _881722)))], (6239 ^ _782652) ^ [_881903, _881905, _881907, _881909] : [hBOOL(hAPP(hAPP(c_member(_881903), _881905), _881907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881903, tc_HOL_Obool)), _881907), _881909)), -(hBOOL(hAPP(hAPP(c_member(_881903), _881905), _881909)))], (6249 ^ _782652) ^ [_882088, _882090, _882092, _882094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882088, tc_HOL_Obool)), _882090), _882092)), hBOOL(hAPP(hAPP(c_member(_882088), _882094), _882090)), -(hBOOL(hAPP(hAPP(c_member(_882088), _882094), _882092)))], (6259 ^ _782652) ^ [_882273, _882275, _882277, _882279, _882281, _882283] : [hBOOL(hAPP(hAPP(c_member(_882273), _882275), _882277)), _882279 = hAPP(_882281, _882275), -(hBOOL(hAPP(hAPP(c_member(_882283), _882279), hAPP(c_Set_Oimage(_882273, _882283, _882281), _882277))))], (6269 ^ _782652) ^ [_882466, _882468, _882470, _882472, _882474] : [hBOOL(hAPP(hAPP(c_member(_882466), _882468), _882470)), -(hBOOL(hAPP(hAPP(c_member(_882472), hAPP(_882474, _882468)), hAPP(c_Set_Oimage(_882466, _882472, _882474), _882470))))], (6275 ^ _782652) ^ [_882621, _882623, _882625, _882627, _882629] : [hBOOL(hAPP(hAPP(c_member(_882621), _882623), hAPP(c_Set_Oimage(_882625, _882621, _882627), _882629))), 6279 ^ _782652 : [(6280 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_882625), 6278 ^ [_882621, _882623, _882625, _882627, _882629]), _882629)))], (6282 ^ _782652) ^ [] : [-(_882623 = hAPP(_882627, 6278 ^ [_882621, _882623, _882625, _882627, _882629]))]]], (6284 ^ _782652) ^ [_882805, _882807, _882809, _882811, _882813] : [-(hBOOL(hAPP(hAPP(c_member(_882805), _882807), hAPP(c_Set_Oimage(_882809, _882805, _882811), _882813)))), 6285 ^ _782652 : [(6286 ^ _782652) ^ [_882875] : [hBOOL(hAPP(hAPP(c_member(_882809), _882875), _882813)), _882807 = hAPP(_882811, _882875)]]], (6294 ^ _782652) ^ [_883023, _883025, _883027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883023, tc_HOL_Obool)), _883025), _883027)), hBOOL(hAPP(c_Finite__Set_Ofinite(_883023), _883027)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_883023), _883025)))], (6304 ^ _782652) ^ [_883192, _883194, _883196] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_883192), _883194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883192, tc_HOL_Obool)), _883196), _883194)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_883192), _883196)))], (6314 ^ _782652) ^ [_883361, _883363, _883365, _883367, _883369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883361, tc_HOL_Obool)), _883363), _883365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883367, tc_HOL_Obool)), hAPP(c_Set_Oimage(_883361, _883367, _883369), _883363)), hAPP(c_Set_Oimage(_883361, _883367, _883369), _883365))))], (6320 ^ _782652) ^ [_883536, _883538, _883540, _883542, _883544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883536, tc_HOL_Obool)), _883538), hAPP(c_Set_Oimage(_883540, _883536, _883542), _883544))), 6324 ^ _782652 : [(6325 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883540, tc_HOL_Obool)), 6323 ^ [_883536, _883538, _883540, _883542, _883544]), _883544)))], (6327 ^ _782652) ^ [] : [-(_883538 = hAPP(c_Set_Oimage(_883540, _883536, _883542), 6323 ^ [_883536, _883538, _883540, _883542, _883544]))]]], (6329 ^ _782652) ^ [_883740, _883742, _883744, _883746, _883748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883740, tc_HOL_Obool)), _883742), hAPP(c_Set_Oimage(_883744, _883740, _883746), _883748)))), 6330 ^ _782652 : [(6331 ^ _782652) ^ [_883820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883744, tc_HOL_Obool)), _883820), _883748)), _883742 = hAPP(c_Set_Oimage(_883744, _883740, _883746), _883820)]]], (6339 ^ _782652) ^ [_883985, _883987] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), _883985), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), _883987)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _883987)), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), _883987)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _883985, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), _883987)))], (6349 ^ _782652) ^ [_884152] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _884152))), -(hAPP(c_Com_Obody, _884152) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 6352 ^ [_884152]))], (6356 ^ _782652) ^ [_884281, _884283, _884285] : [hBOOL(hAPP(hAPP(c_member(_884281), _884283), c_Option_Oset(_884281, _884285))), -(_884285 = hAPP(c_Option_Ooption_OSome(_884281), _884283))], (6362 ^ _782652) ^ [_884386, _884388, _884390] : [_884390 = hAPP(c_Option_Ooption_OSome(_884386), _884388), -(hBOOL(hAPP(hAPP(c_member(_884386), _884388), c_Option_Oset(_884386, _884390))))], (6368 ^ _782652) ^ [_884497, _884499, _884501, _884503, _884505] : [-(hAPP(c_Option_Ooption_Ooption__case(_884497, _884499, _884501, _884503), hAPP(c_Option_Ooption_OSome(_884499), _884505)) = hAPP(_884503, _884505))], (6370 ^ _782652) ^ [_884544, _884546, _884548, _884550, _884552] : [-(c_Option_Ooption_Ooption__rec(_884544, _884546, _884548, _884550, hAPP(c_Option_Ooption_OSome(_884546), _884552)) = hAPP(_884550, _884552))], (6372 ^ _782652) ^ [_884589, _884591, _884593, _884595, _884597, _884599, _884601, _884603] : [c_Finite__Set_Ofolding__image__simple__idem(_884589, _884591, _884593, _884595, _884597, _884599), hBOOL(hAPP(c_Finite__Set_Ofinite(_884591), _884601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884591, tc_HOL_Obool)), _884603), _884601)), -(hAPP(hAPP(_884593, hAPP(_884599, _884603)), hAPP(_884599, _884601)) = hAPP(_884599, _884601))], (6386 ^ _782652) ^ [_884872, _884874, _884876, _884878, _884880, _884882, _884884, _884886] : [c_Finite__Set_Ofolding__image__simple__idem(_884872, _884874, _884876, _884878, _884880, _884882), hBOOL(hAPP(c_Finite__Set_Ofinite(_884874), _884884)), hBOOL(hAPP(hAPP(c_member(_884874), _884886), _884884)), -(hAPP(hAPP(_884876, hAPP(_884880, _884886)), hAPP(_884882, _884884)) = hAPP(_884882, _884884))], (6400 ^ _782652) ^ [_885149, _885151] : [-(hAPP(c_Set_Oimage(_885149, _885149, c_COMBI(_885149)), _885151) = _885151)], (6402 ^ _782652) ^ [_885183, _885185, _885187, _885189, _885191] : [hAPP(_885183, _885185) = hAPP(c_Option_Ooption_OSome(_885187), _885189), -(hBOOL(hAPP(hAPP(c_member(_885187), _885189), c_Map_Oran(_885191, _885187, _885183))))], (6408 ^ _782652) ^ [_885316, _885318] : [c_Option_Ois__none(_885316, hAPP(c_Option_Ooption_OSome(_885316), _885318))], (6410 ^ _782652) ^ [_885346, _885348, _885350, _885352, _885354] : [c_Finite__Set_Ofolding__one__idem(_885346, _885348, _885350), hBOOL(hAPP(c_Finite__Set_Ofinite(_885346), _885352)), hBOOL(hAPP(hAPP(c_member(_885346), _885354), _885352)), -(hAPP(hAPP(_885348, _885354), hAPP(_885350, _885352)) = hAPP(_885350, _885352))], (6424 ^ _782652) ^ [_885593, _885595, _885597, _885599] : [hBOOL(hAPP(hAPP(c_member(_885593), _885595), c_Map_Odom(_885593, _885597, _885599))), -(hAPP(_885599, _885595) = hAPP(c_Option_Ooption_OSome(_885597), 6427 ^ [_885593, _885595, _885597, _885599]))], (6431 ^ _782652) ^ [_885728, _885730, _885732, _885734] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_885728, tc_HOL_Obool)), _885730), _885732), _885734)), -(hBOOL(hAPP(_885730, _885734))), -(hBOOL(hAPP(_885732, _885734)))], (6441 ^ _782652) ^ [_885858, _885860, _885862, _885864] : [6442 ^ _782652 : [(6443 ^ _782652) ^ [] : [hBOOL(hAPP(_885858, _885860))], (6445 ^ _782652) ^ [] : [hBOOL(hAPP(_885862, _885860))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_885864, tc_HOL_Obool)), _885862), _885858), _885860)))], (6449 ^ _782652) ^ [_886013, _886015, _886017, _886019] : [hBOOL(hAPP(hAPP(c_member(_886013), _886015), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886013, tc_HOL_Obool)), _886017), _886019))), -(hBOOL(hAPP(hAPP(c_member(_886013), _886015), _886017))), -(hBOOL(hAPP(hAPP(c_member(_886013), _886015), _886019)))], (6459 ^ _782652) ^ [_886173, _886175, _886177, _886179] : [6460 ^ _782652 : [(6461 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886173), _886175), _886177))], (6463 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886173), _886175), _886179))]], -(hBOOL(hAPP(hAPP(c_member(_886173), _886175), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886173, tc_HOL_Obool)), _886179), _886177))))], (6467 ^ _782652) ^ [_886358, _886360] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886358, tc_HOL_Obool)), _886360), _886360) = _886360)], (6469 ^ _782652) ^ [_886394, _886396, _886398] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886394, tc_HOL_Obool)), _886396), _886398) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886394, tc_HOL_Obool)), _886398), _886396))], (6471 ^ _782652) ^ [_886443, _886445, _886447] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886443, tc_HOL_Obool)), _886445), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886443, tc_HOL_Obool)), _886445), _886447)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886443, tc_HOL_Obool)), _886445), _886447))], (6473 ^ _782652) ^ [_886503, _886505, _886507, _886509] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886503, tc_HOL_Obool)), _886505), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886503, tc_HOL_Obool)), _886507), _886509)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886503, tc_HOL_Obool)), _886507), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886503, tc_HOL_Obool)), _886505), _886509)))], (6475 ^ _782652) ^ [_886576, _886578, _886580, _886582] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886576, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886576, tc_HOL_Obool)), _886578), _886580)), _886582) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886576, tc_HOL_Obool)), _886578), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886576, tc_HOL_Obool)), _886580), _886582)))], (6477 ^ _782652) ^ [_886670, _886672, _886674, _886676] : [6478 ^ _782652 : [(6479 ^ _782652) ^ [_886780] : [hBOOL(hAPP(hAPP(c_member(_886670), _886780), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886670, tc_HOL_Obool)), _886672), _886674))), hBOOL(hAPP(_886676, _886780))]], 6487 ^ _782652 : [(6488 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886670), 6486 ^ [_886670, _886672, _886674, _886676]), _886672)))], (6490 ^ _782652) ^ [] : [-(hBOOL(hAPP(_886676, 6486 ^ [_886670, _886672, _886674, _886676])))]], 6492 ^ _782652 : [(6493 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886670), 6491 ^ [_886670, _886672, _886674, _886676]), _886674)))], (6495 ^ _782652) ^ [] : [-(hBOOL(hAPP(_886676, 6491 ^ [_886670, _886672, _886674, _886676])))]]], (6497 ^ _782652) ^ [_887069, _887071, _887073, _887075] : [6511 ^ _782652 : [(6512 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887069), 6510 ^ [_887069, _887071, _887073, _887075]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887069, tc_HOL_Obool)), _887071), _887073))))], (6514 ^ _782652) ^ [] : [-(hBOOL(hAPP(_887075, 6510 ^ [_887069, _887071, _887073, _887075])))]], 6498 ^ _782652 : [(6499 ^ _782652) ^ [_887182] : [hBOOL(hAPP(hAPP(c_member(_887069), _887182), _887071)), hBOOL(hAPP(_887075, _887182))], (6505 ^ _782652) ^ [_887278] : [hBOOL(hAPP(hAPP(c_member(_887069), _887278), _887073)), hBOOL(hAPP(_887075, _887278))]]], (6535 ^ _782652) ^ [_887915, _887917, _887919, _887921] : [6539 ^ _782652 : [(6540 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887915), 6538 ^ [_887915, _887917, _887919, _887921]), _887917)))], (6542 ^ _782652) ^ [] : [hBOOL(hAPP(_887921, 6538 ^ [_887915, _887917, _887919, _887921]))]], 6544 ^ _782652 : [(6545 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887915), 6543 ^ [_887915, _887917, _887919, _887921]), _887919)))], (6547 ^ _782652) ^ [] : [hBOOL(hAPP(_887921, 6543 ^ [_887915, _887917, _887919, _887921]))]], 6548 ^ _782652 : [(6549 ^ _782652) ^ [_888248] : [hBOOL(hAPP(hAPP(c_member(_887915), _888248), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887915, tc_HOL_Obool)), _887917), _887919))), -(hBOOL(hAPP(_887921, _888248)))]]], (6516 ^ _782652) ^ [_887493, _887495, _887497, _887499] : [6518 ^ _782652 : [(6519 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887493), 6517 ^ [_887493, _887495, _887497, _887499]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_887493, tc_HOL_Obool)), _887495), _887497))))], (6521 ^ _782652) ^ [] : [hBOOL(hAPP(_887499, 6517 ^ [_887493, _887495, _887497, _887499]))]], 6522 ^ _782652 : [(6523 ^ _782652) ^ [_887713] : [hBOOL(hAPP(hAPP(c_member(_887493), _887713), _887495)), -(hBOOL(hAPP(_887499, _887713)))], (6529 ^ _782652) ^ [_887810] : [hBOOL(hAPP(hAPP(c_member(_887493), _887810), _887497)), -(hBOOL(hAPP(_887499, _887810)))]]], (6555 ^ _782652) ^ [_888379, _888381, _888383, _888385] : [hBOOL(hAPP(_888379, _888381)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888383, tc_HOL_Obool)), _888379), _888385), _888381)))], (6561 ^ _782652) ^ [_888490, _888492, _888494, _888496] : [hBOOL(hAPP(_888490, _888492)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888494, tc_HOL_Obool)), _888496), _888490), _888492)))], (6567 ^ _782652) ^ [_888601, _888603, _888605, _888607] : [c_Finite__Set_Ofolding__one__idem(_888601, _888603, _888605), -(hAPP(hAPP(_888603, _888607), _888607) = _888607)], (6573 ^ _782652) ^ [_888696, _888698, _888700, _888702, _888704, _888706, _888708] : [c_Finite__Set_Ofolding__image__simple__idem(_888696, _888698, _888700, _888702, _888704, _888706), -(hAPP(hAPP(_888700, _888708), _888708) = _888708)], (6579 ^ _782652) ^ [_888803, _888805, _888807, _888809, _888811, _888813, _888815, _888817] : [c_Finite__Set_Ofolding__image__simple__idem(_888803, _888805, _888807, _888809, _888811, _888813), hBOOL(hAPP(c_Finite__Set_Ofinite(_888805), _888815)), hBOOL(hAPP(c_Finite__Set_Ofinite(_888805), _888817)), -(hAPP(_888813, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_888805, tc_HOL_Obool)), _888815), _888817)) = hAPP(hAPP(_888807, hAPP(_888813, _888815)), hAPP(_888813, _888817)))], (6603 ^ _782652) ^ [_889271, _889273, _889275, _889277] : [6604 ^ _782652 : [(6605 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889271), _889273), _889275))], (6607 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889271), _889273), _889277))]], -(hBOOL(hAPP(hAPP(c_member(_889271), _889273), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889271, tc_HOL_Obool)), _889275), _889277))))], (6593 ^ _782652) ^ [_889117, _889119, _889121, _889123] : [hBOOL(hAPP(hAPP(c_member(_889117), _889119), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889117, tc_HOL_Obool)), _889121), _889123))), -(hBOOL(hAPP(hAPP(c_member(_889117), _889119), _889121))), -(hBOOL(hAPP(hAPP(c_member(_889117), _889119), _889123)))], (6611 ^ _782652) ^ [_889456, _889458, _889460, _889462] : [hBOOL(hAPP(hAPP(c_member(_889456), _889458), _889460)), -(hBOOL(hAPP(hAPP(c_member(_889456), _889458), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889456, tc_HOL_Obool)), _889460), _889462))))], (6617 ^ _782652) ^ [_889587, _889589, _889591, _889593] : [hBOOL(hAPP(hAPP(c_member(_889587), _889589), _889591)), -(hBOOL(hAPP(hAPP(c_member(_889587), _889589), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889587, tc_HOL_Obool)), _889593), _889591))))], (6623 ^ _782652) ^ [_889736, _889738, _889740] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_889736), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889736, tc_HOL_Obool)), _889738), _889740))), 6626 ^ _782652 : [(6627 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_889736), _889738)))], (6629 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_889736), _889740)))]]], (6631 ^ _782652) ^ [_889883, _889885, _889887] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_889883), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_889883, tc_HOL_Obool)), _889885), _889887)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_889883), _889885)), hBOOL(hAPP(c_Finite__Set_Ofinite(_889883), _889887))], (6641 ^ _782652) ^ [_890064, _890066, _890068] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_890064), _890066)), hBOOL(hAPP(c_Finite__Set_Ofinite(_890064), _890068)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_890064), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890064, tc_HOL_Obool)), _890066), _890068))))], (6651 ^ _782652) ^ [_890243, _890245, _890247] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890243, tc_HOL_Obool)), _890245), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890243, tc_HOL_Obool)), _890245), _890247))))], (6653 ^ _782652) ^ [_890291, _890293, _890295] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890291, tc_HOL_Obool)), _890293), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890291, tc_HOL_Obool)), _890295), _890293))))], (6655 ^ _782652) ^ [_890357, _890359, _890361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890357, tc_HOL_Obool)), _890359), _890361)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890357, tc_HOL_Obool)), _890359), _890361) = _890361)], (6661 ^ _782652) ^ [_890474, _890476, _890478] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890474, tc_HOL_Obool)), _890476), _890478) = _890478, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890474, tc_HOL_Obool)), _890476), _890478)))], (6667 ^ _782652) ^ [_890597, _890599, _890601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890597, tc_HOL_Obool)), _890599), _890601)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890597, tc_HOL_Obool)), _890599), _890601) = _890601)], (6673 ^ _782652) ^ [_890718, _890720, _890722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890718, tc_HOL_Obool)), _890720), _890722)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890718, tc_HOL_Obool)), _890722), _890720) = _890722)], (6679 ^ _782652) ^ [_890839, _890841, _890843, _890845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890839, tc_HOL_Obool)), _890841), _890843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890839, tc_HOL_Obool)), _890845), _890843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890839, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890839, tc_HOL_Obool)), _890841), _890845)), _890843)))], (6689 ^ _782652) ^ [_891058, _891060, _891062, _891064, _891066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891058, tc_HOL_Obool)), _891060), _891062)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891058, tc_HOL_Obool)), _891064), _891066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891058, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891058, tc_HOL_Obool)), _891060), _891064)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891058, tc_HOL_Obool)), _891062), _891066))))], (6699 ^ _782652) ^ [_891303, _891305, _891307, _891309, _891311] : [-(hAPP(c_Set_Oimage(_891303, _891305, _891307), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891303, tc_HOL_Obool)), _891309), _891311)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891305, tc_HOL_Obool)), hAPP(c_Set_Oimage(_891303, _891305, _891307), _891309)), hAPP(c_Set_Oimage(_891303, _891305, _891307), _891311)))], (6701 ^ _782652) ^ [_891398, _891400, _891402, _891404] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891398, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_891398, tc_fun(_891398, tc_HOL_Obool), tc_HOL_Obool), c_member(_891398)), _891400)), hAPP(hAPP(c_COMBC(_891398, tc_fun(_891398, tc_HOL_Obool), tc_HOL_Obool), c_member(_891398)), _891402)), _891404)), -(hBOOL(hAPP(hAPP(c_member(_891398), _891404), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891398, tc_HOL_Obool)), _891400), _891402))))], (6707 ^ _782652) ^ [_891597, _891599, _891601, _891603] : [hBOOL(hAPP(hAPP(c_member(_891597), _891603), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891597, tc_HOL_Obool)), _891599), _891601))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891597, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_891597, tc_fun(_891597, tc_HOL_Obool), tc_HOL_Obool), c_member(_891597)), _891599)), hAPP(hAPP(c_COMBC(_891597, tc_fun(_891597, tc_HOL_Obool), tc_HOL_Obool), c_member(_891597)), _891601)), _891603)))], (6713 ^ _782652) ^ [_891802, _891804, _891806, _891808, _891810] : [class_Lattices_Olattice(_891802), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891804, _891802)), _891806), _891808), _891810) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_891802), hAPP(_891806, _891810)), hAPP(_891808, _891810)))], (6719 ^ _782652) ^ [_891939, _891941, _891943, _891945, _891947] : [c_Hoare__Mirabelle_Ohoare__derivs(_891939, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_891939), tc_HOL_Obool)), _891941), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_891939), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939))), hAPP(hAPP(c_COMBB(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_891939)), _891943)), c_Com_Ocom_OBODY)), _891945)), _891947)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_891939), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939))), hAPP(hAPP(c_COMBB(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_891939)), _891943)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _891945)), _891947)), -(c_Hoare__Mirabelle_Ohoare__derivs(_891939, _891941, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_891939), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939))), hAPP(hAPP(c_COMBB(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_891939, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891939))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_891939)), _891943)), c_Com_Ocom_OBODY)), _891945)), _891947)))], (6725 ^ _782652) ^ [_892460, _892462, _892464, _892466, _892468] : [class_Lattices_Olattice(_892460), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892462, _892460)), _892464), _892466), _892468) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892460), hAPP(_892464, _892468)), hAPP(_892466, _892468)))], (6731 ^ _782652) ^ [_892597, _892599, _892601] : [class_Lattices_Olattice(_892597), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892597), _892599), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892597), _892599), _892601))))], (6737 ^ _782652) ^ [_892704, _892706, _892708] : [class_Lattices_Osemilattice__sup(_892704), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892704), _892706), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892704), _892706), _892708))))], (6743 ^ _782652) ^ [_892811, _892813, _892815] : [class_Lattices_Olattice(_892811), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892811), _892813), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892811), _892815), _892813))))], (6749 ^ _782652) ^ [_892918, _892920, _892922] : [class_Lattices_Osemilattice__sup(_892918), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_892918), _892920), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_892918), _892922), _892920))))], (6755 ^ _782652) ^ [_893025, _893027, _893029] : [class_Lattices_Osemilattice__sup(_893025), 6758 ^ _782652 : [(6759 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893025), _893027), _893029)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893025), _893027), _893029) = _893029)], (6765 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893025), _893027), _893029) = _893029, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893025), _893027), _893029)))]]], (6771 ^ _782652) ^ [_893281, _893283, _893285, _893287] : [class_Lattices_Osemilattice__sup(_893281), 6774 ^ _782652 : [(6775 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893281), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893281), _893283), _893285)), _893287)), 6778 ^ _782652 : [(6779 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893281), _893283), _893287)))], (6781 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893281), _893285), _893287)))]]], (6783 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893281), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893281), _893283), _893285)), _893287))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893281), _893283), _893287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893281), _893285), _893287))]]], (6793 ^ _782652) ^ [_893661, _893663, _893665, _893667] : [class_Lattices_Osemilattice__sup(_893661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893661), _893663), _893665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893661), _893663), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893661), _893665), _893667))))], (6803 ^ _782652) ^ [_893840, _893842, _893844, _893846] : [class_Lattices_Osemilattice__sup(_893840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893840), _893842), _893844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_893840), _893842), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_893840), _893846), _893844))))], (6813 ^ _782652) ^ [_894019, _894021, _894023] : [class_Lattices_Osemilattice__sup(_894019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_894019), _894021), _894023)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894019), _894021), _894023) = _894023)], (6823 ^ _782652) ^ [_894210, _894212, _894214, _894216, _894218, _894220, _894222] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894210), _894212), _894214), _894216) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894210), _894218), _894220), _894222), 6826 ^ _782652 : [(6827 ^ _782652) ^ [] : [-(_894212 = _894218)], (6829 ^ _782652) ^ [] : [-(_894214 = _894220)], (6831 ^ _782652) ^ [] : [-(_894216 = _894222)]]], (6833 ^ _782652) ^ [_894387, _894389, _894391, _894393, _894395, _894397, _894399] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894387), _894389), _894391), _894393) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894387), _894395), _894397), _894399)), _894389 = _894395, _894391 = _894397, _894393 = _894399], (6847 ^ _782652) ^ [_894644, _894646] : [class_Lattices_Osemilattice__sup(_894644), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894644), _894646), _894646) = _894646)], (6853 ^ _782652) ^ [_894735, _894737] : [class_Lattices_Osemilattice__sup(_894735), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894735), _894737), _894737) = _894737)], (6859 ^ _782652) ^ [_894826, _894828, _894830] : [class_Lattices_Osemilattice__sup(_894826), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894826), _894828), _894830) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894826), _894830), _894828))], (6865 ^ _782652) ^ [_894935, _894937, _894939] : [class_Lattices_Olattice(_894935), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894935), _894937), _894939) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_894935), _894939), _894937))], (6871 ^ _782652) ^ [_895044, _895046, _895048] : [class_Lattices_Osemilattice__sup(_895044), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895044), _895046), _895048) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895044), _895048), _895046))], (6877 ^ _782652) ^ [_895153, _895155, _895157] : [class_Lattices_Osemilattice__sup(_895153), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895153), _895155), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895153), _895155), _895157)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895153), _895155), _895157))], (6883 ^ _782652) ^ [_895278, _895280, _895282] : [class_Lattices_Olattice(_895278), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895278), _895280), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895278), _895280), _895282)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895278), _895280), _895282))], (6889 ^ _782652) ^ [_895403, _895405, _895407] : [class_Lattices_Osemilattice__sup(_895403), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895403), _895405), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895403), _895405), _895407)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895403), _895405), _895407))], (6895 ^ _782652) ^ [_895528, _895530, _895532, _895534] : [class_Lattices_Osemilattice__sup(_895528), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895528), _895530), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895528), _895532), _895534)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895528), _895532), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895528), _895530), _895534)))], (6901 ^ _782652) ^ [_895671, _895673, _895675, _895677] : [class_Lattices_Olattice(_895671), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895671), _895673), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895671), _895675), _895677)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895671), _895675), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895671), _895673), _895677)))], (6907 ^ _782652) ^ [_895814, _895816, _895818, _895820] : [class_Lattices_Osemilattice__sup(_895814), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895814), _895816), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895814), _895818), _895820)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895814), _895818), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895814), _895816), _895820)))], (6913 ^ _782652) ^ [_895957, _895959, _895961, _895963] : [class_Lattices_Osemilattice__sup(_895957), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895957), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895957), _895959), _895961)), _895963) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895957), _895959), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895957), _895961), _895963)))], (6919 ^ _782652) ^ [_896100, _896102, _896104, _896106] : [class_Lattices_Olattice(_896100), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896100), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896100), _896102), _896104)), _896106) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896100), _896102), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896100), _896104), _896106)))], (6925 ^ _782652) ^ [_896243, _896245, _896247, _896249] : [class_Lattices_Osemilattice__sup(_896243), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896243), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896243), _896245), _896247)), _896249) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896243), _896245), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896243), _896247), _896249)))], (6931 ^ _782652) ^ [_896386, _896388, _896390, _896392] : [class_Lattices_Osemilattice__sup(_896386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896386), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896386), _896388), _896390)), _896392)), 6938 ^ _782652 : [(6939 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896386), _896388), _896392)))], (6941 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896386), _896390), _896392)))]]], (6943 ^ _782652) ^ [_896609, _896611, _896613, _896615, _896617] : [class_Lattices_Osemilattice__sup(_896609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896609), _896611), _896613)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896609), _896615), _896617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896609), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896609), _896611), _896615)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896609), _896613), _896617))))], (6957 ^ _782652) ^ [_896880, _896882, _896884, _896886] : [class_Lattices_Osemilattice__sup(_896880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896880), _896882), _896884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896880), _896886), _896884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_896880), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896880), _896882), _896886)), _896884)))], (6971 ^ _782652) ^ [_897129, _897131, _897133, _897135] : [class_Lattices_Osemilattice__sup(_897129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897129), _897131), _897133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897129), _897135), _897133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897129), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897129), _897131), _897135)), _897133)))], (6985 ^ _782652) ^ [_897378, _897380, _897382] : [class_Lattices_Osemilattice__sup(_897378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897378), _897380), _897382)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897378), _897382), _897380) = _897382)], (6995 ^ _782652) ^ [_897539, _897541, _897543, _897545, _897547] : [c_Hoare__Mirabelle_Ohoare__valids(_897539, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_897539), tc_HOL_Obool)), _897541), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_897539), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539))), hAPP(hAPP(c_COMBB(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_897539)), _897543)), c_Com_Ocom_OBODY)), _897545)), _897547)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_897539), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539))), hAPP(hAPP(c_COMBB(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_897539)), _897543)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _897545)), _897547)), -(c_Hoare__Mirabelle_Ohoare__valids(_897539, _897541, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_897539), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539))), hAPP(hAPP(c_COMBB(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_897539, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_897539))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_897539)), _897543)), c_Com_Ocom_OBODY)), _897545)), _897547)))], (7001 ^ _782652) ^ [_898060, _898062, _898064, _898066, _898068, _898070] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_898060, _898062, _898064, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_898060), _898066), _898068), _898070)) = hAPP(hAPP(hAPP(_898064, _898066), _898068), _898070))], (7003 ^ _782652) ^ [_898118, _898120, _898122, _898124, _898126, _898128] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_898118, _898120, _898122, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_898118), _898124), _898126), _898128)) = hAPP(hAPP(hAPP(_898122, _898124), _898126), _898128))], (7005 ^ _782652) ^ [_898176, _898178, _898180, _898182, _898184, _898186] : [c_Hoare__Mirabelle_Ohoare__derivs(_898176, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_898176), tc_HOL_Obool)), _898178), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_898176), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_898176, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_898176)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_898176, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_898176))), hAPP(hAPP(c_COMBB(tc_fun(_898176, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_898176, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_898176))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_898176)), _898180)), c_Com_Ocom_OBODY)), _898182)), _898184)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_898176), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_898176, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_898176)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_898176, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_898176))), hAPP(hAPP(c_COMBB(tc_fun(_898176, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_898176, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_898176))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_898176)), _898180)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _898182)), _898184)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _898186), _898184)), -(c_Hoare__Mirabelle_Ohoare__derivs(_898176, _898178, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_898176)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_898176), hAPP(_898180, _898186)), hAPP(c_Com_Ocom_OBODY, _898186)), hAPP(_898182, _898186))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_898176), tc_HOL_Obool)))))], (7015 ^ _782652) ^ [_898728, _898730, _898732, _898734, _898736, _898738] : [hBOOL(hAPP(hAPP(c_member(_898728), _898730), _898732)), -(hAPP(c_Fun_Ooverride__on(_898728, _898734, _898736, _898738, _898732), _898730) = hAPP(_898738, _898730))], (7021 ^ _782652) ^ [_898845, _898847, _898849, _898851, _898853, _898855] : [-(hBOOL(hAPP(hAPP(c_member(_898845), _898847), _898849))), -(hAPP(c_Fun_Ooverride__on(_898845, _898851, _898853, _898855, _898849), _898847) = hAPP(_898853, _898847))], (7027 ^ _782652) ^ [_898910, _898912, _898914, _898916, _898918] : [hBOOL(hAPP(hAPP(c_member(_898910), _898912), hAPP(c_Set_Oimage(_898914, _898910, _898916), _898918))), 7031 ^ _782652 : [(7032 ^ _782652) ^ [] : [-(_898912 = hAPP(_898916, 7030 ^ [_898910, _898912, _898914, _898916, _898918]))], (7034 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898914), 7030 ^ [_898910, _898912, _898914, _898916, _898918]), _898918)))]]], (7036 ^ _782652) ^ [_899102, _899104, _899106, _899108, _899110] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_899102), _899104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899102, tc_HOL_Obool)), _899104), hAPP(c_Set_Oimage(_899106, _899102, _899108), _899110))), 7044 ^ _782652 : [(7045 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899106, tc_HOL_Obool)), 7043 ^ [_899102, _899104, _899106, _899108, _899110]), _899110)))], (7047 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_899106), 7043 ^ [_899102, _899104, _899106, _899108, _899110])))], (7049 ^ _782652) ^ [] : [-(_899104 = hAPP(c_Set_Oimage(_899106, _899102, _899108), 7043 ^ [_899102, _899104, _899106, _899108, _899110]))]]], (7051 ^ _782652) ^ [_899421, _899423, _899425, _899427, _899429] : [7053 ^ _782652 : [(7054 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899421), 7052 ^ [_899421, _899423, _899425, _899427, _899429]), _899423)))], (7056 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899425), hAPP(_899427, 7052 ^ [_899421, _899423, _899425, _899427, _899429])), _899429))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899425, tc_HOL_Obool)), hAPP(c_Set_Oimage(_899421, _899425, _899427), _899423)), _899429)))], (7060 ^ _782652) ^ [_899663, _899665, _899667, _899669, _899671] : [c_Finite__Set_Ofolding__one__idem(_899663, _899665, _899667), hBOOL(hAPP(c_Finite__Set_Ofinite(_899663), _899669)), -(_899669 = c_Orderings_Obot__class_Obot(tc_fun(_899663, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_899663), _899671)), -(_899671 = c_Orderings_Obot__class_Obot(tc_fun(_899663, tc_HOL_Obool))), -(hAPP(_899667, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_899663, tc_HOL_Obool)), _899669), _899671)) = hAPP(hAPP(_899665, hAPP(_899667, _899669)), hAPP(_899667, _899671)))], (7082 ^ _782652) ^ [_900028, _900030, _900032, _900034, _900036] : [c_Finite__Set_Ofolding__one__idem(_900028, _900030, _900032), hBOOL(hAPP(c_Finite__Set_Ofinite(_900028), _900034)), -(_900036 = c_Orderings_Obot__class_Obot(tc_fun(_900028, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900028, tc_HOL_Obool)), _900036), _900034)), -(hAPP(hAPP(_900030, hAPP(_900032, _900036)), hAPP(_900032, _900034)) = hAPP(_900032, _900034))], (7100 ^ _782652) ^ [_900358, _900360, _900362, _900364] : [7102 ^ _782652 : [(7103 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900358), 7101 ^ [_900358, _900360, _900362, _900364]), c_Option_Oset(_900358, _900360))))], (7105 ^ _782652) ^ [] : [hBOOL(hAPP(_900362, 7101 ^ [_900358, _900360, _900362, _900364]))]], _900360 = hAPP(c_Option_Ooption_OSome(_900358), _900364), -(hBOOL(hAPP(_900362, _900364)))], (7113 ^ _782652) ^ [_900622, _900624] : [hBOOL(hAPP(hAPP(c_member(_900622), _900624), c_Orderings_Obot__class_Obot(tc_fun(_900622, tc_HOL_Obool))))], (7115 ^ _782652) ^ [_900659, _900661, _900663, _900665] : [hBOOL(hAPP(hAPP(c_member(_900659), _900661), hAPP(hAPP(c_Set_Oinsert(_900659), _900663), _900665))), -(_900661 = _900663), -(hBOOL(hAPP(hAPP(c_member(_900659), _900661), _900665)))], (7125 ^ _782652) ^ [_900799, _900801, _900803, _900805] : [7126 ^ _782652 : [(7127 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900799), _900801), _900803))], (7129 ^ _782652) ^ [] : [_900801 = _900805]], -(hBOOL(hAPP(hAPP(c_member(_900799), _900801), hAPP(hAPP(c_Set_Oinsert(_900799), _900805), _900803))))], (7133 ^ _782652) ^ [_900964] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_900964), c_Orderings_Obot__class_Obot(tc_fun(_900964, tc_HOL_Obool)))))], (7135 ^ _782652) ^ [_900996, _900998, _901000] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900996), _900998)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_900996), hAPP(hAPP(c_Set_Oinsert(_900996), _901000), _900998))))], (7141 ^ _782652) ^ [_901107, _901109] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901107, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_901107, tc_HOL_Obool))), _901109)))], (7143 ^ _782652) ^ [_901162, _901164, _901166] : [c_Orderings_Obot__class_Obot(tc_fun(_901162, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_901162), _901164), _901166)], (7145 ^ _782652) ^ [_901217, _901219, _901221] : [hAPP(hAPP(c_Set_Oinsert(_901217), _901219), _901221) = c_Orderings_Obot__class_Obot(tc_fun(_901217, tc_HOL_Obool))], (7147 ^ _782652) ^ [_901257, _901259, _901261] : [class_Orderings_Obot(_901257), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_901259, _901257)), _901261) = c_Orderings_Obot__class_Obot(_901257))], (7153 ^ _782652) ^ [_901354, _901356, _901358] : [class_Orderings_Obot(_901354), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_901356, _901354)), _901358) = c_Orderings_Obot__class_Obot(_901354))], (7159 ^ _782652) ^ [_901451, _901453, _901455] : [-(hAPP(hAPP(c_Set_Oinsert(_901451), _901453), hAPP(hAPP(c_Set_Oinsert(_901451), _901453), _901455)) = hAPP(hAPP(c_Set_Oinsert(_901451), _901453), _901455))], (7161 ^ _782652) ^ [_901502, _901504, _901506, _901508] : [-(hAPP(hAPP(c_Set_Oinsert(_901502), _901504), hAPP(hAPP(c_Set_Oinsert(_901502), _901506), _901508)) = hAPP(hAPP(c_Set_Oinsert(_901502), _901506), hAPP(hAPP(c_Set_Oinsert(_901502), _901504), _901508)))], (7163 ^ _782652) ^ [_901587, _901589, _901591, _901593, _901595] : [hAPP(hAPP(c_Set_Oinsert(_901587), _901589), hAPP(hAPP(c_Set_Oinsert(_901587), _901591), c_Orderings_Obot__class_Obot(tc_fun(_901587, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_901587), _901593), hAPP(hAPP(c_Set_Oinsert(_901587), _901595), c_Orderings_Obot__class_Obot(tc_fun(_901587, tc_HOL_Obool)))), 7168 ^ _782652 : [(7169 ^ _782652) ^ [] : [-(_901589 = _901593)], (7171 ^ _782652) ^ [] : [-(_901591 = _901595)]], 7172 ^ _782652 : [(7173 ^ _782652) ^ [] : [-(_901589 = _901595)], (7175 ^ _782652) ^ [] : [-(_901591 = _901593)]]], (7177 ^ _782652) ^ [_901849, _901851, _901853, _901855, _901857] : [-(hAPP(hAPP(c_Set_Oinsert(_901849), _901851), hAPP(hAPP(c_Set_Oinsert(_901849), _901853), c_Orderings_Obot__class_Obot(tc_fun(_901849, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_901849), _901855), hAPP(hAPP(c_Set_Oinsert(_901849), _901857), c_Orderings_Obot__class_Obot(tc_fun(_901849, tc_HOL_Obool))))), 7178 ^ _782652 : [(7179 ^ _782652) ^ [] : [_901851 = _901855, _901853 = _901857], (7185 ^ _782652) ^ [] : [_901851 = _901857, _901853 = _901855]]], (7203 ^ _782652) ^ [_902300, _902302, _902304, _902306] : [7204 ^ _782652 : [(7205 ^ _782652) ^ [] : [_902302 = _902306], (7207 ^ _782652) ^ [] : [hBOOL(hAPP(_902304, _902306))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_902300), _902302), _902304), _902306)))], (7193 ^ _782652) ^ [_902186, _902188, _902190, _902192] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_902186), _902188), _902190), _902192)), -(_902188 = _902192), -(hBOOL(hAPP(_902190, _902192)))], (7211 ^ _782652) ^ [_902445, _902447, _902449] : [hAPP(hAPP(c_Set_Oinsert(_902445), _902447), c_Orderings_Obot__class_Obot(tc_fun(_902445, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_902445), _902449), c_Orderings_Obot__class_Obot(tc_fun(_902445, tc_HOL_Obool))), -(_902447 = _902449)], (7217 ^ _782652) ^ [_902576, _902578, _902580, _902582] : [-(c_Fun_Ooverride__on(_902576, _902578, _902580, _902582, c_Orderings_Obot__class_Obot(tc_fun(_902576, tc_HOL_Obool))) = _902580)], (7219 ^ _782652) ^ [_902616, _902618, _902620] : [hBOOL(hAPP(hAPP(c_member(_902616), _902618), hAPP(hAPP(c_Set_Oinsert(_902616), _902620), c_Orderings_Obot__class_Obot(tc_fun(_902616, tc_HOL_Obool))))), -(_902618 = _902620)], (7225 ^ _782652) ^ [_902753, _902755, _902757] : [hBOOL(hAPP(hAPP(c_member(_902753), _902755), hAPP(hAPP(c_Set_Oinsert(_902753), _902757), c_Orderings_Obot__class_Obot(tc_fun(_902753, tc_HOL_Obool))))), -(_902755 = _902757)], (7231 ^ _782652) ^ [_902868, _902870, _902872] : [_902870 = _902872, -(hBOOL(hAPP(hAPP(c_member(_902868), _902870), hAPP(hAPP(c_Set_Oinsert(_902868), _902872), c_Orderings_Obot__class_Obot(tc_fun(_902868, tc_HOL_Obool))))))], (7237 ^ _782652) ^ [_902989, _902991, _902993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902989, tc_HOL_Obool)), _902991), hAPP(hAPP(c_Set_Oinsert(_902989), _902993), c_Orderings_Obot__class_Obot(tc_fun(_902989, tc_HOL_Obool))))), -(_902991 = c_Orderings_Obot__class_Obot(tc_fun(_902989, tc_HOL_Obool))), -(_902991 = hAPP(hAPP(c_Set_Oinsert(_902989), _902993), c_Orderings_Obot__class_Obot(tc_fun(_902989, tc_HOL_Obool))))], (7247 ^ _782652) ^ [_903163, _903165, _903167] : [-(hAPP(hAPP(c_Set_Oinsert(_903163), _903165), _903167) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903163, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_903163), _903165), c_Orderings_Obot__class_Obot(tc_fun(_903163, tc_HOL_Obool)))), _903167))], (7249 ^ _782652) ^ [_903222, _903224, _903226, _903228] : [c_Hoare__Mirabelle_Ohoare__derivs(_903222, _903224, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_903222)), _903226), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_903222), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_903222, _903224, _903228), -(c_Hoare__Mirabelle_Ohoare__derivs(_903222, _903224, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_903222)), _903226), _903228)))], (7259 ^ _782652) ^ [_903419, _903421, _903423, _903425] : [c_Hoare__Mirabelle_Ohoare__derivs(_903419, _903421, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_903419)), _903423), _903425)), 7262 ^ _782652 : [(7263 ^ _782652) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_903419, _903421, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_903419)), _903423), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_903419), tc_HOL_Obool)))))], (7265 ^ _782652) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_903419, _903421, _903425))]]], (7267 ^ _782652) ^ [_903601, _903603, _903605, _903607] : [_903601 = c_Orderings_Obot__class_Obot(tc_fun(_903603, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_903603, _903605, hAPP(c_COMBK(_903605, _903603), _903607)), _903601) = c_Orderings_Obot__class_Obot(tc_fun(_903605, tc_HOL_Obool)))], (7273 ^ _782652) ^ [_903722, _903724, _903726, _903728] : [-(_903722 = c_Orderings_Obot__class_Obot(tc_fun(_903724, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_903724, _903726, hAPP(c_COMBK(_903726, _903724), _903728)), _903722) = hAPP(hAPP(c_Set_Oinsert(_903726), _903728), c_Orderings_Obot__class_Obot(tc_fun(_903726, tc_HOL_Obool))))], (7279 ^ _782652) ^ [_903795, _903797, _903799] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _903795)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _903797), _903795), _903799)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _903797), _903795), _903799)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (7289 ^ _782652) ^ [_904012, _904014, _904016] : [-(hBOOL(hAPP(hAPP(c_member(_904012), _904014), hAPP(hAPP(c_Set_Oinsert(_904012), _904014), _904016))))], (7301 ^ _782652) ^ [_904209, _904211, _904213, _904215] : [7302 ^ _782652 : [(7303 ^ _782652) ^ [] : [_904211 = _904213], (7305 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_904209), _904211), _904215))]], -(hBOOL(hAPP(hAPP(c_member(_904209), _904211), hAPP(hAPP(c_Set_Oinsert(_904209), _904213), _904215))))], (7291 ^ _782652) ^ [_904075, _904077, _904079, _904081] : [hBOOL(hAPP(hAPP(c_member(_904075), _904077), hAPP(hAPP(c_Set_Oinsert(_904075), _904079), _904081))), -(_904077 = _904079), -(hBOOL(hAPP(hAPP(c_member(_904075), _904077), _904081)))], (7309 ^ _782652) ^ [_904373, _904375, _904377, _904379] : [-(hBOOL(hAPP(hAPP(c_member(_904373), _904375), _904377))), -(hBOOL(hAPP(hAPP(c_member(_904373), _904375), _904379))), 7316 ^ _782652 : [(7317 ^ _782652) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_904373), _904375), _904377) = hAPP(hAPP(c_Set_Oinsert(_904373), _904375), _904379), -(_904377 = _904379)], (7323 ^ _782652) ^ [] : [_904377 = _904379, -(hAPP(hAPP(c_Set_Oinsert(_904373), _904375), _904377) = hAPP(hAPP(c_Set_Oinsert(_904373), _904375), _904379))]]], (7329 ^ _782652) ^ [_904718, _904720, _904722, _904724] : [hBOOL(hAPP(hAPP(c_member(_904718), _904720), _904722)), -(hBOOL(hAPP(hAPP(c_member(_904718), _904720), hAPP(hAPP(c_Set_Oinsert(_904718), _904724), _904722))))], (7335 ^ _782652) ^ [_904843, _904845, _904847] : [hBOOL(hAPP(hAPP(c_member(_904843), _904845), _904847)), -(hAPP(hAPP(c_Set_Oinsert(_904843), _904845), _904847) = _904847)], (7341 ^ _782652) ^ [_904970, _904972, _904974] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_904970), hAPP(hAPP(c_Set_Oinsert(_904970), _904972), _904974))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_904970), _904974)))], (7347 ^ _782652) ^ [_905077, _905079, _905081] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_905077), _905081)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_905077), hAPP(hAPP(c_Set_Oinsert(_905077), _905079), _905081))))], (7353 ^ _782652) ^ [_905190, _905192, _905194] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905190, tc_HOL_Obool)), _905192), hAPP(hAPP(c_Set_Oinsert(_905190), _905194), _905192))))], (7355 ^ _782652) ^ [_905235, _905237, _905239, _905241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905235, tc_HOL_Obool)), _905237), _905239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905235, tc_HOL_Obool)), _905237), hAPP(hAPP(c_Set_Oinsert(_905235), _905241), _905239))))], (7361 ^ _782652) ^ [_905372, _905374, _905376, _905378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905372, tc_HOL_Obool)), _905374), _905376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905372, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_905372), _905378), _905374)), hAPP(hAPP(c_Set_Oinsert(_905372), _905378), _905376))))], (7367 ^ _782652) ^ [_905525, _905527, _905529, _905531, _905533] : [-(hAPP(c_Set_Oimage(_905525, _905527, _905529), hAPP(hAPP(c_Set_Oinsert(_905525), _905531), _905533)) = hAPP(hAPP(c_Set_Oinsert(_905527), hAPP(_905529, _905531)), hAPP(c_Set_Oimage(_905525, _905527, _905529), _905533)))], (7369 ^ _782652) ^ [_905589, _905591, _905593, _905595] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905589, tc_HOL_Obool)), _905591), hAPP(hAPP(c_Set_Oinsert(_905589), _905593), _905595)) = hAPP(hAPP(c_Set_Oinsert(_905589), _905593), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905589, tc_HOL_Obool)), _905591), _905595)))], (7371 ^ _782652) ^ [_905656, _905658, _905660, _905662] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905656, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_905656), _905658), _905660)), _905662) = hAPP(hAPP(c_Set_Oinsert(_905656), _905658), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905656, tc_HOL_Obool)), _905660), _905662)))], (7373 ^ _782652) ^ [_905723, _905725, _905727, _905729, _905731] : [hBOOL(hAPP(hAPP(c_member(_905723), _905725), _905727)), -(hAPP(c_Set_Oimage(_905723, _905729, hAPP(c_COMBK(_905729, _905723), _905731)), _905727) = hAPP(hAPP(c_Set_Oinsert(_905729), _905731), c_Orderings_Obot__class_Obot(tc_fun(_905729, tc_HOL_Obool))))], (7379 ^ _782652) ^ [_905881, _905883] : [-(hBOOL(hAPP(hAPP(c_member(_905881), 7380 ^ [_905881, _905883]), _905883))), -(_905883 = c_Orderings_Obot__class_Obot(tc_fun(_905881, tc_HOL_Obool)))], (7386 ^ _782652) ^ [_905932, _905934] : [_905934 = c_Orderings_Obot__class_Obot(tc_fun(_905932, tc_HOL_Obool)), 7389 ^ _782652 : [(7390 ^ _782652) ^ [_906012] : [hBOOL(hAPP(hAPP(c_member(_905932), _906012), _905934))]]], (7392 ^ _782652) ^ [_906063, _906065] : [7393 ^ _782652 : [(7394 ^ _782652) ^ [_906116] : [hBOOL(hAPP(hAPP(c_member(_906063), _906116), _906065))]], _906065 = c_Orderings_Obot__class_Obot(tc_fun(_906063, tc_HOL_Obool))], (7398 ^ _782652) ^ [_906172, _906174] : [-(_906174 = c_Orderings_Obot__class_Obot(tc_fun(_906172, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_906172), 7401 ^ [_906172, _906174]), _906174)))], (7405 ^ _782652) ^ [_906241, _906243] : [hBOOL(hAPP(hAPP(c_member(_906241), _906243), c_Orderings_Obot__class_Obot(tc_fun(_906241, tc_HOL_Obool))))], (7407 ^ _782652) ^ [_906278, _906280, _906282] : [_906278 = c_Orderings_Obot__class_Obot(tc_fun(_906280, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_906280), _906282), _906278))], (7413 ^ _782652) ^ [_906382] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_906382), c_Orderings_Obot__class_Obot(tc_fun(_906382, tc_HOL_Obool)))))], (7415 ^ _782652) ^ [_906414, _906416, _906418, _906420, _906422] : [c_Finite__Set_Ofolding__one__idem(_906414, _906416, _906418), hBOOL(hAPP(c_Finite__Set_Ofinite(_906414), _906420)), -(_906420 = c_Orderings_Obot__class_Obot(tc_fun(_906414, tc_HOL_Obool))), -(hAPP(_906418, hAPP(hAPP(c_Set_Oinsert(_906414), _906422), _906420)) = hAPP(hAPP(_906416, _906422), hAPP(_906418, _906420)))], (7429 ^ _782652) ^ [_906645, _906647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906645, tc_HOL_Obool)), _906647), c_Orderings_Obot__class_Obot(tc_fun(_906645, tc_HOL_Obool)))), -(_906647 = c_Orderings_Obot__class_Obot(tc_fun(_906645, tc_HOL_Obool)))], (7435 ^ _782652) ^ [_906758, _906760] : [_906760 = c_Orderings_Obot__class_Obot(tc_fun(_906758, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906758, tc_HOL_Obool)), _906760), c_Orderings_Obot__class_Obot(tc_fun(_906758, tc_HOL_Obool)))))], (7441 ^ _782652) ^ [_906898, _906900, _906902, _906904] : [c_Orderings_Obot__class_Obot(tc_fun(_906898, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_906900, _906898, _906902), _906904), -(_906904 = c_Orderings_Obot__class_Obot(tc_fun(_906900, tc_HOL_Obool)))], (7447 ^ _782652) ^ [_907009, _907011, _907013, _907015] : [_907015 = c_Orderings_Obot__class_Obot(tc_fun(_907011, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_907009, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_907011, _907009, _907013), _907015))], (7453 ^ _782652) ^ [_907126, _907128, _907130] : [-(hAPP(c_Set_Oimage(_907126, _907128, _907130), c_Orderings_Obot__class_Obot(tc_fun(_907126, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_907128, tc_HOL_Obool)))], (7455 ^ _782652) ^ [_907191, _907193, _907195, _907197] : [hAPP(c_Set_Oimage(_907191, _907193, _907195), _907197) = c_Orderings_Obot__class_Obot(tc_fun(_907193, tc_HOL_Obool)), -(_907197 = c_Orderings_Obot__class_Obot(tc_fun(_907191, tc_HOL_Obool)))], (7461 ^ _782652) ^ [_907302, _907304, _907306, _907308] : [_907308 = c_Orderings_Obot__class_Obot(tc_fun(_907302, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_907302, _907304, _907306), _907308) = c_Orderings_Obot__class_Obot(tc_fun(_907304, tc_HOL_Obool)))], (7467 ^ _782652) ^ [_907419, _907421] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907419, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_907419, tc_HOL_Obool))), _907421) = _907421)], (7469 ^ _782652) ^ [_907460, _907462] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907460, tc_HOL_Obool)), _907462), c_Orderings_Obot__class_Obot(tc_fun(_907460, tc_HOL_Obool))) = _907462)], (7471 ^ _782652) ^ [_907519, _907521, _907523] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907519, tc_HOL_Obool)), _907521), _907523) = c_Orderings_Obot__class_Obot(tc_fun(_907519, tc_HOL_Obool)), 7474 ^ _782652 : [(7475 ^ _782652) ^ [] : [-(_907521 = c_Orderings_Obot__class_Obot(tc_fun(_907519, tc_HOL_Obool)))], (7477 ^ _782652) ^ [] : [-(_907523 = c_Orderings_Obot__class_Obot(tc_fun(_907519, tc_HOL_Obool)))]]], (7479 ^ _782652) ^ [_907672, _907674, _907676] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907672, tc_HOL_Obool)), _907674), _907676) = c_Orderings_Obot__class_Obot(tc_fun(_907672, tc_HOL_Obool))), _907674 = c_Orderings_Obot__class_Obot(tc_fun(_907672, tc_HOL_Obool)), _907676 = c_Orderings_Obot__class_Obot(tc_fun(_907672, tc_HOL_Obool))], (7489 ^ _782652) ^ [_907859, _907861] : [-(c_Option_Oset(_907859, hAPP(c_Option_Ooption_OSome(_907859), _907861)) = hAPP(hAPP(c_Set_Oinsert(_907859), _907861), c_Orderings_Obot__class_Obot(tc_fun(_907859, tc_HOL_Obool))))], (7491 ^ _782652) ^ [_907905, _907907] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_907905, _907907, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_907905), tc_HOL_Obool))))], (7493 ^ _782652) ^ [_907938, _907940] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_907938, _907940, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_907938), tc_HOL_Obool))))], (7495 ^ _782652) ^ [_907986, _907988] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_907986, tc_HOL_Obool)), _907988)), -(hBOOL(hAPP(hAPP(c_member(_907986), _907988), c_Orderings_Obot__class_Obot(tc_fun(_907986, tc_HOL_Obool)))))], (7501 ^ _782652) ^ [_908097, _908099] : [hBOOL(hAPP(hAPP(c_member(_908097), _908099), c_Orderings_Obot__class_Obot(tc_fun(_908097, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_908097, tc_HOL_Obool)), _908099)))], (7507 ^ _782652) ^ [_908214, _908216] : [class_Orderings_Obot(_908214), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908214), c_Orderings_Obot__class_Obot(_908214)), _908216)))], (7513 ^ _782652) ^ [_908307, _908309, _908311] : [class_Lattices_Obounded__lattice__bot(_908307), 7516 ^ _782652 : [(7517 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908307), _908309), _908311) = c_Orderings_Obot__class_Obot(_908307), 7520 ^ _782652 : [(7521 ^ _782652) ^ [] : [-(_908309 = c_Orderings_Obot__class_Obot(_908307))], (7523 ^ _782652) ^ [] : [-(_908311 = c_Orderings_Obot__class_Obot(_908307))]]], (7525 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908307), _908309), _908311) = c_Orderings_Obot__class_Obot(_908307)), _908309 = c_Orderings_Obot__class_Obot(_908307), _908311 = c_Orderings_Obot__class_Obot(_908307)]]], (7535 ^ _782652) ^ [_908634, _908636] : [class_Lattices_Obounded__lattice__bot(_908634), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908634), _908636), c_Orderings_Obot__class_Obot(_908634)) = _908636)], (7541 ^ _782652) ^ [_908729, _908731] : [class_Lattices_Obounded__lattice__bot(_908729), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908729), c_Orderings_Obot__class_Obot(_908729)), _908731) = _908731)], (7547 ^ _782652) ^ [_908845, _908847, _908849, _908851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908845, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_908845), _908847), _908849)), _908851)), 7550 ^ _782652 : [(7551 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_908845), _908847), _908851)))], (7553 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908845, tc_HOL_Obool)), _908849), _908851)))]]], (7555 ^ _782652) ^ [_909018, _909020, _909022, _909024] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909018, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_909018), _909020), _909022)), _909024))), hBOOL(hAPP(hAPP(c_member(_909018), _909020), _909024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909018, tc_HOL_Obool)), _909022), _909024))], (7565 ^ _782652) ^ [_909226, _909228, _909230, _909232] : [-(hBOOL(hAPP(hAPP(c_member(_909226), _909228), _909230))), 7568 ^ _782652 : [(7569 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909226, tc_HOL_Obool)), _909230), hAPP(hAPP(c_Set_Oinsert(_909226), _909228), _909232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909226, tc_HOL_Obool)), _909230), _909232)))], (7575 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909226, tc_HOL_Obool)), _909230), _909232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909226, tc_HOL_Obool)), _909230), hAPP(hAPP(c_Set_Oinsert(_909226), _909228), _909232))))]]], (7581 ^ _782652) ^ [_909534, _909536, _909538, _909540, _909542] : [hBOOL(hAPP(hAPP(c_member(_909534), _909536), _909538)), -(hAPP(hAPP(c_Set_Oinsert(_909540), hAPP(_909542, _909536)), hAPP(c_Set_Oimage(_909534, _909540, _909542), _909538)) = hAPP(c_Set_Oimage(_909534, _909540, _909542), _909538))], (7587 ^ _782652) ^ [_909681, _909683, _909685, _909687, _909689] : [hAPP(_909681, _909683) = hAPP(c_Option_Ooption_OSome(_909685), _909687), -(hAPP(hAPP(c_Set_Oinsert(_909689), _909683), c_Map_Odom(_909689, _909685, _909681)) = c_Map_Odom(_909689, _909685, _909681))], (7593 ^ _782652) ^ [_909812, _909814, _909816, _909818, _909820, _909822, _909824, _909826] : [c_Finite__Set_Ofolding__image__simple__idem(_909812, _909814, _909816, _909818, _909820, _909822), hBOOL(hAPP(c_Finite__Set_Ofinite(_909814), _909824)), -(hAPP(_909822, hAPP(hAPP(c_Set_Oinsert(_909814), _909826), _909824)) = hAPP(hAPP(_909816, hAPP(_909820, _909826)), hAPP(_909822, _909824)))], (7603 ^ _782652) ^ [_910027, _910029, _910031, _910033, _910035] : [c_Hoare__Mirabelle_Ohoare__derivs(_910027, _910029, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_910027)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910027), _910031), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _910033))), _910035)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_910027), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_910027, _910029, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_910027)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910027), _910031), hAPP(c_Com_Ocom_OBODY, _910033)), _910035)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_910027), tc_HOL_Obool)))))], (7609 ^ _782652) ^ [_910244, _910246, _910248, _910250, _910252] : [c_Hoare__Mirabelle_Ohoare__derivs(_910244, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_910244)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910244), _910246), hAPP(c_Com_Ocom_OBODY, _910248)), _910250)), _910252), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_910244)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910244), _910246), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _910248))), _910250)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_910244), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_910244, _910252, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_910244)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_910244), _910246), hAPP(c_Com_Ocom_OBODY, _910248)), _910250)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_910244), tc_HOL_Obool)))))], (7615 ^ _782652) ^ [_910509, _910511, _910513] : [c_Hoare__Mirabelle_Ohoare__derivs(_910509, _910511, _910513), -(c_Hoare__Mirabelle_Ohoare__valids(_910509, _910511, _910513))], (7621 ^ _782652) ^ [_910588, _910590, _910592, _910594, _910596, _910598] : [-(hBOOL(hAPP(hAPP(c_member(_910588), _910590), _910592))), -(hAPP(c_Fun_Ooverride__on(_910588, _910594, _910596, _910598, _910592), _910590) = hAPP(_910596, _910590))], (7627 ^ _782652) ^ [_910651, _910653, _910655, _910657, _910659, _910661] : [hBOOL(hAPP(hAPP(c_member(_910651), _910653), _910655)), -(hAPP(c_Fun_Ooverride__on(_910651, _910657, _910659, _910661, _910655), _910653) = hAPP(_910661, _910653))], (7633 ^ _782652) ^ [_910774, _910776] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, _910774))), _910776), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _910774)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _910776, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, _910774))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (7639 ^ _782652) ^ [_910933] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(c_Com_OWT, _910933)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _910933)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (7653 ^ _782652) ^ [_911120, _911122, _911124, _911126, _911128, _911130, _911132, _911134, _911136] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_911120), _911122)), 7659 ^ _782652 : [(7660 ^ _782652) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_911124, _911126, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911124)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911124), hAPP(_911128, 7658 ^ [_911120, _911122, _911124, _911126, _911128, _911130, _911132, _911134, _911136])), hAPP(_911130, 7658 ^ [_911120, _911122, _911124, _911126, _911128, _911130, _911132, _911134, _911136])), hAPP(_911132, 7658 ^ [_911120, _911122, _911124, _911126, _911128, _911130, _911132, _911134, _911136]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911124), tc_HOL_Obool)))))], (7662 ^ _782652) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_911124, _911126, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911124)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911124), hAPP(_911134, 7658 ^ [_911120, _911122, _911124, _911126, _911128, _911130, _911132, _911134, _911136])), hAPP(_911130, 7658 ^ [_911120, _911122, _911124, _911126, _911128, _911130, _911132, _911134, _911136])), hAPP(_911136, 7658 ^ [_911120, _911122, _911124, _911126, _911128, _911130, _911132, _911134, _911136]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911124), tc_HOL_Obool))))]], c_Hoare__Mirabelle_Ohoare__derivs(_911124, _911126, hAPP(c_Set_Oimage(_911120, tc_Hoare__Mirabelle_Otriple(_911124), hAPP(hAPP(c_COMBS(_911120, tc_fun(_911124, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_911124)), hAPP(hAPP(c_COMBS(_911120, tc_Com_Ocom, tc_fun(tc_fun(_911124, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_911124))), hAPP(hAPP(c_COMBB(tc_fun(_911124, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_911124, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_911124))), _911120), c_Hoare__Mirabelle_Otriple_Otriple(_911124)), _911128)), _911130)), _911132)), _911122)), -(c_Hoare__Mirabelle_Ohoare__derivs(_911124, _911126, hAPP(c_Set_Oimage(_911120, tc_Hoare__Mirabelle_Otriple(_911124), hAPP(hAPP(c_COMBS(_911120, tc_fun(_911124, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_911124)), hAPP(hAPP(c_COMBS(_911120, tc_Com_Ocom, tc_fun(tc_fun(_911124, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_911124))), hAPP(hAPP(c_COMBB(tc_fun(_911124, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_911124, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_911124))), _911120), c_Hoare__Mirabelle_Otriple_Otriple(_911124)), _911134)), _911130)), _911136)), _911122)))], (7670 ^ _782652) ^ [_912009, _912011] : [-(c_Set_Othe__elem(_912009, hAPP(hAPP(c_Set_Oinsert(_912009), _912011), c_Orderings_Obot__class_Obot(tc_fun(_912009, tc_HOL_Obool)))) = _912011)], (7672 ^ _782652) ^ [_912050, _912052, _912054, _912056, _912058] : [c_Finite__Set_Ofolding__one(_912050, _912052, _912054), hBOOL(hAPP(c_Finite__Set_Ofinite(_912050), _912056)), -(hBOOL(hAPP(hAPP(c_member(_912050), _912058), _912056))), -(_912056 = c_Orderings_Obot__class_Obot(tc_fun(_912050, tc_HOL_Obool))), -(hAPP(_912054, hAPP(hAPP(c_Set_Oinsert(_912050), _912058), _912056)) = hAPP(hAPP(_912052, _912058), hAPP(_912054, _912056)))], (7690 ^ _782652) ^ [_912295, _912297] : [c_Hoare__Mirabelle_Ostate__not__singleton, 7696 ^ _782652 : [(7697 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 7695 ^ [_912295, _912297]), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (7699 ^ _782652) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _912295, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, 7695 ^ [_912295, _912297]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))]], hBOOL(hAPP(c_Com_OWT, _912297)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _912295, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _912297)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (7707 ^ _782652) ^ [_912606, _912608, _912610, _912612] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_912606), _912608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912606, tc_HOL_Obool)), _912608), _912610)), hBOOL(hAPP(_912612, c_Orderings_Obot__class_Obot(tc_fun(_912606, tc_HOL_Obool)))), 7722 ^ _782652 : [(7723 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_912606), 7721 ^ [_912606, _912608, _912610, _912612])))], (7725 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912606), 7720 ^ [_912606, _912608, _912610, _912612]), _912610)))], (7727 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912606), 7720 ^ [_912606, _912608, _912610, _912612]), 7721 ^ [_912606, _912608, _912610, _912612]))], (7729 ^ _782652) ^ [] : [-(hBOOL(hAPP(_912612, 7721 ^ [_912606, _912608, _912610, _912612])))], (7731 ^ _782652) ^ [] : [hBOOL(hAPP(_912612, hAPP(hAPP(c_Set_Oinsert(_912606), 7720 ^ [_912606, _912608, _912610, _912612]), 7721 ^ [_912606, _912608, _912610, _912612])))]], -(hBOOL(hAPP(_912612, _912608)))], (7735 ^ _782652) ^ [_913271, _913273, _913275, _913277, _913279] : [7738 ^ _782652 : [(7739 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_913271, 7736 ^ [_913271, _913273, _913275, _913277, _913279]), 7737 ^ [_913271, _913273, _913275, _913277, _913279])))], (7741 ^ _782652) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_913273, _913275, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913273)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913273), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _913273), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 7737 ^ [_913271, _913273, _913275, _913277, _913279]))), _913277), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _913273), hAPP(_913279, 7736 ^ [_913271, _913273, _913275, _913277, _913279])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913273), tc_HOL_Obool))))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_913273, _913275, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913273)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913273), _913271), _913277), _913279)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913273), tc_HOL_Obool)))))], (7745 ^ _782652) ^ [_913693, _913695, _913697] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_913693, _913695, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913693)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913693), _913697), c_Com_Ocom_OSKIP), _913697)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913693), tc_HOL_Obool)))))], (7747 ^ _782652) ^ [_913749, _913751, _913753] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_913749, _913751, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913749)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913749), _913753), c_Com_Ocom_OSKIP), _913753)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913749), tc_HOL_Obool)))))], (7749 ^ _782652) ^ [_913805, _913807, _913809, _913811, _913813, _913815] : [c_Hoare__Mirabelle_Ohoare__derivs(_913805, _913807, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913805)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913805), _913809), _913811), _913813)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913805), tc_HOL_Obool)))), 7756 ^ _782652 : [(7757 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_913813, 7754 ^ [_913805, _913807, _913809, _913811, _913813, _913815]), 7755 ^ [_913805, _913807, _913809, _913811, _913813, _913815])))], (7759 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_913815, 7754 ^ [_913805, _913807, _913809, _913811, _913813, _913815]), 7755 ^ [_913805, _913807, _913809, _913811, _913813, _913815]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_913805, _913807, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913805)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913805), _913809), _913811), _913815)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913805), tc_HOL_Obool)))))], (7763 ^ _782652) ^ [_914234, _914236, _914238, _914240, _914242, _914244] : [c_Hoare__Mirabelle_Ohoare__derivs(_914234, _914236, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_914234)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_914234), _914238), _914240), _914242)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_914234), tc_HOL_Obool)))), 7770 ^ _782652 : [(7771 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_914244, 7768 ^ [_914234, _914236, _914238, _914240, _914242, _914244]), 7769 ^ [_914234, _914236, _914238, _914240, _914242, _914244])))], (7773 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_914238, 7768 ^ [_914234, _914236, _914238, _914240, _914242, _914244]), 7769 ^ [_914234, _914236, _914238, _914240, _914242, _914244]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_914234, _914236, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_914234)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_914234), _914244), _914240), _914242)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_914234), tc_HOL_Obool)))))], (7777 ^ _782652) ^ [_914672] : [hAPP(c_Com_Ocom_OBODY, _914672) = c_Com_Ocom_OSKIP], (7779 ^ _782652) ^ [_914707] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _914707)], (7781 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (7783 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (7785 ^ _782652) ^ [_914769, _914771, _914773, _914775] : [c_Finite__Set_Ofolding__one(_914769, _914771, _914773), -(hAPP(_914773, hAPP(hAPP(c_Set_Oinsert(_914769), _914775), c_Orderings_Obot__class_Obot(tc_fun(_914769, tc_HOL_Obool)))) = _914775)], (7791 ^ _782652) ^ [_914884, _914886, _914888, _914890] : [c_Finite__Set_Ofolding__one(_914884, _914886, _914888), hBOOL(hAPP(c_Finite__Set_Ofinite(_914884), _914890)), -(_914890 = c_Orderings_Obot__class_Obot(tc_fun(_914884, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_914884), hAPP(hAPP(_914886, 7804 ^ [_914884, _914886, _914888, _914890]), 7805 ^ [_914884, _914886, _914888, _914890])), hAPP(hAPP(c_Set_Oinsert(_914884), 7804 ^ [_914884, _914886, _914888, _914890]), hAPP(hAPP(c_Set_Oinsert(_914884), 7805 ^ [_914884, _914886, _914888, _914890]), c_Orderings_Obot__class_Obot(tc_fun(_914884, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_914884), hAPP(_914888, _914890)), _914890)))], (7811 ^ _782652) ^ [_915370, _915372] : [-(c_Set_Othe__elem(_915370, _915372) = c_HOL_OThe(_915370, hAPP(hAPP(c_COMBB(tc_fun(_915370, tc_HOL_Obool), tc_HOL_Obool, _915370), hAPP(c_fequal, _915372)), hAPP(hAPP(c_COMBC(_915370, tc_fun(_915370, tc_HOL_Obool), tc_fun(_915370, tc_HOL_Obool)), c_Set_Oinsert(_915370)), c_Orderings_Obot__class_Obot(tc_fun(_915370, tc_HOL_Obool))))))], (7813 ^ _782652) ^ [_915440, _915442, _915444, _915446, _915448] : [c_Finite__Set_Ofolding__one__idem(_915440, _915442, _915444), hAPP(_915446, hAPP(hAPP(_915442, 7818 ^ [_915440, _915442, _915444, _915446, _915448]), 7819 ^ [_915440, _915442, _915444, _915446, _915448])) = hAPP(hAPP(_915442, hAPP(_915446, 7818 ^ [_915440, _915442, _915444, _915446, _915448])), hAPP(_915446, 7819 ^ [_915440, _915442, _915444, _915446, _915448])), hBOOL(hAPP(c_Finite__Set_Ofinite(_915440), _915448)), -(_915448 = c_Orderings_Obot__class_Obot(tc_fun(_915440, tc_HOL_Obool))), -(hAPP(_915446, hAPP(_915444, _915448)) = hAPP(_915444, hAPP(c_Set_Oimage(_915440, _915440, _915446), _915448)))], (7833 ^ _782652) ^ [_915875, _915877, _915879, _915881, _915883, _915885, _915887] : [c_Hoare__Mirabelle_Ohoare__derivs(_915875, _915877, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_915875)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_915875), _915879), _915881), _915883)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_915875), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_915875, _915877, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_915875)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_915875), _915883), _915885), _915887)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_915875), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_915875, _915877, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_915875)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_915875), _915879), c_Com_Ocom_OSemi(_915881, _915885)), _915887)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_915875), tc_HOL_Obool)))))], (7843 ^ _782652) ^ [_916204, _916206, _916208, _916210, _916212, _916214, _916216, _916218] : [c_Finite__Set_Ofolding__image__simple(_916204, _916206, _916208, _916210, _916212, _916214), hBOOL(hAPP(c_Finite__Set_Ofinite(_916206), _916216)), -(hBOOL(hAPP(hAPP(c_member(_916206), _916218), _916216))), -(hAPP(_916214, hAPP(hAPP(c_Set_Oinsert(_916206), _916218), _916216)) = hAPP(hAPP(_916208, hAPP(_916212, _916218)), hAPP(_916214, _916216)))], (7857 ^ _782652) ^ [_916448, _916450, _916452, _916454, _916456] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_916448, _916450, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_916448)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_916448), hAPP(hAPP(c_COMBC(_916448, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _916448), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _916448), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _916452))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _916454))), c_Com_Ocom_OWhile(_916454, _916456)), _916452)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_916448), tc_HOL_Obool)))))], (7859 ^ _782652) ^ [_916544, _916546, _916548, _916550, _916552] : [c_Finite__Set_Ofolding__one(_916544, _916546, _916548), hBOOL(hAPP(c_Finite__Set_Ofinite(_916544), _916550)), hBOOL(hAPP(hAPP(c_member(_916544), _916552), _916550)), 7870 ^ _782652 : [(7871 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916544, tc_HOL_Obool)), _916550), hAPP(hAPP(c_Set_Oinsert(_916544), _916552), c_Orderings_Obot__class_Obot(tc_fun(_916544, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_916544, tc_HOL_Obool)), -(hAPP(_916548, _916550) = _916552)], (7877 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916544, tc_HOL_Obool)), _916550), hAPP(hAPP(c_Set_Oinsert(_916544), _916552), c_Orderings_Obot__class_Obot(tc_fun(_916544, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_916544, tc_HOL_Obool))), -(hAPP(_916548, _916550) = hAPP(hAPP(_916546, _916552), hAPP(_916548, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916544, tc_HOL_Obool)), _916550), hAPP(hAPP(c_Set_Oinsert(_916544), _916552), c_Orderings_Obot__class_Obot(tc_fun(_916544, tc_HOL_Obool)))))))]]], (7883 ^ _782652) ^ [_917066, _917068, _917070] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917066), _917068)), hBOOL(hAPP(_917070, c_Orderings_Obot__class_Obot(tc_fun(_917066, tc_HOL_Obool)))), 7894 ^ _782652 : [(7895 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_917066), 7893 ^ [_917066, _917068, _917070])))], (7897 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_917066), 7892 ^ [_917066, _917068, _917070]), 7893 ^ [_917066, _917068, _917070]))], (7899 ^ _782652) ^ [] : [-(hBOOL(hAPP(_917070, 7893 ^ [_917066, _917068, _917070])))], (7901 ^ _782652) ^ [] : [hBOOL(hAPP(_917070, hAPP(hAPP(c_Set_Oinsert(_917066), 7892 ^ [_917066, _917068, _917070]), 7893 ^ [_917066, _917068, _917070])))]], -(hBOOL(hAPP(_917070, _917068)))], (7905 ^ _782652) ^ [_917553, _917555, _917557, _917559, _917561] : [c_Finite__Set_Ofolding__one(_917553, _917555, _917557), hBOOL(hAPP(c_Finite__Set_Ofinite(_917553), _917559)), -(_917559 = c_Orderings_Obot__class_Obot(tc_fun(_917553, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_917553), _917561)), -(_917561 = c_Orderings_Obot__class_Obot(tc_fun(_917553, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_917553, tc_HOL_Obool)), _917559), _917561) = c_Orderings_Obot__class_Obot(tc_fun(_917553, tc_HOL_Obool)), -(hAPP(_917557, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917553, tc_HOL_Obool)), _917559), _917561)) = hAPP(hAPP(_917555, hAPP(_917557, _917559)), hAPP(_917557, _917561)))], (7931 ^ _782652) ^ [_918054, _918056, _918058, _918060, _918062] : [c_Finite__Set_Ofolding__one(_918054, _918056, _918058), hBOOL(hAPP(c_Finite__Set_Ofinite(_918054), _918060)), hBOOL(hAPP(c_Finite__Set_Ofinite(_918054), _918062)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_918054, tc_HOL_Obool)), _918060), _918062) = c_Orderings_Obot__class_Obot(tc_fun(_918054, tc_HOL_Obool))), -(hAPP(hAPP(_918056, hAPP(_918058, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_918054, tc_HOL_Obool)), _918060), _918062))), hAPP(_918058, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_918054, tc_HOL_Obool)), _918060), _918062))) = hAPP(hAPP(_918056, hAPP(_918058, _918060)), hAPP(_918058, _918062)))], (7949 ^ _782652) ^ [_918410, _918412] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _918410, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_Com_Ostate), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies)), c_Natural_Oevalc(_918412))))), c_fequal))), _918412), c_fequal)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _918410, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _918412)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (7959 ^ _782652) ^ [_918625, _918627, _918629, _918631] : [hBOOL(hAPP(_918625, _918627)), hBOOL(hAPP(_918629, _918627)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_918631, tc_HOL_Obool)), _918625), _918629), _918627)))], (7969 ^ _782652) ^ [_918796, _918798, _918800, _918802] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_918796, tc_HOL_Obool)), _918798), _918800), _918802)), 7972 ^ _782652 : [(7973 ^ _782652) ^ [] : [-(hBOOL(hAPP(_918798, _918802)))], (7975 ^ _782652) ^ [] : [-(hBOOL(hAPP(_918800, _918802)))]]], (7977 ^ _782652) ^ [_918941, _918943, _918945, _918947] : [hBOOL(hAPP(hAPP(c_member(_918941), _918943), _918945)), hBOOL(hAPP(hAPP(c_member(_918941), _918943), _918947)), -(hBOOL(hAPP(hAPP(c_member(_918941), _918943), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_918941, tc_HOL_Obool)), _918945), _918947))))], (7987 ^ _782652) ^ [_919142, _919144, _919146, _919148] : [hBOOL(hAPP(hAPP(c_member(_919142), _919144), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919142, tc_HOL_Obool)), _919146), _919148))), 7990 ^ _782652 : [(7991 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_919142), _919144), _919146)))], (7993 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_919142), _919144), _919148)))]]], (7995 ^ _782652) ^ [_919317, _919319, _919321, _919323] : [hBOOL(hAPP(hAPP(c_member(_919317), _919319), _919321)), -(hBOOL(hAPP(hAPP(c_member(_919317), _919319), _919323))), -(hBOOL(hAPP(hAPP(c_member(_919317), _919319), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919317, tc_HOL_Obool)), _919321), _919323))))], (8005 ^ _782652) ^ [_919477, _919479, _919481, _919483] : [hBOOL(hAPP(hAPP(c_member(_919477), _919479), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919477, tc_HOL_Obool)), _919481), _919483))), 8008 ^ _782652 : [(8009 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_919477), _919479), _919481)))], (8011 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_919477), _919479), _919483))]]], (8013 ^ _782652) ^ [_919656, _919658, _919660] : [8014 ^ _782652 : [(8015 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_919656), _919658))], (8017 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_919656), _919660))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_919656), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919656, tc_HOL_Obool)), _919658), _919660))))], (8021 ^ _782652) ^ [_919819, _919821, _919823] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_919819), _919821)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_919819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919819, tc_HOL_Obool)), _919821), _919823))))], (8027 ^ _782652) ^ [_919936, _919938] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_919936, _919938))), -(hBOOL(hAPP(c_Com_OWT, _919938)))], (8033 ^ _782652) ^ [_920027, _920029] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_920027, _920029))), 8036 ^ _782652 : [(8037 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _920027)))], (8039 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _920029)))]]], (8041 ^ _782652) ^ [_920152, _920154] : [class_Lattices_Osemilattice__inf(_920152), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920152), _920154), _920154) = _920154)], (8047 ^ _782652) ^ [_920243, _920245] : [class_Lattices_Osemilattice__inf(_920243), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920243), _920245), _920245) = _920245)], (8053 ^ _782652) ^ [_920334, _920336, _920338, _920340, _920342] : [class_Groups_Ominus(_920334), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920336, _920334)), _920338), _920340), _920342) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_920334), hAPP(_920338, _920342)), hAPP(_920340, _920342)))], (8059 ^ _782652) ^ [_920471, _920473, _920475, _920477, _920479] : [class_Lattices_Olattice(_920471), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_920473, _920471)), _920475), _920477), _920479) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920471), hAPP(_920475, _920479)), hAPP(_920477, _920479)))], (8065 ^ _782652) ^ [_920608, _920610, _920612] : [class_Lattices_Osemilattice__inf(_920608), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920608), _920610), _920612) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920608), _920612), _920610))], (8071 ^ _782652) ^ [_920717, _920719, _920721] : [class_Lattices_Olattice(_920717), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920717), _920719), _920721) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920717), _920721), _920719))], (8077 ^ _782652) ^ [_920826, _920828, _920830] : [class_Lattices_Osemilattice__inf(_920826), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920826), _920828), _920830) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920826), _920830), _920828))], (8083 ^ _782652) ^ [_920935, _920937, _920939] : [class_Lattices_Osemilattice__inf(_920935), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920935), _920937), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920935), _920937), _920939)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_920935), _920937), _920939))], (8089 ^ _782652) ^ [_921060, _921062, _921064] : [class_Lattices_Olattice(_921060), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921060), _921062), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921060), _921062), _921064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921060), _921062), _921064))], (8095 ^ _782652) ^ [_921185, _921187, _921189] : [class_Lattices_Osemilattice__inf(_921185), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921185), _921187), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921185), _921187), _921189)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921185), _921187), _921189))], (8101 ^ _782652) ^ [_921310, _921312, _921314, _921316] : [class_Lattices_Osemilattice__inf(_921310), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921310), _921312), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921310), _921314), _921316)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921310), _921314), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921310), _921312), _921316)))], (8107 ^ _782652) ^ [_921453, _921455, _921457, _921459] : [class_Lattices_Olattice(_921453), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921453), _921455), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921453), _921457), _921459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921453), _921457), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921453), _921455), _921459)))], (8113 ^ _782652) ^ [_921596, _921598, _921600, _921602] : [class_Lattices_Osemilattice__inf(_921596), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921596), _921598), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921596), _921600), _921602)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921596), _921600), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921596), _921598), _921602)))], (8119 ^ _782652) ^ [_921739, _921741, _921743, _921745] : [class_Lattices_Osemilattice__inf(_921739), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921739), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921739), _921741), _921743)), _921745) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921739), _921741), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921739), _921743), _921745)))], (8125 ^ _782652) ^ [_921882, _921884, _921886, _921888] : [class_Lattices_Olattice(_921882), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921882), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921882), _921884), _921886)), _921888) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921882), _921884), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921882), _921886), _921888)))], (8131 ^ _782652) ^ [_922025, _922027, _922029, _922031] : [class_Lattices_Osemilattice__inf(_922025), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922025), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922025), _922027), _922029)), _922031) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922025), _922027), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922025), _922029), _922031)))], (8137 ^ _782652) ^ [_922168, _922170, _922172, _922174, _922176] : [class_Groups_Ominus(_922168), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922170, _922168)), _922172), _922174), _922176) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_922168), hAPP(_922172, _922176)), hAPP(_922174, _922176)))], (8143 ^ _782652) ^ [_922305, _922307, _922309, _922311, _922313] : [class_Lattices_Olattice(_922305), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922307, _922305)), _922309), _922311), _922313) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922305), hAPP(_922309, _922313)), hAPP(_922311, _922313)))], (8149 ^ _782652) ^ [_922460, _922462, _922464, _922466] : [c_Com_Ocom_OSemi(_922460, _922462) = c_Com_Ocom_OWhile(_922464, _922466)], (8151 ^ _782652) ^ [_922513, _922515, _922517, _922519] : [c_Com_Ocom_OWhile(_922513, _922515) = c_Com_Ocom_OSemi(_922517, _922519)], (8153 ^ _782652) ^ [_922548, _922550] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922548, tc_HOL_Obool)), _922550), _922550) = _922550)], (8155 ^ _782652) ^ [_922584, _922586, _922588] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922584, tc_HOL_Obool)), _922586), _922588) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922584, tc_HOL_Obool)), _922588), _922586))], (8157 ^ _782652) ^ [_922633, _922635, _922637] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922633, tc_HOL_Obool)), _922635), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922633, tc_HOL_Obool)), _922635), _922637)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922633, tc_HOL_Obool)), _922635), _922637))], (8159 ^ _782652) ^ [_922693, _922695, _922697, _922699] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922693, tc_HOL_Obool)), _922695), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922693, tc_HOL_Obool)), _922697), _922699)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922693, tc_HOL_Obool)), _922697), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922693, tc_HOL_Obool)), _922695), _922699)))], (8161 ^ _782652) ^ [_922766, _922768, _922770, _922772] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922766, tc_HOL_Obool)), _922768), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922766, tc_HOL_Obool)), _922770), _922772)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922766, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922766, tc_HOL_Obool)), _922768), _922770)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922766, tc_HOL_Obool)), _922768), _922772)))], (8163 ^ _782652) ^ [_922850, _922852, _922854] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922850, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922850, tc_HOL_Obool)), _922852), _922854)), _922854) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922850, tc_HOL_Obool)), _922852), _922854))], (8165 ^ _782652) ^ [_922910, _922912, _922914, _922916] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922910, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922910, tc_HOL_Obool)), _922912), _922914)), _922916) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922910, tc_HOL_Obool)), _922912), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922910, tc_HOL_Obool)), _922914), _922916)))], (8167 ^ _782652) ^ [_922983, _922985, _922987, _922989] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922983, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922983, tc_HOL_Obool)), _922985), _922987)), _922989) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922983, tc_HOL_Obool)), _922985), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_922983, tc_HOL_Obool)), _922987), _922989)))], (8169 ^ _782652) ^ [_923056, _923058, _923060, _923062] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923056, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923056, tc_HOL_Obool)), _923058), _923060)), _923062) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923056, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923056, tc_HOL_Obool)), _923058), _923062)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923056, tc_HOL_Obool)), _923060), _923062)))], (8171 ^ _782652) ^ [_923140, _923142, _923144, _923146] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923140, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923140, tc_HOL_Obool)), _923142), _923144)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923140, tc_HOL_Obool)), _923146), _923144)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923140, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923140, tc_HOL_Obool)), _923142), _923144)), _923146))], (8173 ^ _782652) ^ [_923245, _923247, _923249, _923251] : [c_Com_Ocom_OSemi(_923245, _923247) = c_Com_Ocom_OSemi(_923249, _923251), 8176 ^ _782652 : [(8177 ^ _782652) ^ [] : [-(_923245 = _923249)], (8179 ^ _782652) ^ [] : [-(_923247 = _923251)]]], (8181 ^ _782652) ^ [_923360, _923362, _923364, _923366] : [-(c_Com_Ocom_OSemi(_923360, _923362) = c_Com_Ocom_OSemi(_923364, _923366)), _923360 = _923364, _923362 = _923366], (8191 ^ _782652) ^ [_923532, _923534, _923536, _923538] : [c_Com_Ocom_OWhile(_923532, _923534) = c_Com_Ocom_OWhile(_923536, _923538), 8194 ^ _782652 : [(8195 ^ _782652) ^ [] : [-(_923532 = _923536)], (8197 ^ _782652) ^ [] : [-(_923534 = _923538)]]], (8199 ^ _782652) ^ [_923647, _923649, _923651, _923653] : [-(c_Com_Ocom_OWhile(_923647, _923649) = c_Com_Ocom_OWhile(_923651, _923653)), _923647 = _923651, _923649 = _923653], (8209 ^ _782652) ^ [_923798, _923800, _923802, _923804] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923798, tc_HOL_Obool)), _923800), _923802), _923804)), -(hBOOL(hAPP(_923800, _923804)))], (8215 ^ _782652) ^ [_923909, _923911, _923913, _923915] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_923909, tc_HOL_Obool)), _923911), _923913), _923915)), -(hBOOL(hAPP(_923913, _923915)))], (8221 ^ _782652) ^ [_924020, _924022, _924024] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_924020, tc_HOL_Obool)), _924022), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924020, tc_HOL_Obool)), _924024), _924022)) = c_Orderings_Obot__class_Obot(tc_fun(_924020, tc_HOL_Obool)))], (8223 ^ _782652) ^ [_924074, _924076, _924078] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_924074, tc_HOL_Obool)), _924076), _924078) = c_Orderings_Obot__class_Obot(tc_fun(_924074, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924074, tc_HOL_Obool)), _924076), _924078) = _924076)], (8229 ^ _782652) ^ [_924207, _924209, _924211, _924213] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924207, tc_HOL_Obool)), _924209), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_924207, tc_HOL_Obool)), _924211), _924213)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924207, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924207, tc_HOL_Obool)), _924209), _924211)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924207, tc_HOL_Obool)), _924209), _924213)))], (8231 ^ _782652) ^ [_924291, _924293, _924295, _924297] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924291, tc_HOL_Obool)), _924293), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924291, tc_HOL_Obool)), _924295), _924297)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_924291, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924291, tc_HOL_Obool)), _924293), _924295)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924291, tc_HOL_Obool)), _924293), _924297)))], (8233 ^ _782652) ^ [_924375, _924377, _924379] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924375, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924375, tc_HOL_Obool)), _924377), _924379)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_924375, tc_HOL_Obool)), _924377), _924379)) = _924377)], (8235 ^ _782652) ^ [_924435, _924437, _924439] : [class_Lattices_Olattice(_924435), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924435), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924435), _924437), _924439)), _924437)))], (8241 ^ _782652) ^ [_924542, _924544, _924546] : [class_Lattices_Osemilattice__inf(_924542), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924542), _924544), _924546)), _924544)))], (8247 ^ _782652) ^ [_924649, _924651, _924653] : [class_Lattices_Olattice(_924649), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924649), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924649), _924651), _924653)), _924653)))], (8253 ^ _782652) ^ [_924756, _924758, _924760] : [class_Lattices_Osemilattice__inf(_924756), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924756), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924756), _924758), _924760)), _924760)))], (8259 ^ _782652) ^ [_924863, _924865, _924867] : [class_Lattices_Osemilattice__inf(_924863), 8262 ^ _782652 : [(8263 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924863), _924865), _924867)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924863), _924865), _924867) = _924865)], (8269 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924863), _924865), _924867) = _924865, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924863), _924865), _924867)))]]], (8275 ^ _782652) ^ [_925119, _925121, _925123, _925125] : [class_Lattices_Osemilattice__inf(_925119), 8278 ^ _782652 : [(8279 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925119), _925121), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925119), _925123), _925125))), 8282 ^ _782652 : [(8283 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925119), _925121), _925123)))], (8285 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925119), _925121), _925125)))]]], (8287 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925119), _925121), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925119), _925123), _925125)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925119), _925121), _925123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925119), _925121), _925125))]]], (8297 ^ _782652) ^ [_925499, _925501, _925503, _925505] : [class_Lattices_Osemilattice__inf(_925499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925499), _925501), _925503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925499), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925499), _925501), _925505)), _925503)))], (8307 ^ _782652) ^ [_925678, _925680, _925682, _925684] : [class_Lattices_Osemilattice__inf(_925678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925678), _925680), _925682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925678), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925678), _925684), _925680)), _925682)))], (8317 ^ _782652) ^ [_925857, _925859, _925861] : [class_Lattices_Osemilattice__inf(_925857), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925857), _925859), _925861)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_925857), _925859), _925861) = _925859)], (8327 ^ _782652) ^ [_926018, _926020, _926022] : [class_Lattices_Osemilattice__inf(_926018), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926018), _926020), _926022)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926018), _926022), _926020) = _926020)], (8337 ^ _782652) ^ [_926179, _926181, _926183, _926185] : [class_Lattices_Osemilattice__inf(_926179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926179), _926181), _926183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926179), _926181), _926185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926179), _926181), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926179), _926183), _926185))))], (8351 ^ _782652) ^ [_926428, _926430, _926432, _926434] : [class_Lattices_Osemilattice__inf(_926428), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926428), _926430), _926432)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926428), _926430), _926434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926428), _926430), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926428), _926432), _926434))))], (8365 ^ _782652) ^ [_926677, _926679, _926681, _926683, _926685] : [class_Lattices_Osemilattice__inf(_926677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926677), _926679), _926681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926677), _926683), _926685)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926677), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926677), _926679), _926683)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926677), _926681), _926685))))], (8379 ^ _782652) ^ [_926948, _926950, _926952, _926954] : [class_Lattices_Osemilattice__inf(_926948), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926948), _926950), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_926948), _926952), _926954))), 8386 ^ _782652 : [(8387 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926948), _926950), _926952)))], (8389 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926948), _926950), _926954)))]]], (8391 ^ _782652) ^ [_927171, _927173] : [class_Lattices_Obounded__lattice__bot(_927171), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927171), c_Orderings_Obot__class_Obot(_927171)), _927173) = c_Orderings_Obot__class_Obot(_927171))], (8397 ^ _782652) ^ [_927270, _927272] : [class_Lattices_Obounded__lattice__bot(_927270), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927270), _927272), c_Orderings_Obot__class_Obot(_927270)) = c_Orderings_Obot__class_Obot(_927270))], (8403 ^ _782652) ^ [_927369, _927371, _927373, _927375] : [class_Lattices_Odistrib__lattice(_927369), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927369), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927369), _927371), _927373)), _927375) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927369), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927369), _927371), _927375)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927369), _927373), _927375)))], (8409 ^ _782652) ^ [_927528, _927530, _927532, _927534] : [class_Lattices_Odistrib__lattice(_927528), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927528), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927528), _927530), _927532)), _927534) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927528), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927528), _927530), _927534)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927528), _927532), _927534)))], (8415 ^ _782652) ^ [_927687, _927689, _927691, _927693] : [class_Lattices_Odistrib__lattice(_927687), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927687), _927689), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927687), _927691), _927693)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927687), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927687), _927689), _927691)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927687), _927689), _927693)))], (8421 ^ _782652) ^ [_927846, _927848, _927850, _927852] : [class_Lattices_Odistrib__lattice(_927846), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927846), _927848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927846), _927850), _927852)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927846), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927846), _927848), _927850)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_927846), _927848), _927852)))], (8427 ^ _782652) ^ [_928005, _928007, _928009] : [class_Lattices_Olattice(_928005), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_928005), _928007), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928005), _928007), _928009)) = _928007)], (8433 ^ _782652) ^ [_928114, _928116, _928118] : [class_Lattices_Olattice(_928114), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_928114), _928116), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_928114), _928116), _928118)) = _928116)], (8439 ^ _782652) ^ [_928244, _928246, _928248, _928250] : [hBOOL(hAPP(hAPP(c_member(_928244), _928246), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928244, tc_HOL_Obool)), _928248), _928250))), 8442 ^ _782652 : [(8443 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928244), _928246), _928248)))], (8445 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928244), _928246), _928250))]]], (8447 ^ _782652) ^ [_928419, _928421, _928423, _928425] : [-(hBOOL(hAPP(hAPP(c_member(_928419), _928421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928419, tc_HOL_Obool)), _928423), _928425)))), hBOOL(hAPP(hAPP(c_member(_928419), _928421), _928423)), -(hBOOL(hAPP(hAPP(c_member(_928419), _928421), _928425)))], (8457 ^ _782652) ^ [_928625, _928627, _928629, _928631] : [hBOOL(hAPP(hAPP(c_member(_928625), _928627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928625, tc_HOL_Obool)), _928629), _928631))), -(hBOOL(hAPP(hAPP(c_member(_928625), _928627), _928629)))], (8463 ^ _782652) ^ [_928756, _928758, _928760, _928762] : [hBOOL(hAPP(hAPP(c_member(_928756), _928758), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928756, tc_HOL_Obool)), _928760), _928762))), hBOOL(hAPP(hAPP(c_member(_928756), _928758), _928762))], (8469 ^ _782652) ^ [_928909, _928911, _928913, _928915] : [hBOOL(hAPP(hAPP(c_member(_928909), _928911), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928909, tc_HOL_Obool)), _928913), _928915))), 8472 ^ _782652 : [(8473 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928909), _928911), _928913)))], (8475 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928909), _928911), _928915)))]]], (8477 ^ _782652) ^ [_929076, _929078, _929080, _929082] : [-(hBOOL(hAPP(hAPP(c_member(_929076), _929078), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929076, tc_HOL_Obool)), _929080), _929082)))), hBOOL(hAPP(hAPP(c_member(_929076), _929078), _929080)), hBOOL(hAPP(hAPP(c_member(_929076), _929078), _929082))], (8487 ^ _782652) ^ [_929279, _929281, _929283, _929285] : [hBOOL(hAPP(hAPP(c_member(_929279), _929281), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929279, tc_HOL_Obool)), _929283), _929285))), -(hBOOL(hAPP(hAPP(c_member(_929279), _929281), _929283)))], (8493 ^ _782652) ^ [_929410, _929412, _929414, _929416] : [hBOOL(hAPP(hAPP(c_member(_929410), _929412), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929410, tc_HOL_Obool)), _929414), _929416))), -(hBOOL(hAPP(hAPP(c_member(_929410), _929412), _929416)))], (8499 ^ _782652) ^ [_929541, _929543] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929541, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_929541, tc_HOL_Obool))), _929543) = c_Orderings_Obot__class_Obot(tc_fun(_929541, tc_HOL_Obool)))], (8501 ^ _782652) ^ [_929587, _929589] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929587, tc_HOL_Obool)), _929589), c_Orderings_Obot__class_Obot(tc_fun(_929587, tc_HOL_Obool))) = _929589)], (8503 ^ _782652) ^ [_929628, _929630] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929628, tc_HOL_Obool)), _929630), _929630) = c_Orderings_Obot__class_Obot(tc_fun(_929628, tc_HOL_Obool)))], (8505 ^ _782652) ^ [_929669, _929671, _929673] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_929669), _929671)), 8508 ^ _782652 : [(8509 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_929669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929669, tc_HOL_Obool)), _929673), _929671))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_929669), _929673)))], (8515 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_929669), _929673)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_929669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929669, tc_HOL_Obool)), _929673), _929671))))]]], (8521 ^ _782652) ^ [_929947, _929949] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929947, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_929947, tc_HOL_Obool))), _929949) = c_Orderings_Obot__class_Obot(tc_fun(_929947, tc_HOL_Obool)))], (8523 ^ _782652) ^ [_929993, _929995] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929993, tc_HOL_Obool)), _929995), c_Orderings_Obot__class_Obot(tc_fun(_929993, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_929993, tc_HOL_Obool)))], (8539 ^ _782652) ^ [_930371, _930373, _930375] : [8541 ^ _782652 : [(8542 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_930371), 8540 ^ [_930371, _930373, _930375]), _930373)))], (8545 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_930371), 8543 ^ [_930371, _930373, _930375]), _930375)))], (8547 ^ _782652) ^ [] : [-(8540 ^ [_930371, _930373, _930375] = 8543 ^ [_930371, _930373, _930375])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930371, tc_HOL_Obool)), _930373), _930375) = c_Orderings_Obot__class_Obot(tc_fun(_930371, tc_HOL_Obool)))], (8525 ^ _782652) ^ [_930057, _930059, _930061] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930057, tc_HOL_Obool)), _930059), _930061) = c_Orderings_Obot__class_Obot(tc_fun(_930057, tc_HOL_Obool)), 8528 ^ _782652 : [(8529 ^ _782652) ^ [_930181] : [hBOOL(hAPP(hAPP(c_member(_930057), _930181), _930059)), 8532 ^ _782652 : [(8533 ^ _782652) ^ [_930271] : [hBOOL(hAPP(hAPP(c_member(_930057), _930271), _930061)), _930181 = _930271]]]]], (8551 ^ _782652) ^ [_930532, _930534, _930536] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930532, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930532, tc_HOL_Obool)), _930534), _930536)), _930534)))], (8553 ^ _782652) ^ [_930580, _930582, _930584, _930586, _930588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930580, tc_HOL_Obool)), _930582), _930584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930580, tc_HOL_Obool)), _930586), _930588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930580, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930580, tc_HOL_Obool)), _930582), _930588)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930580, tc_HOL_Obool)), _930584), _930586))))], (8563 ^ _782652) ^ [_930825, _930827, _930829, _930831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930825, tc_HOL_Obool)), _930827), _930829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930825, tc_HOL_Obool)), _930829), _930831)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930825, tc_HOL_Obool)), _930829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930825, tc_HOL_Obool)), _930831), _930827)) = _930827)], (8573 ^ _782652) ^ [_931046, _931048, _931050, _931052] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931046, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_931046), _931048), _931050)), hAPP(hAPP(c_Set_Oinsert(_931046), _931048), _931052)) = hAPP(hAPP(c_Set_Oinsert(_931046), _931048), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931046, tc_HOL_Obool)), _931050), _931052)))], (8575 ^ _782652) ^ [_931121, _931123, _931125] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_931121, tc_HOL_Obool)), _931123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931121, tc_HOL_Obool)), _931125), _931123)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_931121, tc_HOL_Obool)), _931123), _931125))], (8577 ^ _782652) ^ [_931181, _931183, _931185] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_931181, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931181, tc_HOL_Obool)), _931183), _931185)), _931185) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_931181, tc_HOL_Obool)), _931183), _931185))], (8579 ^ _782652) ^ [_931241, _931243, _931245, _931247] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931241, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_931241, tc_HOL_Obool)), _931243), _931245)), _931247) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_931241, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931241, tc_HOL_Obool)), _931243), _931247)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931241, tc_HOL_Obool)), _931245), _931247)))], (8581 ^ _782652) ^ [_931325, _931327, _931329] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931325, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931325, tc_HOL_Obool)), _931327), _931329)), _931327)))], (8583 ^ _782652) ^ [_931373, _931375, _931377] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931373, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931373, tc_HOL_Obool)), _931375), _931377)), _931377)))], (8585 ^ _782652) ^ [_931421, _931423, _931425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931421, tc_HOL_Obool)), _931423), _931425)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931421, tc_HOL_Obool)), _931423), _931425) = _931423)], (8591 ^ _782652) ^ [_931542, _931544, _931546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931542, tc_HOL_Obool)), _931544), _931546)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931542, tc_HOL_Obool)), _931546), _931544) = _931544)], (8597 ^ _782652) ^ [_931663, _931665, _931667, _931669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931663, tc_HOL_Obool)), _931665), _931667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931663, tc_HOL_Obool)), _931665), _931669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931663, tc_HOL_Obool)), _931665), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931663, tc_HOL_Obool)), _931667), _931669))))], (8607 ^ _782652) ^ [_931882, _931884, _931886, _931888, _931890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931882, tc_HOL_Obool)), _931884), _931886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931882, tc_HOL_Obool)), _931888), _931890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931882, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931882, tc_HOL_Obool)), _931884), _931888)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931882, tc_HOL_Obool)), _931886), _931890))))], (8617 ^ _782652) ^ [_932127, _932129, _932131, _932133] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932127, tc_HOL_Obool)), _932129), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932127, tc_HOL_Obool)), _932131), _932133)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932127, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932127, tc_HOL_Obool)), _932129), _932131)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932127, tc_HOL_Obool)), _932129), _932133)))], (8619 ^ _782652) ^ [_932211, _932213, _932215, _932217] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932211, tc_HOL_Obool)), _932213), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932211, tc_HOL_Obool)), _932215), _932217)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932211, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932211, tc_HOL_Obool)), _932213), _932215)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932211, tc_HOL_Obool)), _932213), _932217)))], (8621 ^ _782652) ^ [_932295, _932297, _932299, _932301] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932295, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932295, tc_HOL_Obool)), _932297), _932299)), _932301) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932295, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932295, tc_HOL_Obool)), _932297), _932301)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932295, tc_HOL_Obool)), _932299), _932301)))], (8623 ^ _782652) ^ [_932379, _932381, _932383, _932385] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932379, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932379, tc_HOL_Obool)), _932381), _932383)), _932385) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932379, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932379, tc_HOL_Obool)), _932381), _932385)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932379, tc_HOL_Obool)), _932383), _932385)))], (8625 ^ _782652) ^ [_932463, _932465, _932467, _932469] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932463, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932463, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932463, tc_HOL_Obool)), _932465), _932467)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932463, tc_HOL_Obool)), _932467), _932469))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932463, tc_HOL_Obool)), _932469), _932465)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932463, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932463, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932463, tc_HOL_Obool)), _932465), _932467)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932463, tc_HOL_Obool)), _932467), _932469))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932463, tc_HOL_Obool)), _932469), _932465)))], (8627 ^ _782652) ^ [_932602, _932604, _932606, _932608, _932610, _932612, _932614, _932616] : [c_Finite__Set_Ofolding__image__simple(_932602, _932604, _932606, _932608, _932610, _932612), hBOOL(hAPP(c_Finite__Set_Ofinite(_932604), _932614)), hBOOL(hAPP(c_Finite__Set_Ofinite(_932604), _932616)), -(hAPP(hAPP(_932606, hAPP(_932612, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_932604, tc_HOL_Obool)), _932614), _932616))), hAPP(_932612, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932604, tc_HOL_Obool)), _932614), _932616))) = hAPP(hAPP(_932606, hAPP(_932612, _932614)), hAPP(_932612, _932616)))], (8641 ^ _782652) ^ [_932950, _932952, _932954] : [hAPP(c_Com_Ocom_OBODY, _932950) = c_Com_Ocom_OWhile(_932952, _932954)], (8643 ^ _782652) ^ [_932998, _933000, _933002] : [c_Com_Ocom_OWhile(_932998, _933000) = hAPP(c_Com_Ocom_OBODY, _933002)], (8645 ^ _782652) ^ [_933046, _933048] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_933046, _933048))), -(hBOOL(hAPP(c_Com_OWT, _933048)))], (8651 ^ _782652) ^ [_933133, _933135] : [hBOOL(hAPP(c_Com_OWT, _933135)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_933133, _933135))))], (8657 ^ _782652) ^ [_933226, _933228] : [hBOOL(hAPP(c_Com_OWT, _933226)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_933228, _933226))))], (8663 ^ _782652) ^ [_933338, _933340, _933342, _933344] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933338, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_933338, tc_fun(_933338, tc_HOL_Obool), tc_HOL_Obool), c_member(_933338)), _933340)), hAPP(hAPP(c_COMBC(_933338, tc_fun(_933338, tc_HOL_Obool), tc_HOL_Obool), c_member(_933338)), _933342)), _933344)), -(hBOOL(hAPP(hAPP(c_member(_933338), _933344), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933338, tc_HOL_Obool)), _933340), _933342))))], (8669 ^ _782652) ^ [_933537, _933539, _933541, _933543] : [hBOOL(hAPP(hAPP(c_member(_933537), _933543), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933537, tc_HOL_Obool)), _933539), _933541))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933537, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_933537, tc_fun(_933537, tc_HOL_Obool), tc_HOL_Obool), c_member(_933537)), _933539)), hAPP(hAPP(c_COMBC(_933537, tc_fun(_933537, tc_HOL_Obool), tc_HOL_Obool), c_member(_933537)), _933541)), _933543)))], (8675 ^ _782652) ^ [_933754, _933756] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_933754, _933756)], (8677 ^ _782652) ^ [_933794, _933796] : [c_Com_Ocom_OWhile(_933794, _933796) = c_Com_Ocom_OSKIP], (8679 ^ _782652) ^ [_933837, _933839, _933841] : [hAPP(c_Com_Ocom_OBODY, _933837) = c_Com_Ocom_OSemi(_933839, _933841)], (8681 ^ _782652) ^ [_933885, _933887, _933889] : [c_Com_Ocom_OSemi(_933885, _933887) = hAPP(c_Com_Ocom_OBODY, _933889)], (8683 ^ _782652) ^ [_933933, _933935] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_933933, _933935))), 8686 ^ _782652 : [(8687 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _933933)))], (8689 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _933935)))]]], (8691 ^ _782652) ^ [_934050, _934052] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_934050, _934052)))), hBOOL(hAPP(c_Com_OWT, _934050)), hBOOL(hAPP(c_Com_OWT, _934052))], (8701 ^ _782652) ^ [_934199, _934201] : [hBOOL(hAPP(c_Com_OWT, _934199)), hBOOL(hAPP(c_Com_OWT, _934201)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_934199, _934201))))], (8711 ^ _782652) ^ [_934358, _934360] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_934358, _934360)], (8713 ^ _782652) ^ [_934398, _934400] : [c_Com_Ocom_OSemi(_934398, _934400) = c_Com_Ocom_OSKIP], (8715 ^ _782652) ^ [_934426, _934428, _934430, _934432, _934434, _934436, _934438, _934440] : [c_Finite__Set_Ofolding__image__simple(_934426, _934428, _934430, _934432, _934434, _934436), hBOOL(hAPP(c_Finite__Set_Ofinite(_934428), _934438)), -(hAPP(_934436, hAPP(hAPP(c_Set_Oinsert(_934428), _934440), _934438)) = hAPP(hAPP(_934430, hAPP(_934434, _934440)), hAPP(_934436, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934428, tc_HOL_Obool)), _934438), hAPP(hAPP(c_Set_Oinsert(_934428), _934440), c_Orderings_Obot__class_Obot(tc_fun(_934428, tc_HOL_Obool)))))))], (8725 ^ _782652) ^ [_934689, _934691, _934693, _934695, _934697, _934699, _934701, _934703] : [c_Finite__Set_Ofolding__image__simple(_934689, _934691, _934693, _934695, _934697, _934699), hBOOL(hAPP(c_Finite__Set_Ofinite(_934691), _934701)), hBOOL(hAPP(c_Finite__Set_Ofinite(_934691), _934703)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934691, tc_HOL_Obool)), _934701), _934703) = c_Orderings_Obot__class_Obot(tc_fun(_934691, tc_HOL_Obool)), -(hAPP(_934699, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_934691, tc_HOL_Obool)), _934701), _934703)) = hAPP(hAPP(_934693, hAPP(_934699, _934701)), hAPP(_934699, _934703)))], (8743 ^ _782652) ^ [_935078, _935080, _935082, _935084] : [class_Lattices_Olattice(_935078), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935078), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935078), _935080), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935078), _935082), _935084))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935078), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935078), _935080), _935082)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935078), _935080), _935084)))))], (8749 ^ _782652) ^ [_935251, _935253, _935255, _935257] : [class_Lattices_Olattice(_935251), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935251), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935251), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935251), _935253), _935255)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935251), _935253), _935257))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935251), _935253), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935251), _935255), _935257)))))], (8755 ^ _782652) ^ [_935424, _935426, _935428, _935430] : [hBOOL(hAPP(hAPP(c_member(_935424), _935426), _935428)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935424, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_935424), _935426), _935430)), _935428) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935424, tc_HOL_Obool)), _935430), _935428))], (8761 ^ _782652) ^ [_935594, _935596, _935598, _935600] : [hBOOL(hAPP(hAPP(c_member(_935594), _935596), _935598)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935594, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_935594), _935596), _935600)), _935598) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935594, tc_HOL_Obool)), _935600), _935598))], (8767 ^ _782652) ^ [_935743, _935745, _935747, _935749] : [-(hBOOL(hAPP(hAPP(c_member(_935743), _935745), _935747))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935743, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_935743), _935745), _935749)), _935747) = hAPP(hAPP(c_Set_Oinsert(_935743), _935745), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935743, tc_HOL_Obool)), _935749), _935747)))], (8773 ^ _782652) ^ [_935830, _935832, _935834, _935836] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935830, tc_HOL_Obool)), _935832), hAPP(hAPP(c_Set_Oinsert(_935830), _935834), _935836)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935830, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935830, tc_HOL_Obool)), _935832), _935836)), hAPP(hAPP(c_Set_Oinsert(_935830), _935834), c_Orderings_Obot__class_Obot(tc_fun(_935830, tc_HOL_Obool)))))], (8775 ^ _782652) ^ [_935913, _935915, _935917, _935919] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935913, tc_HOL_Obool)), _935915), hAPP(hAPP(c_Set_Oinsert(_935913), _935917), _935919)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935913, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935913, tc_HOL_Obool)), _935915), hAPP(hAPP(c_Set_Oinsert(_935913), _935917), c_Orderings_Obot__class_Obot(tc_fun(_935913, tc_HOL_Obool))))), _935919))], (8777 ^ _782652) ^ [_935996, _935998, _936000] : [-(hAPP(hAPP(c_Set_Oinsert(_935996), _935998), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_935996, tc_HOL_Obool)), _936000), hAPP(hAPP(c_Set_Oinsert(_935996), _935998), c_Orderings_Obot__class_Obot(tc_fun(_935996, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_935996), _935998), _936000))], (8779 ^ _782652) ^ [_936084, _936086, _936088, _936090] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_936084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936084, tc_HOL_Obool)), _936086), hAPP(hAPP(c_Set_Oinsert(_936084), _936088), _936090)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_936084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936084, tc_HOL_Obool)), _936086), _936090))))], (8785 ^ _782652) ^ [_936237, _936239, _936241, _936243] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_936237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936237, tc_HOL_Obool)), _936239), _936243))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_936237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936237, tc_HOL_Obool)), _936239), hAPP(hAPP(c_Set_Oinsert(_936237), _936241), _936243)))))], (8791 ^ _782652) ^ [_936396, _936398, _936400, _936402] : [hBOOL(hAPP(hAPP(c_member(_936396), _936398), _936400)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936396, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_936396), _936398), _936402)), _936400) = hAPP(hAPP(c_Set_Oinsert(_936396), _936398), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936396, tc_HOL_Obool)), _936402), _936400)))], (8797 ^ _782652) ^ [_936567, _936569, _936571, _936573] : [hBOOL(hAPP(hAPP(c_member(_936567), _936569), _936571)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936567, tc_HOL_Obool)), _936571), hAPP(hAPP(c_Set_Oinsert(_936567), _936569), _936573)) = hAPP(hAPP(c_Set_Oinsert(_936567), _936569), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936567, tc_HOL_Obool)), _936571), _936573)))], (8803 ^ _782652) ^ [_936734, _936736, _936738, _936740] : [-(hBOOL(hAPP(hAPP(c_member(_936734), _936736), _936738))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936734, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_936734), _936736), _936740)), _936738) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936734, tc_HOL_Obool)), _936740), _936738))], (8809 ^ _782652) ^ [_936807, _936809, _936811, _936813] : [-(hBOOL(hAPP(hAPP(c_member(_936807), _936809), _936811))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936807, tc_HOL_Obool)), _936811), hAPP(hAPP(c_Set_Oinsert(_936807), _936809), _936813)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936807, tc_HOL_Obool)), _936811), _936813))], (8815 ^ _782652) ^ [_936899, _936901, _936903, _936905] : [hBOOL(hAPP(hAPP(c_member(_936899), _936901), _936903)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936899, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_936899), _936901), _936905)), _936903) = hAPP(hAPP(c_Set_Oinsert(_936899), _936901), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_936899, tc_HOL_Obool)), _936905), _936903)))], (8821 ^ _782652) ^ [_937064, _937066, _937068, _937070] : [-(hBOOL(hAPP(hAPP(c_member(_937064), _937066), _937068))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937064, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_937064), _937066), _937070)), _937068) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937064, tc_HOL_Obool)), _937070), _937068))], (8827 ^ _782652) ^ [_937158, _937160, _937162, _937164] : [hBOOL(hAPP(hAPP(c_member(_937158), _937160), _937162)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937158, tc_HOL_Obool)), _937162), hAPP(hAPP(c_Set_Oinsert(_937158), _937160), _937164)) = hAPP(hAPP(c_Set_Oinsert(_937158), _937160), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937158, tc_HOL_Obool)), _937162), _937164)))], (8833 ^ _782652) ^ [_937323, _937325, _937327, _937329] : [-(hBOOL(hAPP(hAPP(c_member(_937323), _937325), _937327))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937323, tc_HOL_Obool)), _937327), hAPP(hAPP(c_Set_Oinsert(_937323), _937325), _937329)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937323, tc_HOL_Obool)), _937327), _937329))], (8839 ^ _782652) ^ [_937402, _937404, _937406, _937408, _937410] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937402, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937402, tc_HOL_Obool)), hAPP(c_Set_Oimage(_937404, _937402, _937406), _937408)), hAPP(c_Set_Oimage(_937404, _937402, _937406), _937410))), hAPP(c_Set_Oimage(_937404, _937402, _937406), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937404, tc_HOL_Obool)), _937408), _937410)))))], (8841 ^ _782652) ^ [_937486, _937488, _937490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937486, tc_HOL_Obool)), _937488), _937490)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937486, tc_HOL_Obool)), _937488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937486, tc_HOL_Obool)), _937490), _937488)) = _937490)], (8847 ^ _782652) ^ [_937650, _937652, _937654, _937656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937650, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937650, tc_HOL_Obool)), _937652), _937654)), _937656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937650, tc_HOL_Obool)), _937652), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937650, tc_HOL_Obool)), _937654), _937656))))], (8853 ^ _782652) ^ [_937811, _937813, _937815, _937817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937811, tc_HOL_Obool)), _937813), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937811, tc_HOL_Obool)), _937815), _937817))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937811, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937811, tc_HOL_Obool)), _937813), _937815)), _937817)))], (8859 ^ _782652) ^ [_937978, _937980, _937982, _937984, _937986] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937978, tc_HOL_Obool)), hAPP(c_Set_Oimage(_937980, _937978, _937982), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937980, tc_HOL_Obool)), _937984), _937986))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_937978, tc_HOL_Obool)), hAPP(c_Set_Oimage(_937980, _937978, _937982), _937984)), hAPP(c_Set_Oimage(_937980, _937978, _937982), _937986)))))], (8861 ^ _782652) ^ [_938083, _938085, _938087, _938089] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938083, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938083, tc_HOL_Obool)), _938085), _938087)), _938089) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938083, tc_HOL_Obool)), _938085), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938083, tc_HOL_Obool)), _938087), _938089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938083, tc_HOL_Obool)), _938089), _938085)))], (8867 ^ _782652) ^ [_938268, _938270, _938272, _938274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938268, tc_HOL_Obool)), _938274), _938270)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938268, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938268, tc_HOL_Obool)), _938270), _938272)), _938274) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_938268, tc_HOL_Obool)), _938270), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938268, tc_HOL_Obool)), _938272), _938274)))], (8873 ^ _782652) ^ [_938459, _938461, _938463, _938465, _938467, _938469] : [c_Finite__Set_Ofolding__image__simple(_938459, _938461, _938463, _938465, _938467, _938469), -(hAPP(_938469, c_Orderings_Obot__class_Obot(tc_fun(_938461, tc_HOL_Obool))) = _938465)], (8879 ^ _782652) ^ [_938568, _938570, _938572, _938574, _938576, _938578, _938580, _938582] : [c_Finite__Set_Ofolding__image__simple(_938568, _938570, _938572, _938574, _938576, _938578), hBOOL(hAPP(c_Finite__Set_Ofinite(_938570), _938580)), hBOOL(hAPP(hAPP(c_member(_938570), _938582), _938580)), -(hAPP(_938578, _938580) = hAPP(hAPP(_938572, hAPP(_938576, _938582)), hAPP(_938578, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938570, tc_HOL_Obool)), _938580), hAPP(hAPP(c_Set_Oinsert(_938570), _938582), c_Orderings_Obot__class_Obot(tc_fun(_938570, tc_HOL_Obool)))))))], (8893 ^ _782652) ^ [_938889, _938891, _938893] : [-(hBOOL(hAPP(hAPP(c_member(_938889), _938891), _938893))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938889, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_938889), _938891), _938893)), hAPP(hAPP(c_Set_Oinsert(_938889), _938891), c_Orderings_Obot__class_Obot(tc_fun(_938889, tc_HOL_Obool)))) = _938893)], (8899 ^ _782652) ^ [_938966, _938968, _938970] : [hBOOL(hAPP(hAPP(c_member(_938966), _938968), _938970)), -(hAPP(hAPP(c_Set_Oinsert(_938966), _938968), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938966, tc_HOL_Obool)), _938970), hAPP(hAPP(c_Set_Oinsert(_938966), _938968), c_Orderings_Obot__class_Obot(tc_fun(_938966, tc_HOL_Obool))))) = _938970)], (8905 ^ _782652) ^ [_939123] : [-(hAPP(c_Hoare__Mirabelle_OMGT, _939123) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _939123), c_Natural_Oevalc(_939123)))], (8907 ^ _782652) ^ [_939157, _939159] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _939157, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _939159)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _939157, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_Com_Ostate), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies)), c_Natural_Oevalc(_939159))))), c_fequal))), _939159), c_fequal)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (8929 ^ _782652) ^ [_939679, _939681, _939683, _939685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939679, tc_HOL_Obool)), _939681), hAPP(hAPP(c_Set_Oinsert(_939679), _939683), _939685)))), 8932 ^ _782652 : [(8933 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939679), _939683), _939681)))], (8935 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939679, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939679, tc_HOL_Obool)), _939681), hAPP(hAPP(c_Set_Oinsert(_939679), _939683), c_Orderings_Obot__class_Obot(tc_fun(_939679, tc_HOL_Obool))))), _939685))]], 8936 ^ _782652 : [(8937 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_939679), _939683), _939681))], (8939 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939679, tc_HOL_Obool)), _939681), _939685))]]], (8913 ^ _782652) ^ [_939347, _939349, _939351, _939353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939347, tc_HOL_Obool)), _939349), hAPP(hAPP(c_Set_Oinsert(_939347), _939351), _939353))), 8916 ^ _782652 : [(8917 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_939347), _939351), _939349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939347, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939347, tc_HOL_Obool)), _939349), hAPP(hAPP(c_Set_Oinsert(_939347), _939351), c_Orderings_Obot__class_Obot(tc_fun(_939347, tc_HOL_Obool))))), _939353)))], (8923 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939347), _939351), _939349))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939347, tc_HOL_Obool)), _939349), _939353)))]]], (8943 ^ _782652) ^ [_940043, _940045, _940047, _940049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940043, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940043, tc_HOL_Obool)), _940045), hAPP(hAPP(c_Set_Oinsert(_940043), _940047), c_Orderings_Obot__class_Obot(tc_fun(_940043, tc_HOL_Obool))))), _940049)), hBOOL(hAPP(hAPP(c_member(_940043), _940047), _940045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940043, tc_HOL_Obool)), _940045), hAPP(hAPP(c_Set_Oinsert(_940043), _940047), _940049))))], (8953 ^ _782652) ^ [_940298, _940300, _940302, _940304, _940306] : [c_Finite__Set_Ofolding__one(_940298, _940300, _940302), hBOOL(hAPP(c_Finite__Set_Ofinite(_940298), _940304)), 8960 ^ _782652 : [(8961 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940298, tc_HOL_Obool)), _940304), hAPP(hAPP(c_Set_Oinsert(_940298), _940306), c_Orderings_Obot__class_Obot(tc_fun(_940298, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_940298, tc_HOL_Obool)), -(hAPP(_940302, hAPP(hAPP(c_Set_Oinsert(_940298), _940306), _940304)) = _940306)], (8967 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940298, tc_HOL_Obool)), _940304), hAPP(hAPP(c_Set_Oinsert(_940298), _940306), c_Orderings_Obot__class_Obot(tc_fun(_940298, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_940298, tc_HOL_Obool))), -(hAPP(_940302, hAPP(hAPP(c_Set_Oinsert(_940298), _940306), _940304)) = hAPP(hAPP(_940300, _940306), hAPP(_940302, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940298, tc_HOL_Obool)), _940304), hAPP(hAPP(c_Set_Oinsert(_940298), _940306), c_Orderings_Obot__class_Obot(tc_fun(_940298, tc_HOL_Obool)))))))]]], (8973 ^ _782652) ^ [_940780, _940782, _940784] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _940780)), _940782), _940784)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _940780))), _940782), _940784)))], (8979 ^ _782652) ^ [_940905, _940907, _940909] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _940905))), _940907), _940909)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _940905)), _940907), _940909)))], (8985 ^ _782652) ^ [_941030, _941032] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _941030), _941032)), -(_941032 = _941030)], (8991 ^ _782652) ^ [_941117] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _941117), _941117)))], (8993 ^ _782652) ^ [_941145, _941147, _941149, _941151, _941153] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_941145), _941147), _941149)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_941151), _941149), _941153)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_941145, _941151)), _941147), _941153)))], (9003 ^ _782652) ^ [_941334, _941336, _941338, _941340, _941342] : [hBOOL(hAPP(_941334, _941336)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_941338), _941336), _941340)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_941334, _941338)), _941340), _941342)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_941334, _941338)), _941336), _941342)))], (9017 ^ _782652) ^ [_941587, _941589, _941591] : [-(hBOOL(hAPP(_941587, _941589))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_941587, _941591)), _941589), _941589)))], (9023 ^ _782652) ^ [_941655, _941657, _941659] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _941655)), _941657), _941659)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _941655))), _941657), _941659)))], (9029 ^ _782652) ^ [_941776, _941778, _941780] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _941776))), _941778), _941780)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _941776)), _941778), _941780)))], (9035 ^ _782652) ^ [_941915, _941917, _941919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941915, tc_HOL_Obool)), _941917), hAPP(hAPP(c_Set_Oinsert(_941915), _941919), c_Orderings_Obot__class_Obot(tc_fun(_941915, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_941915, _941919, _941917) = _941919)], (9041 ^ _782652) ^ [_942042, _942044, _942046] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942042, tc_HOL_Obool)), _942044), hAPP(hAPP(c_Set_Oinsert(_942042), _942046), c_Orderings_Obot__class_Obot(tc_fun(_942042, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_942042, _942046, _942044) = c_HOL_OThe(_942042, hAPP(hAPP(c_COMBC(_942042, tc_fun(_942042, tc_HOL_Obool), tc_HOL_Obool), c_member(_942042)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942042, tc_HOL_Obool)), _942044), hAPP(hAPP(c_Set_Oinsert(_942042), _942046), c_Orderings_Obot__class_Obot(tc_fun(_942042, tc_HOL_Obool)))))))], (9047 ^ _782652) ^ [_942151] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _942151), _942151)))], (9049 ^ _782652) ^ [_942200, _942202, _942204, _942206] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_942200, _942202)), _942204), _942206)), 9053 ^ _782652 : [(9054 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_942200), _942204), 9052 ^ [_942200, _942202, _942204, _942206])))], (9056 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_942202), 9052 ^ [_942200, _942202, _942204, _942206]), _942206)))]]], (9058 ^ _782652) ^ [_942378, _942380, _942382, _942384] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_942378, _942380)), _942382), _942384))), 9059 ^ _782652 : [(9060 ^ _782652) ^ [_942446] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_942378), _942382), _942446)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_942380), _942446), _942384))]]], (9068 ^ _782652) ^ [_942596, _942598, _942600, _942602] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_942596), _942598), _942600)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_942596), _942598), _942602)), -(_942602 = _942600)], (9078 ^ _782652) ^ [_942779, _942781, _942783] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_942779, _942781)), _942783), _942783)), hBOOL(hAPP(_942779, _942783)), 9086 ^ _782652 : [(9087 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_942781), _942783), 9085 ^ [_942779, _942781, _942783])))], (9089 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_942779, _942781)), 9085 ^ [_942779, _942781, _942783]), _942783)))]]], (9091 ^ _782652) ^ [_943015, _943017, _943019] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_943015, _943017)), _943019), _943019))), 9092 ^ _782652 : [(9093 ^ _782652) ^ [] : [-(hBOOL(hAPP(_943015, _943019)))], (9095 ^ _782652) ^ [_943115] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_943017), _943019), _943115)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_943015, _943017)), _943115), _943019))]]], (9103 ^ _782652) ^ [_943292, _943294, _943296, _943298] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_943292, _943294)), _943296), _943298)), 9108 ^ _782652 : [(9109 ^ _782652) ^ [] : [-(_943298 = _943296)], (9111 ^ _782652) ^ [] : [hBOOL(hAPP(_943292, _943296))]], 9112 ^ _782652 : [(9113 ^ _782652) ^ [] : [-(hBOOL(hAPP(_943292, _943296)))], (9116 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_943294), _943296), 9114 ^ [_943292, _943294, _943296, _943298])))], (9118 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_943292, _943294)), 9114 ^ [_943292, _943294, _943296, _943298]), _943298)))]]], (9120 ^ _782652) ^ [_943599, _943601, _943603, _943605] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_943599, _943601)), _943603), _943605))), 9121 ^ _782652 : [(9122 ^ _782652) ^ [] : [_943605 = _943603, -(hBOOL(hAPP(_943599, _943603)))], (9128 ^ _782652) ^ [] : [hBOOL(hAPP(_943599, _943603)), 9131 ^ _782652 : [(9132 ^ _782652) ^ [_943818] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_943601), _943603), _943818)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_943599, _943601)), _943818), _943605))]]]]], (9140 ^ _782652) ^ [_943980, _943982, _943984, _943986, _943988] : [class_Groups_Oordered__ab__group__add(_943980), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_943980), _943982), _943984) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_943980), _943986), _943988), 9147 ^ _782652 : [(9148 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943980), _943982), _943984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943980), _943986), _943988)))], (9154 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943980), _943986), _943988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943980), _943982), _943984)))]]], (9160 ^ _782652) ^ [_944356, _944358, _944360, _944362, _944364, _944366] : [hBOOL(hAPP(hAPP(c_member(_944356), _944358), _944360)), -(hAPP(c_Set_Oimage(_944356, _944362, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_944356, _944362), _944364), _944358), _944366)), _944360) = hAPP(hAPP(c_Set_Oinsert(_944362), _944366), hAPP(c_Set_Oimage(_944356, _944362, _944364), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_944356, tc_HOL_Obool)), _944360), hAPP(hAPP(c_Set_Oinsert(_944356), _944358), c_Orderings_Obot__class_Obot(tc_fun(_944356, tc_HOL_Obool)))))))], (9166 ^ _782652) ^ [_944565, _944567, _944569, _944571, _944573, _944575] : [-(hBOOL(hAPP(hAPP(c_member(_944565), _944567), _944569))), -(hAPP(c_Set_Oimage(_944565, _944571, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_944565, _944571), _944573), _944567), _944575)), _944569) = hAPP(c_Set_Oimage(_944565, _944571, _944573), _944569))], (9172 ^ _782652) ^ [_944644, _944646, _944648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_944644), _944646)), hBOOL(hAPP(_944648, _944646)), 9183 ^ _782652 : [(9184 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_944644), 9182 ^ [_944644, _944646, _944648])))], (9186 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944644), 9181 ^ [_944644, _944646, _944648]), 9182 ^ [_944644, _944646, _944648])))], (9188 ^ _782652) ^ [] : [-(hBOOL(hAPP(_944648, 9182 ^ [_944644, _944646, _944648])))], (9190 ^ _782652) ^ [] : [hBOOL(hAPP(_944648, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_944644, tc_HOL_Obool)), 9182 ^ [_944644, _944646, _944648]), hAPP(hAPP(c_Set_Oinsert(_944644), 9181 ^ [_944644, _944646, _944648]), c_Orderings_Obot__class_Obot(tc_fun(_944644, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_944648, c_Orderings_Obot__class_Obot(tc_fun(_944644, tc_HOL_Obool)))))], (9194 ^ _782652) ^ [_945169, _945171, _945173, _945175, _945177, _945179, _945181, _945183] : [c_Finite__Set_Ofolding__image__simple(_945169, _945171, _945173, _945175, _945177, _945179), hBOOL(hAPP(c_Finite__Set_Ofinite(_945171), _945181)), hBOOL(hAPP(c_Finite__Set_Ofinite(_945171), _945183)), 9208 ^ _782652 : [(9209 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_945171), 9207 ^ [_945169, _945171, _945173, _945175, _945177, _945179, _945181, _945183]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945171, tc_HOL_Obool)), _945181), _945183))))], (9211 ^ _782652) ^ [] : [hAPP(_945177, 9207 ^ [_945169, _945171, _945173, _945175, _945177, _945179, _945181, _945183]) = _945175]], -(hAPP(_945179, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945171, tc_HOL_Obool)), _945181), _945183)) = hAPP(hAPP(_945173, hAPP(_945179, _945181)), hAPP(_945179, _945183)))], (9215 ^ _782652) ^ [_945670] : [-(c_Finite__Set_Ofun__left__comm__idem(_945670, tc_fun(_945670, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_945670, tc_HOL_Obool), tc_fun(tc_fun(_945670, tc_HOL_Obool), tc_fun(_945670, tc_HOL_Obool)), _945670), hAPP(c_COMBC(tc_fun(_945670, tc_HOL_Obool), tc_fun(_945670, tc_HOL_Obool), tc_fun(_945670, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_945670, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_945670, tc_fun(_945670, tc_HOL_Obool), tc_fun(_945670, tc_HOL_Obool)), c_Set_Oinsert(_945670)), c_Orderings_Obot__class_Obot(tc_fun(_945670, tc_HOL_Obool))))))], (9217 ^ _782652) ^ [_945763, _945765] : [-(c_HOL_OThe(_945763, hAPP(c_fequal, _945765)) = _945765)], (9219 ^ _782652) ^ [_945794, _945796] : [-(c_HOL_OThe(_945794, hAPP(hAPP(c_COMBC(_945794, _945794, tc_HOL_Obool), c_fequal), _945796)) = _945796)], (9221 ^ _782652) ^ [_945832, _945834, _945836, _945838, _945840] : [-(c_Map_Odom(_945832, _945834, c_Fun_Ooverride__on(_945832, tc_Option_Ooption(_945834), _945836, _945838, _945840)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945832, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945832, tc_HOL_Obool)), c_Map_Odom(_945832, _945834, _945836)), hAPP(c_Set_OCollect(_945832), hAPP(hAPP(c_COMBC(_945832, tc_fun(_945832, tc_HOL_Obool), tc_HOL_Obool), c_member(_945832)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945832, tc_HOL_Obool)), _945840), c_Map_Odom(_945832, _945834, _945838)))))), hAPP(c_Set_OCollect(_945832), hAPP(hAPP(c_COMBC(_945832, tc_fun(_945832, tc_HOL_Obool), tc_HOL_Obool), c_member(_945832)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945832, tc_HOL_Obool)), _945840), c_Map_Odom(_945832, _945834, _945838))))))], (9249 ^ _782652) ^ [_946519, _946521, _946523, _946525] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_946519, tc_HOL_Obool)), _946521), hAPP(hAPP(c_Set_Oinsert(_946519), _946523), _946525)))), 9252 ^ _782652 : [(9253 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_946519), _946523), _946525)))], (9255 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_946519, tc_HOL_Obool)), _946521), _946525))]], 9256 ^ _782652 : [(9257 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_946519), _946523), _946525))], (9259 ^ _782652) ^ [] : [9260 ^ _782652 : [(9261 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_946519), _946523), _946521)))], (9263 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_946519, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946519, tc_HOL_Obool)), _946521), hAPP(hAPP(c_Set_Oinsert(_946519), _946523), c_Orderings_Obot__class_Obot(tc_fun(_946519, tc_HOL_Obool))))), _946525))]], 9264 ^ _782652 : [(9265 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_946519), _946523), _946521))], (9267 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_946519, tc_HOL_Obool)), _946521), _946525))]]]]], (9223 ^ _782652) ^ [_945992, _945994, _945996, _945998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945992, tc_HOL_Obool)), _945994), hAPP(hAPP(c_Set_Oinsert(_945992), _945996), _945998))), 9226 ^ _782652 : [(9227 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_945992), _945996), _945998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945992, tc_HOL_Obool)), _945994), _945998)))], (9233 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_945992), _945996), _945998))), 9236 ^ _782652 : [(9237 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_945992), _945996), _945994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945992, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_945992, tc_HOL_Obool)), _945994), hAPP(hAPP(c_Set_Oinsert(_945992), _945996), c_Orderings_Obot__class_Obot(tc_fun(_945992, tc_HOL_Obool))))), _945998)))], (9243 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_945992), _945996), _945994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945992, tc_HOL_Obool)), _945994), _945998)))]]]]], (9271 ^ _782652) ^ [_947058, _947060, _947062, _947064, _947066, _947068, _947070] : [hBOOL(hAPP(hAPP(c_member(_947058), _947060), _947062)), c_Nitpick_Ofold__graph_H(_947058, _947064, _947066, _947068, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947058, tc_HOL_Obool)), _947062), hAPP(hAPP(c_Set_Oinsert(_947058), _947060), c_Orderings_Obot__class_Obot(tc_fun(_947058, tc_HOL_Obool)))), _947070), -(c_Nitpick_Ofold__graph_H(_947058, _947064, _947066, _947068, _947062, hAPP(hAPP(_947066, _947060), _947070)))], (9281 ^ _782652) ^ [_947297, _947299, _947301, _947303] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_947297, _947299), _947301), _947303), hAPP(_947301, _947303)) = _947301)], (9283 ^ _782652) ^ [_947341, _947343, _947345] : [hBOOL(hAPP(_947341, _947343)), -(hBOOL(hAPP(hAPP(c_member(_947345), _947343), hAPP(c_Set_OCollect(_947345), _947341))))], (9289 ^ _782652) ^ [_947448, _947450, _947452] : [9290 ^ _782652 : [(9291 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947448), hAPP(c_Set_OCollect(_947448), _947450)))], (9293 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947448), hAPP(c_Set_OCollect(_947448), _947452)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_947448), hAPP(c_Set_OCollect(_947448), hAPP(hAPP(c_COMBS(_947448, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _947448), c_fconj), _947450)), _947452)))))], (9297 ^ _782652) ^ [_947659, _947661] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_947659), _947661)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_947659, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_947659, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_947659, tc_HOL_Obool), tc_fun(_947659, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_947659, tc_HOL_Obool))), _947661)))))], (9303 ^ _782652) ^ [_947816, _947818, _947820, _947822, _947824] : [c_Finite__Set_Ofun__left__comm__idem(_947816, _947818, _947820), -(hAPP(hAPP(_947820, _947822), hAPP(hAPP(_947820, _947822), _947824)) = hAPP(hAPP(_947820, _947822), _947824))], (9309 ^ _782652) ^ [_947937, _947939] : [class_Orderings_Opreorder(_947937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947937), _947939), _947939))], (9315 ^ _782652) ^ [_948027, _948029] : [-(hAPP(c_Set_OCollect(_948027), _948029) = _948029)], (9317 ^ _782652) ^ [_948057, _948059, _948061] : [class_Orderings_Olinorder(_948057), 9320 ^ _782652 : [(9331 ^ _782652) ^ [] : [9332 ^ _782652 : [(9333 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948057), _948059), _948061))], (9335 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948057), _948061), _948059))]], _948059 = _948061], (9321 ^ _782652) ^ [] : [-(_948059 = _948061), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948057), _948059), _948061))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948057), _948061), _948059)))]]], (9339 ^ _782652) ^ [_948311, _948313, _948315] : [class_Orderings_Olinorder(_948311), 9342 ^ _782652 : [(9353 ^ _782652) ^ [] : [9354 ^ _782652 : [(9355 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948311), _948315), _948313))], (9357 ^ _782652) ^ [] : [_948313 = _948315]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948311), _948313), _948315))], (9343 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948311), _948313), _948315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948311), _948315), _948313))), -(_948313 = _948315)]]], (9361 ^ _782652) ^ [_948565, _948567, _948569] : [class_Orderings_Olinorder(_948565), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948565), _948567), _948569))), -(_948567 = _948569), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948565), _948569), _948567)))], (9375 ^ _782652) ^ [_948696, _948698, _948700] : [class_Orderings_Olinorder(_948696), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948696), _948698), _948700))), 9382 ^ _782652 : [(9383 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948696), _948700), _948698))), -(_948700 = _948698)], (9389 ^ _782652) ^ [] : [_948700 = _948698, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948696), _948700), _948698))]]], (9395 ^ _782652) ^ [_948955, _948957, _948959] : [class_Orderings_Olinorder(_948955), -(_948957 = _948959), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948955), _948957), _948959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948955), _948959), _948957)))], (9409 ^ _782652) ^ [_949090, _949092, _949094] : [class_Orderings_Oorder(_949090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949090), _949092), _949094)), _949092 = _949094], (9419 ^ _782652) ^ [_949236, _949238, _949240] : [class_Orderings_Opreorder(_949236), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949236), _949238), _949240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949236), _949240), _949238))], (9429 ^ _782652) ^ [_949396, _949398, _949400] : [class_Orderings_Opreorder(_949396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949396), _949398), _949400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949396), _949400), _949398))], (9439 ^ _782652) ^ [_949556, _949558, _949560] : [class_Orderings_Oorder(_949556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949556), _949558), _949560)), _949558 = _949560], (9449 ^ _782652) ^ [_949702, _949704, _949706] : [class_Orderings_Oorder(_949702), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949702), _949704), _949706)), _949706 = _949704], (9459 ^ _782652) ^ [_949848, _949850, _949852] : [class_Orderings_Opreorder(_949848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949848), _949850), _949852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949848), _949852), _949850))], (9469 ^ _782652) ^ [_950008, _950010, _950012] : [class_Orderings_Oorder(_950008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950008), _950010), _950012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950008), _950012), _950010))], (9479 ^ _782652) ^ [_950168, _950170, _950172, _950174] : [class_Orderings_Oord(_950168), _950170 = _950172, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950168), _950172), _950174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950168), _950170), _950174)))], (9493 ^ _782652) ^ [_950387, _950389, _950391, _950393] : [class_Orderings_Oorder(_950387), _950389 = _950391, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950387), _950393), _950391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950387), _950393), _950389)))], (9507 ^ _782652) ^ [_950606, _950608, _950610, _950612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_950606, tc_HOL_Obool)), _950608), _950610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_950606, tc_HOL_Obool)), _950610), _950612)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_950606, tc_HOL_Obool)), _950608), _950612)))], (9517 ^ _782652) ^ [_950803, _950805, _950807, _950809] : [class_Orderings_Oord(_950803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950803), _950805), _950807)), _950807 = _950809, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950803), _950805), _950809)))], (9531 ^ _782652) ^ [_951022, _951024, _951026, _951028] : [class_Orderings_Oorder(_951022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951022), _951024), _951026)), _951024 = _951028, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951022), _951028), _951026)))], (9545 ^ _782652) ^ [_951241, _951243, _951245, _951247] : [class_Orderings_Opreorder(_951241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951241), _951243), _951245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951241), _951245), _951247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951241), _951243), _951247)))], (9559 ^ _782652) ^ [_951474, _951476, _951478, _951480] : [class_Orderings_Oorder(_951474), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951474), _951476), _951478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951474), _951480), _951476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951474), _951480), _951478)))], (9573 ^ _782652) ^ [_951707, _951709, _951711] : [class_Orderings_Opreorder(_951707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951707), _951709), _951711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951707), _951711), _951709))], (9583 ^ _782652) ^ [_951867, _951869, _951871] : [class_Orderings_Olinorder(_951867), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951867), _951869), _951871))), -(_951869 = _951871), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951867), _951871), _951869)))], (9597 ^ _782652) ^ [_952026, _952028, _952030, _952032, _952034] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952026, _952028), _952030), _952032), _952034) = _952030, -(hAPP(_952030, _952032) = _952034)], (9603 ^ _782652) ^ [_952135, _952137, _952139, _952141, _952143] : [hAPP(_952139, _952141) = _952143, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952135, _952137), _952139), _952141), _952143) = _952139)], (9609 ^ _782652) ^ [_952250, _952252, _952254, _952256, _952258, _952260] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952250, _952252), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952250, _952252), _952254), _952256), _952258)), _952256), _952260) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952250, _952252), _952254), _952256), _952260))], (9611 ^ _782652) ^ [_952319, _952321, _952323, _952325, _952327] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952319, _952321), _952323), _952325), _952327), _952325) = _952327)], (9613 ^ _782652) ^ [_952386, _952388, _952390, _952392, _952394, _952396] : [_952386 = _952388, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952390, _952392), _952394), _952388), _952396), _952386) = _952396)], (9619 ^ _782652) ^ [_952495, _952497, _952499, _952501, _952503, _952505] : [-(_952495 = _952497), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952499, _952501), _952503), _952497), _952505), _952495) = hAPP(_952503, _952495))], (9625 ^ _782652) ^ [_952555, _952557, _952559, _952561, _952563, _952565, _952567] : [-(_952555 = _952557), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952559, _952561), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952559, _952561), _952563), _952555), _952565)), _952557), _952567) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952559, _952561), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952559, _952561), _952563), _952557), _952567)), _952555), _952565))], (9631 ^ _782652) ^ [_952645, _952647, _952649, _952651, _952653, _952655] : [-(_952645 = _952647), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952649, _952651), _952653), _952647), _952655), _952645) = hAPP(_952653, _952645))], (9637 ^ _782652) ^ [_952707, _952709, _952711, _952713, _952715] : [hAPP(_952707, _952709) = _952711, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952713, _952715), _952707), _952709), _952711) = _952707)], (9643 ^ _782652) ^ [_952820, _952822, _952824, _952826, _952828] : [class_Groups_Oordered__ab__group__add(_952820), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_952820), _952822), _952824) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_952820), _952826), _952828), 9650 ^ _782652 : [(9651 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952820), _952822), _952824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952820), _952826), _952828)))], (9657 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952820), _952826), _952828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952820), _952822), _952824)))]]], (9663 ^ _782652) ^ [_953196, _953198, _953200, _953202, _953204, _953206] : [_953196 = _953198, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_953200, _953202), _953204), _953198), _953206), _953196) = _953206)], (9669 ^ _782652) ^ [_953305, _953307, _953309, _953311, _953313, _953315] : [-(_953305 = _953307), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_953309, _953311), _953313), _953307), _953315), _953305) = hAPP(_953313, _953305))], (9675 ^ _782652) ^ [_953369, _953371, _953373, _953375, _953377] : [c_Finite__Set_Ofun__left__comm__idem(_953369, _953371, _953373), -(c_Finite__Set_Ofun__left__comm__idem(_953375, _953371, hAPP(hAPP(c_COMBB(_953369, tc_fun(_953371, _953371), _953375), _953373), _953377)))], (9681 ^ _782652) ^ [_953497, _953499] : [c_Orderings_Obot__class_Obot(tc_fun(_953497, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_953497), _953499), 9684 ^ _782652 : [(9685 ^ _782652) ^ [_953582] : [hBOOL(hAPP(_953499, _953582))]]], (9687 ^ _782652) ^ [_953605, _953607] : [-(hBOOL(hAPP(_953607, 9688 ^ [_953605, _953607]))), -(c_Orderings_Obot__class_Obot(tc_fun(_953605, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_953605), _953607))], (9694 ^ _782652) ^ [_953677, _953679] : [hAPP(c_Set_OCollect(_953677), _953679) = c_Orderings_Obot__class_Obot(tc_fun(_953677, tc_HOL_Obool)), 9697 ^ _782652 : [(9698 ^ _782652) ^ [_953762] : [hBOOL(hAPP(_953679, _953762))]]], (9700 ^ _782652) ^ [_953785, _953787] : [-(hBOOL(hAPP(_953787, 9701 ^ [_953785, _953787]))), -(hAPP(c_Set_OCollect(_953785), _953787) = c_Orderings_Obot__class_Obot(tc_fun(_953785, tc_HOL_Obool)))], (9707 ^ _782652) ^ [_953842, _953844, _953846, _953848] : [-(c_Nitpick_Ofold__graph_H(_953842, _953844, _953846, _953848, c_Orderings_Obot__class_Obot(tc_fun(_953842, tc_HOL_Obool)), _953848))], (9709 ^ _782652) ^ [_953880, _953882, _953884, _953886] : [-(c_Nitpick_Ofold__graph_H(_953880, _953882, _953884, _953886, c_Orderings_Obot__class_Obot(tc_fun(_953880, tc_HOL_Obool)), _953886))], (9711 ^ _782652) ^ [_953918, _953920, _953922, _953924] : [class_Orderings_Oord(_953918), 9714 ^ _782652 : [(9715 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953920, _953918)), _953922), _953924)), 9718 ^ _782652 : [(9719 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953920, _953918)), _953922), _953924)))], (9721 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953920, _953918)), _953924), _953922))]]], (9723 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953920, _953918)), _953922), _953924))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953920, _953918)), _953922), _953924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953920, _953918)), _953924), _953922)))]]], (9733 ^ _782652) ^ [_954310, _954312, _954314] : [class_Orderings_Olinorder(_954310), 9736 ^ _782652 : [(9737 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954310), _954312), _954314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954310), _954314), _954312)))], (9743 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954310), _954314), _954312)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954310), _954312), _954314))]]], (9749 ^ _782652) ^ [_954519, _954521, _954523] : [class_Orderings_Olinorder(_954519), 9752 ^ _782652 : [(9753 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954519), _954521), _954523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954519), _954523), _954521)))], (9759 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954519), _954523), _954521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954519), _954521), _954523))]]], (9765 ^ _782652) ^ [_954728, _954730, _954732] : [class_Orderings_Olinorder(_954728), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954728), _954730), _954732))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954728), _954732), _954730)))], (9775 ^ _782652) ^ [_954846, _954848, _954850] : [class_Orderings_Oorder(_954846), 9778 ^ _782652 : [(9779 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954846), _954848), _954850)), 9782 ^ _782652 : [(9783 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954846), _954848), _954850)))], (9785 ^ _782652) ^ [] : [_954848 = _954850]]], (9787 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954846), _954848), _954850))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954846), _954848), _954850)), -(_954848 = _954850)]]], (9797 ^ _782652) ^ [_955182, _955184, _955186] : [class_Orderings_Opreorder(_955182), 9800 ^ _782652 : [(9801 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955182), _955184), _955186)), 9804 ^ _782652 : [(9805 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955182), _955184), _955186)))], (9807 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955182), _955186), _955184))]]], (9809 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955182), _955184), _955186))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955182), _955184), _955186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955182), _955186), _955184)))]]], (9819 ^ _782652) ^ [_955539, _955541, _955543] : [class_Orderings_Oorder(_955539), 9822 ^ _782652 : [(9833 ^ _782652) ^ [] : [9834 ^ _782652 : [(9835 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955539), _955541), _955543))], (9837 ^ _782652) ^ [] : [_955541 = _955543]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955539), _955541), _955543)))], (9823 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955539), _955541), _955543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955539), _955541), _955543))), -(_955541 = _955543)]]], (9841 ^ _782652) ^ [_955837, _955839, _955841] : [class_Orderings_Olinorder(_955837), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955837), _955839), _955841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955837), _955841), _955839)))], (9851 ^ _782652) ^ [_955957, _955959, _955961] : [class_Orderings_Olinorder(_955957), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955957), _955959), _955961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955957), _955961), _955959)))], (9861 ^ _782652) ^ [_956077, _956079, _956081] : [class_Orderings_Olinorder(_956077), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956077), _956079), _956081))), 9868 ^ _782652 : [(9869 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956077), _956079), _956081)), -(_956079 = _956081)], (9875 ^ _782652) ^ [] : [_956079 = _956081, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956077), _956079), _956081)))]]], (9881 ^ _782652) ^ [_956380, _956382, _956384] : [class_Orderings_Oorder(_956380), -(_956382 = _956384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956380), _956382), _956384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956380), _956382), _956384)))], (9895 ^ _782652) ^ [_956596, _956598, _956600] : [class_Orderings_Oorder(_956596), -(_956598 = _956600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956596), _956600), _956598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956596), _956600), _956598)))], (9909 ^ _782652) ^ [_956812, _956814, _956816] : [class_Orderings_Olinorder(_956812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956812), _956814), _956816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956812), _956816), _956814))], (9919 ^ _782652) ^ [_956972, _956974, _956976] : [class_Orderings_Opreorder(_956972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956972), _956974), _956976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956972), _956974), _956976)))], (9929 ^ _782652) ^ [_957131, _957133, _957135] : [class_Orderings_Olinorder(_957131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957131), _957133), _957135)), 9936 ^ _782652 : [(9937 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957131), _957133), _957135))), -(_957133 = _957135)], (9943 ^ _782652) ^ [] : [_957133 = _957135, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957131), _957133), _957135))]]], (9949 ^ _782652) ^ [_957387, _957389, _957391] : [class_Orderings_Oorder(_957387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957387), _957389), _957391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957387), _957389), _957391))), -(_957389 = _957391)], (9963 ^ _782652) ^ [_957559, _957561, _957563] : [class_Orderings_Oorder(_957559), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957559), _957561), _957563)), -(_957561 = _957563), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957559), _957561), _957563)))], (9977 ^ _782652) ^ [_957733, _957735, _957737] : [class_Orderings_Oorder(_957733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957733), _957735), _957737)), -(_957737 = _957735), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957733), _957735), _957737)))], (9991 ^ _782652) ^ [_957907, _957909, _957911, _957913] : [class_Orderings_Opreorder(_957907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957907), _957909), _957911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957907), _957911), _957913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957907), _957909), _957913)))], (10005 ^ _782652) ^ [_958140, _958142, _958144, _958146] : [class_Orderings_Oorder(_958140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958140), _958142), _958144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958140), _958146), _958142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958140), _958146), _958144)))], (10019 ^ _782652) ^ [_958373, _958375, _958377, _958379] : [class_Orderings_Opreorder(_958373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958373), _958375), _958377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958373), _958377), _958379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958373), _958375), _958379)))], (10033 ^ _782652) ^ [_958606, _958608, _958610, _958612] : [class_Orderings_Oorder(_958606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958606), _958608), _958610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958606), _958612), _958608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958606), _958612), _958610)))], (10047 ^ _782652) ^ [_958839, _958841, _958843, _958845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_958839, tc_HOL_Obool)), _958841), _958843)), hBOOL(hAPP(hAPP(c_member(_958839), _958845), _958841)), -(hBOOL(hAPP(hAPP(c_member(_958839), _958845), _958843)))], (10057 ^ _782652) ^ [_959036, _959038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959036, tc_HOL_Obool)), _959038), c_Orderings_Obot__class_Obot(tc_fun(_959036, tc_HOL_Obool))))], (10059 ^ _782652) ^ [_959076, _959078, _959080, _959082] : [class_Lattices_Osemilattice__sup(_959076), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959076), _959078), _959080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959076), _959078), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959076), _959082), _959080))))], (10069 ^ _782652) ^ [_959255, _959257, _959259, _959261] : [class_Lattices_Osemilattice__sup(_959255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959255), _959257), _959259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959255), _959257), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959255), _959259), _959261))))], (10079 ^ _782652) ^ [_959434, _959436, _959438, _959440] : [class_Lattices_Osemilattice__inf(_959434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959434), _959436), _959438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959434), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959434), _959436), _959440)), _959438)))], (10089 ^ _782652) ^ [_959613, _959615, _959617, _959619] : [class_Lattices_Osemilattice__inf(_959613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959613), _959615), _959617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959613), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959613), _959619), _959615)), _959617)))], (10099 ^ _782652) ^ [_959810, _959812, _959814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959810, tc_HOL_Obool)), _959812), _959814)), 10102 ^ _782652 : [(10103 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959810, tc_HOL_Obool)), _959812), _959814)))], (10105 ^ _782652) ^ [] : [_959812 = _959814]]], (10107 ^ _782652) ^ [_959959, _959961, _959963] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_959959, tc_HOL_Obool)), _959961), _959963))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959959, tc_HOL_Obool)), _959961), _959963)), -(_959961 = _959963)], (10127 ^ _782652) ^ [_960283, _960285, _960287] : [10128 ^ _782652 : [(10129 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960283, tc_HOL_Obool)), _960285), _960287))], (10131 ^ _782652) ^ [] : [_960285 = _960287]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960283, tc_HOL_Obool)), _960285), _960287)))], (10117 ^ _782652) ^ [_960155, _960157, _960159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960155, tc_HOL_Obool)), _960157), _960159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960155, tc_HOL_Obool)), _960157), _960159))), -(_960157 = _960159)], (10135 ^ _782652) ^ [_960442, _960444, _960446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960442, tc_HOL_Obool)), _960444), _960446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960442, tc_HOL_Obool)), _960444), _960446)))], (10141 ^ _782652) ^ [_960561, _960563, _960565, _960567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960561, tc_HOL_Obool)), _960563), _960565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960561, tc_HOL_Obool)), _960565), _960567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960561, tc_HOL_Obool)), _960563), _960567)))], (10151 ^ _782652) ^ [_960758, _960760, _960762, _960764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960758, tc_HOL_Obool)), _960760), _960762)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960758, tc_HOL_Obool)), _960762), _960764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960758, tc_HOL_Obool)), _960760), _960764)))], (10161 ^ _782652) ^ [_960985, _960987, _960989, _960991, _960993, _960995, _960997] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_960985, tc_Option_Ooption(_960987)), _960989), _960991), hAPP(c_Option_Ooption_OSome(_960987), _960993)), _960995) = hAPP(c_Option_Ooption_OSome(_960987), _960997), 10166 ^ _782652 : [(10167 ^ _782652) ^ [] : [-(_960995 = _960991)], (10169 ^ _782652) ^ [] : [-(_960993 = _960997)]], 10170 ^ _782652 : [(10171 ^ _782652) ^ [] : [_960995 = _960991], (10173 ^ _782652) ^ [] : [-(hAPP(_960989, _960995) = hAPP(c_Option_Ooption_OSome(_960987), _960997))]]], (10175 ^ _782652) ^ [_961263, _961265, _961267, _961269, _961271, _961273, _961275] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_961263, tc_Option_Ooption(_961265)), _961267), _961269), hAPP(c_Option_Ooption_OSome(_961265), _961271)), _961273) = hAPP(c_Option_Ooption_OSome(_961265), _961275)), 10176 ^ _782652 : [(10177 ^ _782652) ^ [] : [_961273 = _961269, _961271 = _961275], (10183 ^ _782652) ^ [] : [-(_961273 = _961269), hAPP(_961267, _961273) = hAPP(c_Option_Ooption_OSome(_961265), _961275)]]], (10191 ^ _782652) ^ [_961580, _961582, _961584, _961586, _961588] : [hAPP(_961580, _961582) = hAPP(c_Option_Ooption_OSome(_961584), _961586), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_961588, tc_Option_Ooption(_961584)), _961580), _961582), hAPP(c_Option_Ooption_OSome(_961584), _961586)) = _961580)], (10197 ^ _782652) ^ [_961717, _961719, _961721, _961723, _961725, _961727, _961729] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_961717, tc_Option_Ooption(_961719)), _961721), _961723), hAPP(c_Option_Ooption_OSome(_961719), _961725)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_961717, tc_Option_Ooption(_961719)), _961727), _961723), hAPP(c_Option_Ooption_OSome(_961719), _961729)), -(_961725 = _961729)], (10203 ^ _782652) ^ [_961880, _961882] : [-(hAPP(c_Set_OCollect(_961880), hAPP(hAPP(c_COMBC(_961880, tc_fun(_961880, tc_HOL_Obool), tc_HOL_Obool), c_member(_961880)), _961882)) = _961882)], (10205 ^ _782652) ^ [_961943, _961945, _961947] : [hBOOL(hAPP(hAPP(c_member(_961943), _961945), hAPP(c_Set_OCollect(_961943), _961947))), -(hBOOL(hAPP(_961947, _961945)))], (10211 ^ _782652) ^ [_962046, _962048, _962050] : [hBOOL(hAPP(_962050, _962048)), -(hBOOL(hAPP(hAPP(c_member(_962046), _962048), hAPP(c_Set_OCollect(_962046), _962050))))], (10217 ^ _782652) ^ [_962155, _962157, _962159] : [hBOOL(hAPP(hAPP(c_member(_962155), _962157), hAPP(c_Set_OCollect(_962155), _962159))), -(hBOOL(hAPP(_962159, _962157)))], (10223 ^ _782652) ^ [_962262, _962264, _962266] : [hBOOL(hAPP(hAPP(c_member(_962262), _962264), hAPP(c_Set_OCollect(_962262), _962266))), -(hBOOL(hAPP(_962266, _962264)))], (10229 ^ _782652) ^ [_962369] : [-(c_Orderings_Obot__class_Obot(tc_fun(_962369, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_962369), hAPP(c_COMBK(tc_HOL_Obool, _962369), c_fFalse)))], (10231 ^ _782652) ^ [_962426, _962428, _962430] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_962426), hAPP(c_Set_OCollect(_962426), hAPP(hAPP(c_COMBS(_962426, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _962426), c_fdisj), _962428)), _962430)))), 10234 ^ _782652 : [(10235 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_962426), hAPP(c_Set_OCollect(_962426), _962428))))], (10237 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_962426), hAPP(c_Set_OCollect(_962426), _962430))))]]], (10239 ^ _782652) ^ [_962621, _962623, _962625] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_962621), hAPP(c_Set_OCollect(_962621), hAPP(hAPP(c_COMBS(_962621, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _962621), c_fdisj), _962623)), _962625))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_962621), hAPP(c_Set_OCollect(_962621), _962623))), hBOOL(hAPP(c_Finite__Set_Ofinite(_962621), hAPP(c_Set_OCollect(_962621), _962625)))], (10249 ^ _782652) ^ [_962850, _962852, _962854] : [-(hAPP(hAPP(c_Set_Oinsert(_962850), _962852), hAPP(c_Set_OCollect(_962850), _962854)) = hAPP(c_Set_OCollect(_962850), hAPP(hAPP(c_COMBS(_962850, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _962850), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _962850), c_fNot), hAPP(hAPP(c_COMBC(_962850, _962850, tc_HOL_Obool), c_fequal), _962852)))), _962854)))], (10251 ^ _782652) ^ [_962935, _962937, _962939] : [-(hAPP(c_Set_OCollect(_962935), hAPP(hAPP(c_COMBS(_962935, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _962935), c_fdisj), _962937)), _962939)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962935, tc_HOL_Obool)), hAPP(c_Set_OCollect(_962935), _962937)), hAPP(c_Set_OCollect(_962935), _962939)))], (10253 ^ _782652) ^ [_963008, _963010, _963012] : [-(hAPP(c_Set_OCollect(_963008), hAPP(hAPP(c_COMBS(_963008, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _963008), c_fconj), _963010)), _963012)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963008, tc_HOL_Obool)), hAPP(c_Set_OCollect(_963008), _963010)), hAPP(c_Set_OCollect(_963008), _963012)))], (10255 ^ _782652) ^ [_963081] : [-(c_Finite__Set_Ofun__left__comm__idem(_963081, tc_fun(_963081, tc_HOL_Obool), c_Set_Oinsert(_963081)))], (10257 ^ _782652) ^ [_963110] : [class_Lattices_Osemilattice__sup(_963110), -(c_Finite__Set_Ofun__left__comm__idem(_963110, _963110, c_Lattices_Osemilattice__sup__class_Osup(_963110)))], (10263 ^ _782652) ^ [_963189] : [class_Lattices_Osemilattice__inf(_963189), -(c_Finite__Set_Ofun__left__comm__idem(_963189, _963189, c_Lattices_Osemilattice__inf__class_Oinf(_963189)))], (10269 ^ _782652) ^ [_963264, _963266, _963268, _963270, _963272, _963274] : [-(hBOOL(hAPP(hAPP(c_member(_963264), _963266), _963268))), -(hAPP(c_Set_Oimage(_963264, tc_Option_Ooption(_963270), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_963264, tc_Option_Ooption(_963270)), _963272), _963266), hAPP(c_Option_Ooption_OSome(_963270), _963274))), _963268) = hAPP(c_Set_Oimage(_963264, tc_Option_Ooption(_963270), _963272), _963268))], (10275 ^ _782652) ^ [_963352, _963354, _963356] : [-(hAPP(hAPP(c_Set_Oinsert(_963352), _963354), _963356) = hAPP(c_Set_OCollect(_963352), hAPP(hAPP(c_COMBS(_963352, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _963352), c_fdisj), hAPP(hAPP(c_COMBC(_963352, _963352, tc_HOL_Obool), c_fequal), _963354))), hAPP(hAPP(c_COMBC(_963352, tc_fun(_963352, tc_HOL_Obool), tc_HOL_Obool), c_member(_963352)), _963356))))], (10277 ^ _782652) ^ [_963437, _963439, _963441] : [-(hAPP(hAPP(c_Set_Oinsert(_963437), _963439), _963441) = hAPP(c_Set_OCollect(_963437), hAPP(hAPP(c_COMBS(_963437, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _963437), c_fdisj), hAPP(hAPP(c_COMBC(_963437, _963437, tc_HOL_Obool), c_fequal), _963439))), hAPP(hAPP(c_COMBC(_963437, tc_fun(_963437, tc_HOL_Obool), tc_HOL_Obool), c_member(_963437)), _963441))))], (10279 ^ _782652) ^ [_963522, _963524, _963526] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963522, tc_HOL_Obool)), _963524), _963526) = hAPP(c_Set_OCollect(_963522), hAPP(hAPP(c_COMBS(_963522, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _963522), c_fdisj), hAPP(hAPP(c_COMBC(_963522, tc_fun(_963522, tc_HOL_Obool), tc_HOL_Obool), c_member(_963522)), _963524))), hAPP(hAPP(c_COMBC(_963522, tc_fun(_963522, tc_HOL_Obool), tc_HOL_Obool), c_member(_963522)), _963526))))], (10281 ^ _782652) ^ [_963636, _963638, _963640, _963642] : [hBOOL(hAPP(hAPP(c_member(_963636), _963638), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963636, tc_HOL_Obool)), _963640), hAPP(c_Set_OCollect(_963636), _963642)))), 10284 ^ _782652 : [(10285 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_963636), _963638), _963640)))], (10287 ^ _782652) ^ [] : [-(hBOOL(hAPP(_963642, _963638)))]]], (10289 ^ _782652) ^ [_963803, _963805, _963807, _963809] : [-(hBOOL(hAPP(hAPP(c_member(_963803), _963805), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963803, tc_HOL_Obool)), _963807), hAPP(c_Set_OCollect(_963803), _963809))))), hBOOL(hAPP(hAPP(c_member(_963803), _963805), _963807)), hBOOL(hAPP(_963809, _963805))], (10299 ^ _782652) ^ [_964006, _964008, _964010] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964006, tc_HOL_Obool)), _964008), _964010) = hAPP(c_Set_OCollect(_964006), hAPP(hAPP(c_COMBS(_964006, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _964006), c_fconj), hAPP(hAPP(c_COMBC(_964006, tc_fun(_964006, tc_HOL_Obool), tc_HOL_Obool), c_member(_964006)), _964008))), hAPP(hAPP(c_COMBC(_964006, tc_fun(_964006, tc_HOL_Obool), tc_HOL_Obool), c_member(_964006)), _964010))))], (10301 ^ _782652) ^ [_964099, _964101] : [-(hAPP(c_Set_OCollect(_964099), hAPP(c_fequal, _964101)) = hAPP(hAPP(c_Set_Oinsert(_964099), _964101), c_Orderings_Obot__class_Obot(tc_fun(_964099, tc_HOL_Obool))))], (10303 ^ _782652) ^ [_964145, _964147] : [-(hAPP(c_Set_OCollect(_964145), hAPP(hAPP(c_COMBC(_964145, _964145, tc_HOL_Obool), c_fequal), _964147)) = hAPP(hAPP(c_Set_Oinsert(_964145), _964147), c_Orderings_Obot__class_Obot(tc_fun(_964145, tc_HOL_Obool))))], (10305 ^ _782652) ^ [_964210, _964212, _964214] : [hBOOL(hAPP(_964210, _964212)), -(hAPP(c_Set_OCollect(_964214), hAPP(hAPP(c_COMBS(_964214, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _964214), c_fconj), hAPP(c_fequal, _964212))), _964210)) = hAPP(hAPP(c_Set_Oinsert(_964214), _964212), c_Orderings_Obot__class_Obot(tc_fun(_964214, tc_HOL_Obool))))], (10311 ^ _782652) ^ [_964369, _964371, _964373] : [-(hBOOL(hAPP(_964369, _964371))), -(hAPP(c_Set_OCollect(_964373), hAPP(hAPP(c_COMBS(_964373, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _964373), c_fconj), hAPP(c_fequal, _964371))), _964369)) = c_Orderings_Obot__class_Obot(tc_fun(_964373, tc_HOL_Obool)))], (10317 ^ _782652) ^ [_964456, _964458, _964460] : [hBOOL(hAPP(_964456, _964458)), -(hAPP(c_Set_OCollect(_964460), hAPP(hAPP(c_COMBS(_964460, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _964460), c_fconj), hAPP(hAPP(c_COMBC(_964460, _964460, tc_HOL_Obool), c_fequal), _964458))), _964456)) = hAPP(hAPP(c_Set_Oinsert(_964460), _964458), c_Orderings_Obot__class_Obot(tc_fun(_964460, tc_HOL_Obool))))], (10323 ^ _782652) ^ [_964629, _964631, _964633] : [-(hBOOL(hAPP(_964629, _964631))), -(hAPP(c_Set_OCollect(_964633), hAPP(hAPP(c_COMBS(_964633, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _964633), c_fconj), hAPP(hAPP(c_COMBC(_964633, _964633, tc_HOL_Obool), c_fequal), _964631))), _964629)) = c_Orderings_Obot__class_Obot(tc_fun(_964633, tc_HOL_Obool)))], (10329 ^ _782652) ^ [_964711, _964713, _964715] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964711, tc_HOL_Obool)), _964713), _964715) = hAPP(c_Set_OCollect(_964711), hAPP(hAPP(c_COMBS(_964711, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _964711), c_fconj), hAPP(hAPP(c_COMBC(_964711, tc_fun(_964711, tc_HOL_Obool), tc_HOL_Obool), c_member(_964711)), _964713))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _964711), c_fNot), hAPP(hAPP(c_COMBC(_964711, tc_fun(_964711, tc_HOL_Obool), tc_HOL_Obool), c_member(_964711)), _964715)))))], (10331 ^ _782652) ^ [_964814, _964816, _964818] : [-(hAPP(hAPP(c_Set_Oinsert(_964814), _964816), _964818) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964814, tc_HOL_Obool)), hAPP(c_Set_OCollect(_964814), hAPP(hAPP(c_COMBC(_964814, _964814, tc_HOL_Obool), c_fequal), _964816))), _964818))], (10333 ^ _782652) ^ [_964875, _964877, _964879, _964881, _964883, _964885] : [-(hAPP(c_Set_Oimage(_964875, _964877, hAPP(hAPP(c_COMBS(_964875, _964877, _964877), hAPP(hAPP(c_COMBS(_964875, _964877, tc_fun(_964877, _964877)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_964877, tc_fun(_964877, _964877)), _964875), c_If(_964877)), _964879)), _964881)), _964883)), _964885) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964877, tc_HOL_Obool)), hAPP(c_Set_Oimage(_964875, _964877, _964881), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964875, tc_HOL_Obool)), _964885), hAPP(c_Set_OCollect(_964875), _964879)))), hAPP(c_Set_Oimage(_964875, _964877, _964883), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964875, tc_HOL_Obool)), _964885), hAPP(c_Set_OCollect(_964875), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _964875), c_fNot), _964879))))))], (10335 ^ _782652) ^ [_965023, _965025, _965027, _965029, _965031] : [class_Groups_Oab__group__add(_965023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965023), _965025), _965027) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_965023), _965029), _965031), 10342 ^ _782652 : [(10343 ^ _782652) ^ [] : [_965025 = _965027, -(_965029 = _965031)], (10349 ^ _782652) ^ [] : [_965029 = _965031, -(_965025 = _965027)]]], (10355 ^ _782652) ^ [_965336, _965338, _965340, _965342, _965344] : [-(c_Map_Odom(_965336, _965338, hAPP(hAPP(c_COMBS(_965336, tc_Option_Ooption(_965338), tc_Option_Ooption(_965338)), hAPP(hAPP(c_COMBS(_965336, tc_Option_Ooption(_965338), tc_fun(tc_Option_Ooption(_965338), tc_Option_Ooption(_965338))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_965338), tc_fun(tc_Option_Ooption(_965338), tc_Option_Ooption(_965338))), _965336), c_If(tc_Option_Ooption(_965338))), _965340)), _965342)), _965344)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965336, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965336, tc_HOL_Obool)), c_Map_Odom(_965336, _965338, _965342)), hAPP(c_Set_OCollect(_965336), _965340))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965336, tc_HOL_Obool)), c_Map_Odom(_965336, _965338, _965344)), hAPP(c_Set_OCollect(_965336), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _965336), c_fNot), _965340)))))], (10357 ^ _782652) ^ [_965521, _965523, _965525, _965527, _965529, _965531, _965533] : [c_Nitpick_Ofold__graph_H(_965521, _965523, _965525, _965527, _965529, hAPP(hAPP(_965525, _965531), _965533)), 10362 ^ _782652 : [(10363 ^ _782652) ^ [] : [-(_965529 = c_Orderings_Obot__class_Obot(tc_fun(_965521, tc_HOL_Obool)))], (10365 ^ _782652) ^ [] : [-(hAPP(hAPP(_965525, _965531), _965533) = _965527)]], 10368 ^ _782652 : [(10369 ^ _782652) ^ [] : [-(hAPP(hAPP(_965525, _965531), _965533) = hAPP(hAPP(_965525, 10366 ^ [_965521, _965523, _965525, _965527, _965529, _965531, _965533]), 10367 ^ [_965521, _965523, _965525, _965527, _965529, _965531, _965533]))], (10371 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_965521), 10366 ^ [_965521, _965523, _965525, _965527, _965529, _965531, _965533]), _965529)))], (10373 ^ _782652) ^ [] : [-(c_Nitpick_Ofold__graph_H(_965521, _965523, _965525, _965527, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965521, tc_HOL_Obool)), _965529), hAPP(hAPP(c_Set_Oinsert(_965521), 10366 ^ [_965521, _965523, _965525, _965527, _965529, _965531, _965533]), c_Orderings_Obot__class_Obot(tc_fun(_965521, tc_HOL_Obool)))), 10367 ^ [_965521, _965523, _965525, _965527, _965529, _965531, _965533]))]]], (10375 ^ _782652) ^ [_965958, _965960, _965962, _965964, _965966, _965968, _965970] : [-(c_Nitpick_Ofold__graph_H(_965958, _965960, _965962, _965964, _965966, hAPP(hAPP(_965962, _965968), _965970))), 10376 ^ _782652 : [(10377 ^ _782652) ^ [] : [_965966 = c_Orderings_Obot__class_Obot(tc_fun(_965958, tc_HOL_Obool)), hAPP(hAPP(_965962, _965968), _965970) = _965964], (10383 ^ _782652) ^ [_966187, _966189] : [hAPP(hAPP(_965962, _965968), _965970) = hAPP(hAPP(_965962, _966189), _966187), hBOOL(hAPP(hAPP(c_member(_965958), _966189), _965966)), c_Nitpick_Ofold__graph_H(_965958, _965960, _965962, _965964, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965958, tc_HOL_Obool)), _965966), hAPP(hAPP(c_Set_Oinsert(_965958), _966189), c_Orderings_Obot__class_Obot(tc_fun(_965958, tc_HOL_Obool)))), _966187)]]], (10395 ^ _782652) ^ [_966478, _966480, _966482, _966484] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_966478), _966480))), hBOOL(hAPP(c_Finite__Set_Ofinite(_966482), hAPP(c_Set_Oimage(_966478, _966482, _966484), _966480))), 10403 ^ _782652 : [(10404 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_966478), 10402 ^ [_966478, _966480, _966482, _966484]), _966480)))], (10406 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_966478), hAPP(c_Set_OCollect(_966478), hAPP(hAPP(c_COMBS(_966478, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _966478), c_fconj), hAPP(hAPP(c_COMBC(_966478, tc_fun(_966478, tc_HOL_Obool), tc_HOL_Obool), c_member(_966478)), _966480))), hAPP(hAPP(c_COMBC(_966478, _966482, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_966482, tc_fun(_966482, tc_HOL_Obool), _966478), c_fequal), _966484)), hAPP(_966484, 10402 ^ [_966478, _966480, _966482, _966484]))))))]]], (10408 ^ _782652) ^ [_966943, _966945, _966947, _966949, _966951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966943, tc_HOL_Obool)), _966945), _966947)), 10414 ^ _782652 : [(10415 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_966943), 10413 ^ [_966943, _966945, _966947, _966949, _966951]), _966945)))], (10417 ^ _782652) ^ [] : [-(hBOOL(hAPP(_966949, 10413 ^ [_966943, _966945, _966947, _966949, _966951])))], (10419 ^ _782652) ^ [] : [hBOOL(hAPP(_966951, 10413 ^ [_966943, _966945, _966947, _966949, _966951]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966943, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_966943, tc_HOL_Obool)), _966945), hAPP(c_Set_OCollect(_966943), _966949))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_966943, tc_HOL_Obool)), _966947), hAPP(c_Set_OCollect(_966943), _966951)))))], (10423 ^ _782652) ^ [_967343, _967345, _967347] : [class_Lattices_Olattice(_967343), hBOOL(hAPP(c_Finite__Set_Ofinite(_967343), _967345)), hBOOL(hAPP(hAPP(c_member(_967343), _967347), _967345)), 10434 ^ _782652 : [(10435 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967343, tc_HOL_Obool)), _967345), hAPP(hAPP(c_Set_Oinsert(_967343), _967347), c_Orderings_Obot__class_Obot(tc_fun(_967343, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_967343, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_967343, _967345) = _967347)], (10441 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967343, tc_HOL_Obool)), _967345), hAPP(hAPP(c_Set_Oinsert(_967343), _967347), c_Orderings_Obot__class_Obot(tc_fun(_967343, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_967343, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_967343, _967345) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_967343), _967347), c_Big__Operators_Olattice__class_OInf__fin(_967343, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967343, tc_HOL_Obool)), _967345), hAPP(hAPP(c_Set_Oinsert(_967343), _967347), c_Orderings_Obot__class_Obot(tc_fun(_967343, tc_HOL_Obool)))))))]]], (10447 ^ _782652) ^ [_967849, _967851, _967853] : [class_Lattices_Olattice(_967849), hBOOL(hAPP(c_Finite__Set_Ofinite(_967849), _967851)), hBOOL(hAPP(hAPP(c_member(_967849), _967853), _967851)), 10458 ^ _782652 : [(10459 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967849, tc_HOL_Obool)), _967851), hAPP(hAPP(c_Set_Oinsert(_967849), _967853), c_Orderings_Obot__class_Obot(tc_fun(_967849, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_967849, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_967849, _967851) = _967853)], (10465 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967849, tc_HOL_Obool)), _967851), hAPP(hAPP(c_Set_Oinsert(_967849), _967853), c_Orderings_Obot__class_Obot(tc_fun(_967849, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_967849, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_967849, _967851) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967849), _967853), c_Big__Operators_Olattice__class_OSup__fin(_967849, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967849, tc_HOL_Obool)), _967851), hAPP(hAPP(c_Set_Oinsert(_967849), _967853), c_Orderings_Obot__class_Obot(tc_fun(_967849, tc_HOL_Obool)))))))]]], (10471 ^ _782652) ^ [_968376, _968378, _968380, _968382, _968384, _968386] : [hBOOL(hAPP(hAPP(c_member(_968376), _968378), _968380)), -(c_Map_Orestrict__map(_968376, _968382, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968376, tc_Option_Ooption(_968382)), _968384), _968378), _968386), _968380) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968376, tc_Option_Ooption(_968382)), c_Map_Orestrict__map(_968376, _968382, _968384, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968376, tc_HOL_Obool)), _968380), hAPP(hAPP(c_Set_Oinsert(_968376), _968378), c_Orderings_Obot__class_Obot(tc_fun(_968376, tc_HOL_Obool)))))), _968378), _968386))], (10477 ^ _782652) ^ [_968593, _968595, _968597, _968599, _968601, _968603] : [-(hBOOL(hAPP(hAPP(c_member(_968593), _968595), _968597))), -(c_Map_Orestrict__map(_968593, _968599, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968593, tc_Option_Ooption(_968599)), _968601), _968595), _968603), _968597) = c_Map_Orestrict__map(_968593, _968599, _968601, _968597))], (10483 ^ _782652) ^ [_968670, _968672, _968674, _968676, _968678, _968680] : [hBOOL(hAPP(hAPP(c_member(_968670), _968672), _968674)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968670, tc_Option_Ooption(_968676)), c_Map_Orestrict__map(_968670, _968676, _968678, _968674)), _968672), _968680) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968670, tc_Option_Ooption(_968676)), c_Map_Orestrict__map(_968670, _968676, _968678, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968670, tc_HOL_Obool)), _968674), hAPP(hAPP(c_Set_Oinsert(_968670), _968672), c_Orderings_Obot__class_Obot(tc_fun(_968670, tc_HOL_Obool)))))), _968672), _968680))], (10489 ^ _782652) ^ [_968893, _968895, _968897, _968899, _968901, _968903, _968905] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_968893, _968895, _968897, _968899, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968893, tc_HOL_Obool)), _968901), hAPP(hAPP(c_Set_Oinsert(_968893), _968903), c_Orderings_Obot__class_Obot(tc_fun(_968893, tc_HOL_Obool))))), _968905)), hBOOL(hAPP(hAPP(c_member(_968893), _968903), _968901)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_968893, _968895, _968897, _968899, _968901), hAPP(hAPP(_968897, _968903), _968905))))], (10499 ^ _782652) ^ [_969172, _969174, _969176, _969178, _969180] : [c_Fun_Oinj__on(_969172, _969174, _969176, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_969172, tc_HOL_Obool)), _969178), _969180)), 10502 ^ _782652 : [(10503 ^ _782652) ^ [] : [-(c_Fun_Oinj__on(_969172, _969174, _969176, _969178))], (10505 ^ _782652) ^ [] : [-(c_Fun_Oinj__on(_969172, _969174, _969176, _969180))], (10507 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969174, tc_HOL_Obool)), hAPP(c_Set_Oimage(_969172, _969174, _969176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969172, tc_HOL_Obool)), _969178), _969180))), hAPP(c_Set_Oimage(_969172, _969174, _969176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969172, tc_HOL_Obool)), _969180), _969178))) = c_Orderings_Obot__class_Obot(tc_fun(_969174, tc_HOL_Obool)))]]], (10509 ^ _782652) ^ [_969439, _969441, _969443, _969445, _969447] : [-(c_Fun_Oinj__on(_969439, _969441, _969443, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_969439, tc_HOL_Obool)), _969445), _969447))), c_Fun_Oinj__on(_969439, _969441, _969443, _969445), c_Fun_Oinj__on(_969439, _969441, _969443, _969447), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_969441, tc_HOL_Obool)), hAPP(c_Set_Oimage(_969439, _969441, _969443), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969439, tc_HOL_Obool)), _969445), _969447))), hAPP(c_Set_Oimage(_969439, _969441, _969443), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969439, tc_HOL_Obool)), _969447), _969445))) = c_Orderings_Obot__class_Obot(tc_fun(_969441, tc_HOL_Obool))], (10523 ^ _782652) ^ [_969802, _969804, _969806, _969808, _969810] : [c_Fun_Oinj__on(_969802, _969804, _969806, hAPP(hAPP(c_Set_Oinsert(_969802), _969808), _969810)), 10526 ^ _782652 : [(10527 ^ _782652) ^ [] : [-(c_Fun_Oinj__on(_969802, _969804, _969806, _969810))], (10529 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_969804), hAPP(_969806, _969808)), hAPP(c_Set_Oimage(_969802, _969804, _969806), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969802, tc_HOL_Obool)), _969810), hAPP(hAPP(c_Set_Oinsert(_969802), _969808), c_Orderings_Obot__class_Obot(tc_fun(_969802, tc_HOL_Obool)))))))]]], (10531 ^ _782652) ^ [_970021, _970023, _970025, _970027, _970029] : [-(c_Fun_Oinj__on(_970021, _970023, _970025, hAPP(hAPP(c_Set_Oinsert(_970021), _970027), _970029))), c_Fun_Oinj__on(_970021, _970023, _970025, _970029), -(hBOOL(hAPP(hAPP(c_member(_970023), hAPP(_970025, _970027)), hAPP(c_Set_Oimage(_970021, _970023, _970025), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970021, tc_HOL_Obool)), _970029), hAPP(hAPP(c_Set_Oinsert(_970021), _970027), c_Orderings_Obot__class_Obot(tc_fun(_970021, tc_HOL_Obool))))))))], (10541 ^ _782652) ^ [_970273, _970275, _970277] : [-(c_Fun_Oinj__on(_970273, _970275, _970277, c_Orderings_Obot__class_Obot(tc_fun(_970273, tc_HOL_Obool))))], (10561 ^ _782652) ^ [_970713, _970715, _970717, _970719] : [10563 ^ _782652 : [(10564 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_970713), 10562 ^ [_970713, _970715, _970717, _970719]), _970719)))], (10567 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_970713), 10565 ^ [_970713, _970715, _970717, _970719]), _970719)))], (10569 ^ _782652) ^ [] : [-(hAPP(_970717, 10562 ^ [_970713, _970715, _970717, _970719]) = hAPP(_970717, 10565 ^ [_970713, _970715, _970717, _970719]))], (10571 ^ _782652) ^ [] : [10562 ^ [_970713, _970715, _970717, _970719] = 10565 ^ [_970713, _970715, _970717, _970719]]], -(c_Fun_Oinj__on(_970713, _970715, _970717, _970719))], (10543 ^ _782652) ^ [_970328, _970330, _970332, _970334] : [c_Fun_Oinj__on(_970328, _970330, _970332, _970334), 10546 ^ _782652 : [(10547 ^ _782652) ^ [_970436] : [hBOOL(hAPP(hAPP(c_member(_970328), _970436), _970334)), 10550 ^ _782652 : [(10551 ^ _782652) ^ [_970538] : [hBOOL(hAPP(hAPP(c_member(_970328), _970538), _970334)), hAPP(_970332, _970436) = hAPP(_970332, _970538), -(_970436 = _970538)]]]]], (10575 ^ _782652) ^ [_971105, _971107] : [-(c_Fun_Oinj__on(_971105, _971105, c_COMBI(_971105), _971107))], (10577 ^ _782652) ^ [_971134, _971136, _971138, _971140, _971142, _971144] : [c_Fun_Oinj__on(_971134, _971136, _971138, _971140), hAPP(_971138, _971142) = hAPP(_971138, _971144), hBOOL(hAPP(hAPP(c_member(_971134), _971142), _971140)), hBOOL(hAPP(hAPP(c_member(_971134), _971144), _971140)), -(_971142 = _971144)], (10595 ^ _782652) ^ [_971443, _971445, _971447, _971449, _971451, _971453] : [c_Fun_Oinj__on(_971443, _971445, _971447, _971449), hBOOL(hAPP(hAPP(c_member(_971443), _971451), _971449)), hBOOL(hAPP(hAPP(c_member(_971443), _971453), _971449)), 10606 ^ _782652 : [(10607 ^ _782652) ^ [] : [hAPP(_971447, _971451) = hAPP(_971447, _971453), -(_971451 = _971453)], (10613 ^ _782652) ^ [] : [_971451 = _971453, -(hAPP(_971447, _971451) = hAPP(_971447, _971453))]]], (10619 ^ _782652) ^ [_971844, _971846, _971848, _971850, _971852, _971854] : [c_Fun_Oinj__on(_971844, _971846, _971848, _971850), -(_971852 = _971854), hBOOL(hAPP(hAPP(c_member(_971844), _971852), _971850)), hBOOL(hAPP(hAPP(c_member(_971844), _971854), _971850)), hAPP(_971848, _971852) = hAPP(_971848, _971854)], (10637 ^ _782652) ^ [_972157, _972159, _972161, _972163, _972165] : [c_Fun_Oinj__on(_972157, _972159, _972161, _972163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972157, tc_HOL_Obool)), _972165), _972163)), -(c_Fun_Oinj__on(_972157, _972159, _972161, _972165))], (10647 ^ _782652) ^ [_972326, _972328, _972330, _972332, _972334] : [c_Fun_Oinj__on(_972326, _972328, _972330, _972332), c_Fun_Oinj__on(_972326, _972328, _972330, _972334), -(c_Fun_Oinj__on(_972326, _972328, _972330, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972326, tc_HOL_Obool)), _972332), _972334)))], (10657 ^ _782652) ^ [_972501, _972503, _972505, _972507, _972509] : [c_Fun_Oinj__on(_972501, _972503, _972505, _972507), -(c_Fun_Oinj__on(_972501, _972503, _972505, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972501, tc_HOL_Obool)), _972507), _972509)))], (10663 ^ _782652) ^ [_972614, _972616] : [-(c_Fun_Oinj__on(_972614, tc_Option_Ooption(_972614), c_Option_Ooption_OSome(_972614), _972616))], (10665 ^ _782652) ^ [_972645, _972647] : [class_Lattices_Olattice(_972645), hBOOL(hAPP(c_Finite__Set_Ofinite(_972645), _972647)), -(_972647 = c_Orderings_Obot__class_Obot(tc_fun(_972645, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972645), c_Big__Operators_Olattice__class_OInf__fin(_972645, _972647)), c_Big__Operators_Olattice__class_OSup__fin(_972645, _972647))))], (10679 ^ _782652) ^ [_972831, _972833, _972835, _972837, _972839] : [hBOOL(hAPP(hAPP(c_member(_972831), _972833), _972835)), -(hAPP(c_Map_Orestrict__map(_972831, _972837, _972839, _972835), _972833) = hAPP(_972839, _972833))], (10685 ^ _782652) ^ [_972950, _972952, _972954, _972956, _972958] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_972950, _972952, _972954, _972956, c_Orderings_Obot__class_Obot(tc_fun(_972950, tc_HOL_Obool))), _972958)), -(_972958 = _972956)], (10691 ^ _782652) ^ [_973059, _973061, _973063, _973065] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_973059, _973061, _973063, _973065, c_Orderings_Obot__class_Obot(tc_fun(_973059, tc_HOL_Obool))), _973065)))], (10693 ^ _782652) ^ [_973101, _973103, _973105, _973107] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_973101, _973103, _973105, _973107, c_Orderings_Obot__class_Obot(tc_fun(_973101, tc_HOL_Obool))), _973107)))], (10695 ^ _782652) ^ [_973143, _973145, _973147, _973149, _973151, _973153] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_973143, _973145, _973147, _973149, _973151), _973153)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973143), _973151)))], (10701 ^ _782652) ^ [_973252, _973254, _973256, _973258, _973260] : [-(c_Map_Orestrict__map(_973252, _973254, _973256, hAPP(hAPP(c_Set_Oinsert(_973252), _973258), _973260)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_973252, tc_Option_Ooption(_973254)), c_Map_Orestrict__map(_973252, _973254, _973256, _973260)), _973258), hAPP(_973256, _973258)))], (10703 ^ _782652) ^ [_973318, _973320, _973322, _973324, _973326] : [-(c_Map_Orestrict__map(_973318, _973320, c_Map_Orestrict__map(_973318, _973320, _973322, _973324), _973326) = c_Map_Orestrict__map(_973318, _973320, _973322, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973318, tc_HOL_Obool)), _973324), _973326)))], (10705 ^ _782652) ^ [_973375, _973377] : [class_Lattices_Olattice(_973375), -(c_Big__Operators_Olattice__class_OInf__fin(_973375, hAPP(hAPP(c_Set_Oinsert(_973375), _973377), c_Orderings_Obot__class_Obot(tc_fun(_973375, tc_HOL_Obool)))) = _973377)], (10711 ^ _782652) ^ [_973482, _973484] : [class_Lattices_Olattice(_973482), -(c_Big__Operators_Olattice__class_OSup__fin(_973482, hAPP(hAPP(c_Set_Oinsert(_973482), _973484), c_Orderings_Obot__class_Obot(tc_fun(_973482, tc_HOL_Obool)))) = _973484)], (10717 ^ _782652) ^ [_973589, _973591, _973593, _973595] : [_973589 = hAPP(c_Set_Oimage(tc_Nat_Onat, _973591, _973593), 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)), _973595))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973591), _973589)))], (10723 ^ _782652) ^ [_973704, _973706, _973708, _973710] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_973704), hAPP(c_Set_Oimage(_973706, _973704, _973708), _973710))), c_Fun_Oinj__on(_973706, _973704, _973708, _973710), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_973706), _973710)))], (10733 ^ _782652) ^ [_973875, _973877, _973879, _973881, _973883] : [c_Fun_Oinj__on(_973875, _973877, _973879, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_973875, tc_HOL_Obool)), _973881), _973883)), 10736 ^ _782652 : [(10737 ^ _782652) ^ [] : [hAPP(c_Set_Oimage(_973875, _973877, _973879), _973881) = hAPP(c_Set_Oimage(_973875, _973877, _973879), _973883), -(_973881 = _973883)], (10743 ^ _782652) ^ [] : [_973881 = _973883, -(hAPP(c_Set_Oimage(_973875, _973877, _973879), _973881) = hAPP(c_Set_Oimage(_973875, _973877, _973879), _973883))]]], (10749 ^ _782652) ^ [_974168, _974170, _974172, _974174, _974176] : [c_Fun_Oinj__on(_974168, _974170, _974172, _974174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_974168, tc_HOL_Obool)), _974176), _974174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_974170, tc_HOL_Obool)), hAPP(c_Set_Oimage(_974168, _974170, _974172), _974176)), hAPP(c_Set_Oimage(_974168, _974170, _974172), _974174))))], (10759 ^ _782652) ^ [_974381, _974383, _974385] : [class_Lattices_Olattice(_974381), hBOOL(hAPP(c_Finite__Set_Ofinite(_974381), _974383)), hBOOL(hAPP(hAPP(c_member(_974381), _974385), _974383)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_974381), _974385), c_Big__Operators_Olattice__class_OSup__fin(_974381, _974383)) = c_Big__Operators_Olattice__class_OSup__fin(_974381, _974383))], (10773 ^ _782652) ^ [_974616, _974618, _974620] : [class_Lattices_Olattice(_974616), hBOOL(hAPP(c_Finite__Set_Ofinite(_974616), _974618)), hBOOL(hAPP(hAPP(c_member(_974616), _974620), _974618)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_974616), _974620), c_Big__Operators_Olattice__class_OInf__fin(_974616, _974618)) = _974620)], (10787 ^ _782652) ^ [_974845, _974847, _974849] : [class_Lattices_Olattice(_974845), hBOOL(hAPP(c_Finite__Set_Ofinite(_974845), _974847)), hBOOL(hAPP(hAPP(c_member(_974845), _974849), _974847)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_974845), _974849), c_Big__Operators_Olattice__class_OInf__fin(_974845, _974847)) = c_Big__Operators_Olattice__class_OInf__fin(_974845, _974847))], (10801 ^ _782652) ^ [_975080, _975082, _975084] : [class_Lattices_Olattice(_975080), hBOOL(hAPP(c_Finite__Set_Ofinite(_975080), _975082)), hBOOL(hAPP(hAPP(c_member(_975080), _975084), _975082)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_975080), _975084), c_Big__Operators_Olattice__class_OSup__fin(_975080, _975082)) = _975084)], (10815 ^ _782652) ^ [_975308, _975310, _975312, _975314, _975316, _975318, _975320] : [-(hBOOL(hAPP(hAPP(c_member(_975308), _975310), _975312))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975308, _975314, _975316, _975318, _975312), _975320)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_975308, _975314, _975316, _975318, hAPP(hAPP(c_Set_Oinsert(_975308), _975310), _975312)), hAPP(hAPP(_975316, _975310), _975320))))], (10825 ^ _782652) ^ [_975522, _975524, _975526] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975522), _975524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_975522, tc_HOL_Obool)), hAPP(c_Set_Oimage(_975522, _975522, _975526), _975524)), _975524)), c_Fun_Oinj__on(_975522, _975522, _975526, _975524), -(hAPP(c_Set_Oimage(_975522, _975522, _975526), _975524) = _975524)], (10839 ^ _782652) ^ [_975769, _975771, _975773] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975769), _975771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_975769, tc_HOL_Obool)), _975771), hAPP(c_Set_Oimage(_975769, _975769, _975773), _975771))), -(c_Fun_Oinj__on(_975769, _975769, _975773, _975771))], (10849 ^ _782652) ^ [_975948, _975950, _975952, _975954] : [-(c_Map_Odom(_975948, _975950, c_Map_Orestrict__map(_975948, _975950, _975952, _975954)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975948, tc_HOL_Obool)), c_Map_Odom(_975948, _975950, _975952)), _975954))], (10851 ^ _782652) ^ [_976001, _976003, _976005, _976007, _976009, _976011] : [c_Fun_Oinj__on(_976001, _976003, _976005, _976007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976001, tc_HOL_Obool)), _976009), _976007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976001, tc_HOL_Obool)), _976011), _976007)), -(hAPP(c_Set_Oimage(_976001, _976003, _976005), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976001, tc_HOL_Obool)), _976009), _976011)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976003, tc_HOL_Obool)), hAPP(c_Set_Oimage(_976001, _976003, _976005), _976009)), hAPP(c_Set_Oimage(_976001, _976003, _976005), _976011)))], (10865 ^ _782652) ^ [_976336, _976338, _976340, _976342, _976344, _976346] : [c_Fun_Oinj__on(_976336, _976338, _976340, _976342), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976336, tc_HOL_Obool)), _976344), _976342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976336, tc_HOL_Obool)), _976346), _976342)), -(hAPP(c_Set_Oimage(_976336, _976338, _976340), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976336, tc_HOL_Obool)), _976344), _976346)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976338, tc_HOL_Obool)), hAPP(c_Set_Oimage(_976336, _976338, _976340), _976344)), hAPP(c_Set_Oimage(_976336, _976338, _976340), _976346)))], (10879 ^ _782652) ^ [_976671, _976673, _976675, _976677, _976679, _976681] : [c_Fun_Oinj__on(_976671, _976673, _976675, _976677), -(hBOOL(hAPP(hAPP(c_member(_976673), _976679), hAPP(c_Set_Oimage(_976671, _976673, _976675), _976677)))), -(c_Fun_Oinj__on(_976671, _976673, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_976671, _976673), _976675), _976681), _976679), _976677))], (10889 ^ _782652) ^ [_976831, _976833, _976835] : [class_Lattices_Olattice(_976831), hBOOL(hAPP(c_Finite__Set_Ofinite(_976831), _976833)), -(_976833 = c_Orderings_Obot__class_Obot(tc_fun(_976831, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_976831, hAPP(hAPP(c_Set_Oinsert(_976831), _976835), _976833)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976831), _976835), c_Big__Operators_Olattice__class_OSup__fin(_976831, _976833)))], (10903 ^ _782652) ^ [_977039, _977041, _977043] : [class_Lattices_Olattice(_977039), hBOOL(hAPP(c_Finite__Set_Ofinite(_977039), _977041)), -(_977041 = c_Orderings_Obot__class_Obot(tc_fun(_977039, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_977039, hAPP(hAPP(c_Set_Oinsert(_977039), _977043), _977041)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_977039), _977043), c_Big__Operators_Olattice__class_OInf__fin(_977039, _977041)))], (10917 ^ _782652) ^ [_977247, _977249, _977251] : [class_Lattices_Olattice(_977247), hBOOL(hAPP(c_Finite__Set_Ofinite(_977247), _977249)), -(_977251 = c_Orderings_Obot__class_Obot(tc_fun(_977247, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977247, tc_HOL_Obool)), _977251), _977249)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977247), c_Big__Operators_Olattice__class_OSup__fin(_977247, _977251)), c_Big__Operators_Olattice__class_OSup__fin(_977247, _977249)) = c_Big__Operators_Olattice__class_OSup__fin(_977247, _977249))], (10935 ^ _782652) ^ [_977561, _977563, _977565] : [class_Lattices_Olattice(_977561), hBOOL(hAPP(c_Finite__Set_Ofinite(_977561), _977563)), -(_977565 = c_Orderings_Obot__class_Obot(tc_fun(_977561, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977561, tc_HOL_Obool)), _977565), _977563)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_977561), c_Big__Operators_Olattice__class_OInf__fin(_977561, _977565)), c_Big__Operators_Olattice__class_OInf__fin(_977561, _977563)) = c_Big__Operators_Olattice__class_OInf__fin(_977561, _977563))], (10953 ^ _782652) ^ [_977875, _977877, _977879] : [class_Lattices_Olattice(_977875), hBOOL(hAPP(c_Finite__Set_Ofinite(_977875), _977877)), -(_977877 = c_Orderings_Obot__class_Obot(tc_fun(_977875, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_977875), _977879)), -(_977879 = c_Orderings_Obot__class_Obot(tc_fun(_977875, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_977875, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977875, tc_HOL_Obool)), _977877), _977879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977875), c_Big__Operators_Olattice__class_OSup__fin(_977875, _977877)), c_Big__Operators_Olattice__class_OSup__fin(_977875, _977879)))], (10975 ^ _782652) ^ [_978224, _978226, _978228] : [class_Lattices_Olattice(_978224), hBOOL(hAPP(c_Finite__Set_Ofinite(_978224), _978226)), -(_978226 = c_Orderings_Obot__class_Obot(tc_fun(_978224, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978224), _978228)), -(_978228 = c_Orderings_Obot__class_Obot(tc_fun(_978224, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_978224, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978224, tc_HOL_Obool)), _978226), _978228)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978224), c_Big__Operators_Olattice__class_OInf__fin(_978224, _978226)), c_Big__Operators_Olattice__class_OInf__fin(_978224, _978228)))], (10997 ^ _782652) ^ [_978573, _978575] : [class_Lattices_Olattice(_978573), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_978573), _978575), _978575) = _978575)], (11003 ^ _782652) ^ [_978664, _978666] : [class_Lattices_Olattice(_978664), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978664), _978666), _978666) = _978666)], (11009 ^ _782652) ^ [_978755, _978757, _978759, _978761, _978763, _978765] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_978755, tc_Option_Ooption(_978757)), c_Map_Orestrict__map(_978755, _978757, _978759, _978761)), _978763), _978765) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_978755, tc_Option_Ooption(_978757)), c_Map_Orestrict__map(_978755, _978757, _978759, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978755, tc_HOL_Obool)), _978761), hAPP(hAPP(c_Set_Oinsert(_978755), _978763), c_Orderings_Obot__class_Obot(tc_fun(_978755, tc_HOL_Obool)))))), _978763), _978765))], (11011 ^ _782652) ^ [_978850, _978852, _978854] : [class_Lattices_Olattice(_978850), hBOOL(hAPP(c_Finite__Set_Ofinite(_978850), _978852)), -(hBOOL(hAPP(hAPP(c_member(_978850), _978854), _978852))), -(_978852 = c_Orderings_Obot__class_Obot(tc_fun(_978850, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_978850, hAPP(hAPP(c_Set_Oinsert(_978850), _978854), _978852)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_978850), _978854), c_Big__Operators_Olattice__class_OSup__fin(_978850, _978852)))], (11029 ^ _782652) ^ [_979087, _979089, _979091] : [class_Lattices_Olattice(_979087), hBOOL(hAPP(c_Finite__Set_Ofinite(_979087), _979089)), -(hBOOL(hAPP(hAPP(c_member(_979087), _979091), _979089))), -(_979089 = c_Orderings_Obot__class_Obot(tc_fun(_979087, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_979087, hAPP(hAPP(c_Set_Oinsert(_979087), _979091), _979089)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_979087), _979091), c_Big__Operators_Olattice__class_OInf__fin(_979087, _979089)))], (11047 ^ _782652) ^ [_979324, _979326, _979328] : [class_Lattices_Olattice(_979324), hBOOL(hAPP(c_Finite__Set_Ofinite(_979324), _979326)), 11054 ^ _782652 : [(11055 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979324, tc_HOL_Obool)), _979326), hAPP(hAPP(c_Set_Oinsert(_979324), _979328), c_Orderings_Obot__class_Obot(tc_fun(_979324, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_979324, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_979324, hAPP(hAPP(c_Set_Oinsert(_979324), _979328), _979326)) = _979328)], (11061 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979324, tc_HOL_Obool)), _979326), hAPP(hAPP(c_Set_Oinsert(_979324), _979328), c_Orderings_Obot__class_Obot(tc_fun(_979324, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_979324, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_979324, hAPP(hAPP(c_Set_Oinsert(_979324), _979328), _979326)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_979324), _979328), c_Big__Operators_Olattice__class_OSup__fin(_979324, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979324, tc_HOL_Obool)), _979326), hAPP(hAPP(c_Set_Oinsert(_979324), _979328), c_Orderings_Obot__class_Obot(tc_fun(_979324, tc_HOL_Obool)))))))]]], (11067 ^ _782652) ^ [_979794, _979796, _979798] : [class_Lattices_Olattice(_979794), hBOOL(hAPP(c_Finite__Set_Ofinite(_979794), _979796)), 11074 ^ _782652 : [(11075 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979794, tc_HOL_Obool)), _979796), hAPP(hAPP(c_Set_Oinsert(_979794), _979798), c_Orderings_Obot__class_Obot(tc_fun(_979794, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_979794, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_979794, hAPP(hAPP(c_Set_Oinsert(_979794), _979798), _979796)) = _979798)], (11081 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979794, tc_HOL_Obool)), _979796), hAPP(hAPP(c_Set_Oinsert(_979794), _979798), c_Orderings_Obot__class_Obot(tc_fun(_979794, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_979794, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_979794, hAPP(hAPP(c_Set_Oinsert(_979794), _979798), _979796)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_979794), _979798), c_Big__Operators_Olattice__class_OInf__fin(_979794, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979794, tc_HOL_Obool)), _979796), hAPP(hAPP(c_Set_Oinsert(_979794), _979798), c_Orderings_Obot__class_Obot(tc_fun(_979794, tc_HOL_Obool)))))))]]], (11087 ^ _782652) ^ [_980264, _980266, _980268] : [class_Lattices_Olattice(_980264), hBOOL(hAPP(c_Finite__Set_Ofinite(_980264), _980266)), -(_980266 = c_Orderings_Obot__class_Obot(tc_fun(_980264, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_980264), _980268)), -(_980268 = c_Orderings_Obot__class_Obot(tc_fun(_980264, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980264, tc_HOL_Obool)), _980266), _980268) = c_Orderings_Obot__class_Obot(tc_fun(_980264, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_980264, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980264, tc_HOL_Obool)), _980266), _980268)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980264), c_Big__Operators_Olattice__class_OSup__fin(_980264, _980266)), c_Big__Operators_Olattice__class_OSup__fin(_980264, _980268)))], (11113 ^ _782652) ^ [_980741, _980743, _980745] : [class_Lattices_Olattice(_980741), hBOOL(hAPP(c_Finite__Set_Ofinite(_980741), _980743)), hBOOL(hAPP(c_Finite__Set_Ofinite(_980741), _980745)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980741, tc_HOL_Obool)), _980743), _980745) = c_Orderings_Obot__class_Obot(tc_fun(_980741, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980741), c_Big__Operators_Olattice__class_OSup__fin(_980741, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980741, tc_HOL_Obool)), _980743), _980745))), c_Big__Operators_Olattice__class_OSup__fin(_980741, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980741, tc_HOL_Obool)), _980743), _980745))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980741), c_Big__Operators_Olattice__class_OSup__fin(_980741, _980743)), c_Big__Operators_Olattice__class_OSup__fin(_980741, _980745)))], (11131 ^ _782652) ^ [_981089, _981091, _981093] : [class_Lattices_Olattice(_981089), hBOOL(hAPP(c_Finite__Set_Ofinite(_981089), _981091)), -(_981091 = c_Orderings_Obot__class_Obot(tc_fun(_981089, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_981089), _981093)), -(_981093 = c_Orderings_Obot__class_Obot(tc_fun(_981089, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981089, tc_HOL_Obool)), _981091), _981093) = c_Orderings_Obot__class_Obot(tc_fun(_981089, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_981089, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_981089, tc_HOL_Obool)), _981091), _981093)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981089), c_Big__Operators_Olattice__class_OInf__fin(_981089, _981091)), c_Big__Operators_Olattice__class_OInf__fin(_981089, _981093)))], (11157 ^ _782652) ^ [_981566, _981568, _981570] : [class_Lattices_Olattice(_981566), hBOOL(hAPP(c_Finite__Set_Ofinite(_981566), _981568)), hBOOL(hAPP(c_Finite__Set_Ofinite(_981566), _981570)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981566, tc_HOL_Obool)), _981568), _981570) = c_Orderings_Obot__class_Obot(tc_fun(_981566, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981566), c_Big__Operators_Olattice__class_OInf__fin(_981566, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_981566, tc_HOL_Obool)), _981568), _981570))), c_Big__Operators_Olattice__class_OInf__fin(_981566, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981566, tc_HOL_Obool)), _981568), _981570))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981566), c_Big__Operators_Olattice__class_OInf__fin(_981566, _981568)), c_Big__Operators_Olattice__class_OInf__fin(_981566, _981570)))], (11175 ^ _782652) ^ [_981913, _981915, _981917, _981919] : [-(_981913 = c_Orderings_Obot__class_Obot(tc_fun(_981915, tc_HOL_Obool))), 11178 ^ _782652 : [(11190 ^ _782652) ^ [] : [11191 ^ _782652 : [(11192 ^ _782652) ^ [_982246] : [hAPP(c_Set_Oimage(_981917, _981915, _982246), _981919) = _981913]], 11194 ^ _782652 : [(11195 ^ _782652) ^ [] : [-(c_Fun_Oinj__on(_981915, _981917, 11193 ^ [_981913, _981915, _981917, _981919], _981913))], (11197 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_981917, tc_HOL_Obool)), hAPP(c_Set_Oimage(_981915, _981917, 11193 ^ [_981913, _981915, _981917, _981919]), _981913)), _981919)))]]], (11179 ^ _782652) ^ [] : [-(hAPP(c_Set_Oimage(_981917, _981915, 11186 ^ [_981913, _981915, _981917, _981919]), _981919) = _981913), 11180 ^ _782652 : [(11181 ^ _782652) ^ [_982054] : [c_Fun_Oinj__on(_981915, _981917, _982054, _981913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_981917, tc_HOL_Obool)), hAPP(c_Set_Oimage(_981915, _981917, _982054), _981913)), _981919))]]]]], (11199 ^ _782652) ^ [_982371, _982373, _982375, _982377, _982379] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_982371, _982371, _982373, _982375, _982377), _982379)), -(hBOOL(hAPP(hAPP(c_member(_982371), _982375), _982377))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_982371, _982373, hAPP(hAPP(c_Set_Oinsert(_982371), _982375), _982377)), _982379)))], (11209 ^ _782652) ^ [_982527, _982529] : [class_Lattices_Olattice(_982527), hBOOL(hAPP(c_Finite__Set_Ofinite(_982527), _982529)), -(_982529 = c_Orderings_Obot__class_Obot(tc_fun(_982527, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_982527), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_982527), 11222 ^ [_982527, _982529]), 11223 ^ [_982527, _982529])), hAPP(hAPP(c_Set_Oinsert(_982527), 11222 ^ [_982527, _982529]), hAPP(hAPP(c_Set_Oinsert(_982527), 11223 ^ [_982527, _982529]), c_Orderings_Obot__class_Obot(tc_fun(_982527, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_982527), c_Big__Operators_Olattice__class_OInf__fin(_982527, _982529)), _982529)))], (11229 ^ _782652) ^ [_982971, _982973] : [class_Lattices_Olattice(_982971), hBOOL(hAPP(c_Finite__Set_Ofinite(_982971), _982973)), -(_982973 = c_Orderings_Obot__class_Obot(tc_fun(_982971, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_982971), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_982971), 11242 ^ [_982971, _982973]), 11243 ^ [_982971, _982973])), hAPP(hAPP(c_Set_Oinsert(_982971), 11242 ^ [_982971, _982973]), hAPP(hAPP(c_Set_Oinsert(_982971), 11243 ^ [_982971, _982973]), c_Orderings_Obot__class_Obot(tc_fun(_982971, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_982971), c_Big__Operators_Olattice__class_OSup__fin(_982971, _982973)), _982973)))], (11249 ^ _782652) ^ [_983415, _983417, _983419] : [class_Lattices_Odistrib__lattice(_983415), hBOOL(hAPP(c_Finite__Set_Ofinite(_983415), _983417)), -(_983417 = c_Orderings_Obot__class_Obot(tc_fun(_983415, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_983415), _983419), c_Big__Operators_Olattice__class_OSup__fin(_983415, _983417)) = c_Big__Operators_Olattice__class_OSup__fin(_983415, hAPP(c_Set_OCollect(_983415), hAPP(hAPP(c_COMBB(tc_fun(_983415, tc_HOL_Obool), tc_HOL_Obool, _983415), c_HOL_OEx(_983415)), hAPP(hAPP(c_COMBC(_983415, tc_fun(_983415, tc_HOL_Obool), tc_fun(_983415, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_983415, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_983415, tc_HOL_Obool), tc_fun(_983415, tc_HOL_Obool)), _983415), c_COMBS(_983415, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_983415, tc_HOL_Obool), tc_fun(_983415, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _983415), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _983415), c_fconj)), hAPP(hAPP(c_COMBC(_983415, tc_fun(_983415, _983415), tc_fun(_983415, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_983415, tc_HOL_Obool), tc_fun(tc_fun(_983415, _983415), tc_fun(_983415, tc_HOL_Obool)), _983415), c_COMBB(_983415, tc_HOL_Obool, _983415)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_983415), _983419))))), hAPP(hAPP(c_COMBC(_983415, tc_fun(_983415, tc_HOL_Obool), tc_HOL_Obool), c_member(_983415)), _983417))))))], (11263 ^ _782652) ^ [_983901, _983903, _983905] : [class_Lattices_Odistrib__lattice(_983901), hBOOL(hAPP(c_Finite__Set_Ofinite(_983901), _983903)), -(_983903 = c_Orderings_Obot__class_Obot(tc_fun(_983901, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_983901), _983905)), -(_983905 = c_Orderings_Obot__class_Obot(tc_fun(_983901, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_983901), c_Big__Operators_Olattice__class_OSup__fin(_983901, _983903)), c_Big__Operators_Olattice__class_OSup__fin(_983901, _983905)) = c_Big__Operators_Olattice__class_OSup__fin(_983901, hAPP(c_Set_OCollect(_983901), hAPP(hAPP(c_COMBB(tc_fun(_983901, tc_HOL_Obool), tc_HOL_Obool, _983901), c_HOL_OEx(_983901)), hAPP(hAPP(c_COMBB(tc_fun(_983901, tc_fun(_983901, tc_HOL_Obool)), tc_fun(_983901, tc_HOL_Obool), _983901), hAPP(c_COMBB(tc_fun(_983901, tc_HOL_Obool), tc_HOL_Obool, _983901), c_HOL_OEx(_983901))), hAPP(hAPP(c_COMBC(_983901, tc_fun(_983901, tc_fun(_983901, tc_HOL_Obool)), tc_fun(_983901, tc_fun(_983901, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_983901, tc_fun(tc_fun(_983901, tc_HOL_Obool), tc_fun(_983901, tc_HOL_Obool))), tc_fun(tc_fun(_983901, tc_fun(_983901, tc_HOL_Obool)), tc_fun(_983901, tc_fun(_983901, tc_HOL_Obool))), _983901), c_COMBS(_983901, tc_fun(_983901, tc_HOL_Obool), tc_fun(_983901, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_983901, tc_fun(_983901, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_983901, tc_fun(tc_fun(_983901, tc_HOL_Obool), tc_fun(_983901, tc_HOL_Obool))), _983901), hAPP(c_COMBB(tc_fun(_983901, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_983901, tc_HOL_Obool), tc_fun(_983901, tc_HOL_Obool)), _983901), c_COMBS(_983901, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_983901, tc_fun(_983901, tc_HOL_Obool)), tc_fun(_983901, tc_fun(_983901, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _983901), hAPP(c_COMBB(tc_fun(_983901, tc_HOL_Obool), tc_fun(_983901, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _983901), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _983901), c_fconj))), hAPP(hAPP(c_COMBC(_983901, tc_fun(_983901, tc_fun(_983901, _983901)), tc_fun(_983901, tc_fun(_983901, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_983901, _983901), tc_fun(_983901, tc_HOL_Obool)), tc_fun(tc_fun(_983901, tc_fun(_983901, _983901)), tc_fun(_983901, tc_fun(_983901, tc_HOL_Obool))), _983901), c_COMBB(tc_fun(_983901, _983901), tc_fun(_983901, tc_HOL_Obool), _983901)), hAPP(hAPP(c_COMBB(tc_fun(_983901, tc_HOL_Obool), tc_fun(tc_fun(_983901, _983901), tc_fun(_983901, tc_HOL_Obool)), _983901), c_COMBB(_983901, tc_HOL_Obool, _983901)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_983901)))))), hAPP(hAPP(c_COMBC(_983901, tc_fun(_983901, tc_HOL_Obool), tc_fun(_983901, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_983901, tc_HOL_Obool), tc_fun(_983901, tc_HOL_Obool)), _983901), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _983901)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _983901), c_fconj), hAPP(hAPP(c_COMBC(_983901, tc_fun(_983901, tc_HOL_Obool), tc_HOL_Obool), c_member(_983901)), _983903)))), hAPP(hAPP(c_COMBC(_983901, tc_fun(_983901, tc_HOL_Obool), tc_HOL_Obool), c_member(_983901)), _983905))))))))], (11285 ^ _782652) ^ [_985000, _985002, _985004] : [class_Lattices_Odistrib__lattice(_985000), hBOOL(hAPP(c_Finite__Set_Ofinite(_985000), _985002)), -(_985002 = c_Orderings_Obot__class_Obot(tc_fun(_985000, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_985000), _985004)), -(_985004 = c_Orderings_Obot__class_Obot(tc_fun(_985000, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_985000), c_Big__Operators_Olattice__class_OInf__fin(_985000, _985002)), c_Big__Operators_Olattice__class_OInf__fin(_985000, _985004)) = c_Big__Operators_Olattice__class_OInf__fin(_985000, hAPP(c_Set_OCollect(_985000), hAPP(hAPP(c_COMBB(tc_fun(_985000, tc_HOL_Obool), tc_HOL_Obool, _985000), c_HOL_OEx(_985000)), hAPP(hAPP(c_COMBB(tc_fun(_985000, tc_fun(_985000, tc_HOL_Obool)), tc_fun(_985000, tc_HOL_Obool), _985000), hAPP(c_COMBB(tc_fun(_985000, tc_HOL_Obool), tc_HOL_Obool, _985000), c_HOL_OEx(_985000))), hAPP(hAPP(c_COMBC(_985000, tc_fun(_985000, tc_fun(_985000, tc_HOL_Obool)), tc_fun(_985000, tc_fun(_985000, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_985000, tc_fun(tc_fun(_985000, tc_HOL_Obool), tc_fun(_985000, tc_HOL_Obool))), tc_fun(tc_fun(_985000, tc_fun(_985000, tc_HOL_Obool)), tc_fun(_985000, tc_fun(_985000, tc_HOL_Obool))), _985000), c_COMBS(_985000, tc_fun(_985000, tc_HOL_Obool), tc_fun(_985000, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_985000, tc_fun(_985000, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_985000, tc_fun(tc_fun(_985000, tc_HOL_Obool), tc_fun(_985000, tc_HOL_Obool))), _985000), hAPP(c_COMBB(tc_fun(_985000, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_985000, tc_HOL_Obool), tc_fun(_985000, tc_HOL_Obool)), _985000), c_COMBS(_985000, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_985000, tc_fun(_985000, tc_HOL_Obool)), tc_fun(_985000, tc_fun(_985000, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _985000), hAPP(c_COMBB(tc_fun(_985000, tc_HOL_Obool), tc_fun(_985000, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _985000), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _985000), c_fconj))), hAPP(hAPP(c_COMBC(_985000, tc_fun(_985000, tc_fun(_985000, _985000)), tc_fun(_985000, tc_fun(_985000, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_985000, _985000), tc_fun(_985000, tc_HOL_Obool)), tc_fun(tc_fun(_985000, tc_fun(_985000, _985000)), tc_fun(_985000, tc_fun(_985000, tc_HOL_Obool))), _985000), c_COMBB(tc_fun(_985000, _985000), tc_fun(_985000, tc_HOL_Obool), _985000)), hAPP(hAPP(c_COMBB(tc_fun(_985000, tc_HOL_Obool), tc_fun(tc_fun(_985000, _985000), tc_fun(_985000, tc_HOL_Obool)), _985000), c_COMBB(_985000, tc_HOL_Obool, _985000)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_985000)))))), hAPP(hAPP(c_COMBC(_985000, tc_fun(_985000, tc_HOL_Obool), tc_fun(_985000, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_985000, tc_HOL_Obool), tc_fun(_985000, tc_HOL_Obool)), _985000), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _985000)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _985000), c_fconj), hAPP(hAPP(c_COMBC(_985000, tc_fun(_985000, tc_HOL_Obool), tc_HOL_Obool), c_member(_985000)), _985002)))), hAPP(hAPP(c_COMBC(_985000, tc_fun(_985000, tc_HOL_Obool), tc_HOL_Obool), c_member(_985000)), _985004))))))))], (11307 ^ _782652) ^ [_986099, _986101, _986103] : [class_Lattices_Odistrib__lattice(_986099), hBOOL(hAPP(c_Finite__Set_Ofinite(_986099), _986101)), -(_986101 = c_Orderings_Obot__class_Obot(tc_fun(_986099, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_986099), _986103), c_Big__Operators_Olattice__class_OInf__fin(_986099, _986101)) = c_Big__Operators_Olattice__class_OInf__fin(_986099, hAPP(c_Set_OCollect(_986099), hAPP(hAPP(c_COMBB(tc_fun(_986099, tc_HOL_Obool), tc_HOL_Obool, _986099), c_HOL_OEx(_986099)), hAPP(hAPP(c_COMBC(_986099, tc_fun(_986099, tc_HOL_Obool), tc_fun(_986099, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_986099, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_986099, tc_HOL_Obool), tc_fun(_986099, tc_HOL_Obool)), _986099), c_COMBS(_986099, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_986099, tc_HOL_Obool), tc_fun(_986099, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _986099), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _986099), c_fconj)), hAPP(hAPP(c_COMBC(_986099, tc_fun(_986099, _986099), tc_fun(_986099, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_986099, tc_HOL_Obool), tc_fun(tc_fun(_986099, _986099), tc_fun(_986099, tc_HOL_Obool)), _986099), c_COMBB(_986099, tc_HOL_Obool, _986099)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_986099), _986103))))), hAPP(hAPP(c_COMBC(_986099, tc_fun(_986099, tc_HOL_Obool), tc_HOL_Obool), c_member(_986099)), _986101))))))], (11321 ^ _782652) ^ [_986585, _986587, _986589, _986591, _986593, _986595] : [c_Fun_Oinj__on(_986585, _986587, _986589, _986591), hBOOL(hAPP(hAPP(c_member(_986587), _986593), hAPP(c_Set_Oimage(_986585, _986587, _986589), _986591))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986585, tc_HOL_Obool)), _986591), _986595)), -(hBOOL(hAPP(hAPP(c_member(_986585), hAPP(c_Fun_Othe__inv__into(_986585, _986587, _986591, _986589), _986593)), _986595)))], (11335 ^ _782652) ^ [_986872] : [-(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)), _986872)))))], (11337 ^ _782652) ^ [_986903] : [-(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)), _986903)))))], (11339 ^ _782652) ^ [_986949, _986951, _986953] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_986949, _986951, c_Orderings_Obot__class_Obot(tc_fun(_986949, tc_HOL_Obool))), _986953))], (11341 ^ _782652) ^ [_986987, _986989, _986991, _986993] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_986987, _986989, _986991), _986993)), _986991 = c_Orderings_Obot__class_Obot(tc_fun(_986987, tc_HOL_Obool))], (11347 ^ _782652) ^ [_987091, _987093, _987095, _987097] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987091), hAPP(c_Set_OCollect(_987091), _987093))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_987095), hAPP(c_Set_OCollect(_987095), hAPP(hAPP(c_COMBB(tc_fun(_987091, tc_HOL_Obool), tc_HOL_Obool, _987095), c_HOL_OEx(_987091)), hAPP(hAPP(c_COMBC(_987095, tc_fun(_987091, tc_HOL_Obool), tc_fun(_987091, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_987091, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_987091, tc_HOL_Obool), tc_fun(_987091, tc_HOL_Obool)), _987095), c_COMBS(_987091, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_987091, tc_HOL_Obool), tc_fun(_987091, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _987095), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _987091), c_fconj)), hAPP(hAPP(c_COMBC(_987095, tc_fun(_987091, _987095), tc_fun(_987091, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_987095, tc_HOL_Obool), tc_fun(tc_fun(_987091, _987095), tc_fun(_987091, tc_HOL_Obool)), _987095), c_COMBB(_987095, tc_HOL_Obool, _987091)), c_fequal)), _987097)))), _987093))))))], (11353 ^ _782652) ^ [_987452, _987454, _987456, _987458] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987452), hAPP(c_Set_OCollect(_987452), _987454))), 11356 ^ _782652 : [(11367 ^ _782652) ^ [] : [11369 ^ _782652 : [(11370 ^ _782652) ^ [] : [-(hBOOL(hAPP(_987454, 11368 ^ [_987452, _987454, _987456, _987458])))], (11372 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987456), hAPP(c_Set_OCollect(_987456), hAPP(hAPP(c_COMBC(_987456, _987452, tc_HOL_Obool), _987458), 11368 ^ [_987452, _987454, _987456, _987458]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_987456), hAPP(c_Set_OCollect(_987456), hAPP(hAPP(c_COMBB(tc_fun(_987452, tc_HOL_Obool), tc_HOL_Obool, _987456), c_HOL_OEx(_987452)), hAPP(hAPP(c_COMBB(tc_fun(_987452, tc_HOL_Obool), tc_fun(_987452, tc_HOL_Obool), _987456), hAPP(c_COMBS(_987452, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _987452), c_fconj), _987454))), _987458))))))], (11357 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_987456), hAPP(c_Set_OCollect(_987456), hAPP(hAPP(c_COMBB(tc_fun(_987452, tc_HOL_Obool), tc_HOL_Obool, _987456), c_HOL_OEx(_987452)), hAPP(hAPP(c_COMBB(tc_fun(_987452, tc_HOL_Obool), tc_fun(_987452, tc_HOL_Obool), _987456), hAPP(c_COMBS(_987452, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _987452), c_fconj), _987454))), _987458))))), 11360 ^ _782652 : [(11361 ^ _782652) ^ [_987735] : [hBOOL(hAPP(_987454, _987735)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_987456), hAPP(c_Set_OCollect(_987456), hAPP(hAPP(c_COMBC(_987456, _987452, tc_HOL_Obool), _987458), _987735)))))]]]]], (11376 ^ _782652) ^ [_988100, _988102, _988104, _988106, _988108] : [c_Fun_Oinj__on(_988100, _988102, _988104, _988106), hBOOL(hAPP(hAPP(c_member(_988100), _988108), _988106)), -(hAPP(c_Fun_Othe__inv__into(_988100, _988102, _988106, _988104), hAPP(_988104, _988108)) = _988108)], (11386 ^ _782652) ^ [_988281, _988283, _988285, _988287, _988289, _988291] : [c_Fun_Oinj__on(_988281, _988283, _988285, _988287), hAPP(_988285, _988289) = _988291, hBOOL(hAPP(hAPP(c_member(_988281), _988289), _988287)), -(hAPP(c_Fun_Othe__inv__into(_988281, _988283, _988287, _988285), _988291) = _988289)], (11400 ^ _782652) ^ [_988526, _988528, _988530, _988532] : [c_Fun_Oinj__on(_988526, _988528, _988530, _988532), -(c_Fun_Oinj__on(_988528, _988526, c_Fun_Othe__inv__into(_988526, _988528, _988532, _988530), hAPP(c_Set_Oimage(_988526, _988528, _988530), _988532)))], (11406 ^ _782652) ^ [_988639, _988641, _988643, _988645] : [c_Fun_Oinj__on(_988639, _988641, _988643, _988645), -(hAPP(c_Set_Oimage(_988641, _988639, c_Fun_Othe__inv__into(_988639, _988641, _988645, _988643)), hAPP(c_Set_Oimage(_988639, _988641, _988643), _988645)) = _988645)], (11412 ^ _782652) ^ [_988783, _988785, _988787, _988789] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_988783, _988785, hAPP(hAPP(c_Set_Oinsert(_988783), _988787), c_Orderings_Obot__class_Obot(tc_fun(_988783, tc_HOL_Obool)))), _988789)), -(_988787 = _988789)], (11418 ^ _782652) ^ [_988898, _988900, _988902, _988904] : [_988902 = _988904, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_988898, _988900, hAPP(hAPP(c_Set_Oinsert(_988898), _988902), c_Orderings_Obot__class_Obot(tc_fun(_988898, tc_HOL_Obool)))), _988904)))], (11424 ^ _782652) ^ [_989019, _989021, _989023] : [-(c_Map_Oran(_989019, _989021, _989023) = hAPP(c_Set_OCollect(_989021), hAPP(hAPP(c_COMBB(tc_fun(_989019, tc_HOL_Obool), tc_HOL_Obool, _989021), c_HOL_OEx(_989019)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_989021), tc_fun(_989019, tc_HOL_Obool), _989021), hAPP(c_COMBC(_989019, tc_Option_Ooption(_989021), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_989021), tc_fun(tc_Option_Ooption(_989021), tc_HOL_Obool), _989019), c_fequal), _989023))), c_Option_Ooption_OSome(_989021)))))], (11426 ^ _782652) ^ [_989113, _989115, _989117, _989119, _989121] : [-(hAPP(c_Fun_Othe__inv__into(_989113, _989115, _989117, _989119), _989121) = c_HOL_OThe(_989113, hAPP(hAPP(c_COMBS(_989113, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _989113), c_fconj), hAPP(hAPP(c_COMBC(_989113, tc_fun(_989113, tc_HOL_Obool), tc_HOL_Obool), c_member(_989113)), _989117))), hAPP(hAPP(c_COMBC(_989113, _989115, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_989115, tc_fun(_989115, tc_HOL_Obool), _989113), c_fequal), _989119)), _989121))))], (11428 ^ _782652) ^ [_989213, _989215, _989217, _989219, _989221] : [c_Fun_Oinj__on(_989213, _989215, _989217, _989219), hBOOL(hAPP(hAPP(c_member(_989215), _989221), hAPP(c_Set_Oimage(_989213, _989215, _989217), _989219))), -(hAPP(_989217, hAPP(c_Fun_Othe__inv__into(_989213, _989215, _989219, _989217), _989221)) = _989221)], (11438 ^ _782652) ^ [_989408, _989410] : [-(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), _989408)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _989410))))))], (11440 ^ _782652) ^ [_989450, _989452, _989454] : [class_Lattices_Olattice(_989450), hAPP(_989452, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_989450), 11445 ^ [_989450, _989452, _989454]), 11446 ^ [_989450, _989452, _989454])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_989450), hAPP(_989452, 11445 ^ [_989450, _989452, _989454])), hAPP(_989452, 11446 ^ [_989450, _989452, _989454])), hBOOL(hAPP(c_Finite__Set_Ofinite(_989450), _989454)), -(_989454 = c_Orderings_Obot__class_Obot(tc_fun(_989450, tc_HOL_Obool))), -(hAPP(_989452, c_Big__Operators_Olattice__class_OInf__fin(_989450, _989454)) = c_Big__Operators_Olattice__class_OInf__fin(_989450, hAPP(c_Set_Oimage(_989450, _989450, _989452), _989454)))], (11460 ^ _782652) ^ [_989853, _989855, _989857] : [class_Lattices_Olattice(_989853), hAPP(_989855, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_989853), 11465 ^ [_989853, _989855, _989857]), 11466 ^ [_989853, _989855, _989857])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_989853), hAPP(_989855, 11465 ^ [_989853, _989855, _989857])), hAPP(_989855, 11466 ^ [_989853, _989855, _989857])), hBOOL(hAPP(c_Finite__Set_Ofinite(_989853), _989857)), -(_989857 = c_Orderings_Obot__class_Obot(tc_fun(_989853, tc_HOL_Obool))), -(hAPP(_989855, c_Big__Operators_Olattice__class_OSup__fin(_989853, _989857)) = c_Big__Operators_Olattice__class_OSup__fin(_989853, hAPP(c_Set_Oimage(_989853, _989853, _989855), _989857)))], (11480 ^ _782652) ^ [_990274, _990276, _990278, _990280, _990282] : [hBOOL(hAPP(hAPP(c_member(_990274), _990276), _990278)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_990274, tc_Option_Ooption(_990280)), c_Map_Orestrict__map(_990274, _990280, _990282, _990278)), _990276), c_Option_Ooption_ONone(_990280)) = c_Map_Orestrict__map(_990274, _990280, _990282, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990274, tc_HOL_Obool)), _990278), hAPP(hAPP(c_Set_Oinsert(_990274), _990276), c_Orderings_Obot__class_Obot(tc_fun(_990274, tc_HOL_Obool))))))], (11486 ^ _782652) ^ [_990465, _990467, _990469, _990471, _990473] : [-(hBOOL(hAPP(hAPP(c_member(_990465), _990467), _990469))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_990465, tc_Option_Ooption(_990471)), c_Map_Orestrict__map(_990465, _990471, _990473, _990469)), _990467), c_Option_Ooption_ONone(_990471)) = c_Map_Orestrict__map(_990465, _990471, _990473, _990469))], (11492 ^ _782652) ^ [_990557, _990559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_990557), _990559)), -(_990559 = hAPP(c_Set_Oimage(tc_Nat_Onat, _990557, 11496 ^ [_990557, _990559]), 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)), 11495 ^ [_990557, _990559]))))], (11500 ^ _782652) ^ [_990688, _990690] : [11501 ^ _782652 : [(11502 ^ _782652) ^ [_990752, _990754] : [_990690 = hAPP(c_Set_Oimage(tc_Nat_Onat, _990688, _990752), 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)), _990754)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_990688), _990690)))], (11506 ^ _782652) ^ [_990824, _990826, _990828, _990830, _990832] : [hBOOL(hAPP(hAPP(c_member(_990824), _990826), c_Map_Oran(_990828, _990824, c_Map_Orestrict__map(_990828, _990824, _990830, _990832)))), 11510 ^ _782652 : [(11511 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_990828), 11509 ^ [_990824, _990826, _990828, _990830, _990832]), _990832)))], (11513 ^ _782652) ^ [] : [-(hAPP(_990830, 11509 ^ [_990824, _990826, _990828, _990830, _990832]) = hAPP(c_Option_Ooption_OSome(_990824), _990826))]]], (11515 ^ _782652) ^ [_991026, _991028, _991030, _991032] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_991026), _991028)), -(hAPP(c_Set_Oimage(_991026, _991030, _991032), _991028) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_991030, tc_HOL_Obool), _991026, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_991030, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_991026, tc_fun(_991030, tc_HOL_Obool), tc_fun(_991030, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_991030, tc_fun(tc_fun(_991030, tc_HOL_Obool), tc_fun(_991030, tc_HOL_Obool)), _991026), c_Set_Oinsert(_991030)), _991032)), c_Orderings_Obot__class_Obot(tc_fun(_991030, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_991030, tc_HOL_Obool))), _991028))], (11521 ^ _782652) ^ [_991289, _991291, _991293, _991295, _991297] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_991289, _991291, hAPP(hAPP(c_Set_Oinsert(_991289), _991293), _991295)), _991297)), 11526 ^ _782652 : [(11527 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_991289), _991293), _991295) = hAPP(hAPP(c_Set_Oinsert(_991289), 11524 ^ [_991289, _991291, _991293, _991295, _991297]), 11525 ^ [_991289, _991291, _991293, _991295, _991297]))], (11529 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_991289, _991289, _991291, 11524 ^ [_991289, _991291, _991293, _991295, _991297], 11525 ^ [_991289, _991291, _991293, _991295, _991297]), _991297)))], (11531 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_991289), 11524 ^ [_991289, _991291, _991293, _991295, _991297]), 11525 ^ [_991289, _991291, _991293, _991295, _991297]))]]], (11533 ^ _782652) ^ [_991680, _991682, _991684, _991686, _991688] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_991680, _991682, hAPP(hAPP(c_Set_Oinsert(_991680), _991684), _991686)), _991688))), 11534 ^ _782652 : [(11535 ^ _782652) ^ [_991784, _991786] : [hAPP(hAPP(c_Set_Oinsert(_991680), _991684), _991686) = hAPP(hAPP(c_Set_Oinsert(_991680), _991786), _991784), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_991680, _991680, _991682, _991786, _991784), _991688)), -(hBOOL(hAPP(hAPP(c_member(_991680), _991786), _991784)))]]], (11547 ^ _782652) ^ [_992041, _992043, _992045, _992047, _992049] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_992041, _992043, hAPP(hAPP(c_Set_Oinsert(_992041), _992045), _992047)), _992049)), 11552 ^ _782652 : [(11553 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_992041), _992045), _992047) = hAPP(hAPP(c_Set_Oinsert(_992041), 11550 ^ [_992041, _992043, _992045, _992047, _992049]), 11551 ^ [_992041, _992043, _992045, _992047, _992049]))], (11555 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_992041, _992041, _992043, 11550 ^ [_992041, _992043, _992045, _992047, _992049], 11551 ^ [_992041, _992043, _992045, _992047, _992049]), _992049)))], (11557 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_992041), 11550 ^ [_992041, _992043, _992045, _992047, _992049]), 11551 ^ [_992041, _992043, _992045, _992047, _992049]))]]], (11570 ^ _782652) ^ [_992633] : [11572 ^ _782652 : [(11573 ^ _782652) ^ [_992709] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 11571 ^ [_992633, _992709]), _992633)))], (11575 ^ _782652) ^ [_992743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 11571 ^ [_992633, _992743]), _992743))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _992633)))], (11559 ^ _782652) ^ [_992446] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _992446)), 11563 ^ _782652 : [(11564 ^ _782652) ^ [_992526] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _992526), _992446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992526), 11562 ^ [_992446])))]]], (11579 ^ _782652) ^ [_992821, _992823] : [-(_992821 = c_Option_Ooption_ONone(_992823)), -(_992821 = hAPP(c_Option_Ooption_OSome(_992823), 11582 ^ [_992821, _992823]))], (11586 ^ _782652) ^ [_992867, _992869] : [11587 ^ _782652 : [(11588 ^ _782652) ^ [_992915] : [_992867 = hAPP(c_Option_Ooption_OSome(_992869), _992915)]], _992867 = c_Option_Ooption_ONone(_992869)], (11592 ^ _782652) ^ [_992983, _992985] : [-(_992983 = hAPP(c_Option_Ooption_OSome(_992985), 11593 ^ [_992983, _992985])), -(_992983 = c_Option_Ooption_ONone(_992985))], (11599 ^ _782652) ^ [_993029, _993031] : [_993029 = c_Option_Ooption_ONone(_993031), 11602 ^ _782652 : [(11603 ^ _782652) ^ [_993101] : [_993029 = hAPP(c_Option_Ooption_OSome(_993031), _993101)]]], (11605 ^ _782652) ^ [_993147, _993149] : [hAPP(c_Option_Ooption_OSome(_993147), _993149) = c_Option_Ooption_ONone(_993147)], (11607 ^ _782652) ^ [_993191, _993193] : [c_Option_Ooption_ONone(_993191) = hAPP(c_Option_Ooption_OSome(_993191), _993193)], (11609 ^ _782652) ^ [_993223, _993225, _993227, _993229, _993231] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_993223, _993225, _993227), _993229), _993231), c_Orderings_Obot__class_Obot(tc_fun(_993225, tc_HOL_Obool))) = _993231)], (11611 ^ _782652) ^ [_993272, _993274, _993276, _993278] : [-(hAPP(c_Option_Ooption_Ooption__case(_993272, _993274, _993276, _993278), c_Option_Ooption_ONone(_993274)) = _993276)], (11613 ^ _782652) ^ [_993311, _993313, _993315, _993317] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_993311, tc_Option_Ooption(_993313)), hAPP(c_COMBK(tc_Option_Ooption(_993313), _993311), c_Option_Ooption_ONone(_993313))), _993315), c_Option_Ooption_ONone(_993313)), _993317) = c_Option_Ooption_ONone(_993313))], (11615 ^ _782652) ^ [_993371, _993373, _993375, _993377] : [-(hAPP(c_Map_Orestrict__map(_993371, _993373, hAPP(c_COMBK(tc_Option_Ooption(_993373), _993371), c_Option_Ooption_ONone(_993373)), _993375), _993377) = c_Option_Ooption_ONone(_993373))], (11617 ^ _782652) ^ [_993435, _993437] : [c_Option_Ois__none(_993435, _993437), -(_993437 = c_Option_Ooption_ONone(_993435))], (11623 ^ _782652) ^ [_993512, _993514] : [_993514 = c_Option_Ooption_ONone(_993512), -(c_Option_Ois__none(_993512, _993514))], (11629 ^ _782652) ^ [_993595] : [-(c_Option_Ois__none(_993595, c_Option_Ooption_ONone(_993595)))], (11631 ^ _782652) ^ [_993641, _993643, _993645, _993647] : [hBOOL(hAPP(hAPP(c_member(_993641), _993643), c_Map_Odom(_993641, _993645, _993647))), hAPP(_993647, _993643) = c_Option_Ooption_ONone(_993645)], (11637 ^ _782652) ^ [_993749, _993751, _993753, _993755] : [-(hAPP(_993755, _993751) = c_Option_Ooption_ONone(_993753)), -(hBOOL(hAPP(hAPP(c_member(_993749), _993751), c_Map_Odom(_993749, _993753, _993755))))], (11643 ^ _782652) ^ [_993807, _993809, _993811, _993813] : [-(c_Option_Ooption_Ooption__rec(_993807, _993809, _993811, _993813, c_Option_Ooption_ONone(_993809)) = _993811)], (11645 ^ _782652) ^ [_993840, _993842, _993844, _993846, _993848] : [-(hBOOL(hAPP(hAPP(c_member(_993840), _993842), _993844))), -(hAPP(c_Map_Orestrict__map(_993840, _993846, _993848, _993844), _993842) = c_Option_Ooption_ONone(_993846))], (11651 ^ _782652) ^ [_993917, _993919, _993921] : [c_Map_Odom(_993917, _993919, _993921) = c_Orderings_Obot__class_Obot(tc_fun(_993917, tc_HOL_Obool)), -(_993921 = hAPP(c_COMBK(tc_Option_Ooption(_993919), _993917), c_Option_Ooption_ONone(_993919)))], (11657 ^ _782652) ^ [_994030, _994032, _994034] : [_994034 = hAPP(c_COMBK(tc_Option_Ooption(_994032), _994030), c_Option_Ooption_ONone(_994032)), -(c_Map_Odom(_994030, _994032, _994034) = c_Orderings_Obot__class_Obot(tc_fun(_994030, tc_HOL_Obool)))], (11663 ^ _782652) ^ [_994149, _994151] : [-(c_Map_Odom(_994149, _994151, hAPP(c_COMBK(tc_Option_Ooption(_994151), _994149), c_Option_Ooption_ONone(_994151))) = c_Orderings_Obot__class_Obot(tc_fun(_994149, tc_HOL_Obool)))], (11665 ^ _782652) ^ [_994193, _994195, _994197] : [-(c_Map_Odom(_994193, _994195, _994197) = hAPP(c_Set_OCollect(_994193), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _994193), c_fNot), hAPP(hAPP(c_COMBC(_994193, tc_Option_Ooption(_994195), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_994195), tc_fun(tc_Option_Ooption(_994195), tc_HOL_Obool), _994193), c_fequal), _994197)), c_Option_Ooption_ONone(_994195)))))], (11667 ^ _782652) ^ [_994288, _994290, _994292, _994294, _994296] : [hBOOL(hAPP(hAPP(c_member(_994288), _994290), _994292)), -(hAPP(c_Map_Orestrict__map(_994288, _994294, _994296, _994292), _994290) = hAPP(_994296, _994290))], (11673 ^ _782652) ^ [_994401, _994403, _994405, _994407, _994409] : [-(hBOOL(hAPP(hAPP(c_member(_994401), _994403), _994405))), -(hAPP(c_Map_Orestrict__map(_994401, _994407, _994409, _994405), _994403) = c_Option_Ooption_ONone(_994407))], (11679 ^ _782652) ^ [_994462, _994464, _994466, _994468] : [-(hAPP(c_Map_Orestrict__map(_994462, _994464, _994466, c_Orderings_Obot__class_Obot(tc_fun(_994462, tc_HOL_Obool))), _994468) = c_Option_Ooption_ONone(_994464))], (11681 ^ _782652) ^ [_994521, _994523] : [c_Option_Oset(_994521, _994523) = c_Orderings_Obot__class_Obot(tc_fun(_994521, tc_HOL_Obool)), -(_994523 = c_Option_Ooption_ONone(_994521))], (11687 ^ _782652) ^ [_994614, _994616] : [_994616 = c_Option_Ooption_ONone(_994614), -(c_Option_Oset(_994614, _994616) = c_Orderings_Obot__class_Obot(tc_fun(_994614, tc_HOL_Obool)))], (11693 ^ _782652) ^ [_994713] : [-(c_Option_Oset(_994713, c_Option_Ooption_ONone(_994713)) = c_Orderings_Obot__class_Obot(tc_fun(_994713, tc_HOL_Obool)))], (11695 ^ _782652) ^ [_994767, _994769, _994771, _994773, _994775] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_994767, tc_Option_Ooption(_994769)), _994771), _994773), hAPP(c_Option_Ooption_OSome(_994769), _994775)) = hAPP(c_COMBK(tc_Option_Ooption(_994769), _994767), c_Option_Ooption_ONone(_994769))], (11697 ^ _782652) ^ [_994827, _994829, _994831, _994833, _994835, _994837, _994839] : [c_Finite__Set_Ofolding__image__simple(_994827, _994829, _994831, _994833, _994835, _994837), hBOOL(hAPP(c_Finite__Set_Ofinite(_994829), _994839)), -(hAPP(_994837, _994839) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_994827, _994829, _994831), _994835), _994833), _994839))], (11707 ^ _782652) ^ [_995024, _995026] : [-(c_Map_Oran(_995024, _995026, hAPP(c_COMBK(tc_Option_Ooption(_995026), _995024), c_Option_Ooption_ONone(_995026))) = c_Orderings_Obot__class_Obot(tc_fun(_995026, tc_HOL_Obool)))], (11709 ^ _782652) ^ [_995068, _995070, _995072, _995074, _995076] : [hAPP(_995068, _995070) = c_Option_Ooption_ONone(_995072), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995074, tc_HOL_Obool)), c_Map_Odom(_995074, _995072, _995068)), hAPP(hAPP(c_Set_Oinsert(_995074), _995070), _995076)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995074, tc_HOL_Obool)), c_Map_Odom(_995074, _995072, _995068)), _995076))], (11726 ^ _782652) ^ [_995436] : [11728 ^ _782652 : [(11729 ^ _782652) ^ [_995512] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 11727 ^ [_995436, _995512]), _995436)))], (11731 ^ _782652) ^ [_995546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 11727 ^ [_995436, _995546]), _995546))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _995436)))], (11715 ^ _782652) ^ [_995249] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _995249)), 11719 ^ _782652 : [(11720 ^ _782652) ^ [_995329] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _995329), _995249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995329), 11718 ^ [_995249])))]]], (11735 ^ _782652) ^ [_995611] : [-(hAPP(c_Com_Obody, _995611) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _995611))))], (11741 ^ _782652) ^ [_995653, _995655, _995657, _995659, _995661] : [hAPP(_995653, _995655) = c_Option_Ooption_ONone(_995657), -(c_Map_Oran(_995659, _995657, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_995659, tc_Option_Ooption(_995657)), _995653), _995655), hAPP(c_Option_Ooption_OSome(_995657), _995661))) = hAPP(hAPP(c_Set_Oinsert(_995657), _995661), c_Map_Oran(_995659, _995657, _995653)))], (11747 ^ _782652) ^ [_995834, _995836, _995838, _995840, _995842] : [_995834 = c_Option_Ooption_ONone(_995836), -(c_Map_Odom(_995838, _995836, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_995838, tc_Option_Ooption(_995836)), _995840), _995842), _995834)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995838, tc_HOL_Obool)), c_Map_Odom(_995838, _995836, _995840)), hAPP(hAPP(c_Set_Oinsert(_995838), _995842), c_Orderings_Obot__class_Obot(tc_fun(_995838, tc_HOL_Obool)))))], (11753 ^ _782652) ^ [_996007, _996009, _996011, _996013, _996015] : [-(_996007 = c_Option_Ooption_ONone(_996009)), -(c_Map_Odom(_996011, _996009, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_996011, tc_Option_Ooption(_996009)), _996013), _996015), _996007)) = hAPP(hAPP(c_Set_Oinsert(_996011), _996015), c_Map_Odom(_996011, _996009, _996013)))], (11759 ^ _782652) ^ [_996104, _996106, _996108, _996110] : [c_Map_Odom(_996104, _996106, _996108) = hAPP(hAPP(c_Set_Oinsert(_996104), _996110), c_Orderings_Obot__class_Obot(tc_fun(_996104, tc_HOL_Obool))), -(_996108 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_996104, tc_Option_Ooption(_996106)), hAPP(c_COMBK(tc_Option_Ooption(_996106), _996104), c_Option_Ooption_ONone(_996106))), _996110), hAPP(c_Option_Ooption_OSome(_996106), 11762 ^ [_996104, _996106, _996108, _996110])))], (11766 ^ _782652) ^ [_996289, _996291, _996293, _996295] : [11767 ^ _782652 : [(11768 ^ _782652) ^ [_996378] : [_996293 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_996289, tc_Option_Ooption(_996291)), hAPP(c_COMBK(tc_Option_Ooption(_996291), _996289), c_Option_Ooption_ONone(_996291))), _996295), hAPP(c_Option_Ooption_OSome(_996291), _996378))]], -(c_Map_Odom(_996289, _996291, _996293) = hAPP(hAPP(c_Set_Oinsert(_996289), _996295), c_Orderings_Obot__class_Obot(tc_fun(_996289, tc_HOL_Obool))))], (11772 ^ _782652) ^ [_996477, _996479, _996481, _996483, _996485, _996487, _996489] : [c_Big__Operators_Ocomm__monoid__big(_996477, _996479, _996481, _996483, _996485), 11775 ^ _782652 : [(11776 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_996479), _996487)), -(hAPP(hAPP(_996485, _996489), _996487) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_996477, _996479, _996481), _996489), _996483), _996487))], (11782 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_996479), _996487))), -(hAPP(hAPP(_996485, _996489), _996487) = _996483)]]], (11788 ^ _782652) ^ [_996772, _996774, _996776, _996778, _996780, _996782] : [hBOOL(hAPP(hAPP(c_member(_996772), _996774), c_SetInterval_Oord_OgreaterThanAtMost(_996772, _996776, _996778, _996780, _996782))), 11791 ^ _782652 : [(11792 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_996778, _996780), _996774)))], (11794 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_996776, _996774), _996782)))]]], (11796 ^ _782652) ^ [_996925, _996927, _996929, _996931, _996933, _996935] : [-(hBOOL(hAPP(hAPP(c_member(_996925), _996927), c_SetInterval_Oord_OgreaterThanAtMost(_996925, _996929, _996931, _996933, _996935)))), hBOOL(hAPP(hAPP(_996931, _996933), _996927)), hBOOL(hAPP(hAPP(_996929, _996927), _996935))], (11806 ^ _782652) ^ [_997145, _997147, _997149, _997151, _997153, _997155] : [hBOOL(hAPP(hAPP(c_member(_997145), _997147), c_SetInterval_Oord_OatLeastLessThan(_997145, _997149, _997151, _997153, _997155))), 11809 ^ _782652 : [(11810 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_997149, _997153), _997147)))], (11812 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_997151, _997147), _997155)))]]], (11814 ^ _782652) ^ [_997298, _997300, _997302, _997304, _997306, _997308] : [-(hBOOL(hAPP(hAPP(c_member(_997298), _997300), c_SetInterval_Oord_OatLeastLessThan(_997298, _997302, _997304, _997306, _997308)))), hBOOL(hAPP(hAPP(_997302, _997306), _997300)), hBOOL(hAPP(hAPP(_997304, _997300), _997308))], (11824 ^ _782652) ^ [_997515, _997517, _997519, _997521, _997523] : [hBOOL(hAPP(hAPP(c_member(_997515), _997517), c_SetInterval_Oord_OgreaterThanLessThan(_997515, _997519, _997521, _997523))), 11827 ^ _782652 : [(11828 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_997519, _997521), _997517)))], (11830 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_997519, _997517), _997523)))]]], (11832 ^ _782652) ^ [_997664, _997666, _997668, _997670, _997672] : [-(hBOOL(hAPP(hAPP(c_member(_997664), _997666), c_SetInterval_Oord_OgreaterThanLessThan(_997664, _997668, _997670, _997672)))), hBOOL(hAPP(hAPP(_997668, _997670), _997666)), hBOOL(hAPP(hAPP(_997668, _997666), _997672))], (11842 ^ _782652) ^ [_997875, _997877, _997879, _997881, _997883] : [hBOOL(hAPP(hAPP(c_member(_997875), _997877), c_SetInterval_Oord_OatLeastAtMost(_997875, _997879, _997881, _997883))), 11845 ^ _782652 : [(11846 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_997879, _997881), _997877)))], (11848 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_997879, _997877), _997883)))]]], (11850 ^ _782652) ^ [_998024, _998026, _998028, _998030, _998032] : [-(hBOOL(hAPP(hAPP(c_member(_998024), _998026), c_SetInterval_Oord_OatLeastAtMost(_998024, _998028, _998030, _998032)))), hBOOL(hAPP(hAPP(_998028, _998030), _998026)), hBOOL(hAPP(hAPP(_998028, _998026), _998032))], (11860 ^ _782652) ^ [_998232, _998234, _998236, _998238] : [hBOOL(hAPP(hAPP(c_member(_998232), _998234), c_SetInterval_Oord_OgreaterThan(_998232, _998236, _998238))), -(hBOOL(hAPP(hAPP(_998236, _998238), _998234)))], (11866 ^ _782652) ^ [_998341, _998343, _998345, _998347] : [hBOOL(hAPP(hAPP(_998345, _998347), _998343)), -(hBOOL(hAPP(hAPP(c_member(_998341), _998343), c_SetInterval_Oord_OgreaterThan(_998341, _998345, _998347))))], (11872 ^ _782652) ^ [_998477, _998479, _998481, _998483] : [hBOOL(hAPP(hAPP(c_member(_998477), _998479), c_SetInterval_Oord_OlessThan(_998477, _998481, _998483))), -(hBOOL(hAPP(hAPP(_998481, _998479), _998483)))], (11878 ^ _782652) ^ [_998586, _998588, _998590, _998592] : [hBOOL(hAPP(hAPP(_998590, _998588), _998592)), -(hBOOL(hAPP(hAPP(c_member(_998586), _998588), c_SetInterval_Oord_OlessThan(_998586, _998590, _998592))))], (11884 ^ _782652) ^ [_998722, _998724, _998726, _998728] : [hBOOL(hAPP(hAPP(c_member(_998722), _998724), c_SetInterval_Oord_OatLeast(_998722, _998726, _998728))), -(hBOOL(hAPP(hAPP(_998726, _998728), _998724)))], (11890 ^ _782652) ^ [_998831, _998833, _998835, _998837] : [hBOOL(hAPP(hAPP(_998835, _998837), _998833)), -(hBOOL(hAPP(hAPP(c_member(_998831), _998833), c_SetInterval_Oord_OatLeast(_998831, _998835, _998837))))], (11896 ^ _782652) ^ [_998967, _998969, _998971, _998973] : [hBOOL(hAPP(hAPP(c_member(_998967), _998969), c_SetInterval_Oord_OatMost(_998967, _998971, _998973))), -(hBOOL(hAPP(hAPP(_998971, _998969), _998973)))], (11902 ^ _782652) ^ [_999076, _999078, _999080, _999082] : [hBOOL(hAPP(hAPP(_999080, _999078), _999082)), -(hBOOL(hAPP(hAPP(c_member(_999076), _999078), c_SetInterval_Oord_OatMost(_999076, _999080, _999082))))], (11908 ^ _782652) ^ [_999191, _999193, _999195, _999197, _999199, _999201, _999203] : [c_Big__Operators_Ocomm__monoid__big(_999191, _999193, _999195, _999197, _999199), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_999193), _999201))), -(hAPP(hAPP(_999199, _999203), _999201) = _999197)], (11918 ^ _782652) ^ [_999319, _999321, _999323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999319), _999321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999319), _999323)), 11925 ^ _782652 : [(11926 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999321), _999319)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999323), _999319))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999321), _999323)))], (11932 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999321), _999323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999321), _999319)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999323), _999319))))]]], (11938 ^ _782652) ^ [_999672, _999674, _999676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999672), _999674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999676), _999672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999672), _999676)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999674), _999676))))], (11948 ^ _782652) ^ [_999859, _999861] : [11949 ^ _782652 : [(11950 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999859), _999861))], (11952 ^ _782652) ^ [] : [_999859 = _999861]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999859), _999861)))], (11956 ^ _782652) ^ [_999994, _999996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _999994), _999996)), -(_999994 = _999996), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999994), _999996)))], (11966 ^ _782652) ^ [_1000106, _1000108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000106), _1000108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000106), _1000108)))], (11972 ^ _782652) ^ [_1000203, _1000205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000203), _1000205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000203), _1000205)))], (11988 ^ _782652) ^ [_1000421, _1000423] : [11989 ^ _782652 : [(11990 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000421), _1000423))], (11992 ^ _782652) ^ [] : [_1000421 = _1000423]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000421), _1000423)))], (11978 ^ _782652) ^ [_1000315, _1000317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000315), _1000317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000315), _1000317))), -(_1000315 = _1000317)], (11996 ^ _782652) ^ [_1000573, _1000575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000573), _1000575)), 11999 ^ _782652 : [(12000 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000573), _1000575)))], (12002 ^ _782652) ^ [] : [_1000573 = _1000575]]], (12004 ^ _782652) ^ [_1000700, _1000702] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000700), _1000702))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000700), _1000702)), -(_1000700 = _1000702)], (12014 ^ _782652) ^ [_1000854, _1000856, _1000858, _1000860] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1000854), _1000856)), hBOOL(hAPP(hAPP(c_member(_1000854), _1000858), _1000856)), hBOOL(hAPP(hAPP(c_member(_1000854), _1000860), _1000856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1000854), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1000854, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1000854, tc_HOL_Obool)), _1000856), hAPP(hAPP(c_Set_Oinsert(_1000854), _1000858), c_Orderings_Obot__class_Obot(tc_fun(_1000854, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1000854), _1000860), c_Orderings_Obot__class_Obot(tc_fun(_1000854, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1000854), _1000856))))], (12028 ^ _782652) ^ [_1001209, _1001211, _1001213] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001209), _1001211)), _1001213) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001209), _1001213)), _1001211))], (12030 ^ _782652) ^ [_1001260, _1001262, _1001264, _1001266] : [c_Fun_Oinj__on(_1001260, _1001262, _1001264, _1001266), -(hAPP(c_Finite__Set_Ocard(_1001262), hAPP(c_Set_Oimage(_1001260, _1001262, _1001264), _1001266)) = hAPP(c_Finite__Set_Ocard(_1001260), _1001266))], (12036 ^ _782652) ^ [_1001379, _1001381, _1001383] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1001379), _1001381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1001379), _1001381)), hAPP(c_Finite__Set_Ocard(_1001379), hAPP(hAPP(c_Set_Oinsert(_1001379), _1001383), _1001381)))))], (12042 ^ _782652) ^ [_1001512, _1001514, _1001516] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1001512), _1001514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001512, tc_HOL_Obool)), _1001516), _1001514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1001512), _1001514)), hAPP(c_Finite__Set_Ocard(_1001512), _1001516))), -(_1001516 = _1001514)], (12056 ^ _782652) ^ [_1001757, _1001759, _1001761] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1001757), _1001759)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001757, tc_HOL_Obool)), _1001761), _1001759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1001757), _1001761)), hAPP(c_Finite__Set_Ocard(_1001757), _1001759))))], (12066 ^ _782652) ^ [_1001948, _1001950, _1001952, _1001954] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1001948), _1001950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1001952), hAPP(c_Set_Oimage(_1001948, _1001952, _1001954), _1001950))), hAPP(c_Finite__Set_Ocard(_1001948), _1001950))))], (12072 ^ _782652) ^ [_1002081, _1002083, _1002085] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002081), _1002083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002081, tc_HOL_Obool)), _1002083), _1002085)), -(hAPP(c_Finite__Set_Ocard(_1002081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002081, tc_HOL_Obool)), _1002085), _1002083)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1002081), _1002085)), hAPP(c_Finite__Set_Ocard(_1002081), _1002083)))], (12082 ^ _782652) ^ [_1002306, _1002308, _1002310] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1002306, tc_HOL_Obool)), _1002308), _1002310))), -(hAPP(c_Finite__Set_Ocard(_1002306), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002306, tc_HOL_Obool)), _1002308), _1002310)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1002306), _1002308)), hAPP(c_Finite__Set_Ocard(_1002306), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1002306, tc_HOL_Obool)), _1002308), _1002310))))], (12088 ^ _782652) ^ [_1002501, _1002503, _1002505, _1002507] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002501), _1002503)), hAPP(c_Finite__Set_Ocard(_1002505), hAPP(c_Set_Oimage(_1002501, _1002505, _1002507), _1002503)) = hAPP(c_Finite__Set_Ocard(_1002501), _1002503), -(c_Fun_Oinj__on(_1002501, _1002505, _1002507, _1002503))], (12098 ^ _782652) ^ [_1002684, _1002686, _1002688, _1002690] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002684), _1002686)), 12101 ^ _782652 : [(12102 ^ _782652) ^ [] : [c_Fun_Oinj__on(_1002684, _1002688, _1002690, _1002686), -(hAPP(c_Finite__Set_Ocard(_1002688), hAPP(c_Set_Oimage(_1002684, _1002688, _1002690), _1002686)) = hAPP(c_Finite__Set_Ocard(_1002684), _1002686))], (12108 ^ _782652) ^ [] : [hAPP(c_Finite__Set_Ocard(_1002688), hAPP(c_Set_Oimage(_1002684, _1002688, _1002690), _1002686)) = hAPP(c_Finite__Set_Ocard(_1002684), _1002686), -(c_Fun_Oinj__on(_1002684, _1002688, _1002690, _1002686))]]], (12114 ^ _782652) ^ [_1002968, _1002970, _1002972] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002968), _1002970)), -(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(_1002968), _1002972)), hAPP(c_Finite__Set_Ocard(_1002968), _1002970))), hAPP(c_Finite__Set_Ocard(_1002968), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002968, tc_HOL_Obool)), _1002972), _1002970)))))], (12120 ^ _782652) ^ [_1003129, _1003131, _1003133, _1003135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1003129), hAPP(c_Set_Oimage(_1003131, _1003129, _1003133), _1003135))), hAPP(c_Finite__Set_Ocard(_1003131), _1003135))), c_Fun_Oinj__on(_1003131, _1003129, _1003133, _1003135)], (12126 ^ _782652) ^ [_1003259, _1003261, _1003263] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1003259), _1003261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1003259, tc_HOL_Obool)), _1003263), _1003261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1003259), _1003263)), hAPP(c_Finite__Set_Ocard(_1003259), _1003261))))], (12136 ^ _782652) ^ [_1003459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003459), _1003459))], (12148 ^ _782652) ^ [_1003545, _1003547] : [12149 ^ _782652 : [(12150 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003545), _1003547))], (12152 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003547), _1003545))]], _1003545 = _1003547], (12138 ^ _782652) ^ [_1003496, _1003498] : [-(_1003496 = _1003498), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003496), _1003498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003498), _1003496)))], (12156 ^ _782652) ^ [_1003679, _1003681] : [-(_1003679 = _1003681), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003679), _1003681))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003681), _1003679)))], (12166 ^ _782652) ^ [_1003741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003741), _1003741))], (12168 ^ _782652) ^ [_1003769, _1003771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003769), _1003771)), _1003771 = _1003769], (12174 ^ _782652) ^ [_1003857, _1003859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003857), _1003859)), _1003857 = _1003859], (12180 ^ _782652) ^ [_1003945, _1003947, _1003949] : [12181 ^ _782652 : [(12182 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003945), _1003947)))], (12184 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1003949, _1003947), _1003945))]], 12187 ^ _782652 : [(12188 ^ _782652) ^ [] : [-(_1003945 = _1003947)], (12190 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1003949, _1003947), _1003945))]], 12193 ^ _782652 : [(12194 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003947), _1003945)))], (12196 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1003949, _1003947), _1003945))]], -(hBOOL(hAPP(hAPP(_1003949, _1003947), _1003945)))], (12200 ^ _782652) ^ [_1004291, _1004293, _1004295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004291), _1004293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004291), _1004295)), _1004293)))], (12206 ^ _782652) ^ [_1004402, _1004404, _1004406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004402), _1004404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004402), _1004406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004406), _1004404)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004406), _1004402))))], (12216 ^ _782652) ^ [_1004589] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004589), _1004589)))], (12218 ^ _782652) ^ [_1004613, _1004615] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004613), _1004615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004615), _1004613)))], (12224 ^ _782652) ^ [_1004659, _1004661] : [_1004659 = _1004661, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004659), _1004661)))], (12230 ^ _782652) ^ [_1004746, _1004748, _1004750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004746), _1004748)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004748), _1004750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004746), _1004750)))], (12240 ^ _782652) ^ [_1004909, _1004911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004909), _1004911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004911), _1004909)), -(_1004909 = _1004911)], (12250 ^ _782652) ^ [_1005058, _1005060] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005058), _1005060)), _1005058)))], (12252 ^ _782652) ^ [_1005094, _1005096, _1005098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005094), _1005096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005098), _1005096)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005098), _1005094))))], (12258 ^ _782652) ^ [_1005217, _1005219, _1005221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005217), _1005219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005217), _1005221)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005219), _1005221))))], (12264 ^ _782652) ^ [_1005340, 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-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005977), _1005979)))], (12314 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005977), _1005979)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005977), _1005975)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005979), _1005975))))]]], (12320 ^ _782652) ^ [_1006328, _1006330, _1006332, _1006334, _1006336, _1006338] : [c_Fun_Oinj__on(_1006328, _1006330, _1006332, _1006334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1006330, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1006328, _1006330, _1006332), _1006334)), _1006336)), c_Fun_Oinj__on(_1006330, _1006328, _1006338, _1006336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1006328, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1006330, _1006328, _1006338), _1006336)), _1006334)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006328), _1006334)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006330), _1006336)), -(hAPP(c_Finite__Set_Ocard(_1006328), _1006334) = hAPP(c_Finite__Set_Ocard(_1006330), _1006336))], (12346 ^ _782652) ^ [_1006825, _1006827, _1006829] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1006825), _1006827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1006825, tc_HOL_Obool)), _1006829), _1006827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1006825), _1006829)), hAPP(c_Finite__Set_Ocard(_1006825), _1006827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1006825, tc_HOL_Obool)), _1006829), _1006827)))], (12360 ^ _782652) ^ [_1007090, _1007092, _1007094] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007090), _1007092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1007090), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007090, tc_HOL_Obool)), _1007092), hAPP(hAPP(c_Set_Oinsert(_1007090), _1007094), c_Orderings_Obot__class_Obot(tc_fun(_1007090, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1007090), _1007092))))], (12366 ^ _782652) ^ [_1007255, _1007257, _1007259, _1007261] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007255), _1007257)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007259), _1007261)), 12373 ^ _782652 : [(12384 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1007255), _1007257)), hAPP(c_Finite__Set_Ocard(_1007259), _1007261))), 12388 ^ _782652 : [(12389 ^ _782652) ^ [] : [-(c_Fun_Oinj__on(_1007255, _1007259, 12387 ^ [_1007255, _1007257, _1007259, _1007261], _1007257))], (12391 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1007259, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1007255, _1007259, 12387 ^ [_1007255, _1007257, _1007259, _1007261]), _1007257)), _1007261)))]]], (12374 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1007255), _1007257)), hAPP(c_Finite__Set_Ocard(_1007259), _1007261)))), 12375 ^ _782652 : [(12376 ^ _782652) ^ [_1007466] : [c_Fun_Oinj__on(_1007255, _1007259, _1007466, _1007257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1007259, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1007255, _1007259, _1007466), _1007257)), _1007261))]]]]], (12393 ^ _782652) ^ [_1007782, _1007784, _1007786, _1007788, _1007790] : [c_Fun_Oinj__on(_1007782, _1007784, _1007786, _1007788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1007784, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1007782, _1007784, _1007786), _1007788)), _1007790)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007784), _1007790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1007782), _1007788)), hAPP(c_Finite__Set_Ocard(_1007784), _1007790))))], (12407 ^ _782652) ^ [_1008057, _1008059, _1008061] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1008057), _1008059)), hBOOL(hAPP(hAPP(c_member(_1008057), _1008061), _1008059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1008057), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008057, tc_HOL_Obool)), _1008059), hAPP(hAPP(c_Set_Oinsert(_1008057), _1008061), c_Orderings_Obot__class_Obot(tc_fun(_1008057, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1008057), _1008059))))], (12417 ^ _782652) ^ [_1008290, _1008292, _1008294] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1008290), _1008292)), 12420 ^ _782652 : [(12421 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008290), _1008294), _1008292)), -(hAPP(c_Finite__Set_Ocard(_1008290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008290, tc_HOL_Obool)), _1008292), hAPP(hAPP(c_Set_Oinsert(_1008290), _1008294), c_Orderings_Obot__class_Obot(tc_fun(_1008290, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1008290), _1008292)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12427 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008290), _1008294), _1008292))), -(hAPP(c_Finite__Set_Ocard(_1008290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008290, tc_HOL_Obool)), _1008292), hAPP(hAPP(c_Set_Oinsert(_1008290), _1008294), c_Orderings_Obot__class_Obot(tc_fun(_1008290, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1008290), _1008292))]]], (12433 ^ _782652) ^ [_1008654, _1008656, _1008658] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1008654), _1008656)), hBOOL(hAPP(hAPP(c_member(_1008654), _1008658), _1008656)), -(hAPP(c_Finite__Set_Ocard(_1008654), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008654, tc_HOL_Obool)), _1008656), hAPP(hAPP(c_Set_Oinsert(_1008654), _1008658), c_Orderings_Obot__class_Obot(tc_fun(_1008654, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1008654), _1008656)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12443 ^ _782652) ^ [_1008889, _1008891, _1008893, _1008895] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1008889), _1008891)), hBOOL(hAPP(hAPP(c_member(_1008889), _1008893), _1008891)), -(hBOOL(hAPP(hAPP(c_member(_1008889), _1008893), _1008895))), -(hAPP(c_Finite__Set_Ocard(_1008889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008889, tc_HOL_Obool)), _1008891), hAPP(hAPP(c_Set_Oinsert(_1008889), _1008893), _1008895))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1008889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008889, tc_HOL_Obool)), _1008891), _1008895))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12457 ^ _782652) ^ [_1009169, _1009171, _1009173] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1009169), _1009171)), hBOOL(hAPP(hAPP(c_member(_1009169), _1009173), _1009171)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1009169), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009169, tc_HOL_Obool)), _1009171), hAPP(hAPP(c_Set_Oinsert(_1009169), _1009173), c_Orderings_Obot__class_Obot(tc_fun(_1009169, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1009169), _1009171))], (12467 ^ _782652) ^ [_1009398, _1009400, _1009402, _1009404, _1009406] : [class_Groups_Oab__group__add(_1009398), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009400), _1009402)), 12474 ^ _782652 : [(12475 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1009400), _1009404), _1009402)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009400, _1009398), _1009406), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009400, tc_HOL_Obool)), _1009402), hAPP(hAPP(c_Set_Oinsert(_1009400), _1009404), c_Orderings_Obot__class_Obot(tc_fun(_1009400, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1009398), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009400, _1009398), _1009406), _1009402)), hAPP(_1009406, _1009404)))], (12481 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1009400), _1009404), _1009402))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009400, _1009398), _1009406), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009400, tc_HOL_Obool)), _1009402), hAPP(hAPP(c_Set_Oinsert(_1009400), _1009404), c_Orderings_Obot__class_Obot(tc_fun(_1009400, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009400, _1009398), _1009406), _1009402))]]], (12487 ^ _782652) ^ [_1009868, _1009870, _1009872, _1009874, _1009876] : [class_Rings_Oring(_1009868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009870), _1009872)), hBOOL(hAPP(hAPP(c_member(_1009870), _1009874), _1009872)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009870, _1009868), _1009876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009870, tc_HOL_Obool)), _1009872), hAPP(hAPP(c_Set_Oinsert(_1009870), _1009874), c_Orderings_Obot__class_Obot(tc_fun(_1009870, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1009868), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009870, _1009868), _1009876), _1009872)), hAPP(_1009876, _1009874)))], (12501 ^ _782652) ^ [_1010193, _1010195, _1010197, _1010199, _1010201] : [-(c_Map_Orestrict__map(_1010193, _1010195, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1010193, tc_Option_Ooption(_1010195)), _1010197), _1010199), hAPP(c_Option_Ooption_OSome(_1010195), _1010201)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1010193, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1010193), _1010199), c_Orderings_Obot__class_Obot(tc_fun(_1010193, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1010193, _1010195, _1010197, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1010193, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1010193), _1010199), c_Orderings_Obot__class_Obot(tc_fun(_1010193, tc_HOL_Obool))))))], (12503 ^ _782652) ^ [_1010295, _1010297, _1010299, _1010301] : [-(c_Map_Orestrict__map(_1010295, _1010297, _1010299, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1010295, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1010295), _1010301), c_Orderings_Obot__class_Obot(tc_fun(_1010295, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1010295, tc_Option_Ooption(_1010297)), _1010299), _1010301), c_Option_Ooption_ONone(_1010297)))], (12505 ^ _782652) ^ [_1010366, _1010368, _1010370, _1010372, _1010374] : [class_Groups_Oab__semigroup__mult(_1010366), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1010366, _1010366, c_Groups_Otimes__class_Otimes(_1010366), _1010368, _1010370), _1010372)), hBOOL(hAPP(hAPP(c_member(_1010366), _1010374), _1010370)), -(hBOOL(hAPP(hAPP(c_member(_1010366), _1010368), _1010370))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1010366, _1010366, c_Groups_Otimes__class_Otimes(_1010366), _1010374, hAPP(hAPP(c_Set_Oinsert(_1010366), _1010368), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010366, tc_HOL_Obool)), _1010370), hAPP(hAPP(c_Set_Oinsert(_1010366), _1010374), c_Orderings_Obot__class_Obot(tc_fun(_1010366, tc_HOL_Obool)))))), _1010372)))], (12523 ^ _782652) ^ [_1010710, _1010712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1010710), _1010712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1010710)), hAPP(c_Nat_OSuc, _1010712))))], (12529 ^ _782652) ^ [_1010819] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1010819), hAPP(c_Nat_OSuc, _1010819))))], (12531 ^ _782652) ^ [_1010850, _1010852] : [class_Groups_Oordered__ab__group__add(_1010850), -(c_Fun_Oinj__on(_1010850, _1010850, c_Groups_Ouminus__class_Ouminus(_1010850), _1010852))], (12537 ^ _782652) ^ [_1010929, _1010931, _1010933] : [-(hBOOL(hAPP(hAPP(c_member(_1010929), _1010931), _1010933))), -(hBOOL(hAPP(hAPP(c_member(_1010929), _1010931), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1010929, tc_HOL_Obool)), _1010933))))], (12543 ^ _782652) ^ [_1011007, _1011009, _1011011] : [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, _1011007)), _1011009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1011007)), _1011011))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1011009), _1011011)))], (12549 ^ _782652) ^ [_1011138, _1011140, _1011142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1011140), _1011142)), -(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, _1011138)), _1011140)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1011138)), _1011142))))], (12555 ^ _782652) ^ [_1011275] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1011275))], (12557 ^ _782652) ^ [_1011309] : [_1011309 = hAPP(c_Nat_OSuc, _1011309)], (12559 ^ _782652) ^ [_1011344] : [hAPP(c_Nat_OSuc, _1011344) = _1011344], (12561 ^ _782652) ^ [_1011370] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1011370) = _1011370)], (12563 ^ _782652) ^ [_1011411, _1011413] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011411), _1011413), 12566 ^ _782652 : [(12567 ^ _782652) ^ [] : [-(_1011411 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12569 ^ _782652) ^ [] : [-(_1011413 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12571 ^ _782652) ^ [_1011522, _1011524] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011522), _1011524)), _1011522 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1011524 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12581 ^ _782652) ^ [_1011665] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011665), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1011665)], (12583 ^ _782652) ^ [_1011709, _1011711] : [hAPP(c_Nat_OSuc, _1011709) = hAPP(c_Nat_OSuc, _1011711), -(_1011709 = _1011711)], (12589 ^ _782652) ^ [_1011794, _1011796] : [_1011794 = _1011796, -(hAPP(c_Nat_OSuc, _1011794) = hAPP(c_Nat_OSuc, _1011796))], (12595 ^ _782652) ^ [_1011900, _1011902] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011900), _1011902) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12598 ^ _782652 : [(12599 ^ _782652) ^ [] : [-(_1011900 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12601 ^ _782652) ^ [] : [-(_1011902 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12603 ^ _782652) ^ [_1012011, _1012013] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1012011), _1012013) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1012011 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1012013 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12613 ^ _782652) ^ [_1012172, _1012174, _1012176] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012172)), _1012174) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012172)), _1012176), -(_1012174 = _1012176)], (12619 ^ _782652) ^ [_1012283, _1012285, _1012287] : [_1012285 = _1012287, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012283)), _1012285) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012283)), _1012287))], (12625 ^ _782652) ^ [_1012400, _1012402] : [hAPP(c_Nat_OSuc, _1012400) = hAPP(c_Nat_OSuc, _1012402), -(_1012400 = _1012402)], (12631 ^ _782652) ^ [_1012489] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012489)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1012489)], (12633 ^ _782652) ^ [_1012539, _1012541, _1012543] : [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, _1012539)), _1012541)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012539)), _1012543))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1012541), _1012543)))], (12639 ^ _782652) ^ [_1012670, _1012672, _1012674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1012672), _1012674)), -(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, _1012670)), _1012672)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1012670)), _1012674))))], (12645 ^ _782652) ^ [_1012807, _1012809, _1012811, _1012813, _1012815] : [class_Rings_Osemiring__0(_1012807), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012807), _1012809), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012811, _1012807), _1012813), _1012815)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012811, _1012807), hAPP(hAPP(c_COMBB(_1012807, _1012807, _1012811), hAPP(c_Groups_Otimes__class_Otimes(_1012807), _1012809)), _1012813)), _1012815))], (12651 ^ _782652) ^ [_1012970, _1012972, _1012974, _1012976] : [class_Groups_Oab__group__add(_1012970), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012972, _1012970), hAPP(hAPP(c_COMBB(_1012970, _1012970, _1012972), c_Groups_Ouminus__class_Ouminus(_1012970)), _1012974)), _1012976) = hAPP(c_Groups_Ouminus__class_Ouminus(_1012970), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012972, _1012970), _1012974), _1012976)))], (12657 ^ _782652) ^ [_1013119, _1013121, _1013123, _1013125, _1013127, _1013129] : [class_Groups_Ocomm__monoid__add(_1013119), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013121, _1013119), hAPP(hAPP(c_COMBC(_1013121, tc_fun(_1013123, tc_HOL_Obool), _1013119), hAPP(hAPP(c_COMBB(tc_fun(_1013123, _1013119), tc_fun(tc_fun(_1013123, tc_HOL_Obool), _1013119), _1013121), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013123, _1013119)), _1013125)), _1013127)), _1013129) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013123, _1013119), hAPP(hAPP(c_COMBC(_1013123, tc_fun(_1013121, tc_HOL_Obool), _1013119), hAPP(hAPP(c_COMBB(tc_fun(_1013121, _1013119), tc_fun(tc_fun(_1013121, tc_HOL_Obool), _1013119), _1013123), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013121, _1013119)), hAPP(c_COMBC(_1013121, _1013123, _1013119), _1013125))), _1013129)), _1013127))], (12663 ^ _782652) ^ [_1013392, _1013394, _1013396, _1013398, _1013400] : [class_Rings_Osemiring__0(_1013392), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013392), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013394, _1013392), _1013396), _1013398)), _1013400) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013394, _1013392), hAPP(hAPP(c_COMBC(_1013394, _1013392, _1013392), hAPP(hAPP(c_COMBB(_1013392, tc_fun(_1013392, _1013392), _1013394), c_Groups_Otimes__class_Otimes(_1013392)), _1013396)), _1013400)), _1013398))], (12669 ^ _782652) ^ [_1013575, _1013577, _1013579, _1013581, _1013583, _1013585, _1013587] : [class_Rings_Osemiring__0(_1013575), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013575), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013577, _1013575), _1013579), _1013581)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013583, _1013575), _1013585), _1013587)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013577, _1013575), hAPP(hAPP(c_COMBC(_1013577, tc_fun(_1013583, tc_HOL_Obool), _1013575), hAPP(hAPP(c_COMBB(tc_fun(_1013583, _1013575), tc_fun(tc_fun(_1013583, tc_HOL_Obool), _1013575), _1013577), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013583, _1013575)), hAPP(hAPP(c_COMBC(_1013577, tc_fun(_1013583, _1013575), tc_fun(_1013583, _1013575)), hAPP(hAPP(c_COMBB(tc_fun(_1013575, _1013575), tc_fun(tc_fun(_1013583, _1013575), tc_fun(_1013583, _1013575)), _1013577), c_COMBB(_1013575, _1013575, _1013583)), hAPP(hAPP(c_COMBB(_1013575, tc_fun(_1013575, _1013575), _1013577), c_Groups_Otimes__class_Otimes(_1013575)), _1013579))), _1013585))), _1013587)), _1013581))], (12675 ^ _782652) ^ [_1013914, _1013916, _1013918, _1013920] : [class_Groups_Ouminus(_1013914), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1013916, _1013914)), _1013918), _1013920) = hAPP(c_Groups_Ouminus__class_Ouminus(_1013914), hAPP(_1013918, _1013920)))], (12681 ^ _782652) ^ [_1014031, _1014033] : [class_Lattices_Oboolean__algebra(_1014031), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1014031), hAPP(c_Groups_Ouminus__class_Ouminus(_1014031), _1014033)) = _1014033)], (12687 ^ _782652) ^ [_1014126, _1014128] : [class_Lattices_Oab__semigroup__idem__mult(_1014126), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014126), _1014128), _1014128) = _1014128)], (12693 ^ _782652) ^ [_1014217, _1014219] : [class_Lattices_Oab__semigroup__idem__mult(_1014217), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014217), _1014219), _1014219) = _1014219)], (12699 ^ _782652) ^ [_1014308, _1014310, _1014312, _1014314] : [class_Groups_Ouminus(_1014308), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1014310, _1014308)), _1014312), _1014314) = hAPP(c_Groups_Ouminus__class_Ouminus(_1014308), hAPP(_1014312, _1014314)))], (12705 ^ _782652) ^ [_1014425, _1014427, _1014429] : [class_Lattices_Oab__semigroup__idem__mult(_1014425), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014425), _1014427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014425), _1014427), _1014429)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014425), _1014427), _1014429))], (12711 ^ _782652) ^ [_1014550, _1014552, _1014554] : [class_Lattices_Oboolean__algebra(_1014550), 12714 ^ _782652 : [(12715 ^ _782652) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1014550), _1014552) = hAPP(c_Groups_Ouminus__class_Ouminus(_1014550), _1014554), -(_1014552 = _1014554)], (12721 ^ _782652) ^ [] : [_1014552 = _1014554, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1014550), _1014552) = hAPP(c_Groups_Ouminus__class_Ouminus(_1014550), _1014554))]]], (12727 ^ _782652) ^ [_1014791, _1014793] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1014791, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1014791, tc_HOL_Obool)), _1014793)) = _1014793)], (12729 ^ _782652) ^ [_1014850, _1014852, _1014854] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1014850, tc_HOL_Obool)), _1014852) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1014850, tc_HOL_Obool)), _1014854), -(_1014852 = _1014854)], (12735 ^ _782652) ^ [_1014957, _1014959, _1014961] : [_1014959 = _1014961, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1014957, tc_HOL_Obool)), _1014959) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1014957, tc_HOL_Obool)), _1014961))], (12741 ^ _782652) ^ [_1015070, _1015072] : [class_Groups_Ogroup__add(_1015070), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1015070), hAPP(c_Groups_Ouminus__class_Ouminus(_1015070), _1015072)) = _1015072)], (12747 ^ _782652) ^ [_1015165, _1015167] : [class_Groups_Omonoid__mult(_1015165), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015165), c_Groups_Oone__class_Oone(_1015165)), _1015167) = _1015167)], (12753 ^ _782652) ^ [_1015260, _1015262] : [class_Groups_Ocomm__monoid__mult(_1015260), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015260), c_Groups_Oone__class_Oone(_1015260)), _1015262) = _1015262)], (12759 ^ _782652) ^ [_1015355, _1015357] : [class_Groups_Oone(_1015355), 12762 ^ _782652 : [(12763 ^ _782652) ^ [] : [c_Groups_Oone__class_Oone(_1015355) = _1015357, -(_1015357 = c_Groups_Oone__class_Oone(_1015355))], (12769 ^ _782652) ^ [] : [_1015357 = c_Groups_Oone__class_Oone(_1015355), -(c_Groups_Oone__class_Oone(_1015355) = _1015357)]]], (12775 ^ _782652) ^ [_1015572, _1015574] : [class_Groups_Omonoid__mult(_1015572), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015572), _1015574), c_Groups_Oone__class_Oone(_1015572)) = _1015574)], (12781 ^ _782652) ^ [_1015667, _1015669] : [class_Groups_Ocomm__monoid__mult(_1015667), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015667), _1015669), c_Groups_Oone__class_Oone(_1015667)) = _1015669)], (12787 ^ _782652) ^ [_1015762, _1015764, _1015766] : [class_Groups_Ogroup__add(_1015762), 12790 ^ _782652 : [(12791 ^ _782652) ^ [] : [_1015764 = hAPP(c_Groups_Ouminus__class_Ouminus(_1015762), _1015766), -(_1015766 = hAPP(c_Groups_Ouminus__class_Ouminus(_1015762), _1015764))], (12797 ^ _782652) ^ [] : [_1015766 = hAPP(c_Groups_Ouminus__class_Ouminus(_1015762), _1015764), -(_1015764 = hAPP(c_Groups_Ouminus__class_Ouminus(_1015762), _1015766))]]], (12803 ^ _782652) ^ [_1016003, _1016005, _1016007] : [class_Groups_Ogroup__add(_1016003), 12806 ^ _782652 : [(12807 ^ _782652) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1016003), _1016005) = _1016007, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1016003), _1016007) = _1016005)], (12813 ^ _782652) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1016003), _1016007) = _1016005, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1016003), _1016005) = _1016007)]]], (12819 ^ _782652) ^ [_1016244, _1016246, _1016248] : [class_Groups_Ogroup__add(_1016244), 12822 ^ _782652 : [(12823 ^ _782652) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1016244), _1016246) = hAPP(c_Groups_Ouminus__class_Ouminus(_1016244), _1016248), -(_1016246 = _1016248)], (12829 ^ _782652) ^ [] : [_1016246 = _1016248, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1016244), _1016246) = hAPP(c_Groups_Ouminus__class_Ouminus(_1016244), _1016248))]]], (12835 ^ _782652) ^ [_1016485, _1016487, _1016489, _1016491] : [class_Groups_Oab__semigroup__mult(_1016485), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016485), _1016487), _1016489)), _1016491) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016485), _1016487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016485), _1016489), _1016491)))], (12841 ^ _782652) ^ [_1016628, _1016630] : [-(hAPP(c_Finite__Set_Ocard(_1016628), _1016630) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1016628, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1016628), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1016630))], (12843 ^ _782652) ^ [_1016673, _1016675, _1016677] : [class_Groups_Oordered__ab__group__add(_1016673), 12846 ^ _782652 : [(12847 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016673), _1016675), hAPP(c_Groups_Ouminus__class_Ouminus(_1016673), _1016677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016673), _1016677), hAPP(c_Groups_Ouminus__class_Ouminus(_1016673), _1016675))))], (12853 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016673), _1016677), hAPP(c_Groups_Ouminus__class_Ouminus(_1016673), _1016675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016673), _1016675), hAPP(c_Groups_Ouminus__class_Ouminus(_1016673), _1016677))))]]], (12859 ^ _782652) ^ [_1016956, _1016958, _1016960] : [class_Groups_Oordered__ab__group__add(_1016956), 12862 ^ _782652 : [(12863 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016956), hAPP(c_Groups_Ouminus__class_Ouminus(_1016956), _1016958)), _1016960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016956), hAPP(c_Groups_Ouminus__class_Ouminus(_1016956), _1016960)), _1016958)))], (12869 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016956), hAPP(c_Groups_Ouminus__class_Ouminus(_1016956), _1016960)), _1016958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016956), hAPP(c_Groups_Ouminus__class_Ouminus(_1016956), _1016958)), _1016960)))]]], (12875 ^ _782652) ^ [_1017239, _1017241, _1017243] : [class_Groups_Oordered__ab__group__add(_1017239), 12878 ^ _782652 : [(12879 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017239), hAPP(c_Groups_Ouminus__class_Ouminus(_1017239), _1017241)), hAPP(c_Groups_Ouminus__class_Ouminus(_1017239), _1017243))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017239), _1017243), _1017241)))], (12885 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017239), _1017243), _1017241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017239), hAPP(c_Groups_Ouminus__class_Ouminus(_1017239), _1017241)), hAPP(c_Groups_Ouminus__class_Ouminus(_1017239), _1017243))))]]], (12891 ^ _782652) ^ [_1017522, _1017524, _1017526] : [class_Groups_Oordered__ab__group__add(_1017522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017522), _1017524), _1017526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017522), hAPP(c_Groups_Ouminus__class_Ouminus(_1017522), _1017526)), hAPP(c_Groups_Ouminus__class_Ouminus(_1017522), _1017524))))], (12901 ^ _782652) ^ [_1017701, _1017703, _1017705] : [class_Lattices_Oboolean__algebra(_1017701), 12904 ^ _782652 : [(12905 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017701), hAPP(c_Groups_Ouminus__class_Ouminus(_1017701), _1017703)), hAPP(c_Groups_Ouminus__class_Ouminus(_1017701), _1017705))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017701), _1017705), _1017703)))], (12911 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017701), _1017705), _1017703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017701), hAPP(c_Groups_Ouminus__class_Ouminus(_1017701), _1017703)), hAPP(c_Groups_Ouminus__class_Ouminus(_1017701), _1017705))))]]], (12917 ^ _782652) ^ [_1017984, _1017986, _1017988] : [class_Lattices_Oboolean__algebra(_1017984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017984), _1017986), _1017988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017984), hAPP(c_Groups_Ouminus__class_Ouminus(_1017984), _1017988)), hAPP(c_Groups_Ouminus__class_Ouminus(_1017984), _1017986))))], (12927 ^ _782652) ^ [_1018163, _1018165, _1018167] : [class_Groups_Oordered__ab__group__add(_1018163), 12930 ^ _782652 : [(12931 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018163), hAPP(c_Groups_Ouminus__class_Ouminus(_1018163), _1018165)), hAPP(c_Groups_Ouminus__class_Ouminus(_1018163), _1018167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018163), _1018167), _1018165)))], (12937 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018163), _1018167), _1018165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018163), hAPP(c_Groups_Ouminus__class_Ouminus(_1018163), _1018165)), hAPP(c_Groups_Ouminus__class_Ouminus(_1018163), _1018167))))]]], (12943 ^ _782652) ^ [_1018446, _1018448, _1018450] : [class_Groups_Oordered__ab__group__add(_1018446), 12946 ^ _782652 : [(12947 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018446), hAPP(c_Groups_Ouminus__class_Ouminus(_1018446), _1018448)), _1018450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018446), hAPP(c_Groups_Ouminus__class_Ouminus(_1018446), _1018450)), _1018448)))], (12953 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018446), hAPP(c_Groups_Ouminus__class_Ouminus(_1018446), _1018450)), _1018448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018446), hAPP(c_Groups_Ouminus__class_Ouminus(_1018446), _1018448)), _1018450)))]]], (12959 ^ _782652) ^ [_1018729, _1018731, _1018733] : [class_Groups_Oordered__ab__group__add(_1018729), 12962 ^ _782652 : [(12963 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018729), _1018731), hAPP(c_Groups_Ouminus__class_Ouminus(_1018729), _1018733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018729), _1018733), hAPP(c_Groups_Ouminus__class_Ouminus(_1018729), _1018731))))], (12969 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018729), _1018733), hAPP(c_Groups_Ouminus__class_Ouminus(_1018729), _1018731))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018729), _1018731), hAPP(c_Groups_Ouminus__class_Ouminus(_1018729), _1018733))))]]], (12975 ^ _782652) ^ [_1019030, _1019032, _1019034] : [hBOOL(hAPP(hAPP(c_member(_1019030), _1019032), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019030, tc_HOL_Obool)), _1019034))), hBOOL(hAPP(hAPP(c_member(_1019030), _1019032), _1019034))], (12981 ^ _782652) ^ [_1019148, _1019150, _1019152] : [-(hBOOL(hAPP(hAPP(c_member(_1019148), _1019150), _1019152))), -(hBOOL(hAPP(hAPP(c_member(_1019148), _1019150), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019148, tc_HOL_Obool)), _1019152))))], (12987 ^ _782652) ^ [_1019210, _1019212, _1019214] : [hBOOL(hAPP(hAPP(c_member(_1019210), _1019212), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019210, tc_HOL_Obool)), _1019214))), hBOOL(hAPP(hAPP(c_member(_1019210), _1019212), _1019214))], (12993 ^ _782652) ^ [_1019334, _1019336, _1019338] : [hBOOL(hAPP(hAPP(c_member(_1019334), _1019336), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019334, tc_HOL_Obool)), _1019338))), hBOOL(hAPP(hAPP(c_member(_1019334), _1019336), _1019338))], (12999 ^ _782652) ^ [_1019458, _1019460, _1019462] : [class_Groups_Oab__group__add(_1019458), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1019458), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019458), _1019460), _1019462)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1019458), _1019462), _1019460))], (13005 ^ _782652) ^ [_1019595, _1019597, _1019599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019595, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019595, tc_HOL_Obool)), _1019597)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019595, tc_HOL_Obool)), _1019599))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019595, tc_HOL_Obool)), _1019599), _1019597)))], (13011 ^ _782652) ^ [_1019742, _1019744, _1019746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019742, tc_HOL_Obool)), _1019746), _1019744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019742, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019742, tc_HOL_Obool)), _1019744)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019742, tc_HOL_Obool)), _1019746))))], (13017 ^ _782652) ^ [_1019895, _1019897, _1019899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019895, tc_HOL_Obool)), _1019897), _1019899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019895, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019895, tc_HOL_Obool)), _1019899)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019895, tc_HOL_Obool)), _1019897))))], (13023 ^ _782652) ^ [_1020055, _1020057] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020055), _1020057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020057), hAPP(c_Nat_OSuc, _1020055))))], (13029 ^ _782652) ^ [_1020100, _1020102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020102), hAPP(c_Nat_OSuc, _1020100))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020100), _1020102))], (13045 ^ _782652) ^ [_1020333, _1020335] : [13046 ^ _782652 : [(13047 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020333), _1020335))], (13049 ^ _782652) ^ [] : [_1020333 = _1020335]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020333), hAPP(c_Nat_OSuc, _1020335))))], (13035 ^ _782652) ^ [_1020221, _1020223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020221), hAPP(c_Nat_OSuc, _1020223))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020221), _1020223))), -(_1020221 = _1020223)], (13053 ^ _782652) ^ [_1020491, _1020493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1020491)), hAPP(c_Nat_OSuc, _1020493))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020491), _1020493)))], (13059 ^ _782652) ^ [_1020596, _1020598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020596), _1020598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1020596)), hAPP(c_Nat_OSuc, _1020598))))], (13065 ^ _782652) ^ [_1020706, _1020708] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020706), _1020708))), 13068 ^ _782652 : [(13069 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020706), hAPP(c_Nat_OSuc, _1020708))), -(_1020706 = _1020708)], (13075 ^ _782652) ^ [] : [_1020706 = _1020708, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020706), hAPP(c_Nat_OSuc, _1020708))))]]], (13081 ^ _782652) ^ [_1020939, _1020941] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020939), _1020941))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1020939), hAPP(c_Nat_OSuc, _1020941))), -(_1020941 = _1020939)], (13091 ^ _782652) ^ [_1021087, _1021089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021087), _1021089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021087), hAPP(c_Nat_OSuc, _1021089))))], (13097 ^ _782652) ^ [_1021190, _1021192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021190), _1021192)), -(hAPP(c_Nat_OSuc, _1021190) = _1021192), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1021190)), _1021192)))], (13107 ^ _782652) ^ [_1021314, _1021316, _1021318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021314), _1021316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021316), _1021318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1021314)), _1021318)))], (13117 ^ _782652) ^ [_1021483, _1021485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021483), hAPP(c_Nat_OSuc, _1021485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021483), _1021485))), -(_1021483 = _1021485)], (13127 ^ _782652) ^ [_1021601, _1021603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1021601)), _1021603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021601), _1021603)))], (13133 ^ _782652) ^ [_1021704, _1021706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1021704)), hAPP(c_Nat_OSuc, _1021706))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1021704), _1021706)))], (13139 ^ _782652) ^ [_1021822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1021822)), _1021822))], (13141 ^ _782652) ^ [_1021862, _1021864] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1021862), _1021864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1021864)), _1021862)))], (13147 ^ _782652) ^ [_1021907, _1021909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1021909)), _1021907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1021907), _1021909))], (13163 ^ _782652) ^ [_1022146, _1022148] : [13164 ^ _782652 : [(13165 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022146), _1022148))], (13167 ^ _782652) ^ [] : [_1022146 = hAPP(c_Nat_OSuc, _1022148)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022146), hAPP(c_Nat_OSuc, _1022148))))], (13153 ^ _782652) ^ [_1022028, _1022030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022028), hAPP(c_Nat_OSuc, _1022030))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022028), _1022030))), -(_1022028 = hAPP(c_Nat_OSuc, _1022030))], (13171 ^ _782652) ^ [_1022310, _1022312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1022310)), hAPP(c_Nat_OSuc, _1022312))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022310), _1022312)))], (13177 ^ _782652) ^ [_1022415, _1022417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022415), _1022417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1022415)), hAPP(c_Nat_OSuc, _1022417))))], (13183 ^ _782652) ^ [_1022526, _1022528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022526), _1022528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022526), hAPP(c_Nat_OSuc, _1022528))))], (13189 ^ _782652) ^ [_1022629, _1022631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022629), hAPP(c_Nat_OSuc, _1022631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022629), _1022631))), -(_1022629 = hAPP(c_Nat_OSuc, _1022631))], (13199 ^ _782652) ^ [_1022753, _1022755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1022753)), _1022755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022753), _1022755)))], (13205 ^ _782652) ^ [_1022856, _1022858, _1022860] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1022856)), _1022858)), hAPP(c_Nat_OSuc, _1022860)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1022856), _1022858)), _1022860))], (13207 ^ _782652) ^ [_1022913, _1022915] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1022913)), hAPP(c_Nat_OSuc, _1022915)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1022913), _1022915))], (13209 ^ _782652) ^ [_1022956, _1022958, _1022960, _1022962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022956), _1022958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1022960), _1022962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022956), _1022960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022958), _1022962))))], (13219 ^ _782652) ^ [_1023147, _1023149, _1023151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1023147), _1023149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023151), _1023147)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023151), _1023149))))], (13225 ^ _782652) ^ [_1023270, _1023272, _1023274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1023270), _1023272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023270), _1023274)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023272), _1023274))))], (13231 ^ _782652) ^ [_1023393] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1023393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023393), _1023393)))))], (13233 ^ _782652) ^ [_1023433] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1023433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023433), _1023433))))], (13235 ^ _782652) ^ [_1023467, _1023469, _1023471] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1023467), _1023469)), _1023471) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023467), _1023471)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023469), _1023471)))], (13237 ^ _782652) ^ [_1023524, _1023526, _1023528] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023524), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1023526), _1023528)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023524), _1023526)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1023524), _1023528)))], (13239 ^ _782652) ^ [_1023581, _1023583, _1023585, _1023587, _1023589] : [class_Groups_Ocomm__monoid__mult(_1023581), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023583), _1023585)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023581, _1023583, c_Groups_Otimes__class_Otimes(_1023581)), hAPP(hAPP(c_COMBS(_1023583, _1023581, _1023581), hAPP(hAPP(c_COMBB(_1023581, tc_fun(_1023581, _1023581), _1023583), c_Groups_Otimes__class_Otimes(_1023581)), _1023587)), _1023589)), c_Groups_Oone__class_Oone(_1023581)), _1023585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1023581), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023581, _1023583, c_Groups_Otimes__class_Otimes(_1023581)), _1023587), c_Groups_Oone__class_Oone(_1023581)), _1023585)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023581, _1023583, c_Groups_Otimes__class_Otimes(_1023581)), _1023589), c_Groups_Oone__class_Oone(_1023581)), _1023585)))], (13249 ^ _782652) ^ [_1023896, _1023898, _1023900, _1023902, _1023904] : [class_Groups_Oab__group__add(_1023896), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1023898, _1023896), hAPP(hAPP(c_COMBS(_1023898, _1023896, _1023896), hAPP(hAPP(c_COMBB(_1023896, tc_fun(_1023896, _1023896), _1023898), c_Groups_Ominus__class_Ominus(_1023896)), _1023900)), _1023902)), _1023904) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1023896), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1023898, _1023896), _1023900), _1023904)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1023898, _1023896), _1023902), _1023904)))], (13255 ^ _782652) ^ [_1024097] : [class_Lattices_Oab__semigroup__idem__mult(_1024097), -(c_Finite__Set_Ofun__left__comm__idem(_1024097, _1024097, c_Groups_Otimes__class_Otimes(_1024097)))], (13261 ^ _782652) ^ [_1024176, _1024178] : [-(hAPP(c_Set_OCollect(_1024176), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1024176), c_fNot), _1024178)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1024176, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1024176), _1024178)))], (13263 ^ _782652) ^ [_1024229, _1024231] : [class_Lattices_Oboolean__algebra(_1024229), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1024229), hAPP(c_Groups_Ouminus__class_Ouminus(_1024229), _1024231)), _1024231) = c_Orderings_Obot__class_Obot(_1024229))], (13269 ^ _782652) ^ [_1024334, _1024336] : [class_Lattices_Oboolean__algebra(_1024334), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1024334), _1024336), hAPP(c_Groups_Ouminus__class_Ouminus(_1024334), _1024336)) = c_Orderings_Obot__class_Obot(_1024334))], (13275 ^ _782652) ^ [_1024439, _1024441, _1024443] : [class_Lattices_Oboolean__algebra(_1024439), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1024439), _1024441), _1024443) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1024439), _1024441), hAPP(c_Groups_Ouminus__class_Ouminus(_1024439), _1024443)))], (13281 ^ _782652) ^ [_1024558, _1024560, _1024562] : [class_Lattices_Oboolean__algebra(_1024558), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1024558), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1024558), _1024560), _1024562)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1024558), hAPP(c_Groups_Ouminus__class_Ouminus(_1024558), _1024560)), hAPP(c_Groups_Ouminus__class_Ouminus(_1024558), _1024562)))], (13287 ^ _782652) ^ [_1024697, _1024699, _1024701] : [class_Lattices_Oboolean__algebra(_1024697), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1024697), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1024697), _1024699), _1024701)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1024697), hAPP(c_Groups_Ouminus__class_Ouminus(_1024697), _1024699)), hAPP(c_Groups_Ouminus__class_Ouminus(_1024697), _1024701)))], (13293 ^ _782652) ^ [_1024836, _1024838, _1024840, _1024842, _1024844] : [class_Groups_Ocomm__monoid__mult(_1024836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024838), _1024840)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024838), _1024842)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024836), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1024836, _1024838, c_Groups_Otimes__class_Otimes(_1024836)), _1024844), c_Groups_Oone__class_Oone(_1024836)), _1024840)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1024836, _1024838, c_Groups_Otimes__class_Otimes(_1024836)), _1024844), c_Groups_Oone__class_Oone(_1024836)), _1024842)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024836), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1024836, _1024838, c_Groups_Otimes__class_Otimes(_1024836)), _1024844), c_Groups_Oone__class_Oone(_1024836)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1024838, tc_HOL_Obool)), _1024840), _1024842))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1024836, _1024838, c_Groups_Otimes__class_Otimes(_1024836)), _1024844), c_Groups_Oone__class_Oone(_1024836)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024838, tc_HOL_Obool)), _1024840), _1024842))))], (13307 ^ _782652) ^ [_1025276, _1025278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025276, tc_HOL_Obool)), _1025278), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025276, tc_HOL_Obool)), _1025278))), -(_1025278 = c_Orderings_Obot__class_Obot(tc_fun(_1025276, tc_HOL_Obool)))], (13313 ^ _782652) ^ [_1025395, _1025397] : [_1025397 = c_Orderings_Obot__class_Obot(tc_fun(_1025395, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025395, tc_HOL_Obool)), _1025397), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025395, tc_HOL_Obool)), _1025397))))], (13319 ^ _782652) ^ [_1025520, _1025522] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1025520, tc_HOL_Obool)), _1025522), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025520, tc_HOL_Obool)), _1025522)) = c_Orderings_Obot__class_Obot(tc_fun(_1025520, tc_HOL_Obool)))], (13321 ^ _782652) ^ [_1025569, _1025571] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1025569, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025569, tc_HOL_Obool)), _1025571)), _1025571) = c_Orderings_Obot__class_Obot(tc_fun(_1025569, tc_HOL_Obool)))], (13323 ^ _782652) ^ [_1025618, _1025620, _1025622] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025618, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1025618, tc_HOL_Obool)), _1025620), _1025622)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025618, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025618, tc_HOL_Obool)), _1025620)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025618, tc_HOL_Obool)), _1025622)))], (13325 ^ _782652) ^ [_1025691, _1025693, _1025695] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025691, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025691, tc_HOL_Obool)), _1025693), _1025695)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1025691, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025691, tc_HOL_Obool)), _1025693)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025691, tc_HOL_Obool)), _1025695)))], (13327 ^ _782652) ^ [_1025764, _1025766, _1025768] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025764, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025764, tc_HOL_Obool)), _1025766), _1025768)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025764, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025764, tc_HOL_Obool)), _1025766)), _1025768))], (13329 ^ _782652) ^ [_1025829, _1025831, _1025833] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025829, tc_HOL_Obool)), _1025831), _1025833) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1025829, tc_HOL_Obool)), _1025831), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025829, tc_HOL_Obool)), _1025833)))], (13331 ^ _782652) ^ [_1025886, _1025888, _1025890] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025886, tc_HOL_Obool)), _1025888), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1025886, tc_HOL_Obool)), _1025890)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1025886, tc_HOL_Obool)), _1025888), _1025890))], (13333 ^ _782652) ^ [_1025943, _1025945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1025943)), _1025945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1025943), _1025945)))], (13339 ^ _782652) ^ [_1026046, _1026048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026046), _1026048)), 13342 ^ _782652 : [(13343 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026048), hAPP(c_Nat_OSuc, _1026046))), -(_1026048 = _1026046)], (13349 ^ _782652) ^ [] : [_1026048 = _1026046, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026048), hAPP(c_Nat_OSuc, _1026046))))]]], (13355 ^ _782652) ^ [_1026287, _1026289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026287), _1026289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026287)), _1026289)))], (13361 ^ _782652) ^ [_1026390, _1026392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026390), _1026392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026390), hAPP(c_Nat_OSuc, _1026392))))], (13367 ^ _782652) ^ [_1026508, _1026510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026508)), _1026510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026508), _1026510)))], (13373 ^ _782652) ^ [_1026607, _1026609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026607), _1026609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026607)), _1026609)))], (13379 ^ _782652) ^ [_1026727, _1026729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026727), hAPP(c_Nat_OSuc, _1026729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026727), _1026729)))], (13385 ^ _782652) ^ [_1026826, _1026828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026826), _1026828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026826), hAPP(c_Nat_OSuc, _1026828))))], (13391 ^ _782652) ^ [_1026946, _1026948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026946), _1026948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1026946)), _1026948)))], (13397 ^ _782652) ^ [_1027045, _1027047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027045)), _1027047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027045), _1027047)))], (13403 ^ _782652) ^ [_1027150, _1027152] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027150), _1027152)), hAPP(c_Nat_OSuc, _1027150))))], (13405 ^ _782652) ^ [_1027189, _1027191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027189), _1027191)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027191)), _1027189) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027191), _1027189)))], (13411 ^ _782652) ^ [_1027312, _1027314] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1027312, tc_HOL_Obool)), _1027314) = hAPP(c_Set_OCollect(_1027312), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1027312), c_fNot), hAPP(hAPP(c_COMBC(_1027312, tc_fun(_1027312, tc_HOL_Obool), tc_HOL_Obool), c_member(_1027312)), _1027314))))], (13413 ^ _782652) ^ [_1027375, _1027377, _1027379] : [-(hAPP(c_Set_OCollect(_1027375), hAPP(hAPP(c_COMBS(_1027375, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1027375), c_fimplies), _1027377)), _1027379)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027375, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1027375, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1027375), _1027377))), hAPP(c_Set_OCollect(_1027375), _1027379)))], (13415 ^ _782652) ^ [_1027456] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027456) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1027456)))], (13417 ^ _782652) ^ [_1027488, _1027490, _1027492, _1027494, _1027496] : [class_Groups_Ocomm__monoid__mult(_1027488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027490), _1027492)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027490), _1027494)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1027490, tc_HOL_Obool)), _1027492), _1027494) = c_Orderings_Obot__class_Obot(tc_fun(_1027490, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1027488, _1027490, c_Groups_Otimes__class_Otimes(_1027488)), _1027496), c_Groups_Oone__class_Oone(_1027488)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027490, tc_HOL_Obool)), _1027492), _1027494)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1027488), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1027488, _1027490, c_Groups_Otimes__class_Otimes(_1027488)), _1027496), c_Groups_Oone__class_Oone(_1027488)), _1027492)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1027488, _1027490, c_Groups_Otimes__class_Otimes(_1027488)), _1027496), c_Groups_Oone__class_Oone(_1027488)), _1027494)))], (13435 ^ _782652) ^ [_1027949, _1027951, _1027953] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1027949, tc_HOL_Obool)), _1027951), _1027953) = c_Orderings_Obot__class_Obot(tc_fun(_1027949, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027949, tc_HOL_Obool)), _1027951), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1027949, tc_HOL_Obool)), _1027953))))], (13441 ^ _782652) ^ [_1028092, _1028094, _1028096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028092, tc_HOL_Obool)), _1028094), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1028092, tc_HOL_Obool)), _1028096))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1028092, tc_HOL_Obool)), _1028094), _1028096) = c_Orderings_Obot__class_Obot(tc_fun(_1028092, tc_HOL_Obool)))], (13447 ^ _782652) ^ [_1028241, _1028243, _1028245, _1028247, _1028249, _1028251, _1028253] : [class_Groups_Ocomm__monoid__add(_1028241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028243), _1028245)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028247), _1028249)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028243, _1028241), hAPP(hAPP(c_COMBS(_1028243, tc_fun(_1028247, tc_HOL_Obool), _1028241), hAPP(hAPP(c_COMBB(tc_fun(_1028247, _1028241), tc_fun(tc_fun(_1028247, tc_HOL_Obool), _1028241), _1028243), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028247, _1028241)), _1028251)), hAPP(hAPP(c_COMBB(tc_fun(_1028247, tc_HOL_Obool), tc_fun(_1028247, tc_HOL_Obool), _1028243), c_Set_OCollect(_1028247)), hAPP(hAPP(c_COMBB(tc_fun(_1028247, tc_HOL_Obool), tc_fun(_1028247, tc_HOL_Obool), _1028243), hAPP(c_COMBS(_1028247, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1028247), c_fconj), hAPP(hAPP(c_COMBC(_1028247, tc_fun(_1028247, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028247)), _1028249)))), _1028253)))), _1028245) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028247, _1028241), hAPP(hAPP(c_COMBS(_1028247, tc_fun(_1028243, tc_HOL_Obool), _1028241), hAPP(hAPP(c_COMBB(tc_fun(_1028243, _1028241), tc_fun(tc_fun(_1028243, tc_HOL_Obool), _1028241), _1028247), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1028243, _1028241)), hAPP(c_COMBC(_1028243, _1028247, _1028241), _1028251))), hAPP(hAPP(c_COMBB(tc_fun(_1028243, tc_HOL_Obool), tc_fun(_1028243, tc_HOL_Obool), _1028247), c_Set_OCollect(_1028243)), hAPP(hAPP(c_COMBB(tc_fun(_1028243, tc_HOL_Obool), tc_fun(_1028243, tc_HOL_Obool), _1028247), hAPP(c_COMBS(_1028243, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1028243), c_fconj), hAPP(hAPP(c_COMBC(_1028243, tc_fun(_1028243, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028243)), _1028245)))), hAPP(c_COMBC(_1028243, _1028247, tc_HOL_Obool), _1028253))))), _1028249))], (13461 ^ _782652) ^ [_1028934, _1028936, _1028938, _1028940, _1028942] : [class_Groups_Oab__semigroup__mult(_1028934), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1028934, _1028934, c_Groups_Otimes__class_Otimes(_1028934), _1028936, _1028938), _1028940)), -(hBOOL(hAPP(hAPP(c_member(_1028934), _1028936), _1028938))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1028934, _1028934, c_Groups_Otimes__class_Otimes(_1028934), _1028942, hAPP(hAPP(c_Set_Oinsert(_1028934), _1028936), _1028938)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028934), _1028942), _1028940))))], (13475 ^ _782652) ^ [_1029174, _1029176, _1029178, _1029180, _1029182] : [class_Groups_Oab__group__add(_1029174), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029176), _1029178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1029176, tc_HOL_Obool)), _1029180), _1029178)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029176, _1029174), _1029182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1029176, tc_HOL_Obool)), _1029178), _1029180)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1029174), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029176, _1029174), _1029182), _1029178)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029176, _1029174), _1029182), _1029180)))], (13489 ^ _782652) ^ [_1029491, _1029493, _1029495, _1029497] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1029491), _1029493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1029491, tc_HOL_Obool)), _1029493), _1029495)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029491, tc_Nat_Onat), _1029497), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1029491, tc_HOL_Obool)), _1029495), _1029493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029491, tc_Nat_Onat), _1029497), _1029495)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029491, tc_Nat_Onat), _1029497), _1029493)))], (13499 ^ _782652) ^ [_1029744, _1029746, _1029748, _1029750, _1029752, _1029754] : [class_Groups_Ocomm__monoid__add(_1029744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029746), _1029748)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029746, _1029744), _1029750), _1029748) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029752, _1029744), hAPP(hAPP(c_COMBB(tc_fun(_1029746, tc_HOL_Obool), _1029744, _1029752), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1029746, _1029744), _1029750)), hAPP(hAPP(c_COMBB(tc_fun(_1029746, tc_HOL_Obool), tc_fun(_1029746, tc_HOL_Obool), _1029752), c_Set_OCollect(_1029746)), hAPP(hAPP(c_COMBB(tc_fun(_1029746, tc_HOL_Obool), tc_fun(_1029746, tc_HOL_Obool), _1029752), hAPP(c_COMBS(_1029746, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1029746), c_fconj), hAPP(hAPP(c_COMBC(_1029746, tc_fun(_1029746, tc_HOL_Obool), tc_HOL_Obool), c_member(_1029746)), _1029748)))), hAPP(c_COMBC(_1029746, _1029752, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1029752, tc_fun(_1029752, tc_HOL_Obool), _1029746), c_fequal), _1029754)))))), hAPP(c_Set_Oimage(_1029746, _1029752, _1029754), _1029748)))], (13509 ^ _782652) ^ [_1030155, _1030157, _1030159] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1030155), _1030157)), 13512 ^ _782652 : [(13513 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1030155), _1030159), _1030157)), -(hAPP(c_Finite__Set_Ocard(_1030155), hAPP(hAPP(c_Set_Oinsert(_1030155), _1030159), _1030157)) = hAPP(c_Finite__Set_Ocard(_1030155), _1030157))], (13519 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1030155), _1030159), _1030157))), -(hAPP(c_Finite__Set_Ocard(_1030155), hAPP(hAPP(c_Set_Oinsert(_1030155), _1030159), _1030157)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1030155), _1030157)))]]], (13525 ^ _782652) ^ [_1030449, _1030451, _1030453] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1030449), _1030451)), -(hBOOL(hAPP(hAPP(c_member(_1030449), _1030453), _1030451))), -(hAPP(c_Finite__Set_Ocard(_1030449), hAPP(hAPP(c_Set_Oinsert(_1030449), _1030453), _1030451)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1030449), _1030451)))], (13535 ^ _782652) ^ [_1030607, _1030609, _1030611, _1030613, _1030615, _1030617] : [class_Groups_Oab__semigroup__mult(_1030607), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030609), _1030611)), -(hBOOL(hAPP(hAPP(c_member(_1030609), _1030613), _1030611))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030607, _1030609, c_Groups_Otimes__class_Otimes(_1030607)), _1030615), _1030617), hAPP(hAPP(c_Set_Oinsert(_1030609), _1030613), _1030611)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030607), hAPP(_1030615, _1030613)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1030607, _1030609, c_Groups_Otimes__class_Otimes(_1030607)), _1030615), _1030617), _1030611)))], (13549 ^ _782652) ^ [_1030900, _1030902, _1030904, _1030906] : [hBOOL(hAPP(hAPP(c_member(_1030900), _1030902), _1030904)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1030900, tc_Nat_Onat), _1030906), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1030900, tc_HOL_Obool)), _1030904), hAPP(hAPP(c_Set_Oinsert(_1030900), _1030902), c_Orderings_Obot__class_Obot(tc_fun(_1030900, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1030900, tc_Nat_Onat), _1030906), _1030904)), hAPP(_1030906, _1030902)))], (13555 ^ _782652) ^ [_1031091, _1031093, _1031095, _1031097] : [-(hBOOL(hAPP(hAPP(c_member(_1031091), _1031093), _1031095))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1031091, tc_Nat_Onat), _1031097), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031091, tc_HOL_Obool)), _1031095), hAPP(hAPP(c_Set_Oinsert(_1031091), _1031093), c_Orderings_Obot__class_Obot(tc_fun(_1031091, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1031091, tc_Nat_Onat), _1031097), _1031095))], (13561 ^ _782652) ^ [_1031182, _1031184, _1031186] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031182), _1031184)), -(hAPP(c_Finite__Set_Ocard(_1031182), hAPP(hAPP(c_Set_Oinsert(_1031182), _1031186), _1031184)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1031182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031182, tc_HOL_Obool)), _1031184), hAPP(hAPP(c_Set_Oinsert(_1031182), _1031186), c_Orderings_Obot__class_Obot(tc_fun(_1031182, tc_HOL_Obool)))))))], (13567 ^ _782652) ^ [_1031359, _1031361] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031359), hAPP(c_Nat_OSuc, _1031361)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031359), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1031361))], (13569 ^ _782652) ^ [_1031405, _1031407] : [class_Rings_Oring__1__no__zero__divisors(_1031405), 13572 ^ _782652 : [(13583 ^ _782652) ^ [] : [13584 ^ _782652 : [(13585 ^ _782652) ^ [] : [_1031407 = c_Groups_Oone__class_Oone(_1031405)], (13587 ^ _782652) ^ [] : [_1031407 = hAPP(c_Groups_Ouminus__class_Ouminus(_1031405), c_Groups_Oone__class_Oone(_1031405))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031405), _1031407), _1031407) = c_Groups_Oone__class_Oone(_1031405))], (13573 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031405), _1031407), _1031407) = c_Groups_Oone__class_Oone(_1031405), -(_1031407 = c_Groups_Oone__class_Oone(_1031405)), -(_1031407 = hAPP(c_Groups_Ouminus__class_Ouminus(_1031405), c_Groups_Oone__class_Oone(_1031405)))]]], (13591 ^ _782652) ^ [_1031712, _1031714] : [class_Rings_Ocomm__ring__1(_1031712), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1031712), _1031714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031712), hAPP(c_Groups_Ouminus__class_Ouminus(_1031712), c_Groups_Oone__class_Oone(_1031712))), _1031714))], (13597 ^ _782652) ^ [_1031827, _1031829, _1031831] : [class_Rings_Olinordered__semidom(_1031827), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031827), c_Groups_Oone__class_Oone(_1031827)), _1031829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031827), c_Groups_Oone__class_Oone(_1031827)), _1031831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031827), c_Groups_Oone__class_Oone(_1031827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031827), _1031829), _1031831))))], (13611 ^ _782652) ^ [_1032106, _1032108, _1032110, _1032112, _1032114] : [c_Hoare__Mirabelle_Otriple__valid(_1032106, _1032108, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1032106), _1032110), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1032112))), _1032114)), -(c_Hoare__Mirabelle_Otriple__valid(_1032106, hAPP(c_Nat_OSuc, _1032108), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1032106), _1032110), hAPP(c_Com_Ocom_OBODY, _1032112)), _1032114)))], (13617 ^ _782652) ^ [_1032257, _1032259, _1032261, _1032263, _1032265] : [c_Hoare__Mirabelle_Otriple__valid(_1032257, hAPP(c_Nat_OSuc, _1032259), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1032257), _1032261), hAPP(c_Com_Ocom_OBODY, _1032263)), _1032265)), -(c_Hoare__Mirabelle_Otriple__valid(_1032257, _1032259, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1032257), _1032261), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1032263))), _1032265)))], (13623 ^ _782652) ^ [_1032414, _1032416, _1032418, _1032420, _1032422] : [class_Groups_Ocomm__monoid__mult(_1032414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032416), _1032418)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032416), _1032420)), 13637 ^ _782652 : [(13638 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1032416), 13636 ^ [_1032414, _1032416, _1032418, _1032420, _1032422]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1032416, tc_HOL_Obool)), _1032418), _1032420))))], (13640 ^ _782652) ^ [] : [hAPP(_1032422, 13636 ^ [_1032414, _1032416, _1032418, _1032420, _1032422]) = c_Groups_Oone__class_Oone(_1032414)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1032414, _1032416, c_Groups_Otimes__class_Otimes(_1032414)), _1032422), c_Groups_Oone__class_Oone(_1032414)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1032416, tc_HOL_Obool)), _1032418), _1032420)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032414), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1032414, _1032416, c_Groups_Otimes__class_Otimes(_1032414)), _1032422), c_Groups_Oone__class_Oone(_1032414)), _1032418)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1032414, _1032416, c_Groups_Otimes__class_Otimes(_1032414)), _1032422), c_Groups_Oone__class_Oone(_1032414)), _1032420)))], (13644 ^ _782652) ^ [_1032957, _1032959, _1032961] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032957), _1032959)), hBOOL(hAPP(hAPP(c_member(_1032957), _1032961), _1032959)), -(hAPP(c_Finite__Set_Ocard(_1032957), _1032959) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1032957), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1032957, tc_HOL_Obool)), _1032959), hAPP(hAPP(c_Set_Oinsert(_1032957), _1032961), c_Orderings_Obot__class_Obot(tc_fun(_1032957, tc_HOL_Obool)))))))], (13654 ^ _782652) ^ [_1033186, _1033188, _1033190] : [class_Rings_Oidom(_1033186), 13657 ^ _782652 : [(13668 ^ _782652) ^ [] : [13669 ^ _782652 : [(13670 ^ _782652) ^ [] : [_1033188 = _1033190], (13672 ^ _782652) ^ [] : [_1033188 = hAPP(c_Groups_Ouminus__class_Ouminus(_1033186), _1033190)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033186), _1033188), _1033188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033186), _1033190), _1033190))], (13658 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033186), _1033188), _1033188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033186), _1033190), _1033190), -(_1033188 = _1033190), -(_1033188 = hAPP(c_Groups_Ouminus__class_Ouminus(_1033186), _1033190))]]], (13676 ^ _782652) ^ [_1033505, _1033507] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033505), _1033507) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033507), _1033505))], (13678 ^ _782652) ^ [_1033542, _1033544, _1033546] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033542), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1033544), _1033546)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033542), _1033544)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033542), _1033546)))], (13680 ^ _782652) ^ [_1033599, _1033601, _1033603] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033599), _1033601)), _1033603) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033601), _1033603)))], (13682 ^ _782652) ^ [_1033650, _1033652, _1033654] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1033650), _1033652)), _1033654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033650), _1033654)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033652), _1033654)))], (13684 ^ _782652) ^ [_1033707, _1033709, _1033711, _1033713, _1033715] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1033707), 13687 ^ _782652 : [(13698 ^ _782652) ^ [] : [13699 ^ _782652 : [(13700 ^ _782652) ^ [] : [_1033709 = _1033713], (13702 ^ _782652) ^ [] : [_1033711 = _1033715]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033709), _1033711)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033713), _1033715)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033709), _1033715)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033713), _1033711)))], (13688 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033709), _1033711)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033713), _1033715)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033707), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033709), _1033715)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033707), _1033713), _1033711)), -(_1033709 = _1033713), -(_1033711 = _1033715)]]], (13706 ^ _782652) ^ [_1034119, _1034121, _1034123, _1034125, _1034127] : [class_Rings_Osemiring(_1034119), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034119), _1034121), _1034123)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034119), _1034125), _1034123)), _1034127)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034119), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034119), _1034121), _1034125)), _1034123)), _1034127))], (13712 ^ _782652) ^ [_1034312, _1034314, _1034316, _1034318] : [class_Rings_Ocomm__semiring__1(_1034312), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034312), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034312), _1034314), _1034316)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034312), _1034318), _1034316)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034312), _1034314), _1034318)), _1034316))], (13718 ^ _782652) ^ [_1034471, _1034473, _1034475, _1034477] : [class_Rings_Ocomm__semiring__1(_1034471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034471), _1034473), _1034475)), _1034477) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034471), _1034473), _1034477)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034471), _1034475), _1034477)))], (13724 ^ _782652) ^ [_1034630, _1034632, _1034634, _1034636] : [class_Rings_Ocomm__semiring(_1034630), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034630), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034630), _1034632), _1034634)), _1034636) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034630), _1034632), _1034636)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034630), _1034634), _1034636)))], (13730 ^ _782652) ^ [_1034789, _1034791, _1034793, _1034795, _1034797] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1034789), 13733 ^ _782652 : [(13744 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034789), _1034791), _1034795)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034789), _1034793), _1034797)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034789), _1034791), _1034797)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034789), _1034793), _1034795))), 13747 ^ _782652 : [(13748 ^ _782652) ^ [] : [_1034791 = _1034793], (13750 ^ _782652) ^ [] : [_1034795 = _1034797]]], (13734 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034789), _1034791), _1034795)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034789), _1034793), _1034797)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034789), _1034791), _1034797)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034789), _1034793), _1034795)), -(_1034791 = _1034793), -(_1034795 = _1034797)]]], (13752 ^ _782652) ^ [_1035207, _1035209, _1035211, _1035213] : [class_Rings_Ocomm__semiring__1(_1035207), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035207), _1035209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035207), _1035211), _1035213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035207), _1035209), _1035211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035207), _1035209), _1035213)))], (13758 ^ _782652) ^ [_1035366, _1035368, _1035370, _1035372] : [class_Groups_Ocancel__semigroup__add(_1035366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035366), _1035368), _1035370) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035366), _1035372), _1035370), -(_1035368 = _1035372)], (13768 ^ _782652) ^ [_1035533, _1035535, _1035537, _1035539] : [class_Groups_Ocancel__ab__semigroup__add(_1035533), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035533), _1035535), _1035537) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035533), _1035535), _1035539), -(_1035537 = _1035539)], (13778 ^ _782652) ^ [_1035700, _1035702, _1035704, _1035706] : [class_Groups_Ocancel__semigroup__add(_1035700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035700), _1035702), _1035704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035700), _1035702), _1035706), -(_1035704 = _1035706)], (13788 ^ _782652) ^ [_1035867, _1035869, _1035871, _1035873] : [class_Groups_Ocancel__semigroup__add(_1035867), 13791 ^ _782652 : [(13792 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035867), _1035869), _1035871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035867), _1035873), _1035871), -(_1035869 = _1035873)], (13798 ^ _782652) ^ [] : [_1035869 = _1035873, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035867), _1035869), _1035871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035867), _1035873), _1035871))]]], (13804 ^ _782652) ^ [_1036132, _1036134, _1036136, _1036138] : [class_Groups_Ocancel__semigroup__add(_1036132), 13807 ^ _782652 : [(13808 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036132), _1036134), _1036136) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036132), _1036134), _1036138), -(_1036136 = _1036138)], (13814 ^ _782652) ^ [] : [_1036136 = _1036138, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036132), _1036134), _1036136) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036132), _1036134), _1036138))]]], (13820 ^ _782652) ^ [_1036397, _1036399, _1036401, _1036403] : [class_Groups_Oab__semigroup__add(_1036397), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036397), _1036399), _1036401)), _1036403) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036397), _1036399), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036397), _1036401), _1036403)))], (13826 ^ _782652) ^ [_1036540, _1036542, _1036544] : [class_Rings_Ocomm__semiring__1(_1036540), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036540), _1036542), _1036544) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036540), _1036544), _1036542))], (13832 ^ _782652) ^ [_1036649, _1036651, _1036653, _1036655] : [class_Rings_Ocomm__semiring__1(_1036649), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036649), _1036651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036649), _1036653), _1036655)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036649), _1036653), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036649), _1036651), _1036655)))], (13838 ^ _782652) ^ [_1036792, _1036794, _1036796, _1036798] : [class_Rings_Ocomm__semiring__1(_1036792), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036792), _1036794), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036792), _1036796), _1036798)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036792), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036792), _1036794), _1036796)), _1036798))], (13844 ^ _782652) ^ [_1036935, _1036937, _1036939, _1036941] : [class_Rings_Ocomm__semiring__1(_1036935), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036935), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036935), _1036937), _1036939)), _1036941) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036935), _1036937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036935), _1036939), _1036941)))], (13850 ^ _782652) ^ [_1037078, _1037080, _1037082, _1037084] : [class_Rings_Ocomm__semiring__1(_1037078), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037078), _1037080), _1037082)), _1037084) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037078), _1037080), _1037084)), _1037082))], (13856 ^ _782652) ^ [_1037221, _1037223, _1037225, _1037227, _1037229] : [class_Rings_Ocomm__semiring__1(_1037221), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037221), _1037223), _1037225)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037221), _1037227), _1037229)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037221), _1037223), _1037227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037221), _1037225), _1037229)))], (13862 ^ _782652) ^ [_1037416, _1037418, _1037420] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037416), _1037418) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037420), _1037418), -(_1037416 = _1037420)], (13868 ^ _782652) ^ [_1037515, _1037517, _1037519] : [_1037515 = _1037519, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037515), _1037517) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037519), _1037517))], (13874 ^ _782652) ^ [_1037638, _1037640, _1037642] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037638), _1037640) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037638), _1037642), -(_1037640 = _1037642)], (13880 ^ _782652) ^ [_1037737, _1037739, _1037741] : [_1037739 = _1037741, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037737), _1037739) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037737), _1037741))], (13886 ^ _782652) ^ [_1037842, _1037844, _1037846] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037842), _1037844)), _1037846) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037842), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037844), _1037846)))], (13888 ^ _782652) ^ [_1037893, _1037895, _1037897] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037893), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037895), _1037897)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037895), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037893), _1037897)))], (13890 ^ _782652) ^ [_1037944, _1037946] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037944), _1037946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037946), _1037944))], (13892 ^ _782652) ^ [_1037981, _1037983] : [-(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)), _1037981), _1037983))], (13894 ^ _782652) ^ [_1038011, _1038013, _1038015, _1038017] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1038011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038011), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038011), _1038013), _1038015)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038011), _1038013), _1038017))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038011), _1038015), _1038017)))], (13904 ^ _782652) ^ [_1038206, _1038208, _1038210, _1038212] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1038206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038206), _1038208), _1038210)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038206), _1038212), _1038210))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038206), _1038208), _1038212)))], (13914 ^ _782652) ^ [_1038401, _1038403, _1038405, _1038407, _1038409] : [class_Groups_Oordered__ab__semigroup__add(_1038401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038401), _1038403), _1038405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038401), _1038407), _1038409)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038401), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038401), _1038403), _1038407)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038401), _1038405), _1038409))))], (13928 ^ _782652) ^ [_1038672, _1038674, _1038676, _1038678] : [class_Groups_Oordered__ab__semigroup__add(_1038672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038672), _1038674), _1038676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038672), _1038678), _1038674)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038672), _1038678), _1038676))))], (13938 ^ _782652) ^ [_1038867, _1038869, _1038871, _1038873] : [class_Groups_Oordered__ab__semigroup__add(_1038867), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038867), _1038869), _1038871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038867), _1038869), _1038873)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1038867), _1038871), _1038873))))], (13948 ^ _782652) ^ [_1039062, _1039064, _1039066, _1039068] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1039062), 13951 ^ _782652 : [(13952 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039062), _1039064), _1039066)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039062), _1039064), _1039068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039062), _1039066), _1039068)))], (13958 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039062), _1039066), _1039068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039062), _1039064), _1039066)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039062), _1039064), _1039068))))]]], (13964 ^ _782652) ^ [_1039369, _1039371, _1039373, _1039375] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1039369), 13967 ^ _782652 : [(13968 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039369), _1039371), _1039373)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039369), _1039375), _1039373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039369), _1039371), _1039375)))], (13974 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039369), _1039371), _1039375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039369), _1039371), _1039373)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039369), _1039375), _1039373))))]]], (13980 ^ _782652) ^ [_1039676, _1039678, _1039680, _1039682] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1039676), 13983 ^ _782652 : [(13984 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039676), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039676), _1039678), _1039680)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039676), _1039682), _1039680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039676), _1039678), _1039682)))], (13990 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039676), _1039678), _1039682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039676), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039676), _1039678), _1039680)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039676), _1039682), _1039680))))]]], (13996 ^ _782652) ^ [_1039983, _1039985, _1039987, _1039989] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1039983), 13999 ^ _782652 : [(14000 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039983), _1039985), _1039987)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039983), _1039985), _1039989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039983), _1039987), _1039989)))], (14006 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039983), _1039987), _1039989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039983), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039983), _1039985), _1039987)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1039983), _1039985), _1039989))))]]], (14012 ^ _782652) ^ [_1040290, _1040292, _1040294, _1040296] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1040290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040290), _1040292), _1040294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040290), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040290), _1040292), _1040296)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040290), _1040294), _1040296))))], (14022 ^ _782652) ^ [_1040485, _1040487, _1040489, _1040491] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1040485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040485), _1040487), _1040489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040485), _1040491), _1040487)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040485), _1040491), _1040489))))], (14032 ^ _782652) ^ [_1040680, _1040682, _1040684, _1040686, _1040688] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1040680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040680), _1040682), _1040684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040680), _1040686), _1040688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040680), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040680), _1040682), _1040686)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040680), _1040684), _1040688))))], (14046 ^ _782652) ^ [_1040951, _1040953, _1040955, _1040957] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1040951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040951), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040951), _1040953), _1040955)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040951), _1040957), _1040955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040951), _1040953), _1040957)))], (14056 ^ _782652) ^ [_1041146, _1041148, _1041150, _1041152] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1041146), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041146), _1041148), _1041150)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041146), _1041148), _1041152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041146), _1041150), _1041152)))], (14066 ^ _782652) ^ [_1041341, _1041343, _1041345] : [class_Groups_Ogroup__add(_1041341), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041341), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041341), _1041343), _1041345)), _1041345) = _1041343)], (14072 ^ _782652) ^ [_1041450, _1041452, _1041454] : [class_Groups_Ogroup__add(_1041450), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041450), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041450), _1041452), _1041454)), _1041454) = _1041452)], (14078 ^ _782652) ^ [_1041559, _1041561, _1041563] : [class_Groups_Ogroup__add(_1041559), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041559), hAPP(c_Groups_Ouminus__class_Ouminus(_1041559), _1041561)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041559), _1041561), _1041563)) = _1041563)], (14084 ^ _782652) ^ [_1041678, _1041680, _1041682] : [class_Groups_Ogroup__add(_1041678), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041678), _1041680), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041678), hAPP(c_Groups_Ouminus__class_Ouminus(_1041678), _1041680)), _1041682)) = _1041682)], (14090 ^ _782652) ^ [_1041797, _1041799, _1041801] : [class_Groups_Ogroup__add(_1041797), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1041797), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041797), _1041799), _1041801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041797), hAPP(c_Groups_Ouminus__class_Ouminus(_1041797), _1041801)), hAPP(c_Groups_Ouminus__class_Ouminus(_1041797), _1041799)))], (14096 ^ _782652) ^ [_1041936, _1041938, _1041940] : [class_Groups_Oab__group__add(_1041936), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1041936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041936), _1041938), _1041940)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041936), hAPP(c_Groups_Ouminus__class_Ouminus(_1041936), _1041938)), hAPP(c_Groups_Ouminus__class_Ouminus(_1041936), _1041940)))], (14102 ^ _782652) ^ [_1042075, _1042077] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1042075)), _1042077) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042075), _1042077)))], (14104 ^ _782652) ^ [_1042121, _1042123] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1042121)), _1042123) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042121), hAPP(c_Nat_OSuc, _1042123)))], (14106 ^ _782652) ^ [_1042164, _1042166] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1042164)), _1042166) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042164), _1042166)))], (14108 ^ _782652) ^ [_1042207, _1042209] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042207), hAPP(c_Nat_OSuc, _1042209)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1042207), _1042209)))], (14110 ^ _782652) ^ [_1042253, _1042255] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042253), hAPP(c_Nat_OSuc, _1042255)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042253), _1042255)))], (14112 ^ _782652) ^ [_1042296, _1042298, _1042300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042296), _1042298)), _1042300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042296), _1042300)))], (14118 ^ _782652) ^ [_1042407, _1042409, _1042411, _1042413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042407), _1042409)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042411), _1042409) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042407), _1042413), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042411), _1042413)))], (14128 ^ _782652) ^ [_1042588, _1042590, _1042592, _1042594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042588), _1042590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042592), _1042594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042588), _1042592)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042590), _1042594))))], (14138 ^ _782652) ^ [_1042779, _1042781, _1042783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042779), _1042781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042779), _1042783)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042781), _1042783))))], (14144 ^ _782652) ^ [_1042902, _1042904, _1042906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042902), _1042904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1042902), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042906), _1042904))))], (14150 ^ _782652) ^ [_1043013, _1043015, _1043017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043013), _1043015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043015), _1043017))))], (14156 ^ _782652) ^ [_1043124, _1043126, _1043128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043124), _1043126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043124), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043128), _1043126))))], (14162 ^ _782652) ^ [_1043235, _1043237, _1043239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043235), _1043237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043235), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043237), _1043239))))], (14168 ^ _782652) ^ [_1043364, _1043366, _1043368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043364), _1043366)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043364), _1043368))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043366), _1043368)))], (14174 ^ _782652) ^ [_1043483, _1043485, _1043487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1043485), _1043487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043483), _1043485)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043483), _1043487))))], (14180 ^ _782652) ^ [_1043620, _1043622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043620), _1043622)), _1043622))], (14182 ^ _782652) ^ [_1043668, _1043670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043668), _1043670)), _1043668))], (14184 ^ _782652) ^ [_1043704, _1043706] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043704), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043706), _1043704))))], (14186 ^ _782652) ^ [_1043740, _1043742] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043740), _1043742))))], (14188 ^ _782652) ^ [_1043791, _1043793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043791), _1043793)), -(_1043793 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043791), 14191 ^ [_1043791, _1043793]))], (14195 ^ _782652) ^ [_1043898, _1043900] : [14196 ^ _782652 : [(14197 ^ _782652) ^ [_1043948] : [_1043900 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043898), _1043948)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043898), _1043900)))], (14201 ^ _782652) ^ [_1044030, _1044032, _1044034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044030), _1044032)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044030), _1044034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044032), _1044034)))], (14207 ^ _782652) ^ [_1044149, _1044151, _1044153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044151), _1044153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044149), _1044151)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044149), _1044153))))], (14213 ^ _782652) ^ [_1044274, _1044276, _1044278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044274), _1044276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044274), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044276), _1044278))))], (14219 ^ _782652) ^ [_1044385, _1044387, _1044389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044385), _1044387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044389), _1044387))))], (14225 ^ _782652) ^ [_1044496, _1044498, _1044500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044496), _1044498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044498), _1044500))))], (14231 ^ _782652) ^ [_1044607, _1044609, _1044611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044607), _1044609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044611), _1044609))))], (14237 ^ _782652) ^ [_1044718, _1044720, _1044722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044718), _1044720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044718), _1044722)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044720), _1044722))))], (14243 ^ _782652) ^ [_1044841, _1044843, _1044845, _1044847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044841), _1044843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1044845), _1044847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044841), _1044845)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1044843), _1044847))))], (14253 ^ _782652) ^ [_1045032, _1045034, _1045036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045032), _1045034)), _1045036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045034), _1045036)))], (14259 ^ _782652) ^ [_1045143, _1045145, _1045147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045143), _1045145)), _1045147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045143), _1045147)))], (14265 ^ _782652) ^ [_1045254, _1045256, _1045258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045254), _1045256)), _1045258)), 14268 ^ _782652 : [(14269 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045254), _1045258)))], (14271 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045256), _1045258)))]]], (14273 ^ _782652) ^ [_1045405, _1045407] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045405), _1045407)), _1045407) = _1045405)], (14275 ^ _782652) ^ [_1045442, _1045444] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045442), _1045444)), _1045442) = _1045444)], (14277 ^ _782652) ^ [_1045479, _1045481, _1045483] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045479), _1045481)), _1045483) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045479), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045481), _1045483)))], (14279 ^ _782652) ^ [_1045530, _1045532, _1045534] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045530), _1045532)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045530), _1045534)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045532), _1045534))], (14281 ^ _782652) ^ [_1045581, _1045583, _1045585] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045581), _1045583)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1045585), _1045583)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1045581), _1045585))], (14283 ^ _782652) ^ [_1045632, _1045634] : [class_Rings_Olinordered__semidom(_1045632), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045632), _1045634), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045632), _1045634), c_Groups_Oone__class_Oone(_1045632)))))], (14289 ^ _782652) ^ [_1045741, _1045743, _1045745, _1045747, _1045749, _1045751] : [class_Rings_Oring(_1045741), 14292 ^ _782652 : [(14293 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045741), _1045743), _1045745)), _1045747) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045741), _1045749), _1045745)), _1045751), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045741), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045741), _1045743), _1045749)), _1045745)), _1045747) = _1045751)], (14299 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045741), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045741), _1045743), _1045749)), _1045745)), _1045747) = _1045751, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045741), _1045743), _1045745)), _1045747) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045741), _1045749), _1045745)), _1045751))]]], (14305 ^ _782652) ^ [_1046138, _1046140, _1046142, _1046144, _1046146, _1046148] : [class_Rings_Oring(_1046138), 14308 ^ _782652 : [(14309 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046138), _1046140), _1046142)), _1046144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046138), _1046146), _1046142)), _1046148), -(_1046144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046138), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046138), _1046146), _1046140)), _1046142)), _1046148))], (14315 ^ _782652) ^ [] : [_1046144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046138), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046138), _1046146), _1046140)), _1046142)), _1046148), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046138), _1046140), _1046142)), _1046144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046138), _1046146), _1046142)), _1046148))]]], (14321 ^ _782652) ^ [_1046535, _1046537] : [class_Rings_Ocomm__semiring__1(_1046535), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046535), _1046537), _1046537) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046535), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046535), c_Groups_Oone__class_Oone(_1046535)), c_Groups_Oone__class_Oone(_1046535))), _1046537))], (14327 ^ _782652) ^ [_1046666, _1046668, _1046670] : [class_Rings_Ocomm__semiring__1(_1046666), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046666), _1046668), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046666), _1046670), _1046668)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046666), _1046670), c_Groups_Oone__class_Oone(_1046666))), _1046668))], (14333 ^ _782652) ^ [_1046811, _1046813, _1046815] : [class_Rings_Ocomm__semiring__1(_1046811), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046811), _1046813), _1046815)), _1046815) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046811), _1046813), c_Groups_Oone__class_Oone(_1046811))), _1046815))], (14339 ^ _782652) ^ [_1046956, _1046958, _1046960] : [class_Rings_Ocomm__ring__1(_1046956), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1046956), _1046958), _1046960) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046956), _1046958), hAPP(c_Groups_Ouminus__class_Ouminus(_1046956), _1046960)))], (14345 ^ _782652) ^ [_1047075] : [-(hAPP(c_Nat_OSuc, _1047075) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1047075))], (14347 ^ _782652) ^ [_1047104] : [-(hAPP(c_Nat_OSuc, _1047104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047104), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (14349 ^ _782652) ^ [_1047136, _1047138, _1047140, _1047142, _1047144] : [class_Groups_Ocomm__monoid__add(_1047136), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047138, _1047136), hAPP(hAPP(c_COMBS(_1047138, _1047136, _1047136), hAPP(hAPP(c_COMBB(_1047136, tc_fun(_1047136, _1047136), _1047138), c_Groups_Oplus__class_Oplus(_1047136)), _1047140)), _1047142)), _1047144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047136), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047138, _1047136), _1047140), _1047144)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1047138, _1047136), _1047142), _1047144)))], (14355 ^ _782652) ^ [_1047337, _1047339, _1047341, _1047343, _1047345] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1047337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047337), _1047339), _1047341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047337), _1047343), _1047345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047337), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047337), _1047339), _1047343)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047337), _1047341), _1047345))))], (14369 ^ _782652) ^ [_1047608, _1047610, _1047612, _1047614, _1047616] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1047608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047608), _1047610), _1047612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047608), _1047614), _1047616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047608), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047608), _1047610), _1047614)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047608), _1047612), _1047616))))], (14383 ^ _782652) ^ [_1047879, _1047881, _1047883, _1047885, _1047887, _1047889] : [class_Rings_Oordered__ring(_1047879), 14386 ^ _782652 : [(14387 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047879), _1047881), _1047883)), _1047885)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047879), _1047887), _1047883)), _1047889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047879), _1047885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047879), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047879), _1047887), _1047881)), _1047883)), _1047889))))], (14393 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047879), _1047885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047879), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1047879), _1047887), _1047881)), _1047883)), _1047889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047879), _1047881), _1047883)), _1047885)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047879), _1047887), _1047883)), _1047889))))]]], (14399 ^ _782652) ^ [_1048318, _1048320, _1048322, _1048324, _1048326, _1048328] : [class_Rings_Oordered__ring(_1048318), 14402 ^ _782652 : [(14403 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048318), _1048320), _1048322)), _1048324)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048318), _1048326), _1048322)), _1048328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048318), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048318), _1048320), _1048326)), _1048322)), _1048324)), _1048328)))], (14409 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048318), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048318), _1048320), _1048326)), _1048322)), _1048324)), _1048328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1048318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048318), _1048320), _1048322)), _1048324)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048318), _1048326), _1048322)), _1048328))))]]], (14415 ^ _782652) ^ [_1048757, _1048759, _1048761, _1048763, _1048765, _1048767] : [class_Rings_Oordered__ring(_1048757), 14418 ^ _782652 : [(14419 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048757), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048757), _1048759), _1048761)), _1048763)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048757), _1048765), _1048761)), _1048767))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048757), _1048763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048757), _1048765), _1048759)), _1048761)), _1048767))))], (14425 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048757), _1048763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1048757), _1048765), _1048759)), _1048761)), _1048767))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1048757), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048757), _1048759), _1048761)), _1048763)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048757), _1048765), _1048761)), _1048767))))]]], (14431 ^ _782652) ^ [_1049196, _1049198, _1049200, _1049202, _1049204, _1049206] : [class_Rings_Oordered__ring(_1049196), 14434 ^ _782652 : [(14435 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049196), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049196), _1049198), _1049200)), _1049202)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049196), _1049204), _1049200)), _1049206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049196), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049196), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049196), _1049198), _1049204)), _1049200)), _1049202)), _1049206)))], (14441 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049196), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049196), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049196), _1049198), _1049204)), _1049200)), _1049202)), _1049206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049196), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049196), _1049198), _1049200)), _1049202)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1049196), _1049204), _1049200)), _1049206))))]]], (14447 ^ _782652) ^ [_1049635, _1049637, _1049639] : [class_Groups_Ogroup__add(_1049635), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049635), _1049637), _1049639) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049635), _1049637), hAPP(c_Groups_Ouminus__class_Ouminus(_1049635), _1049639)))], (14453 ^ _782652) ^ [_1049754, _1049756, _1049758] : [class_Groups_Oab__group__add(_1049754), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049754), _1049756), _1049758) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049754), _1049756), hAPP(c_Groups_Ouminus__class_Ouminus(_1049754), _1049758)))], (14459 ^ _782652) ^ [_1049873, _1049875, _1049877] : [class_Groups_Ogroup__add(_1049873), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049873), _1049875), hAPP(c_Groups_Ouminus__class_Ouminus(_1049873), _1049877)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1049873), _1049875), _1049877))], (14465 ^ _782652) ^ [_1049992, _1049994, _1049996] : [c_Hoare__Mirabelle_Otriple__valid(_1049992, hAPP(c_Nat_OSuc, _1049994), _1049996), -(c_Hoare__Mirabelle_Otriple__valid(_1049992, _1049994, _1049996))], (14471 ^ _782652) ^ [_1050081, _1050083] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050081), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050081), _1050083)))))], (14473 ^ _782652) ^ [_1050120, _1050122] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050120), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050122), _1050120)))))], (14475 ^ _782652) ^ [_1050174, _1050176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050174), _1050176)), -(_1050176 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050174), 14478 ^ [_1050174, _1050176])))], (14482 ^ _782652) ^ [_1050287, _1050289] : [14483 ^ _782652 : [(14484 ^ _782652) ^ [_1050340] : [_1050289 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050287), _1050340))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050287), _1050289)))], (14488 ^ _782652) ^ [_1050403, _1050405] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050403), _1050405))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050405), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050403), _1050405)) = _1050403)], (14494 ^ _782652) ^ [_1050474, _1050476, _1050478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050476), _1050478))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050474), _1050478)), _1050476)))], (14500 ^ _782652) ^ [_1050593, _1050595, _1050597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050593), _1050597)), _1050595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050593), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050595), _1050597))))], (14506 ^ _782652) ^ [_1050718, _1050720, _1050722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050718), _1050720)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050722), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050720), _1050718)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050722), _1050718)), _1050720))], (14512 ^ _782652) ^ [_1050873, _1050875, _1050877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050873), _1050875)), _1050877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050873), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050877), _1050875))))], (14518 ^ _782652) ^ [_1050992, _1050994, _1050996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050992), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050996), _1050994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050992), _1050994)), _1050996)))], (14524 ^ _782652) ^ [_1051117, _1051119, _1051121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051117), _1051119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051121), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051119), _1051121)), _1051117))))], (14530 ^ _782652) ^ [_1051240, _1051242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051240), _1051242)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051240), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051242), _1051240)) = _1051242)], (14536 ^ _782652) ^ [_1051351, _1051353, _1051355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051351), _1051353)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051355), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051353), _1051351)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051355), _1051353)), _1051351))], (14542 ^ _782652) ^ [_1051488, _1051490, _1051492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051488), _1051490)), 14545 ^ _782652 : [(14546 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051492), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051490), _1051488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051492), _1051488)), _1051490)))], (14552 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051492), _1051488)), _1051490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051492), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051490), _1051488))))]]], (14558 ^ _782652) ^ [_1051777, _1051779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051777), _1051779)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051779), _1051777)), _1051777) = _1051779)], (14564 ^ _782652) ^ [_1051888, _1051890, _1051892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051888), _1051890)), 14567 ^ _782652 : [(14568 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051890), _1051888) = _1051892, -(_1051890 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051892), _1051888))], (14574 ^ _782652) ^ [] : [_1051890 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051892), _1051888), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1051890), _1051888) = _1051892)]]], (14580 ^ _782652) ^ [_1052147, _1052149, _1052151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052147), _1052149)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052151), _1052149)), _1052147) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052151), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052149), _1052147)))], (14586 ^ _782652) ^ [_1052284, _1052286, _1052288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052284), _1052286)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052286), _1052284)), _1052288) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052286), _1052288)), _1052284))], (14592 ^ _782652) ^ [_1052421, _1052423, _1052425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052421), _1052423)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052423), _1052425)), _1052421) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052423), _1052421)), _1052425))], (14598 ^ _782652) ^ [_1052558, _1052560, _1052562, _1052564, _1052566] : [class_Groups_Ocomm__monoid__add(_1052558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052560), _1052562)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1052560, _1052558), hAPP(hAPP(c_COMBS(_1052560, _1052558, _1052558), hAPP(hAPP(c_COMBB(_1052558, tc_fun(_1052558, _1052558), _1052560), c_Groups_Oplus__class_Oplus(_1052558)), _1052564)), _1052566)), _1052562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052558), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1052560, _1052558), _1052564), _1052562)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1052560, _1052558), _1052566), _1052562)))], (14608 ^ _782652) ^ [_1052825, _1052827, _1052829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052825), _1052827)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052827), _1052825))), _1052829) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1052827)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052825), _1052829)))], (14614 ^ _782652) ^ [_1052974, _1052976, _1052978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052974), _1052976)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052978), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052976), _1052974))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052978), _1052974)), hAPP(c_Nat_OSuc, _1052976)))], (14620 ^ _782652) ^ [_1053123, _1053125, _1053127] : [class_Rings_Olinordered__idom(_1053123), -(_1053125 = _1053127), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053123), _1053125), _1053127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053123), _1053127), _1053125)))], (14634 ^ _782652) ^ [_1053258, _1053260, _1053262] : [class_Rings_Ocomm__semiring__1(_1053258), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053258), _1053260), _1053262) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053258), _1053262), _1053260))], (14640 ^ _782652) ^ [_1053367, _1053369, _1053371, _1053373] : [class_Rings_Ocomm__semiring__1(_1053367), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053367), _1053369), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053367), _1053371), _1053373)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053367), _1053371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053367), _1053369), _1053373)))], (14646 ^ _782652) ^ [_1053510, _1053512, _1053514, _1053516] : [class_Rings_Ocomm__semiring__1(_1053510), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053510), _1053512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053510), _1053514), _1053516)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053510), _1053512), _1053514)), _1053516))], (14652 ^ _782652) ^ [_1053653, _1053655, _1053657, _1053659] : [class_Rings_Ocomm__semiring__1(_1053653), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053653), _1053655), _1053657)), _1053659) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053653), _1053655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053653), _1053657), _1053659)))], (14658 ^ _782652) ^ [_1053796, _1053798, _1053800, _1053802] : [class_Rings_Ocomm__semiring__1(_1053796), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053796), _1053798), _1053800)), _1053802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053796), _1053798), _1053802)), _1053800))], (14664 ^ _782652) ^ [_1053939, _1053941, _1053943, _1053945, _1053947] : [class_Rings_Ocomm__semiring__1(_1053939), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053939), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053939), _1053941), _1053943)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053939), _1053945), _1053947)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053939), _1053941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053939), _1053943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053939), _1053945), _1053947))))], (14670 ^ _782652) ^ [_1054116, _1054118, _1054120, _1054122, _1054124] : [class_Rings_Ocomm__semiring__1(_1054116), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054116), _1054118), _1054120)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054116), _1054122), _1054124)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054116), _1054122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054116), _1054118), _1054120)), _1054124)))], (14676 ^ _782652) ^ [_1054293, _1054295, _1054297, _1054299, _1054301] : [class_Rings_Ocomm__semiring__1(_1054293), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054293), _1054295), _1054297)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054293), _1054299), _1054301)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054293), _1054295), _1054299)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054293), _1054297), _1054301)))], (14682 ^ _782652) ^ [_1054470, _1054472, _1054474, _1054476, _1054478] : [class_Groups_Ocomm__monoid__add(_1054470), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054472), _1054474)), -(hBOOL(hAPP(hAPP(c_member(_1054472), _1054476), _1054474))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1054472, _1054470), _1054478), hAPP(hAPP(c_Set_Oinsert(_1054472), _1054476), _1054474)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054470), hAPP(_1054478, _1054476)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1054472, _1054470), _1054478), _1054474)))], (14696 ^ _782652) ^ [_1054720, _1054722, _1054724, _1054726, _1054728] : [class_Groups_Ocomm__monoid__add(_1054720), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054722), _1054724)), -(hBOOL(hAPP(hAPP(c_member(_1054722), _1054726), _1054724))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1054722, _1054720), _1054728), hAPP(hAPP(c_Set_Oinsert(_1054722), _1054726), _1054724)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054720), hAPP(_1054728, _1054726)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1054722, _1054720), _1054728), _1054724)))], (14710 ^ _782652) ^ [_1054970, _1054972, _1054974, _1054976, _1054978] : [class_Groups_Ocomm__monoid__add(_1054970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054972), _1054974)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054972), _1054976)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054970), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1054972, _1054970), _1054978), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054972, tc_HOL_Obool)), _1054974), _1054976))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1054972, _1054970), _1054978), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054972, tc_HOL_Obool)), _1054974), _1054976))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054970), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1054972, _1054970), _1054978), _1054974)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1054972, _1054970), _1054978), _1054976)))], (14724 ^ _782652) ^ [_1055331, _1055333, _1055335, _1055337] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055331), _1055333)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055331), _1055335)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1055331, tc_Nat_Onat), _1055337), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055331, tc_HOL_Obool)), _1055333), _1055335)) = 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(_1055331, tc_Nat_Onat), _1055337), _1055333)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1055331, tc_Nat_Onat), _1055337), _1055335))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1055331, tc_Nat_Onat), _1055337), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055331, tc_HOL_Obool)), _1055333), _1055335))))], (14734 ^ _782652) ^ [_1055624, _1055626, _1055628] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055624), _1055626)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055624), _1055628)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055624), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055624, tc_HOL_Obool)), _1055626), _1055628))), hAPP(c_Finite__Set_Ocard(_1055624), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055624, tc_HOL_Obool)), _1055626), _1055628))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055624), _1055626)), hAPP(c_Finite__Set_Ocard(_1055624), _1055628)))], (14744 ^ _782652) ^ [_1055881, _1055883, _1055885] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055881), _1055883)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055881), _1055885)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055881), _1055883)), hAPP(c_Finite__Set_Ocard(_1055881), _1055885)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1055881), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055881, tc_HOL_Obool)), _1055883), _1055885))), hAPP(c_Finite__Set_Ocard(_1055881), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055881, tc_HOL_Obool)), _1055883), _1055885))))], (14754 ^ _782652) ^ [_1056138, _1056140, _1056142, _1056144, _1056146] : [class_Groups_Ocomm__monoid__add(_1056138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056140), _1056142)), 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_1056802), _1056810), _1056806)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1056804, _1056802), _1056810), _1056808))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1056804, _1056802), _1056810), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056804, tc_HOL_Obool)), _1056806), _1056808))))], (14796 ^ _782652) ^ [_1057163, _1057165, _1057167] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1057163), _1057165)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057163), _1057167)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057163, tc_HOL_Obool)), _1057165), _1057167) = c_Orderings_Obot__class_Obot(tc_fun(_1057163, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1057163), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1057163, tc_HOL_Obool)), _1057165), _1057167)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1057163), _1057165)), hAPP(c_Finite__Set_Ocard(_1057163), _1057167)))], (14810 ^ _782652) ^ [_1057462, _1057464, _1057466] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1057462), _1057464)), -(hBOOL(hAPP(hAPP(c_member(_1057462), _1057466), _1057464))), -(hAPP(c_Finite__Set_Ocard(_1057462), hAPP(hAPP(c_Set_Oinsert(_1057462), _1057466), _1057464)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1057462), _1057464)))], (14820 ^ _782652) ^ [_1057620, _1057622, _1057624, _1057626, _1057628, _1057630] : [class_Groups_Ocomm__monoid__add(_1057620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057622), _1057624)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057622, _1057620), hAPP(hAPP(c_COMBS(_1057622, _1057620, _1057620), hAPP(hAPP(c_COMBS(_1057622, _1057620, tc_fun(_1057620, _1057620)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1057620, tc_fun(_1057620, _1057620)), _1057622), c_If(_1057620)), _1057626)), _1057628)), _1057630)), _1057624) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057620), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057622, _1057620), _1057628), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057622, tc_HOL_Obool)), _1057624), hAPP(c_Set_OCollect(_1057622), _1057626)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1057622, _1057620), _1057630), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057622, tc_HOL_Obool)), _1057624), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1057622, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1057622), _1057626))))))], (14830 ^ _782652) ^ [_1058003, _1058005, _1058007, _1058009, _1058011] : [class_Groups_Ocomm__monoid__add(_1058003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058005), _1058007)), hBOOL(hAPP(hAPP(c_member(_1058005), _1058009), _1058007)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058005, _1058003), _1058011), _1058007) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058003), hAPP(_1058011, _1058009)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058005, _1058003), _1058011), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058005, tc_HOL_Obool)), _1058007), hAPP(hAPP(c_Set_Oinsert(_1058005), _1058009), c_Orderings_Obot__class_Obot(tc_fun(_1058005, tc_HOL_Obool)))))))], (14844 ^ _782652) ^ [_1058328, _1058330, _1058332, _1058334, _1058336] : [class_Groups_Ocomm__monoid__add(_1058328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058330), _1058332)), hBOOL(hAPP(hAPP(c_member(_1058330), _1058334), _1058332)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058330, _1058328), _1058336), _1058332) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058328), hAPP(_1058336, _1058334)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1058330, _1058328), _1058336), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058330, tc_HOL_Obool)), _1058332), hAPP(hAPP(c_Set_Oinsert(_1058330), _1058334), c_Orderings_Obot__class_Obot(tc_fun(_1058330, tc_HOL_Obool)))))))], (14858 ^ _782652) ^ [_1058653, _1058655, _1058657] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1058653), _1058655)), -(hAPP(c_Finite__Set_Ocard(_1058653), hAPP(hAPP(c_Set_Oinsert(_1058653), _1058657), _1058655)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1058653), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1058653, tc_HOL_Obool)), _1058655), hAPP(hAPP(c_Set_Oinsert(_1058653), _1058657), c_Orderings_Obot__class_Obot(tc_fun(_1058653, tc_HOL_Obool)))))))], (14864 ^ _782652) ^ [_1058830, _1058832] : [class_Rings_Ocomm__semiring__1(_1058830), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058830), c_Groups_Oone__class_Oone(_1058830)), _1058832) = _1058832)], (14870 ^ _782652) ^ [_1058925, _1058927] : [class_Rings_Ocomm__semiring__1(_1058925), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058925), _1058927), c_Groups_Oone__class_Oone(_1058925)) = _1058927)], (14876 ^ _782652) ^ [_1059020, _1059022, _1059024] : [class_Rings_Oring(_1059020), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1059020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059020), _1059022), _1059024)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059020), _1059022), hAPP(c_Groups_Ouminus__class_Ouminus(_1059020), _1059024)))], (14882 ^ _782652) ^ [_1059149, _1059151, _1059153] : [class_Rings_Oring(_1059149), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1059149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059149), _1059151), _1059153)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059149), hAPP(c_Groups_Ouminus__class_Ouminus(_1059149), _1059151)), _1059153))], (14888 ^ _782652) ^ [_1059278, _1059280, _1059282] : [class_Rings_Oring(_1059278), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059278), hAPP(c_Groups_Ouminus__class_Ouminus(_1059278), _1059280)), _1059282) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059278), _1059280), hAPP(c_Groups_Ouminus__class_Ouminus(_1059278), _1059282)))], (14894 ^ _782652) ^ [_1059407, _1059409, _1059411] : [class_Rings_Oring(_1059407), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059407), hAPP(c_Groups_Ouminus__class_Ouminus(_1059407), _1059409)), hAPP(c_Groups_Ouminus__class_Ouminus(_1059407), _1059411)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059407), _1059409), _1059411))], (14900 ^ _782652) ^ [_1059536, _1059538, _1059540, _1059542, _1059544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059536), _1059538)), 14903 ^ _782652 : [(14904 ^ _782652) ^ [] : [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), _1059538), _1059540)), _1059542)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059536), _1059540)), _1059544))), -(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), _1059538), _1059536)), _1059540)), _1059542)), _1059544)))], (14910 ^ _782652) ^ [] : [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), _1059538), _1059536)), _1059540)), _1059542)), _1059544)), -(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), _1059538), _1059540)), _1059542)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059536), _1059540)), _1059544))))]]], (14916 ^ _782652) ^ [_1059927, _1059929, _1059931, _1059933, _1059935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059927), _1059929)), 14919 ^ _782652 : [(14920 ^ _782652) ^ [] : 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059927), _1059931)), _1059933)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059929), _1059931)), _1059935))))]]], (14932 ^ _782652) ^ [_1060318, _1060320, _1060322, _1060324, _1060326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060318), _1060320)), 14935 ^ _782652 : [(14936 ^ _782652) ^ [] : [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), _1060320), _1060322)), _1060324)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060318), _1060322)), _1060326))), -(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), _1060320), _1060318)), _1060322)), _1060324)), _1060326)))], (14942 ^ _782652) ^ [] : [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), _1060320), _1060318)), _1060322)), _1060324)), _1060326)), -(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), _1060320), _1060322)), _1060324)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060318), _1060322)), _1060326))))]]], (14948 ^ _782652) ^ [_1060709, _1060711, _1060713, _1060715, _1060717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060709), _1060711)), 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060910), _1060914)), _1060918), -(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), _1060912), _1060910)), _1060914)), _1060916) = _1060918)], (14964 ^ _782652) ^ [] : [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), _1060912), _1060910)), _1060914)), _1060916) = _1060918, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060912), _1060914)), _1060916) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060910), _1060914)), _1060918))]]], (14970 ^ _782652) ^ [_1061271, _1061273, _1061275, _1061277, _1061279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061271), _1061273)), 14973 ^ _782652 : [(14974 ^ _782652) ^ [] : [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), _1061271), _1061275)), _1061277)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061273), _1061275)), _1061279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061277), 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), _1061273), _1061271)), _1061275)), _1061279))))], (14980 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061277), 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), _1061273), _1061271)), _1061275)), _1061279))), -(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), _1061271), _1061275)), _1061277)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061273), _1061275)), _1061279))))]]], (14986 ^ _782652) ^ [_1061662, _1061664, _1061666, _1061668, _1061670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061662), _1061664)), -(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), _1061662), _1061666)), _1061668)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061664), _1061666)), _1061670)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061668), 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), _1061664), _1061662)), _1061666)), _1061670)))], (14992 ^ _782652) ^ [_1061863, _1061865, _1061867, _1061869, _1061871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061863), _1061865)), 14995 ^ _782652 : [(14996 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061863), _1061867)), _1061869) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061865), _1061867)), _1061871), -(_1061869 = 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), _1061865), _1061863)), _1061867)), _1061871))], (15002 ^ _782652) ^ [] : [_1061869 = 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), _1061865), _1061863)), _1061867)), _1061871), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061863), _1061867)), _1061869) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061865), _1061867)), _1061871))]]], (15008 ^ _782652) ^ [_1062224, _1062226, _1062228, _1062230] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062224), _1062226)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062228), _1062226)), _1062230)) = 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), _1062224), _1062228)), _1062226)), _1062230))], (15010 ^ _782652) ^ [_1062295, _1062297, _1062299, _1062301, _1062303, _1062305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062295), _1062297)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062299), _1062301)), 15020 ^ _782652 : [(15021 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062299), 15019 ^ [_1062295, _1062297, _1062299, _1062301, _1062303, _1062305]), _1062301)))], (15023 ^ _782652) ^ [] : [hAPP(c_Finite__Set_Ocard(_1062295), hAPP(c_Set_OCollect(_1062295), hAPP(hAPP(c_COMBS(_1062295, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1062295), c_fconj), hAPP(hAPP(c_COMBC(_1062295, tc_fun(_1062295, tc_HOL_Obool), tc_HOL_Obool), c_member(_1062295)), _1062297))), hAPP(hAPP(c_COMBC(_1062295, _1062299, tc_HOL_Obool), _1062303), 15019 ^ [_1062295, _1062297, _1062299, _1062301, _1062303, _1062305])))) = _1062305]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1062295, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1062299, tc_HOL_Obool), tc_Nat_Onat, _1062295), c_Finite__Set_Ocard(_1062299)), hAPP(hAPP(c_COMBB(tc_fun(_1062299, tc_HOL_Obool), tc_fun(_1062299, tc_HOL_Obool), _1062295), c_Set_OCollect(_1062299)), hAPP(hAPP(c_COMBB(tc_fun(_1062299, tc_HOL_Obool), tc_fun(_1062299, tc_HOL_Obool), _1062295), hAPP(c_COMBS(_1062299, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1062299), c_fconj), hAPP(hAPP(c_COMBC(_1062299, tc_fun(_1062299, tc_HOL_Obool), tc_HOL_Obool), c_member(_1062299)), _1062301)))), _1062303)))), _1062297) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062305), hAPP(c_Finite__Set_Ocard(_1062299), _1062301)))], (15027 ^ _782652) ^ [_1062985, _1062987, _1062989] : [class_Groups_Olinordered__ab__semigroup__add(_1062985), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062985), _1062987)), -(_1062987 = c_Orderings_Obot__class_Obot(tc_fun(_1062985, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1062985), _1062989), c_Big__Operators_Olinorder__class_OMin(_1062985, _1062987)) = c_Big__Operators_Olinorder__class_OMin(_1062985, hAPP(c_Set_OCollect(_1062985), hAPP(hAPP(c_COMBB(tc_fun(_1062985, tc_HOL_Obool), tc_HOL_Obool, _1062985), c_HOL_OEx(_1062985)), hAPP(hAPP(c_COMBC(_1062985, tc_fun(_1062985, tc_HOL_Obool), tc_fun(_1062985, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1062985, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1062985, tc_HOL_Obool), tc_fun(_1062985, tc_HOL_Obool)), _1062985), c_COMBS(_1062985, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1062985, tc_HOL_Obool), tc_fun(_1062985, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1062985), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1062985), c_fconj)), hAPP(hAPP(c_COMBC(_1062985, tc_fun(_1062985, _1062985), tc_fun(_1062985, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1062985, tc_HOL_Obool), tc_fun(tc_fun(_1062985, _1062985), tc_fun(_1062985, tc_HOL_Obool)), _1062985), c_COMBB(_1062985, tc_HOL_Obool, _1062985)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1062985), _1062989))))), hAPP(hAPP(c_COMBC(_1062985, tc_fun(_1062985, tc_HOL_Obool), tc_HOL_Obool), c_member(_1062985)), _1062987))))))], (15041 ^ _782652) ^ [_1063471, _1063473, _1063475] : [class_Groups_Olinordered__ab__semigroup__add(_1063471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063471), _1063473)), -(_1063473 = c_Orderings_Obot__class_Obot(tc_fun(_1063471, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1063471), _1063475), c_Big__Operators_Olinorder__class_OMax(_1063471, _1063473)) = c_Big__Operators_Olinorder__class_OMax(_1063471, hAPP(c_Set_OCollect(_1063471), hAPP(hAPP(c_COMBB(tc_fun(_1063471, tc_HOL_Obool), tc_HOL_Obool, _1063471), c_HOL_OEx(_1063471)), hAPP(hAPP(c_COMBC(_1063471, tc_fun(_1063471, tc_HOL_Obool), tc_fun(_1063471, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1063471, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1063471, tc_HOL_Obool), tc_fun(_1063471, tc_HOL_Obool)), _1063471), c_COMBS(_1063471, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1063471, tc_HOL_Obool), tc_fun(_1063471, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1063471), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1063471), c_fconj)), hAPP(hAPP(c_COMBC(_1063471, tc_fun(_1063471, _1063471), tc_fun(_1063471, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1063471, tc_HOL_Obool), tc_fun(tc_fun(_1063471, _1063471), tc_fun(_1063471, tc_HOL_Obool)), _1063471), c_COMBB(_1063471, tc_HOL_Obool, _1063471)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1063471), _1063475))))), hAPP(hAPP(c_COMBC(_1063471, tc_fun(_1063471, tc_HOL_Obool), tc_HOL_Obool), c_member(_1063471)), _1063473))))))], (15055 ^ _782652) ^ [_1063957, _1063959, _1063961, _1063963, _1063965, _1063967] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1063957), _1063959)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063961), _1063963)), 15065 ^ _782652 : [(15066 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1063961), 15064 ^ [_1063957, _1063959, _1063961, _1063963, _1063965, _1063967]), _1063963)))], (15068 ^ _782652) ^ [] : [hAPP(c_Finite__Set_Ocard(_1063957), hAPP(c_Set_OCollect(_1063957), hAPP(hAPP(c_COMBS(_1063957, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1063957), c_fconj), hAPP(hAPP(c_COMBC(_1063957, tc_fun(_1063957, tc_HOL_Obool), tc_HOL_Obool), c_member(_1063957)), _1063959))), hAPP(hAPP(c_COMBC(_1063957, _1063961, tc_HOL_Obool), _1063965), 15064 ^ [_1063957, _1063959, _1063961, _1063963, _1063965, _1063967])))) = hAPP(_1063967, 15064 ^ [_1063957, _1063959, _1063961, _1063963, _1063965, _1063967])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1063957, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1063961, tc_HOL_Obool), tc_Nat_Onat, _1063957), c_Finite__Set_Ocard(_1063961)), hAPP(hAPP(c_COMBB(tc_fun(_1063961, tc_HOL_Obool), tc_fun(_1063961, tc_HOL_Obool), _1063957), c_Set_OCollect(_1063961)), hAPP(hAPP(c_COMBB(tc_fun(_1063961, tc_HOL_Obool), tc_fun(_1063961, tc_HOL_Obool), _1063957), hAPP(c_COMBS(_1063961, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1063961), c_fconj), hAPP(hAPP(c_COMBC(_1063961, tc_fun(_1063961, tc_HOL_Obool), tc_HOL_Obool), c_member(_1063961)), _1063963)))), _1063965)))), _1063959) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1063961, tc_Nat_Onat), _1063967), _1063963))], (15072 ^ _782652) ^ [_1064667, _1064669, _1064671, _1064673, _1064675] : [class_Groups_Ocomm__monoid__add(_1064667), class_Groups_Oordered__cancel__ab__semigroup__add(_1064667), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064669), _1064671)), -(_1064671 = c_Orderings_Obot__class_Obot(tc_fun(_1064669, tc_HOL_Obool))), 15090 ^ _782652 : [(15091 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1064669), 15089 ^ [_1064667, _1064669, _1064671, _1064673, _1064675]), _1064671)))], (15093 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064667), hAPP(_1064673, 15089 ^ [_1064667, _1064669, _1064671, _1064673, _1064675])), hAPP(_1064675, 15089 ^ [_1064667, _1064669, _1064671, _1064673, _1064675])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1064667), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1064669, _1064667), _1064673), _1064671)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1064669, _1064667), _1064675), _1064671))))], (15097 ^ _782652) ^ [_1065198, _1065200, _1065202] : [class_Lattices_Oboolean__algebra(_1065198), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065198), _1065200), _1065202) = c_Orderings_Obot__class_Obot(_1065198), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065198), _1065200), _1065202) = c_Orderings_Otop__class_Otop(_1065198), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1065198), _1065200) = _1065202)], (15111 ^ _782652) ^ [_1065433, _1065435, _1065437] : [class_Groups_Oab__semigroup__mult(_1065433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065433), _1065435)), -(_1065435 = c_Orderings_Obot__class_Obot(tc_fun(_1065433, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065433), _1065437)), -(_1065437 = c_Orderings_Obot__class_Obot(tc_fun(_1065433, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1065433, tc_HOL_Obool)), _1065435), _1065437) = c_Orderings_Obot__class_Obot(tc_fun(_1065433, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1065433, c_Groups_Otimes__class_Otimes(_1065433)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1065433, tc_HOL_Obool)), _1065435), _1065437)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065433), hAPP(c_Finite__Set_Ofold1(_1065433, c_Groups_Otimes__class_Otimes(_1065433)), _1065435)), hAPP(c_Finite__Set_Ofold1(_1065433, c_Groups_Otimes__class_Otimes(_1065433)), _1065437)))], (15137 ^ _782652) ^ [_1065940, _1065942, _1065944, _1065946] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1065940))), _1065942), _1065944), _1065946)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _1065940)), _1065942), hAPP(c_Nat_OSuc, _1065944)), _1065946)))], (15143 ^ _782652) ^ [_1066089, _1066091] : [-(hBOOL(hAPP(hAPP(c_member(_1066089), _1066091), c_Orderings_Otop__class_Otop(tc_fun(_1066089, tc_HOL_Obool)))))], (15145 ^ _782652) ^ [_1066122, _1066124, _1066126, _1066128] : [-(hBOOL(hAPP(_1066122, _1066124))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1066122, _1066126)), _1066124), _1066128), _1066124)))], (15151 ^ _782652) ^ [_1066178, _1066180, _1066182, _1066184, _1066186, _1066188] : [hBOOL(hAPP(_1066178, _1066180)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1066182), _1066180), _1066184), _1066186)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1066178, _1066182)), _1066186), _1066184), _1066188)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1066178, _1066182)), _1066180), _1066184), _1066188)))], (15165 ^ _782652) ^ [_1066465, _1066467, _1066469, _1066471, _1066473, _1066475] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1066465), _1066467), _1066469), _1066471)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1066473), _1066471), _1066469), _1066475)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_1066465, _1066473)), _1066467), _1066469), _1066475)))], (15175 ^ _782652) ^ [_1066682, _1066684] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _1066682), _1066684), _1066682)))], (15177 ^ _782652) ^ [_1066715, _1066717, _1066719] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _1066715), _1066717), _1066719)), -(_1066719 = _1066715)], (15183 ^ _782652) ^ [_1066810, _1066812, _1066814] : [class_Orderings_Otop(_1066810), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1066812, _1066810)), _1066814) = c_Orderings_Otop__class_Otop(_1066810))], (15189 ^ _782652) ^ [_1066907, _1066909] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1066907), c_Orderings_Otop__class_Otop(tc_fun(_1066907, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066909), c_Orderings_Otop__class_Otop(tc_fun(_1066909, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1066907, _1066909)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1066907, _1066909), tc_HOL_Obool)))))], (15199 ^ _782652) ^ [_1067117, _1067119] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1067117, _1067119)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1067117, _1067119), tc_HOL_Obool)))), 15202 ^ _782652 : [(15203 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1067117), c_Orderings_Otop__class_Otop(tc_fun(_1067117, tc_HOL_Obool)))))], (15205 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1067119), c_Orderings_Otop__class_Otop(tc_fun(_1067119, tc_HOL_Obool)))))]]], (15207 ^ _782652) ^ [_1067282, _1067284] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1067282, _1067284)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1067282, _1067284), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067282), c_Orderings_Otop__class_Otop(tc_fun(_1067282, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067284), c_Orderings_Otop__class_Otop(tc_fun(_1067284, tc_HOL_Obool))))], (15217 ^ _782652) ^ [_1067491] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1067491)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1067491), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1067491), c_Orderings_Otop__class_Otop(tc_fun(_1067491, tc_HOL_Obool)))))], (15223 ^ _782652) ^ [_1067606] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1067606), c_Orderings_Otop__class_Otop(tc_fun(_1067606, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1067606)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1067606), tc_HOL_Obool)))))], (15229 ^ _782652) ^ [_1067727, _1067729, _1067731, _1067733] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1067727), _1067729), _1067731), _1067733)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1067727), _1067729), hAPP(c_Nat_OSuc, _1067731)), _1067733)))], (15235 ^ _782652) ^ [_1067858, _1067860] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1067858, _1067860)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1067858, _1067860), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1067860), c_Orderings_Otop__class_Otop(tc_fun(_1067860, tc_HOL_Obool)))))], (15241 ^ _782652) ^ [_1067983, _1067985, _1067987, _1067989, _1067991] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1067983), _1067985), _1067987), _1067989)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1067987), _1067991)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1067983), _1067985), _1067991), _1067989)))], (15251 ^ _782652) ^ [_1068187] : [c_Orderings_Otop__class_Otop(tc_fun(_1068187, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1068187, tc_HOL_Obool))], (15253 ^ _782652) ^ [_1068220] : [class_Finite__Set_Ofinite(_1068220), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1068220), c_Orderings_Otop__class_Otop(tc_fun(_1068220, tc_HOL_Obool)))))], (15259 ^ _782652) ^ [_1068311, _1068313] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1068311, tc_HOL_Obool)), _1068313), c_Orderings_Otop__class_Otop(tc_fun(_1068311, tc_HOL_Obool)))))], (15261 ^ _782652) ^ [_1068351, _1068353] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1068351, tc_HOL_Obool)), _1068353), c_Orderings_Otop__class_Otop(tc_fun(_1068351, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1068351, tc_HOL_Obool)))], (15263 ^ _782652) ^ [_1068397, _1068399] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1068397, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1068397, tc_HOL_Obool))), _1068399) = c_Orderings_Otop__class_Otop(tc_fun(_1068397, tc_HOL_Obool)))], (15265 ^ _782652) ^ [_1068443, _1068445] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1068443, tc_HOL_Obool)), _1068445), c_Orderings_Otop__class_Otop(tc_fun(_1068443, tc_HOL_Obool))) = _1068445)], (15267 ^ _782652) ^ [_1068484, _1068486] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1068484, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1068484, tc_HOL_Obool))), _1068486) = _1068486)], (15269 ^ _782652) ^ [_1068525, _1068527, _1068529, _1068531, _1068533] : [c_Fun_Oinj__on(_1068525, _1068527, _1068529, c_Orderings_Otop__class_Otop(tc_fun(_1068525, tc_HOL_Obool))), hAPP(_1068529, _1068531) = hAPP(_1068529, _1068533), -(_1068531 = _1068533)], (15279 ^ _782652) ^ [_1068692, _1068694, _1068696, _1068698, _1068700] : [c_Fun_Oinj__on(_1068692, _1068694, _1068696, c_Orderings_Otop__class_Otop(tc_fun(_1068692, tc_HOL_Obool))), 15282 ^ _782652 : [(15283 ^ _782652) ^ [] : [hAPP(_1068696, _1068698) = hAPP(_1068696, _1068700), -(_1068698 = _1068700)], (15289 ^ _782652) ^ [] : [_1068698 = _1068700, -(hAPP(_1068696, _1068698) = hAPP(_1068696, _1068700))]]], (15295 ^ _782652) ^ [_1068967, _1068969, _1068971] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1068967), _1068969), _1068971)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1068967), _1068969), 15298 ^ [_1068967, _1068969, _1068971]), _1068971)))], (15302 ^ _782652) ^ [_1069092, _1069094, _1069096] : [15303 ^ _782652 : [(15304 ^ _782652) ^ [_1069151] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1069092), _1069094), _1069151), _1069096))]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1069092), _1069094), _1069096)))], (15308 ^ _782652) ^ [_1069222, _1069224, _1069226, _1069228] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1069222), _1069224), _1069226), _1069228)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1069222), _1069224), _1069228)))], (15314 ^ _782652) ^ [] : [-(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))], (15316 ^ _782652) ^ [_1069378, _1069380, _1069382, _1069384] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1069378, _1069380)), _1069382), _1069384), _1069382)), hBOOL(hAPP(_1069378, _1069382)), 15324 ^ _782652 : [(15325 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1069380), _1069382), _1069384), 15323 ^ [_1069378, _1069380, _1069382, _1069384])))], (15327 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1069378, _1069380)), 15323 ^ [_1069378, _1069380, _1069382, _1069384]), _1069384), _1069382)))]]], (15329 ^ _782652) ^ [_1069646, _1069648, _1069650, _1069652] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1069646, _1069648)), _1069650), _1069652), _1069650))), 15330 ^ _782652 : [(15331 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1069646, _1069650)))], (15333 ^ _782652) ^ [_1069760] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1069648), _1069650), _1069652), _1069760)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1069646, _1069648)), _1069760), _1069652), _1069650))]]], (15341 ^ _782652) ^ [_1069962, _1069964, _1069966, _1069968, _1069970] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1069962, _1069964)), _1069966), _1069968), _1069970)), 15346 ^ _782652 : [(15347 ^ _782652) ^ [] : [-(_1069970 = _1069966)], (15349 ^ _782652) ^ [] : [hBOOL(hAPP(_1069962, _1069966))]], 15350 ^ _782652 : [(15351 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1069962, _1069966)))], (15354 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1069964), _1069966), _1069968), 15352 ^ [_1069962, _1069964, _1069966, _1069968, _1069970])))], (15356 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1069962, _1069964)), 15352 ^ [_1069962, _1069964, _1069966, _1069968, _1069970]), _1069968), _1069970)))]]], (15358 ^ _782652) ^ [_1070301, _1070303, _1070305, _1070307, _1070309] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1070301, _1070303)), _1070305), _1070307), _1070309))), 15359 ^ _782652 : [(15360 ^ _782652) ^ [] : [_1070309 = _1070305, -(hBOOL(hAPP(_1070301, _1070305)))], (15366 ^ _782652) ^ [] : [hBOOL(hAPP(_1070301, _1070305)), 15369 ^ _782652 : [(15370 ^ _782652) ^ [_1070538] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1070303), _1070305), _1070307), _1070538)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_1070301, _1070303)), _1070538), _1070307), _1070309))]]]]], (15378 ^ _782652) ^ [_1070746, _1070748, _1070750, _1070752, _1070754] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_1070746, _1070748)), _1070750), _1070752), _1070754)), 15382 ^ _782652 : [(15383 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1070746), _1070750), _1070752), 15381 ^ [_1070746, _1070748, _1070750, _1070752, _1070754])))], (15385 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1070748), 15381 ^ [_1070746, _1070748, _1070750, _1070752, _1070754]), _1070752), _1070754)))]]], (15387 ^ _782652) ^ [_1070954, _1070956, _1070958, _1070960, _1070962] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_1070954, _1070956)), _1070958), _1070960), _1070962))), 15388 ^ _782652 : [(15389 ^ _782652) ^ [_1071036] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1070954), _1070958), _1070960), _1071036)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1070956), _1071036), _1070960), _1070962))]]], (15397 ^ _782652) ^ [_1071208, _1071210] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _1071208), _1071210), _1071208)))], (15399 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (15401 ^ _782652) ^ [_1071265] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1071265, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1071265), hAPP(c_COMBK(tc_HOL_Obool, _1071265), c_fTrue)))], (15403 ^ _782652) ^ [_1071304, _1071306, _1071308, _1071310, _1071312] : [-(hAPP(c_Set_Oimage(_1071304, _1071306, hAPP(hAPP(c_COMBB(_1071308, _1071306, _1071304), _1071310), _1071312)), c_Orderings_Otop__class_Otop(tc_fun(_1071304, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1071308, _1071306, _1071310), hAPP(c_Set_Oimage(_1071304, _1071308, _1071312), c_Orderings_Otop__class_Otop(tc_fun(_1071304, tc_HOL_Obool)))))], (15405 ^ _782652) ^ [_1071376, _1071378, _1071380, _1071382] : [c_Fun_Oinj__on(_1071376, _1071378, _1071380, c_Orderings_Otop__class_Otop(tc_fun(_1071376, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1071376, tc_fun(_1071382, _1071378), hAPP(hAPP(c_COMBB(_1071378, tc_fun(_1071382, _1071378), _1071376), c_COMBK(_1071378, _1071382)), _1071380), c_Orderings_Otop__class_Otop(tc_fun(_1071376, tc_HOL_Obool))))], (15411 ^ _782652) ^ [_1071523, _1071525] : [class_Orderings_Otop(_1071523), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071523), _1071525), c_Orderings_Otop__class_Otop(_1071523))))], (15417 ^ _782652) ^ [_1071616, _1071618] : [class_Lattices_Obounded__lattice__top(_1071616), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1071616), c_Orderings_Otop__class_Otop(_1071616)), _1071618) = c_Orderings_Otop__class_Otop(_1071616))], (15423 ^ _782652) ^ [_1071715, _1071717] : [class_Lattices_Obounded__lattice__top(_1071715), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1071715), _1071717), c_Orderings_Otop__class_Otop(_1071715)) = c_Orderings_Otop__class_Otop(_1071715))], (15429 ^ _782652) ^ [_1071814, _1071816, _1071818] : [class_Lattices_Obounded__lattice__top(_1071814), 15432 ^ _782652 : [(15433 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1071814), _1071816), _1071818) = c_Orderings_Otop__class_Otop(_1071814), 15436 ^ _782652 : [(15437 ^ _782652) ^ [] : [-(_1071816 = c_Orderings_Otop__class_Otop(_1071814))], (15439 ^ _782652) ^ [] : [-(_1071818 = c_Orderings_Otop__class_Otop(_1071814))]]], (15441 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1071814), _1071816), _1071818) = c_Orderings_Otop__class_Otop(_1071814)), _1071816 = c_Orderings_Otop__class_Otop(_1071814), _1071818 = c_Orderings_Otop__class_Otop(_1071814)]]], (15451 ^ _782652) ^ [_1072141, _1072143] : [class_Lattices_Obounded__lattice__top(_1072141), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1072141), _1072143), c_Orderings_Otop__class_Otop(_1072141)) = _1072143)], (15457 ^ _782652) ^ [_1072236, _1072238] : [class_Lattices_Obounded__lattice__top(_1072236), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1072236), c_Orderings_Otop__class_Otop(_1072236)), _1072238) = _1072238)], (15463 ^ _782652) ^ [_1072331] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1072331), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1072331)), c_Option_Ooption_ONone(_1072331)), hAPP(c_Set_Oimage(_1072331, tc_Option_Ooption(_1072331), c_Option_Ooption_OSome(_1072331)), c_Orderings_Otop__class_Otop(tc_fun(_1072331, tc_HOL_Obool)))))], (15465 ^ _782652) ^ [_1072389, _1072391, _1072393, _1072395, _1072397] : [_1072389 = hAPP(_1072391, _1072393), -(hBOOL(hAPP(hAPP(c_member(_1072395), _1072389), hAPP(c_Set_Oimage(_1072397, _1072395, _1072391), c_Orderings_Otop__class_Otop(tc_fun(_1072397, tc_HOL_Obool))))))], (15471 ^ _782652) ^ [_1072516, _1072518, _1072520, _1072522] : [-(hBOOL(hAPP(hAPP(c_member(_1072516), hAPP(_1072518, _1072520)), hAPP(c_Set_Oimage(_1072522, _1072516, _1072518), c_Orderings_Otop__class_Otop(tc_fun(_1072522, tc_HOL_Obool))))))], (15473 ^ _782652) ^ [_1072567, _1072569] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1072567, tc_HOL_Obool)), _1072569), c_Orderings_Otop__class_Otop(tc_fun(_1072567, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1072567, tc_HOL_Obool)))], (15475 ^ _782652) ^ [_1072613, _1072615] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1072613), c_Orderings_Otop__class_Otop(tc_fun(_1072613, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1072613), _1072615) = hAPP(c_Finite__Set_Ocard(_1072613), c_Orderings_Otop__class_Otop(tc_fun(_1072613, tc_HOL_Obool))), -(_1072615 = c_Orderings_Otop__class_Otop(tc_fun(_1072613, tc_HOL_Obool)))], (15485 ^ _782652) ^ [_1072800, _1072802] : [class_Groups_Olinordered__ab__group__add(_1072800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1072800), _1072802)), -(_1072802 = c_Orderings_Obot__class_Obot(tc_fun(_1072800, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1072800), c_Big__Operators_Olinorder__class_OMin(_1072800, _1072802)) = c_Big__Operators_Olinorder__class_OMax(_1072800, hAPP(c_Set_Oimage(_1072800, _1072800, c_Groups_Ouminus__class_Ouminus(_1072800)), _1072802)))], (15499 ^ _782652) ^ [_1073000, _1073002] : [class_Groups_Olinordered__ab__group__add(_1073000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073000), _1073002)), -(_1073002 = c_Orderings_Obot__class_Obot(tc_fun(_1073000, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1073000), c_Big__Operators_Olinorder__class_OMax(_1073000, _1073002)) = c_Big__Operators_Olinorder__class_OMin(_1073000, hAPP(c_Set_Oimage(_1073000, _1073000, c_Groups_Ouminus__class_Ouminus(_1073000)), _1073002)))], (15513 ^ _782652) ^ [_1073200, _1073202, _1073204, _1073206, _1073208] : [c_Fun_Oinj__on(_1073200, _1073202, _1073204, c_Orderings_Otop__class_Otop(tc_fun(_1073200, tc_HOL_Obool))), 15516 ^ _782652 : [(15517 ^ _782652) ^ [] : [hAPP(c_Set_Oimage(_1073200, _1073202, _1073204), _1073206) = hAPP(c_Set_Oimage(_1073200, _1073202, _1073204), _1073208), -(_1073206 = _1073208)], (15523 ^ _782652) ^ [] : [_1073206 = _1073208, -(hAPP(c_Set_Oimage(_1073200, _1073202, _1073204), _1073206) = hAPP(c_Set_Oimage(_1073200, _1073202, _1073204), _1073208))]]], (15529 ^ _782652) ^ [_1073481] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1073481, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1073481, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1073481, tc_HOL_Obool)))], (15531 ^ _782652) ^ [_1073522] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1073522, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1073522, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1073522, tc_HOL_Obool)))], (15533 ^ _782652) ^ [_1073563, _1073565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1073563), _1073565)), 15536 ^ _782652 : [(15537 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1073563), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1073563, tc_HOL_Obool)), _1073565))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1073563), c_Orderings_Otop__class_Otop(tc_fun(_1073563, tc_HOL_Obool)))))], (15543 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1073563), c_Orderings_Otop__class_Otop(tc_fun(_1073563, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1073563), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1073563, tc_HOL_Obool)), _1073565))))]]], (15549 ^ _782652) ^ [_1073841, _1073843] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073841, tc_HOL_Obool)), _1073843), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1073841, tc_HOL_Obool)), _1073843)) = c_Orderings_Otop__class_Otop(tc_fun(_1073841, tc_HOL_Obool)))], (15551 ^ _782652) ^ [_1073890, _1073892] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073890, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1073890, tc_HOL_Obool)), _1073892)), _1073892) = c_Orderings_Otop__class_Otop(tc_fun(_1073890, tc_HOL_Obool)))], (15553 ^ _782652) ^ [_1073939, _1073941] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1073939, tc_HOL_Obool)), _1073941) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1073939, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1073939, tc_HOL_Obool))), _1073941))], (15555 ^ _782652) ^ [_1073988, _1073990, _1073992, _1073994] : [_1073988 = c_Finite__Set_Ofold1(_1073990, _1073992), -(hAPP(_1073988, hAPP(hAPP(c_Set_Oinsert(_1073990), _1073994), c_Orderings_Obot__class_Obot(tc_fun(_1073990, tc_HOL_Obool)))) = _1073994)], (15561 ^ _782652) ^ [_1074107, _1074109, _1074111] : [-(hAPP(c_Finite__Set_Ofold1(_1074107, _1074109), hAPP(hAPP(c_Set_Oinsert(_1074107), _1074111), c_Orderings_Obot__class_Obot(tc_fun(_1074107, tc_HOL_Obool)))) = _1074111)], (15563 ^ _782652) ^ [_1074153, _1074155] : [class_Orderings_Olinorder(_1074153), -(c_Big__Operators_Olinorder__class_OMax(_1074153, hAPP(hAPP(c_Set_Oinsert(_1074153), _1074155), c_Orderings_Obot__class_Obot(tc_fun(_1074153, tc_HOL_Obool)))) = _1074155)], (15569 ^ _782652) ^ [_1074260, _1074262] : [class_Orderings_Olinorder(_1074260), -(c_Big__Operators_Olinorder__class_OMin(_1074260, hAPP(hAPP(c_Set_Oinsert(_1074260), _1074262), c_Orderings_Obot__class_Obot(tc_fun(_1074260, tc_HOL_Obool)))) = _1074262)], (15575 ^ _782652) ^ [_1074367] : [-(c_Fun_Oinj__on(_1074367, tc_fun(_1074367, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1074367, tc_fun(_1074367, tc_HOL_Obool), tc_fun(_1074367, tc_HOL_Obool)), c_Set_Oinsert(_1074367)), c_Orderings_Obot__class_Obot(tc_fun(_1074367, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1074367, tc_HOL_Obool))))], (15591 ^ _782652) ^ [_1074801, _1074803, _1074805, _1074807, _1074809] : [15594 ^ _782652 : [(15595 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1074805, 15592 ^ [_1074801, _1074803, _1074805, _1074807, _1074809]), 15593 ^ [_1074801, _1074803, _1074805, _1074807, _1074809])))], (15598 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1074807), 15593 ^ [_1074801, _1074803, _1074805, _1074807, _1074809]), _1074803), 15596 ^ [_1074801, _1074803, _1074805, _1074807, _1074809])))], (15600 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1074809, 15592 ^ [_1074801, _1074803, _1074805, _1074807, _1074809]), 15596 ^ [_1074801, _1074803, _1074805, _1074807, _1074809]))]], -(c_Hoare__Mirabelle_Otriple__valid(_1074801, _1074803, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1074801), _1074805), _1074807), _1074809)))], (15577 ^ _782652) ^ [_1074447, _1074449, _1074451, _1074453, _1074455] : [c_Hoare__Mirabelle_Otriple__valid(_1074447, _1074449, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1074447), _1074451), _1074453), _1074455)), 15580 ^ _782652 : [(15581 ^ _782652) ^ [_1074577, _1074579] : [hBOOL(hAPP(hAPP(_1074451, _1074579), _1074577)), 15584 ^ _782652 : [(15585 ^ _782652) ^ [_1074676] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1074453), _1074577), _1074449), _1074676)), -(hBOOL(hAPP(hAPP(_1074455, _1074579), _1074676)))]]]]], (15604 ^ _782652) ^ [_1075209, _1075211] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075209), hAPP(c_Set_OCollect(_1075209), _1075211))), 15607 ^ _782652 : [(15608 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075209), hAPP(c_Set_OCollect(_1075209), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1075209), c_fNot), _1075211)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1075209), c_Orderings_Otop__class_Otop(tc_fun(_1075209, tc_HOL_Obool)))))], (15614 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075209), c_Orderings_Otop__class_Otop(tc_fun(_1075209, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1075209), hAPP(c_Set_OCollect(_1075209), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1075209), c_fNot), _1075211)))))]]], (15620 ^ _782652) ^ [_1075518, _1075520, _1075522, _1075524, _1075526] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075518), hAPP(c_Set_Oimage(_1075520, _1075518, _1075522), c_Orderings_Otop__class_Otop(tc_fun(_1075520, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1075524), hAPP(c_Set_Oimage(_1075520, _1075524, hAPP(hAPP(c_COMBB(_1075518, _1075524, _1075520), _1075526), _1075522)), c_Orderings_Otop__class_Otop(tc_fun(_1075520, tc_HOL_Obool))))))], (15626 ^ _782652) ^ [_1075685, _1075687, _1075689, _1075691] : [c_Fun_Oinj__on(_1075685, _1075687, _1075689, c_Orderings_Otop__class_Otop(tc_fun(_1075685, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1075685, _1075687, c_Orderings_Otop__class_Otop(tc_fun(_1075685, tc_HOL_Obool)), _1075689), hAPP(_1075689, _1075691)) = _1075691)], (15632 ^ _782652) ^ [_1075812, _1075814, _1075816] : [-(c_Map_Odom(_1075812, _1075814, hAPP(hAPP(c_COMBB(_1075814, tc_Option_Ooption(_1075814), _1075812), c_Option_Ooption_OSome(_1075814)), _1075816)) = c_Orderings_Otop__class_Otop(tc_fun(_1075812, tc_HOL_Obool)))], (15634 ^ _782652) ^ [_1075862, _1075864, _1075866, _1075868] : [c_Finite__Set_Ofolding__one(_1075862, _1075864, _1075866), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075862), _1075868)), -(hAPP(_1075866, _1075868) = hAPP(c_Finite__Set_Ofold1(_1075862, _1075864), _1075868))], (15644 ^ _782652) ^ [_1076027] : [class_Lattices_Oboolean__algebra(_1076027), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1076027), c_Orderings_Obot__class_Obot(_1076027)) = c_Orderings_Otop__class_Otop(_1076027))], (15650 ^ _782652) ^ [_1076118] : [class_Lattices_Oboolean__algebra(_1076118), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1076118), c_Orderings_Otop__class_Otop(_1076118)) = c_Orderings_Obot__class_Obot(_1076118))], (15656 ^ _782652) ^ [_1076209, _1076211] : [class_Lattices_Oboolean__algebra(_1076209), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076209), _1076211), hAPP(c_Groups_Ouminus__class_Ouminus(_1076209), _1076211)) = c_Orderings_Otop__class_Otop(_1076209))], (15662 ^ _782652) ^ [_1076314, _1076316] : [class_Lattices_Oboolean__algebra(_1076314), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076314), hAPP(c_Groups_Ouminus__class_Ouminus(_1076314), _1076316)), _1076316) = c_Orderings_Otop__class_Otop(_1076314))], (15668 ^ _782652) ^ [_1076419, _1076421, _1076423, _1076425, _1076427] : [c_Fun_Oinj__on(_1076419, _1076421, _1076423, c_Orderings_Otop__class_Otop(tc_fun(_1076419, tc_HOL_Obool))), 15671 ^ _782652 : [(15672 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1076421), hAPP(_1076423, _1076425)), hAPP(c_Set_Oimage(_1076419, _1076421, _1076423), _1076427))), -(hBOOL(hAPP(hAPP(c_member(_1076419), _1076425), _1076427)))], (15678 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1076419), _1076425), _1076427)), -(hBOOL(hAPP(hAPP(c_member(_1076421), hAPP(_1076423, _1076425)), hAPP(c_Set_Oimage(_1076419, _1076421, _1076423), _1076427))))]]], (15684 ^ _782652) ^ [_1076730, _1076732, _1076734, _1076736] : [c_Fun_Oinj__on(_1076730, _1076732, _1076734, c_Orderings_Otop__class_Otop(tc_fun(_1076730, tc_HOL_Obool))), 15687 ^ _782652 : [(15688 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1076732), _1076736), hAPP(c_Set_Oimage(_1076730, _1076732, _1076734), c_Orderings_Otop__class_Otop(tc_fun(_1076730, tc_HOL_Obool))))), 15692 ^ _782652 : [(15693 ^ _782652) ^ [] : [-(_1076736 = hAPP(_1076734, 15691 ^ [_1076730, _1076732, _1076734, _1076736]))], (15695 ^ _782652) ^ [_1076995] : [_1076736 = hAPP(_1076734, _1076995), -(_1076995 = 15691 ^ [_1076730, _1076732, _1076734, _1076736])]]], (15701 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1076732), _1076736), hAPP(c_Set_Oimage(_1076730, _1076732, _1076734), c_Orderings_Otop__class_Otop(tc_fun(_1076730, tc_HOL_Obool)))))), 15702 ^ _782652 : [(15703 ^ _782652) ^ [_1077133] : [_1076736 = hAPP(_1076734, _1077133), 15707 ^ _782652 : [(15708 ^ _782652) ^ [] : [-(_1076736 = hAPP(_1076734, 15706 ^ [_1076730, _1076732, _1076734, _1076736, _1077133]))], (15710 ^ _782652) ^ [] : [15706 ^ [_1076730, _1076732, _1076734, _1076736, _1077133] = _1077133]]]]]]], (15714 ^ _782652) ^ [_1077361, _1077363] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1077361), c_Orderings_Otop__class_Otop(tc_fun(_1077361, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1077361, _1077361, _1077363), c_Orderings_Otop__class_Otop(tc_fun(_1077361, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1077361, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1077361, _1077361, _1077363, c_Orderings_Otop__class_Otop(tc_fun(_1077361, tc_HOL_Obool))))], (15724 ^ _782652) ^ [_1077556, _1077558] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1077556), c_Orderings_Otop__class_Otop(tc_fun(_1077556, tc_HOL_Obool)))), c_Fun_Oinj__on(_1077556, _1077556, _1077558, c_Orderings_Otop__class_Otop(tc_fun(_1077556, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1077556, _1077556, _1077558), c_Orderings_Otop__class_Otop(tc_fun(_1077556, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1077556, tc_HOL_Obool)))], (15734 ^ _782652) ^ [_1077751, _1077753, _1077755, _1077757, _1077759] : [c_Fun_Oinj__on(_1077751, _1077753, _1077755, c_Orderings_Otop__class_Otop(tc_fun(_1077751, tc_HOL_Obool))), 15737 ^ _782652 : [(15738 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1077753, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1077751, _1077753, _1077755), _1077757)), hAPP(c_Set_Oimage(_1077751, _1077753, _1077755), _1077759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1077751, tc_HOL_Obool)), _1077757), _1077759)))], (15744 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1077751, tc_HOL_Obool)), _1077757), _1077759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1077753, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1077751, _1077753, _1077755), _1077757)), hAPP(c_Set_Oimage(_1077751, _1077753, _1077755), _1077759))))]]], (15750 ^ _782652) ^ [_1078092, _1078094, _1078096, _1078098, _1078100] : [c_Fun_Oinj__on(_1078092, _1078094, _1078096, c_Orderings_Otop__class_Otop(tc_fun(_1078092, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1078092, _1078094, _1078096), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078092, tc_HOL_Obool)), _1078098), _1078100)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078094, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1078092, _1078094, _1078096), _1078098)), hAPP(c_Set_Oimage(_1078092, _1078094, _1078096), _1078100)))], (15756 ^ _782652) ^ [_1078275, _1078277, _1078279, _1078281, _1078283] : [c_Fun_Oinj__on(_1078275, _1078277, _1078279, c_Orderings_Otop__class_Otop(tc_fun(_1078275, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1078275, _1078277, _1078279), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078275, tc_HOL_Obool)), _1078281), _1078283)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078277, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1078275, _1078277, _1078279), _1078281)), hAPP(c_Set_Oimage(_1078275, _1078277, _1078279), _1078283)))], (15762 ^ _782652) ^ [_1078458, _1078460, _1078462, _1078464] : [hAPP(c_Set_Oimage(_1078458, _1078460, _1078462), c_Orderings_Otop__class_Otop(tc_fun(_1078458, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1078460, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1078460, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1078460, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1078458, _1078460, _1078462), _1078464))), hAPP(c_Set_Oimage(_1078458, _1078460, _1078462), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1078458, tc_HOL_Obool)), _1078464)))))], (15768 ^ _782652) ^ [_1078653, _1078655, _1078657] : [class_Orderings_Olinorder(_1078653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078653), _1078655)), hBOOL(hAPP(hAPP(c_member(_1078653), _1078657), _1078655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078653), c_Big__Operators_Olinorder__class_OMin(_1078653, _1078655)), _1078657)))], (15782 ^ _782652) ^ [_1078880, _1078882, _1078884] : [class_Orderings_Olinorder(_1078880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078880), _1078882)), hBOOL(hAPP(hAPP(c_member(_1078880), _1078884), _1078882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078880), _1078884), c_Big__Operators_Olinorder__class_OMax(_1078880, _1078882))))], (15796 ^ _782652) ^ [_1079107, _1079109, _1079111] : [-(hAPP(c_Finite__Set_Ofold1(_1079107, _1079109), _1079111) = c_HOL_OThe(_1079107, c_Finite__Set_Ofold1Set(_1079107, _1079109, _1079111)))], (15798 ^ _782652) ^ [_1079147, _1079149] : [class_Orderings_Olinorder(_1079147), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079147), _1079149)), -(_1079149 = c_Orderings_Obot__class_Obot(tc_fun(_1079147, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1079147), c_Big__Operators_Olinorder__class_OMin(_1079147, _1079149)), _1079149)))], (15812 ^ _782652) ^ [_1079327, _1079329] : [class_Orderings_Olinorder(_1079327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079327), _1079329)), -(_1079329 = c_Orderings_Obot__class_Obot(tc_fun(_1079327, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1079327), c_Big__Operators_Olinorder__class_OMax(_1079327, _1079329)), _1079329)))], (15826 ^ _782652) ^ [_1079507, _1079509] : [class_Lattices_Olattice(_1079507), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079507), _1079509)), -(c_Big__Operators_Olattice__class_OSup__fin(_1079507, _1079509) = hAPP(c_Finite__Set_Ofold1(_1079507, c_Lattices_Osemilattice__sup__class_Osup(_1079507)), _1079509))], (15836 ^ _782652) ^ [_1079664, _1079666] : [class_Lattices_Olattice(_1079664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079664), _1079666)), -(c_Big__Operators_Olattice__class_OInf__fin(_1079664, _1079666) = hAPP(c_Finite__Set_Ofold1(_1079664, c_Lattices_Osemilattice__inf__class_Oinf(_1079664)), _1079666))], (15846 ^ _782652) ^ [_1079821, _1079823, _1079825, _1079827, _1079829] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1079821)), hAPP(c_Set_Oimage(_1079823, tc_Option_Ooption(_1079821), _1079825), c_Orderings_Otop__class_Otop(tc_fun(_1079823, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1079821)), hAPP(c_Set_Oimage(_1079823, tc_Option_Ooption(_1079821), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1079823, tc_Option_Ooption(_1079821)), _1079825), _1079827), hAPP(c_Option_Ooption_OSome(_1079821), _1079829))), c_Orderings_Otop__class_Otop(tc_fun(_1079823, tc_HOL_Obool))))))], (15852 ^ _782652) ^ [_1080022, _1080024, _1080026, _1080028] : [c_Fun_Oinj__on(_1080022, _1080024, _1080026, c_Orderings_Otop__class_Otop(tc_fun(_1080022, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1080024, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1080022, _1080024, _1080026), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1080022, tc_HOL_Obool)), _1080028))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1080024, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1080022, _1080024, _1080026), _1080028)))))], (15858 ^ _782652) ^ [_1080215, _1080217, _1080219] : [c_Hoare__Mirabelle_Otriple__valid(_1080215, _1080217, _1080219), -(hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(_1080215, tc_HOL_Obool, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_HOL_Obool))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_HOL_Obool)), tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1080215, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_HOL_OAll(_1080215)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_HOL_Obool))), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_HOL_Obool)), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_HOL_Obool), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, _1080215), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBC(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(_1080215, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBS(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1080215, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1080215), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1080215), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1080215), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1080215, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_Com_Ocom), c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1080215)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))), hAPP(hAPP(c_COMBC(tc_Com_Ocom, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_Natural_Oevaln)), _1080217))))))))), _1080219)))], (15864 ^ _782652) ^ [_1081260, _1081262, _1081264] : [hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(_1081260, tc_HOL_Obool, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_HOL_Obool))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_HOL_Obool)), tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1081260, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_HOL_OAll(_1081260)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_HOL_Obool))), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_HOL_Obool)), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_HOL_Obool), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, _1081260), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBC(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(_1081260, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBS(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1081260, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1081260), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1081260), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1081260), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_1081260, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_Com_Ocom), c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1081260)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))), hAPP(hAPP(c_COMBC(tc_Com_Ocom, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_Natural_Oevaln)), _1081262))))))))), _1081264)), -(c_Hoare__Mirabelle_Otriple__valid(_1081260, _1081262, _1081264))], (15870 ^ _782652) ^ [_1082311, _1082313, _1082315] : [class_Lattices_Osemilattice__inf(_1082311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082311), _1082313)), hBOOL(hAPP(hAPP(c_member(_1082311), _1082315), _1082313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082311), hAPP(c_Finite__Set_Ofold1(_1082311, c_Lattices_Osemilattice__inf__class_Oinf(_1082311)), _1082313)), _1082315)))], (15884 ^ _782652) ^ [_1082548, _1082550, _1082552] : [class_Lattices_Osemilattice__inf(_1082548), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082548), _1082550)), -(_1082550 = c_Orderings_Obot__class_Obot(tc_fun(_1082548, tc_HOL_Obool))), 15895 ^ _782652 : [(15906 ^ _782652) ^ [] : [15908 ^ _782652 : [(15909 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1082548), 15907 ^ [_1082548, _1082550, _1082552]), _1082550)))], (15911 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082548), _1082552), 15907 ^ [_1082548, _1082550, _1082552]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082548), _1082552), hAPP(c_Finite__Set_Ofold1(_1082548, c_Lattices_Osemilattice__inf__class_Oinf(_1082548)), _1082550))))], (15896 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082548), _1082552), hAPP(c_Finite__Set_Ofold1(_1082548, c_Lattices_Osemilattice__inf__class_Oinf(_1082548)), _1082550))), 15899 ^ _782652 : [(15900 ^ _782652) ^ [_1082841] : [hBOOL(hAPP(hAPP(c_member(_1082548), _1082841), _1082550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082548), _1082552), _1082841)))]]]]], (15915 ^ _782652) ^ [_1083126, _1083128, _1083130] : [class_Lattices_Oab__semigroup__idem__mult(_1083126), -(_1083128 = c_Orderings_Obot__class_Obot(tc_fun(_1083126, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083126), _1083128)), -(hAPP(c_Finite__Set_Ofold1(_1083126, c_Groups_Otimes__class_Otimes(_1083126)), hAPP(hAPP(c_Set_Oinsert(_1083126), _1083130), _1083128)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083126), _1083130), hAPP(c_Finite__Set_Ofold1(_1083126, c_Groups_Otimes__class_Otimes(_1083126)), _1083128)))], (15929 ^ _782652) ^ [_1083396, _1083398, _1083400] : [class_Lattices_Oab__semigroup__idem__mult(_1083396), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083396), _1083398)), -(_1083398 = c_Orderings_Obot__class_Obot(tc_fun(_1083396, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083396), _1083400)), -(_1083400 = c_Orderings_Obot__class_Obot(tc_fun(_1083396, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1083396, c_Groups_Otimes__class_Otimes(_1083396)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1083396, tc_HOL_Obool)), _1083398), _1083400)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083396), hAPP(c_Finite__Set_Ofold1(_1083396, c_Groups_Otimes__class_Otimes(_1083396)), _1083398)), hAPP(c_Finite__Set_Ofold1(_1083396, c_Groups_Otimes__class_Otimes(_1083396)), _1083400)))], (15951 ^ _782652) ^ [_1083775, _1083777, _1083779] : [class_Orderings_Olinorder(_1083775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1083775, tc_HOL_Obool)), _1083777), _1083779)), -(_1083777 = c_Orderings_Obot__class_Obot(tc_fun(_1083775, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083775), _1083779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083775), c_Big__Operators_Olinorder__class_OMin(_1083775, _1083779)), c_Big__Operators_Olinorder__class_OMin(_1083775, _1083777))))], (15969 ^ _782652) ^ [_1084081, _1084083, _1084085] : [class_Orderings_Olinorder(_1084081), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084081, tc_HOL_Obool)), _1084083), _1084085)), -(_1084083 = c_Orderings_Obot__class_Obot(tc_fun(_1084081, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084081), _1084085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084081), c_Big__Operators_Olinorder__class_OMax(_1084081, _1084083)), c_Big__Operators_Olinorder__class_OMax(_1084081, _1084085))))], (15987 ^ _782652) ^ [_1084408, _1084410, _1084412, _1084414] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _1084408)), _1084410), hAPP(c_Nat_OSuc, _1084412)), _1084414)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1084408))), _1084410), _1084412), _1084414)))], (15993 ^ _782652) ^ [_1084553, _1084555, _1084557, _1084559] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1084553))), _1084555), _1084557), _1084559)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _1084553)), _1084555), hAPP(c_Nat_OSuc, _1084557)), _1084559)))], (15999 ^ _782652) ^ [_1084704, _1084706, _1084708] : [class_Groups_Oab__semigroup__mult(_1084704), -(_1084706 = c_Orderings_Obot__class_Obot(tc_fun(_1084704, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084704), _1084706)), -(hBOOL(hAPP(hAPP(c_member(_1084704), _1084708), _1084706))), -(hAPP(c_Finite__Set_Ofold1(_1084704, c_Groups_Otimes__class_Otimes(_1084704)), hAPP(hAPP(c_Set_Oinsert(_1084704), _1084708), _1084706)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084704), _1084708), hAPP(c_Finite__Set_Ofold1(_1084704, c_Groups_Otimes__class_Otimes(_1084704)), _1084706)))], (16017 ^ _782652) ^ [_1085003, _1085005, _1085007, _1085009] : [c_Big__Operators_Osemilattice__big(_1085003, _1085005, _1085007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085003), _1085009)), -(hAPP(_1085007, _1085009) = hAPP(c_Finite__Set_Ofold1(_1085003, _1085005), _1085009))], (16027 ^ _782652) ^ [_1085168, _1085170, _1085172, _1085174] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _1085168)), _1085170), _1085172), _1085174)), 16031 ^ _782652 : [(16032 ^ _782652) ^ [] : [-(_1085172 = hAPP(c_Nat_OSuc, 16030 ^ [_1085168, _1085170, _1085172, _1085174]))], (16034 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1085168))), _1085170), 16030 ^ [_1085168, _1085170, _1085172, _1085174]), _1085174)))]]], (16036 ^ _782652) ^ [_1085374, _1085376] : [class_Groups_Oab__semigroup__mult(_1085374), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085374), _1085376)), -(_1085376 = c_Orderings_Obot__class_Obot(tc_fun(_1085374, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1085374), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085374), 16049 ^ [_1085374, _1085376]), 16050 ^ [_1085374, _1085376])), hAPP(hAPP(c_Set_Oinsert(_1085374), 16049 ^ [_1085374, _1085376]), hAPP(hAPP(c_Set_Oinsert(_1085374), 16050 ^ [_1085374, _1085376]), c_Orderings_Obot__class_Obot(tc_fun(_1085374, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1085374), hAPP(c_Finite__Set_Ofold1(_1085374, c_Groups_Otimes__class_Otimes(_1085374)), _1085376)), _1085376)))], (16056 ^ _782652) ^ [_1085828, _1085830, _1085832] : [class_Lattices_Oab__semigroup__idem__mult(_1085828), hAPP(_1085830, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085828), 16061 ^ [_1085828, _1085830, _1085832]), 16062 ^ [_1085828, _1085830, _1085832])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085828), hAPP(_1085830, 16061 ^ [_1085828, _1085830, _1085832])), hAPP(_1085830, 16062 ^ [_1085828, _1085830, _1085832])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085828), _1085832)), -(_1085832 = c_Orderings_Obot__class_Obot(tc_fun(_1085828, tc_HOL_Obool))), -(hAPP(_1085830, hAPP(c_Finite__Set_Ofold1(_1085828, c_Groups_Otimes__class_Otimes(_1085828)), _1085832)) = hAPP(c_Finite__Set_Ofold1(_1085828, c_Groups_Otimes__class_Otimes(_1085828)), hAPP(c_Set_Oimage(_1085828, _1085828, _1085830), _1085832)))], (16076 ^ _782652) ^ [_1086251, _1086253, _1086255] : [class_Orderings_Olinorder(_1086251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086251), _1086253)), hBOOL(hAPP(hAPP(c_member(_1086251), _1086255), _1086253)), 16087 ^ _782652 : [(16088 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1086251, tc_HOL_Obool)), _1086253), hAPP(hAPP(c_Set_Oinsert(_1086251), _1086255), c_Orderings_Obot__class_Obot(tc_fun(_1086251, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1086251, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1086251, _1086253) = _1086255)], (16094 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1086251, tc_HOL_Obool)), _1086253), hAPP(hAPP(c_Set_Oinsert(_1086251), _1086255), c_Orderings_Obot__class_Obot(tc_fun(_1086251, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1086251, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1086251, _1086253) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1086251), _1086255), c_Big__Operators_Olinorder__class_OMin(_1086251, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1086251, tc_HOL_Obool)), _1086253), hAPP(hAPP(c_Set_Oinsert(_1086251), _1086255), c_Orderings_Obot__class_Obot(tc_fun(_1086251, tc_HOL_Obool)))))))]]], (16100 ^ _782652) ^ [_1086757, _1086759, _1086761] : [class_Orderings_Olinorder(_1086757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086757), _1086759)), hBOOL(hAPP(hAPP(c_member(_1086757), _1086761), _1086759)), 16111 ^ _782652 : [(16112 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1086757, tc_HOL_Obool)), _1086759), hAPP(hAPP(c_Set_Oinsert(_1086757), _1086761), c_Orderings_Obot__class_Obot(tc_fun(_1086757, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1086757, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1086757, _1086759) = _1086761)], (16118 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1086757, tc_HOL_Obool)), _1086759), hAPP(hAPP(c_Set_Oinsert(_1086757), _1086761), c_Orderings_Obot__class_Obot(tc_fun(_1086757, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1086757, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1086757, _1086759) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1086757), _1086761), c_Big__Operators_Olinorder__class_OMax(_1086757, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1086757, tc_HOL_Obool)), _1086759), hAPP(hAPP(c_Set_Oinsert(_1086757), _1086761), c_Orderings_Obot__class_Obot(tc_fun(_1086757, tc_HOL_Obool)))))))]]], (16124 ^ _782652) ^ [_1087263, _1087265, _1087267, _1087269] : [c_Fun_Oinj__on(_1087263, _1087265, _1087267, c_Orderings_Otop__class_Otop(tc_fun(_1087263, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1087263, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1087263, _1087265, _1087267), hAPP(hAPP(c_Set_Oinsert(_1087265), _1087269), c_Orderings_Obot__class_Obot(tc_fun(_1087265, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1087263), c_HOL_OThe(_1087263, hAPP(hAPP(c_COMBC(_1087263, _1087265, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1087265, tc_fun(_1087265, tc_HOL_Obool), _1087263), c_fequal), _1087267)), _1087269))), c_Orderings_Obot__class_Obot(tc_fun(_1087263, tc_HOL_Obool))))))], (16130 ^ _782652) ^ [_1087496, _1087498] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1087496, tc_HOL_Obool)), _1087498)))], (16132 ^ _782652) ^ [_1087528, _1087530, _1087532, _1087534, _1087536, _1087538] : [hAPP(_1087528, _1087530) = _1087532, hBOOL(hAPP(hAPP(c_member(_1087534), _1087532), _1087536)), -(hBOOL(hAPP(hAPP(c_member(_1087538), _1087530), hAPP(c_Set_Ovimage(_1087538, _1087534, _1087528), _1087536))))], (16142 ^ _782652) ^ [_1087721, _1087723, _1087725] : [-(hAPP(c_Set_Ovimage(_1087721, _1087723, _1087725), c_Orderings_Otop__class_Otop(tc_fun(_1087723, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1087721, tc_HOL_Obool)))], (16144 ^ _782652) ^ [_1087765, _1087767, _1087769] : [class_Groups_Olinordered__ab__group__add(_1087765), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1087765), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1087765), _1087767), _1087769)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1087765), hAPP(c_Groups_Ouminus__class_Ouminus(_1087765), _1087767)), hAPP(c_Groups_Ouminus__class_Ouminus(_1087765), _1087769)))], (16150 ^ _782652) ^ [_1087904, _1087906, _1087908] : [class_Groups_Olinordered__ab__group__add(_1087904), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1087904), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1087904), _1087906), _1087908)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1087904), hAPP(c_Groups_Ouminus__class_Ouminus(_1087904), _1087906)), hAPP(c_Groups_Ouminus__class_Ouminus(_1087904), _1087908)))], (16156 ^ _782652) ^ [_1088043, _1088045, _1088047, _1088049] : [class_Orderings_Olinorder(_1088043), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088043), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088043), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1088043), _1088045), _1088047)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1088043), _1088045), _1088049))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1088043), _1088045), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088043), _1088047), _1088049)))))], (16162 ^ _782652) ^ [_1088216, _1088218, _1088220, _1088222] : [class_Orderings_Olinorder(_1088216), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088216), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088216), _1088218), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1088216), _1088220), _1088222))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1088216), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088216), _1088218), _1088220)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088216), _1088218), _1088222)))))], (16168 ^ _782652) ^ [_1088389, _1088391] : [class_Orderings_Olinorder(_1088389), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088389), _1088391), _1088391) = _1088391)], (16174 ^ _782652) ^ [_1088480, _1088482] : [class_Orderings_Olinorder(_1088480), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1088480), _1088482), _1088482) = _1088482)], (16180 ^ _782652) ^ [_1088571, _1088573] : [-(hAPP(c_Set_Ovimage(_1088571, _1088571, c_COMBI(_1088571)), _1088573) = _1088573)], (16182 ^ _782652) ^ [_1088605, _1088607] : [class_Orderings_Olinorder(_1088605), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088605), _1088607), _1088607) = _1088607)], (16188 ^ _782652) ^ [_1088696, _1088698] : [class_Orderings_Olinorder(_1088696), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1088696), _1088698), _1088698) = _1088698)], (16194 ^ _782652) ^ [_1088787, _1088789, _1088791] : [class_Orderings_Olinorder(_1088787), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088787), _1088789), _1088791) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088787), _1088791), _1088789))], (16200 ^ _782652) ^ [_1088896, _1088898, _1088900] : [class_Orderings_Olinorder(_1088896), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088896), _1088898), _1088900) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088896), _1088900), _1088898))], (16206 ^ _782652) ^ [_1089005, _1089007, _1089009] : [class_Orderings_Olinorder(_1089005), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089005), _1089007), _1089009) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089005), _1089009), _1089007))], (16212 ^ _782652) ^ [_1089114, _1089116, _1089118] : [class_Orderings_Olinorder(_1089114), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089114), _1089116), _1089118) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089114), _1089118), _1089116))], (16218 ^ _782652) ^ [_1089223, _1089225, _1089227] : [class_Orderings_Olinorder(_1089223), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089223), _1089225), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089223), _1089225), _1089227)) = _1089225)], (16224 ^ _782652) ^ [_1089332, _1089334, _1089336] : [class_Orderings_Olinorder(_1089332), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089332), _1089334), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089332), _1089334), _1089336)) = _1089334)], (16230 ^ _782652) ^ [_1089441, _1089443, _1089445] : [class_Orderings_Olinorder(_1089441), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089441), _1089443), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089441), _1089443), _1089445)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089441), _1089443), _1089445))], (16236 ^ _782652) ^ [_1089566, _1089568, _1089570] : [class_Orderings_Olinorder(_1089566), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089566), _1089568), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089566), _1089568), _1089570)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089566), _1089568), _1089570))], (16242 ^ _782652) ^ [_1089691, _1089693, _1089695] : [class_Orderings_Olinorder(_1089691), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089691), _1089693), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089691), _1089693), _1089695)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089691), _1089693), _1089695))], (16248 ^ _782652) ^ [_1089816, _1089818, _1089820] : [class_Orderings_Olinorder(_1089816), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089816), _1089818), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089816), _1089818), _1089820)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089816), _1089818), _1089820))], (16254 ^ _782652) ^ [_1089941, _1089943, _1089945, _1089947] : [class_Orderings_Olinorder(_1089941), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089941), _1089943), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089941), _1089945), _1089947)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089941), _1089945), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089941), _1089943), _1089947)))], (16260 ^ _782652) ^ [_1090084, _1090086, _1090088, _1090090] : [class_Orderings_Olinorder(_1090084), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090084), _1090086), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090084), _1090088), _1090090)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090084), _1090088), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090084), _1090086), _1090090)))], (16266 ^ _782652) ^ [_1090227, _1090229, _1090231, _1090233] : [class_Orderings_Olinorder(_1090227), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090227), _1090229), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090227), _1090231), _1090233)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090227), _1090231), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090227), _1090229), _1090233)))], (16272 ^ _782652) ^ [_1090370, _1090372, _1090374, _1090376] : [class_Orderings_Olinorder(_1090370), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090370), _1090372), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090370), _1090374), _1090376)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090370), _1090374), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090370), _1090372), _1090376)))], (16278 ^ _782652) ^ [_1090513, _1090515, _1090517, _1090519] : [class_Orderings_Olinorder(_1090513), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090513), _1090515), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090513), _1090517), _1090519)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090513), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090513), _1090515), _1090517)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090513), _1090515), _1090519)))], (16284 ^ _782652) ^ [_1090672, _1090674, _1090676, _1090678] : [class_Orderings_Olinorder(_1090672), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090672), _1090674), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090672), _1090676), _1090678)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090672), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090672), _1090674), _1090676)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090672), _1090674), _1090678)))], (16290 ^ _782652) ^ [_1090831, _1090833, _1090835, _1090837] : [class_Orderings_Olinorder(_1090831), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090831), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090831), _1090833), _1090835)), _1090837) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090831), _1090833), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090831), _1090835), _1090837)))], (16296 ^ _782652) ^ [_1090974, _1090976, _1090978, _1090980] : [class_Orderings_Olinorder(_1090974), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090974), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090974), _1090976), _1090978)), _1090980) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090974), _1090976), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090974), _1090978), _1090980)))], (16302 ^ _782652) ^ [_1091117, _1091119, _1091121, _1091123] : [class_Orderings_Olinorder(_1091117), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091117), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091117), _1091119), _1091121)), _1091123) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091117), _1091119), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091117), _1091121), _1091123)))], (16308 ^ _782652) ^ [_1091260, _1091262, _1091264, _1091266] : [class_Orderings_Olinorder(_1091260), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091260), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091260), _1091262), _1091264)), _1091266) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091260), _1091262), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091260), _1091264), _1091266)))], (16314 ^ _782652) ^ [_1091403, _1091405, _1091407, _1091409] : [class_Orderings_Olinorder(_1091403), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091403), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091403), _1091405), _1091407)), _1091409) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091403), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091403), _1091405), _1091409)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091403), _1091407), _1091409)))], (16320 ^ _782652) ^ [_1091562, _1091564, _1091566, _1091568] : [class_Orderings_Olinorder(_1091562), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091562), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091562), _1091564), _1091566)), _1091568) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091562), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091562), _1091564), _1091568)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091562), _1091566), _1091568)))], (16326 ^ _782652) ^ [_1091745, _1091747, _1091749, _1091751, _1091753] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1091745, _1091747, _1091749), _1091751), _1091753)), -(hBOOL(hAPP(_1091751, hAPP(_1091749, _1091753))))], (16332 ^ _782652) ^ [_1091852, _1091854, _1091856, _1091858, _1091860] : [hBOOL(hAPP(_1091858, hAPP(_1091856, _1091860))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1091852, _1091854, _1091856), _1091858), _1091860)))], (16338 ^ _782652) ^ [_1091965, _1091967, _1091969, _1091971] : [class_Orderings_Olinorder(_1091965), 16341 ^ _782652 : [(16352 ^ _782652) ^ [] : [16353 ^ _782652 : [(16354 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091965), _1091967), _1091969))], (16356 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091965), _1091967), _1091971))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091965), _1091967), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091965), _1091969), _1091971))))], (16342 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091965), _1091967), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091965), _1091969), _1091971))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091965), _1091967), _1091969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091965), _1091967), _1091971)))]]], (16360 ^ _782652) ^ [_1092314, _1092316, _1092318] : [class_Orderings_Olinorder(_1092314), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092314), _1092316), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092314), _1092316), _1092318))))], (16366 ^ _782652) ^ [_1092421, _1092423, _1092425] : [class_Orderings_Olinorder(_1092421), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092421), _1092423), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092421), _1092425), _1092423))))], (16372 ^ _782652) ^ [_1092528, _1092530, _1092532] : [class_Orderings_Olinorder(_1092528), 16375 ^ _782652 : [(16376 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092528), _1092530), _1092532)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092528), _1092530), _1092532) = _1092532)], (16382 ^ _782652) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092528), _1092530), _1092532) = _1092532, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092528), _1092530), _1092532)))]]], (16388 ^ _782652) ^ [_1092784, _1092786, _1092788, _1092790] : [class_Orderings_Olinorder(_1092784), 16391 ^ _782652 : [(16392 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092784), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092784), _1092786), _1092788)), _1092790)), 16395 ^ _782652 : [(16396 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092784), _1092786), _1092790)))], (16398 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092784), _1092788), _1092790)))]]], (16400 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092784), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092784), _1092786), _1092788)), _1092790))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092784), _1092786), _1092790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092784), _1092788), _1092790))]]], (16410 ^ _782652) ^ [_1093164, _1093166, _1093168, _1093170] : [class_Orderings_Olinorder(_1093164), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093164), _1093166), _1093168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093164), _1093166), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093164), _1093168), _1093170))))], (16420 ^ _782652) ^ [_1093343, _1093345, _1093347, _1093349] : [class_Orderings_Olinorder(_1093343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093343), _1093345), _1093347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093343), _1093345), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093343), _1093349), _1093347))))], (16430 ^ _782652) ^ [_1093522, _1093524, _1093526] : [class_Orderings_Olinorder(_1093522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093522), _1093524), _1093526)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093522), _1093524), _1093526) = _1093526)], (16440 ^ _782652) ^ [_1093683, _1093685, _1093687] : [class_Orderings_Olinorder(_1093683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093683), _1093685), _1093687)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093683), _1093687), _1093685) = _1093687)], (16450 ^ _782652) ^ [_1093844, _1093846, _1093848, _1093850] : [class_Orderings_Olinorder(_1093844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093844), _1093846), _1093848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093844), _1093850), _1093848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093844), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093844), _1093846), _1093850)), _1093848)))], (16464 ^ _782652) ^ [_1094093, _1094095, _1094097, _1094099] : [class_Orderings_Olinorder(_1094093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094093), _1094095), _1094097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094093), _1094099), _1094097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094093), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094093), _1094095), _1094099)), _1094097)))], (16478 ^ _782652) ^ [_1094342, _1094344, _1094346, _1094348, _1094350] : [class_Orderings_Olinorder(_1094342), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094342), _1094344), _1094346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094342), _1094348), _1094350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094342), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094342), _1094344), _1094348)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094342), _1094346), _1094350))))], (16492 ^ _782652) ^ [_1094613, _1094615, _1094617, _1094619] : [class_Orderings_Olinorder(_1094613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094613), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094613), _1094615), _1094617)), _1094619)), 16499 ^ _782652 : [(16500 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094613), _1094615), _1094619)))], (16502 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094613), _1094617), _1094619)))]]], (16504 ^ _782652) ^ [_1094836, _1094838, _1094840, _1094842] : [class_Orderings_Olinorder(_1094836), 16507 ^ _782652 : [(16518 ^ _782652) ^ [] : [16519 ^ _782652 : [(16520 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094836), _1094838), _1094842))], (16522 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094836), _1094840), _1094842))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094836), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094836), _1094838), _1094840)), _1094842)))], (16508 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094836), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094836), _1094838), _1094840)), _1094842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094836), _1094838), _1094842))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094836), _1094840), _1094842)))]]], (16526 ^ _782652) ^ [_1095185, _1095187, _1095189] : [class_Orderings_Olinorder(_1095185), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095185), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095185), _1095187), _1095189)), _1095187)))], (16532 ^ _782652) ^ [_1095292, _1095294, _1095296] : [class_Orderings_Olinorder(_1095292), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095292), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095292), _1095294), _1095296)), _1095296)))], (16538 ^ _782652) ^ [_1095399, _1095401, _1095403] : [class_Orderings_Olinorder(_1095399), 16541 ^ _782652 : [(16542 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095399), _1095401), _1095403)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095399), _1095401), _1095403) = _1095401)], (16548 ^ _782652) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095399), _1095401), _1095403) = _1095401, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095399), _1095401), _1095403)))]]], (16554 ^ _782652) ^ [_1095655, _1095657, _1095659, _1095661] : [class_Orderings_Olinorder(_1095655), 16557 ^ _782652 : [(16558 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095655), _1095657), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095655), _1095659), _1095661))), 16561 ^ _782652 : [(16562 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095655), _1095657), _1095659)))], (16564 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095655), _1095657), _1095661)))]]], (16566 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095655), _1095657), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095655), _1095659), _1095661)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095655), _1095657), _1095659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095655), _1095657), _1095661))]]], (16576 ^ _782652) ^ [_1096035, _1096037, _1096039, _1096041] : [class_Orderings_Olinorder(_1096035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096035), _1096037), _1096039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096035), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096035), _1096037), _1096041)), _1096039)))], (16586 ^ _782652) ^ [_1096214, _1096216, _1096218, _1096220] : [class_Orderings_Olinorder(_1096214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096214), _1096216), _1096218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096214), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096214), _1096220), _1096216)), _1096218)))], (16596 ^ _782652) ^ [_1096393, _1096395, _1096397] : [class_Orderings_Olinorder(_1096393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096393), _1096395), _1096397)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096393), _1096395), _1096397) = _1096395)], (16606 ^ _782652) ^ [_1096554, _1096556, _1096558] : [class_Orderings_Olinorder(_1096554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096554), _1096556), _1096558)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096554), _1096558), _1096556) = _1096556)], (16616 ^ _782652) ^ [_1096715, _1096717, _1096719, _1096721] : [class_Orderings_Olinorder(_1096715), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096715), _1096717), _1096719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096715), _1096717), _1096721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096715), _1096717), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096715), _1096719), _1096721))))], (16630 ^ _782652) ^ [_1096964, _1096966, _1096968, _1096970] : [class_Orderings_Olinorder(_1096964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096964), _1096966), _1096968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096964), _1096966), _1096970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096964), _1096966), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096964), _1096968), _1096970))))], (16644 ^ _782652) ^ [_1097213, _1097215, _1097217, _1097219, _1097221] : [class_Orderings_Olinorder(_1097213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097213), _1097215), _1097217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097213), _1097219), _1097221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097213), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097213), _1097215), _1097219)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097213), _1097217), _1097221))))], (16658 ^ _782652) ^ [_1097484, _1097486, _1097488, _1097490] : [class_Orderings_Olinorder(_1097484), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097484), _1097486), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097484), _1097488), _1097490))), 16665 ^ _782652 : [(16666 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097484), _1097486), _1097488)))], (16668 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097484), _1097486), _1097490)))]]], (16670 ^ _782652) ^ [_1097707, _1097709, _1097711, _1097713] : [class_Orderings_Olinorder(_1097707), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097707), _1097709), _1097711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097707), _1097709), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097707), _1097711), _1097713))))], (16680 ^ _782652) ^ [_1097886, _1097888, _1097890, _1097892] : [class_Orderings_Olinorder(_1097886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097886), _1097888), _1097890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097886), _1097888), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097886), _1097892), _1097890))))], (16690 ^ _782652) ^ [_1098065, _1098067, _1098069, _1098071] : [class_Orderings_Olinorder(_1098065), 16693 ^ _782652 : [(16704 ^ _782652) ^ [] : [16705 ^ _782652 : [(16706 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098065), _1098067), _1098069))], (16708 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098065), _1098067), _1098071))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098065), _1098067), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1098065), _1098069), _1098071))))], (16694 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098065), _1098067), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1098065), _1098069), _1098071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098065), _1098067), _1098069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098065), _1098067), _1098071)))]]], (16712 ^ _782652) ^ [_1098414, _1098416, _1098418, _1098420] : [class_Orderings_Olinorder(_1098414), 16715 ^ _782652 : [(16716 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098414), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1098414), _1098416), _1098418)), _1098420)), 16719 ^ _782652 : [(16720 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098414), _1098416), _1098420)))], (16722 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098414), _1098418), _1098420)))]]], (16724 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098414), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1098414), _1098416), _1098418)), _1098420))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098414), _1098416), _1098420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098414), _1098418), _1098420))]]], (16734 ^ _782652) ^ [_1098794, _1098796, _1098798, _1098800] : [class_Orderings_Olinorder(_1098794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098794), _1098796), _1098798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098794), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098794), _1098796), _1098800)), _1098798)))], (16744 ^ _782652) ^ [_1098973, _1098975, _1098977, _1098979] : [class_Orderings_Olinorder(_1098973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098973), _1098975), _1098977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098973), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098973), _1098979), _1098975)), _1098977)))], (16754 ^ _782652) ^ [_1099152, _1099154, _1099156, _1099158] : [class_Orderings_Olinorder(_1099152), 16757 ^ _782652 : [(16758 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099152), _1099154), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099152), _1099156), _1099158))), 16761 ^ _782652 : [(16762 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099152), _1099154), _1099156)))], (16764 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099152), _1099154), _1099158)))]]], (16766 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099152), _1099154), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099152), _1099156), _1099158)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099152), _1099154), _1099156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099152), _1099154), _1099158))]]], (16776 ^ _782652) ^ [_1099532, _1099534, _1099536, _1099538] : [class_Orderings_Olinorder(_1099532), 16779 ^ _782652 : [(16790 ^ _782652) ^ [] : [16791 ^ _782652 : [(16792 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099532), _1099534), _1099538))], (16794 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099532), _1099536), _1099538))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099532), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099532), _1099534), _1099536)), _1099538)))], (16780 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099532), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099532), _1099534), _1099536)), _1099538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099532), _1099534), _1099538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099532), _1099536), _1099538)))]]], (16798 ^ _782652) ^ [_1099881, _1099883, _1099885, _1099887] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1099881), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099881), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1099881), _1099883), _1099885)), _1099887) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1099881), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099881), _1099883), _1099887)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099881), _1099885), _1099887)))], (16804 ^ _782652) ^ [_1100040, _1100042, _1100044, _1100046] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1100040), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100040), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100040), _1100042), _1100044)), _1100046) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100040), _1100042), _1100046)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100040), _1100044), _1100046)))], (16810 ^ _782652) ^ [_1100199, _1100201, _1100203, _1100205] : [class_Groups_Oordered__ab__group__add(_1100199), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100199), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1100199), _1100201), _1100203)), _1100205) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1100199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100199), _1100201), _1100205)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100199), _1100203), _1100205)))], (16816 ^ _782652) ^ [_1100358, _1100360, _1100362, _1100364] : [class_Groups_Oordered__ab__group__add(_1100358), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100358), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100358), _1100360), _1100362)), _1100364) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100358), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100358), _1100360), _1100364)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100358), _1100362), _1100364)))], (16822 ^ _782652) ^ [_1100541, _1100543, _1100545, _1100547, _1100549] : [hBOOL(hAPP(hAPP(c_member(_1100541), _1100543), hAPP(c_Set_Ovimage(_1100541, _1100545, _1100547), _1100549))), -(hBOOL(hAPP(hAPP(c_member(_1100545), hAPP(_1100547, _1100543)), _1100549)))], (16828 ^ _782652) ^ [_1100668, _1100670, _1100672, _1100674, _1100676] : [hBOOL(hAPP(hAPP(c_member(_1100672), hAPP(_1100674, _1100670)), _1100676)), -(hBOOL(hAPP(hAPP(c_member(_1100668), _1100670), hAPP(c_Set_Ovimage(_1100668, _1100672, _1100674), _1100676))))], (16834 ^ _782652) ^ [_1100801, _1100803, _1100805, _1100807, _1100809] : [hBOOL(hAPP(hAPP(c_member(_1100801), _1100803), hAPP(c_Set_Ovimage(_1100801, _1100805, _1100807), _1100809))), -(hBOOL(hAPP(hAPP(c_member(_1100805), hAPP(_1100807, _1100803)), _1100809)))], (16840 ^ _782652) ^ [_1100932, _1100934, _1100936, _1100938, _1100940] : [hBOOL(hAPP(hAPP(c_member(_1100932), hAPP(_1100934, _1100936)), _1100938)), -(hBOOL(hAPP(hAPP(c_member(_1100940), _1100936), hAPP(c_Set_Ovimage(_1100940, _1100932, _1100934), _1100938))))], (16846 ^ _782652) ^ [_1101063] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1101063) = c_Orderings_Oord__class_Omax(_1101063)), class_Lattices_Osemilattice__sup(_1101063), class_Orderings_Olinorder(_1101063)], (16856 ^ _782652) ^ [_1101192] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1101192) = c_Orderings_Oord__class_Omin(_1101192)), class_Lattices_Osemilattice__inf(_1101192), class_Orderings_Olinorder(_1101192)], (16866 ^ _782652) ^ [_1101321, _1101323] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1101321)), hAPP(c_Nat_OSuc, _1101323)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1101321), _1101323)))], (16868 ^ _782652) ^ [_1101367, _1101369] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1101367)), hAPP(c_Nat_OSuc, _1101369)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1101367), _1101369)))], (16870 ^ _782652) ^ [_1101413, _1101415, _1101417] : [-(hAPP(c_Set_Ovimage(_1101413, _1101415, _1101417), c_Orderings_Obot__class_Obot(tc_fun(_1101415, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1101413, tc_HOL_Obool)))], (16872 ^ _782652) ^ [_1101457, _1101459, _1101461] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1101457), _1101459)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1101461), _1101459)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1101457), _1101461)), _1101459))], (16874 ^ _782652) ^ [_1101514, _1101516, _1101518, _1101520, _1101522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101514, tc_HOL_Obool)), _1101516), _1101518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101520, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1101520, _1101514, _1101522), _1101516)), hAPP(c_Set_Ovimage(_1101520, _1101514, _1101522), _1101518))))], (16880 ^ _782652) ^ [_1101665, _1101667, _1101669, _1101671] : [hAPP(c_Set_Oimage(_1101665, _1101667, _1101669), c_Orderings_Otop__class_Otop(tc_fun(_1101665, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1101667, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1101665, _1101667, _1101669), hAPP(c_Set_Ovimage(_1101665, _1101667, _1101669), _1101671)) = _1101671)], (16886 ^ _782652) ^ [_1101808, _1101810, _1101812, _1101814, _1101816] : [-(hAPP(c_Set_Ovimage(_1101808, _1101810, _1101812), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1101810, tc_HOL_Obool)), _1101814), _1101816)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1101808, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1101808, _1101810, _1101812), _1101814)), hAPP(c_Set_Ovimage(_1101808, _1101810, _1101812), _1101816)))], (16888 ^ _782652) ^ [_1101882, _1101884, _1101886, _1101888, _1101890] : [-(hAPP(c_Set_Ovimage(_1101882, _1101884, _1101886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1101884, tc_HOL_Obool)), _1101888), _1101890)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1101882, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1101882, _1101884, _1101886), _1101888)), hAPP(c_Set_Ovimage(_1101882, _1101884, _1101886), _1101890)))], (16890 ^ _782652) ^ [_1101956, _1101958, _1101960, _1101962, _1101964] : [-(hAPP(c_Set_Ovimage(_1101956, _1101958, _1101960), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1101958, tc_HOL_Obool)), _1101962), _1101964)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1101956, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1101956, _1101958, _1101960), _1101962)), hAPP(c_Set_Ovimage(_1101956, _1101958, _1101960), _1101964)))], (16892 ^ _782652) ^ [_1102030, _1102032, _1102034, _1102036] : [-(hAPP(c_Set_Ovimage(_1102030, _1102032, _1102034), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1102032, tc_HOL_Obool)), _1102036)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1102030, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1102030, _1102032, _1102034), _1102036)))], (16894 ^ _782652) ^ [_1102089] : [class_Orderings_Olinorder(_1102089), -(c_Finite__Set_Ofun__left__comm__idem(_1102089, _1102089, c_Orderings_Oord__class_Omax(_1102089)))], (16900 ^ _782652) ^ [_1102168] : [class_Orderings_Olinorder(_1102168), -(c_Finite__Set_Ofun__left__comm__idem(_1102168, _1102168, c_Orderings_Oord__class_Omin(_1102168)))], (16906 ^ _782652) ^ [_1102247, _1102249, _1102251, _1102253] : [-(hAPP(c_Set_Ovimage(_1102247, _1102249, _1102251), hAPP(c_Set_OCollect(_1102249), _1102253)) = hAPP(c_Set_OCollect(_1102247), hAPP(hAPP(c_COMBB(_1102249, tc_HOL_Obool, _1102247), _1102253), _1102251)))], (16908 ^ _782652) ^ [_1102303, _1102305] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1102303), _1102305)), _1102305) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1102303), _1102305))], (16910 ^ _782652) ^ [_1102346, _1102348, _1102350, _1102352] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102346), hAPP(c_Set_Ovimage(_1102346, _1102348, _1102350), _1102352))), hAPP(c_Set_Oimage(_1102346, _1102348, _1102350), c_Orderings_Otop__class_Otop(tc_fun(_1102346, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1102348, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1102348), _1102352)))], (16920 ^ _782652) ^ [_1102547, _1102549, _1102551, _1102553] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1102547, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1102549, _1102547, _1102551), hAPP(c_Set_Ovimage(_1102549, _1102547, _1102551), _1102553))), _1102553)))], (16922 ^ _782652) ^ [_1102600, _1102602, _1102604, _1102606, _1102608] : [hAPP(c_Set_Oimage(_1102600, _1102602, _1102604), c_Orderings_Otop__class_Otop(tc_fun(_1102600, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1102602, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1102600, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1102600, _1102602, _1102604), _1102606)), _1102608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1102602, tc_HOL_Obool)), _1102606), hAPP(c_Set_Oimage(_1102600, _1102602, _1102604), _1102608))))], (16932 ^ _782652) ^ [_1102843, _1102845, _1102847, _1102849] : [-(hAPP(c_Set_Oimage(_1102843, _1102845, _1102847), hAPP(c_Set_Ovimage(_1102843, _1102845, _1102847), _1102849)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102845, tc_HOL_Obool)), _1102849), hAPP(c_Set_Oimage(_1102843, _1102845, _1102847), c_Orderings_Otop__class_Otop(tc_fun(_1102843, tc_HOL_Obool)))))], (16934 ^ _782652) ^ [_1102909, _1102911, _1102913, _1102915] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102909), _1102911)), c_Fun_Oinj__on(_1102913, _1102909, _1102915, c_Orderings_Otop__class_Otop(tc_fun(_1102913, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1102913), hAPP(c_Set_Ovimage(_1102913, _1102909, _1102915), _1102911))))], (16944 ^ _782652) ^ [_1103090, _1103092, _1103094, _1103096] : [c_Fun_Oinj__on(_1103090, _1103092, _1103094, c_Orderings_Otop__class_Otop(tc_fun(_1103090, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1103090, _1103092, _1103094), hAPP(c_Set_Oimage(_1103090, _1103092, _1103094), _1103096)) = _1103096)], (16950 ^ _782652) ^ [_1103228, _1103230, _1103232, _1103234] : [hBOOL(hAPP(hAPP(c_member(_1103228), _1103230), _1103232)), -(hAPP(c_Set_Ovimage(_1103234, _1103228, hAPP(c_COMBK(_1103228, _1103234), _1103230)), _1103232) = c_Orderings_Otop__class_Otop(tc_fun(_1103234, tc_HOL_Obool)))], (16956 ^ _782652) ^ [_1103353, _1103355, _1103357, _1103359] : [-(hBOOL(hAPP(hAPP(c_member(_1103353), _1103355), _1103357))), -(hAPP(c_Set_Ovimage(_1103359, _1103353, hAPP(c_COMBK(_1103353, _1103359), _1103355)), _1103357) = c_Orderings_Obot__class_Obot(tc_fun(_1103359, tc_HOL_Obool)))], (16962 ^ _782652) ^ [_1103420, _1103422, _1103424, _1103426] : [-(hAPP(c_Set_Ovimage(_1103420, _1103422, _1103424), _1103426) = hAPP(c_Set_OCollect(_1103420), hAPP(hAPP(c_COMBC(_1103420, tc_fun(_1103422, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1103422, tc_fun(tc_fun(_1103422, tc_HOL_Obool), tc_HOL_Obool), _1103420), c_member(_1103422)), _1103424)), _1103426)))], (16964 ^ _782652) ^ [_1103516, _1103518, _1103520, _1103522, _1103524] : [hBOOL(hAPP(hAPP(c_member(_1103516), _1103518), hAPP(c_Set_Ovimage(_1103516, _1103520, _1103522), hAPP(hAPP(c_Set_Oinsert(_1103520), _1103524), c_Orderings_Obot__class_Obot(tc_fun(_1103520, tc_HOL_Obool)))))), -(hAPP(_1103522, _1103518) = _1103524)], (16970 ^ _782652) ^ [_1103655, _1103657, _1103659, _1103661, _1103663] : [hAPP(_1103661, _1103657) = _1103663, -(hBOOL(hAPP(hAPP(c_member(_1103655), _1103657), hAPP(c_Set_Ovimage(_1103655, _1103659, _1103661), hAPP(hAPP(c_Set_Oinsert(_1103659), _1103663), c_Orderings_Obot__class_Obot(tc_fun(_1103659, tc_HOL_Obool)))))))], (16976 ^ _782652) ^ [_1103800, _1103802, _1103804, _1103806, _1103808] : [-(hAPP(c_Set_Ovimage(_1103800, _1103802, _1103804), hAPP(hAPP(c_Set_Oinsert(_1103802), _1103806), _1103808)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1103800, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1103800, _1103802, _1103804), hAPP(hAPP(c_Set_Oinsert(_1103802), _1103806), c_Orderings_Obot__class_Obot(tc_fun(_1103802, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1103800, _1103802, _1103804), _1103808)))], (16978 ^ _782652) ^ [_1103884, _1103886, _1103888] : [class_Orderings_Olinorder(_1103884), hBOOL(hAPP(c_Finite__Set_Ofinite(_1103884), _1103886)), hBOOL(hAPP(hAPP(c_member(_1103884), _1103888), _1103886)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1103884), _1103888), c_Big__Operators_Olinorder__class_OMax(_1103884, _1103886)) = c_Big__Operators_Olinorder__class_OMax(_1103884, _1103886))], (16992 ^ _782652) ^ [_1104119, _1104121, _1104123] : [class_Orderings_Olinorder(_1104119), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104119), _1104121)), hBOOL(hAPP(hAPP(c_member(_1104119), _1104123), _1104121)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1104119), _1104123), c_Big__Operators_Olinorder__class_OMin(_1104119, _1104121)) = c_Big__Operators_Olinorder__class_OMin(_1104119, _1104121))], (17006 ^ _782652) ^ [_1104354, _1104356, _1104358, _1104360, _1104362] : [c_Fun_Oinj__on(_1104354, _1104356, _1104358, c_Orderings_Otop__class_Otop(tc_fun(_1104354, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104356, tc_HOL_Obool)), _1104360), hAPP(c_Set_Oimage(_1104354, _1104356, _1104358), _1104362))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104354, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1104354, _1104356, _1104358), _1104360)), _1104362)))], (17016 ^ _782652) ^ [_1104577, _1104579] : [class_Orderings_Olinorder(_1104577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104577), _1104579)), -(c_Big__Operators_Olinorder__class_OMax(_1104577, _1104579) = hAPP(c_Finite__Set_Ofold1(_1104577, c_Orderings_Oord__class_Omax(_1104577)), _1104579))], (17026 ^ _782652) ^ [_1104734, _1104736] : [class_Orderings_Olinorder(_1104734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104734), _1104736)), -(c_Big__Operators_Olinorder__class_OMin(_1104734, _1104736) = hAPP(c_Finite__Set_Ofold1(_1104734, c_Orderings_Oord__class_Omin(_1104734)), _1104736))], (17036 ^ _782652) ^ [_1104912, _1104914, _1104916, _1104918, _1104920, _1104922] : [hBOOL(hAPP(hAPP(c_member(_1104912), _1104914), _1104916)), 17039 ^ _782652 : [(17040 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1104912), _1104918), _1104916)), -(hAPP(c_Set_Ovimage(_1104920, _1104912, hAPP(hAPP(c_COMBC(_1104920, _1104912, _1104912), hAPP(hAPP(c_COMBC(_1104920, _1104912, tc_fun(_1104912, _1104912)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1104912, tc_fun(_1104912, _1104912)), _1104920), c_If(_1104912)), hAPP(hAPP(c_COMBC(_1104920, tc_fun(_1104920, tc_HOL_Obool), tc_HOL_Obool), c_member(_1104920)), _1104922))), _1104914)), _1104918)), _1104916) = c_Orderings_Otop__class_Otop(tc_fun(_1104920, tc_HOL_Obool)))], (17046 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1104912), _1104918), _1104916))), -(hAPP(c_Set_Ovimage(_1104920, _1104912, hAPP(hAPP(c_COMBC(_1104920, _1104912, _1104912), hAPP(hAPP(c_COMBC(_1104920, _1104912, tc_fun(_1104912, _1104912)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1104912, tc_fun(_1104912, _1104912)), _1104920), c_If(_1104912)), hAPP(hAPP(c_COMBC(_1104920, tc_fun(_1104920, tc_HOL_Obool), tc_HOL_Obool), c_member(_1104920)), _1104922))), _1104914)), _1104918)), _1104916) = _1104922)]]], (17052 ^ _782652) ^ [_1105403, _1105405, _1105407, _1105409, _1105411, _1105413] : [-(hBOOL(hAPP(hAPP(c_member(_1105403), _1105405), _1105407))), 17055 ^ _782652 : [(17056 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1105403), _1105409), _1105407)), -(hAPP(c_Set_Ovimage(_1105411, _1105403, hAPP(hAPP(c_COMBC(_1105411, _1105403, _1105403), hAPP(hAPP(c_COMBC(_1105411, _1105403, tc_fun(_1105403, _1105403)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1105403, tc_fun(_1105403, _1105403)), _1105411), c_If(_1105403)), hAPP(hAPP(c_COMBC(_1105411, tc_fun(_1105411, tc_HOL_Obool), tc_HOL_Obool), c_member(_1105411)), _1105413))), _1105405)), _1105409)), _1105407) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1105411, tc_HOL_Obool)), _1105413))], (17062 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105403), _1105409), _1105407))), -(hAPP(c_Set_Ovimage(_1105411, _1105403, hAPP(hAPP(c_COMBC(_1105411, _1105403, _1105403), hAPP(hAPP(c_COMBC(_1105411, _1105403, tc_fun(_1105403, _1105403)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1105403, tc_fun(_1105403, _1105403)), _1105411), c_If(_1105403)), hAPP(hAPP(c_COMBC(_1105411, tc_fun(_1105411, tc_HOL_Obool), tc_HOL_Obool), c_member(_1105411)), _1105413))), _1105405)), _1105409)), _1105407) = c_Orderings_Obot__class_Obot(tc_fun(_1105411, tc_HOL_Obool)))]]], (17068 ^ _782652) ^ [_1105908, _1105910, _1105912] : [class_Orderings_Olinorder(_1105908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105908), _1105910)), hBOOL(hAPP(hAPP(c_member(_1105908), _1105912), _1105910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105908), hAPP(c_Finite__Set_Ofold1(_1105908, c_Orderings_Oord__class_Omin(_1105908)), _1105910)), _1105912)))], (17082 ^ _782652) ^ [_1106145, _1106147, _1106149] : [class_Orderings_Olinorder(_1106145), hBOOL(hAPP(c_Finite__Set_Ofinite(_1106145), _1106147)), -(_1106147 = c_Orderings_Obot__class_Obot(tc_fun(_1106145, tc_HOL_Obool))), 17093 ^ _782652 : [(17104 ^ _782652) ^ [] : [17106 ^ _782652 : [(17107 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1106145), 17105 ^ [_1106145, _1106147, _1106149]), _1106147)))], (17109 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106145), _1106149), 17105 ^ [_1106145, _1106147, _1106149]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106145), _1106149), hAPP(c_Finite__Set_Ofold1(_1106145, c_Orderings_Oord__class_Omin(_1106145)), _1106147))))], (17094 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106145), _1106149), hAPP(c_Finite__Set_Ofold1(_1106145, c_Orderings_Oord__class_Omin(_1106145)), _1106147))), 17097 ^ _782652 : [(17098 ^ _782652) ^ [_1106438] : [hBOOL(hAPP(hAPP(c_member(_1106145), _1106438), _1106147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106145), _1106149), _1106438)))]]]]], (17113 ^ _782652) ^ [_1106723, _1106725, _1106727] : [class_Orderings_Olinorder(_1106723), hBOOL(hAPP(c_Finite__Set_Ofinite(_1106723), _1106725)), -(_1106725 = c_Orderings_Obot__class_Obot(tc_fun(_1106723, tc_HOL_Obool))), 17124 ^ _782652 : [(17125 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106723), hAPP(c_Finite__Set_Ofold1(_1106723, c_Orderings_Oord__class_Omin(_1106723)), _1106725)), _1106727)), 17129 ^ _782652 : [(17130 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1106723), 17128 ^ [_1106723, _1106725, _1106727]), _1106725)))], (17132 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106723), 17128 ^ [_1106723, _1106725, _1106727]), _1106727)))]]], (17134 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106723), hAPP(c_Finite__Set_Ofold1(_1106723, c_Orderings_Oord__class_Omin(_1106723)), _1106725)), _1106727))), 17135 ^ _782652 : [(17136 ^ _782652) ^ [_1107112] : [hBOOL(hAPP(hAPP(c_member(_1106723), _1107112), _1106725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106723), _1107112), _1106727))]]]]], (17144 ^ _782652) ^ [_1107273, _1107275, _1107277] : [class_Orderings_Olinorder(_1107273), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107273), _1107275)), -(_1107275 = c_Orderings_Obot__class_Obot(tc_fun(_1107273, tc_HOL_Obool))), 17155 ^ _782652 : [(17156 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107273), hAPP(c_Finite__Set_Ofold1(_1107273, c_Orderings_Oord__class_Omin(_1107273)), _1107275)), _1107277)), 17160 ^ _782652 : [(17161 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1107273), 17159 ^ [_1107273, _1107275, _1107277]), _1107275)))], (17163 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107273), 17159 ^ [_1107273, _1107275, _1107277]), _1107277)))]]], (17165 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107273), hAPP(c_Finite__Set_Ofold1(_1107273, c_Orderings_Oord__class_Omin(_1107273)), _1107275)), _1107277))), 17166 ^ _782652 : [(17167 ^ _782652) ^ [_1107662] : [hBOOL(hAPP(hAPP(c_member(_1107273), _1107662), _1107275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107273), _1107662), _1107277))]]]]], (17175 ^ _782652) ^ [_1107823, _1107825, _1107827] : [class_Orderings_Olinorder(_1107823), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107823), _1107825)), -(_1107825 = c_Orderings_Obot__class_Obot(tc_fun(_1107823, tc_HOL_Obool))), 17186 ^ _782652 : [(17197 ^ _782652) ^ [] : [17199 ^ _782652 : [(17200 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1107823), 17198 ^ [_1107823, _1107825, _1107827]), _1107825)))], (17202 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107823), _1107827), 17198 ^ [_1107823, _1107825, _1107827]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107823), _1107827), hAPP(c_Finite__Set_Ofold1(_1107823, c_Orderings_Oord__class_Omin(_1107823)), _1107825))))], (17187 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107823), _1107827), hAPP(c_Finite__Set_Ofold1(_1107823, c_Orderings_Oord__class_Omin(_1107823)), _1107825))), 17190 ^ _782652 : [(17191 ^ _782652) ^ [_1108116] : [hBOOL(hAPP(hAPP(c_member(_1107823), _1108116), _1107825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107823), _1107827), _1108116)))]]]]], (17206 ^ _782652) ^ [_1108401, _1108403, _1108405] : [class_Orderings_Olinorder(_1108401), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108401), _1108403)), -(_1108403 = c_Orderings_Obot__class_Obot(tc_fun(_1108401, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1108401, hAPP(hAPP(c_Set_Oinsert(_1108401), _1108405), _1108403)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1108401), _1108405), c_Big__Operators_Olinorder__class_OMax(_1108401, _1108403)))], (17220 ^ _782652) ^ [_1108609, _1108611, _1108613] : [class_Orderings_Olinorder(_1108609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108609), _1108611)), -(_1108611 = c_Orderings_Obot__class_Obot(tc_fun(_1108609, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1108609, hAPP(hAPP(c_Set_Oinsert(_1108609), _1108613), _1108611)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108609), _1108613), c_Big__Operators_Olinorder__class_OMin(_1108609, _1108611)))], (17234 ^ _782652) ^ [_1108817, _1108819, _1108821] : [class_Orderings_Olinorder(_1108817), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108817), _1108819)), -(_1108821 = c_Orderings_Obot__class_Obot(tc_fun(_1108817, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1108817, tc_HOL_Obool)), _1108821), _1108819)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1108817), c_Big__Operators_Olinorder__class_OMax(_1108817, _1108821)), c_Big__Operators_Olinorder__class_OMax(_1108817, _1108819)) = c_Big__Operators_Olinorder__class_OMax(_1108817, _1108819))], (17252 ^ _782652) ^ [_1109131, _1109133, _1109135] : [class_Orderings_Olinorder(_1109131), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109131), _1109133)), -(_1109135 = c_Orderings_Obot__class_Obot(tc_fun(_1109131, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1109131, tc_HOL_Obool)), _1109135), _1109133)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109131), c_Big__Operators_Olinorder__class_OMin(_1109131, _1109135)), c_Big__Operators_Olinorder__class_OMin(_1109131, _1109133)) = c_Big__Operators_Olinorder__class_OMin(_1109131, _1109133))], (17270 ^ _782652) ^ [_1109445, _1109447, _1109449] : [class_Orderings_Olinorder(_1109445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109445), _1109447)), -(_1109447 = c_Orderings_Obot__class_Obot(tc_fun(_1109445, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109445), _1109449)), -(_1109449 = c_Orderings_Obot__class_Obot(tc_fun(_1109445, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1109445, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1109445, tc_HOL_Obool)), _1109447), _1109449)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1109445), c_Big__Operators_Olinorder__class_OMax(_1109445, _1109447)), c_Big__Operators_Olinorder__class_OMax(_1109445, _1109449)))], (17292 ^ _782652) ^ [_1109794, _1109796, _1109798] : [class_Orderings_Olinorder(_1109794), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109794), _1109796)), -(_1109796 = c_Orderings_Obot__class_Obot(tc_fun(_1109794, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109794), _1109798)), -(_1109798 = c_Orderings_Obot__class_Obot(tc_fun(_1109794, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1109794, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1109794, tc_HOL_Obool)), _1109796), _1109798)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1109794), c_Big__Operators_Olinorder__class_OMin(_1109794, _1109796)), c_Big__Operators_Olinorder__class_OMin(_1109794, _1109798)))], (17314 ^ _782652) ^ [_1110143, _1110145, _1110147] : [class_Orderings_Olinorder(_1110143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110143), _1110145)), -(hBOOL(hAPP(hAPP(c_member(_1110143), _1110147), _1110145))), -(_1110145 = c_Orderings_Obot__class_Obot(tc_fun(_1110143, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1110143, hAPP(hAPP(c_Set_Oinsert(_1110143), _1110147), _1110145)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1110143), _1110147), c_Big__Operators_Olinorder__class_OMax(_1110143, _1110145)))], (17332 ^ _782652) ^ [_1110380, _1110382, _1110384] : [class_Orderings_Olinorder(_1110380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110380), _1110382)), -(hBOOL(hAPP(hAPP(c_member(_1110380), _1110384), _1110382))), -(_1110382 = c_Orderings_Obot__class_Obot(tc_fun(_1110380, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1110380, hAPP(hAPP(c_Set_Oinsert(_1110380), _1110384), _1110382)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110380), _1110384), c_Big__Operators_Olinorder__class_OMin(_1110380, _1110382)))], (17350 ^ _782652) ^ [_1110617, _1110619, _1110621] : [class_Orderings_Olinorder(_1110617), -(_1110619 = c_Orderings_Obot__class_Obot(tc_fun(_1110617, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1110617, tc_HOL_Obool)), _1110619), _1110621)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110617), _1110621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110617), hAPP(c_Finite__Set_Ofold1(_1110617, c_Orderings_Oord__class_Omin(_1110617)), _1110621)), hAPP(c_Finite__Set_Ofold1(_1110617, c_Orderings_Oord__class_Omin(_1110617)), _1110619))))], (17368 ^ _782652) ^ [_1110943, _1110945, _1110947] : [class_Orderings_Olinorder(_1110943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110943), _1110945)), 17375 ^ _782652 : [(17376 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1110943, tc_HOL_Obool)), _1110945), hAPP(hAPP(c_Set_Oinsert(_1110943), _1110947), c_Orderings_Obot__class_Obot(tc_fun(_1110943, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1110943, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1110943, hAPP(hAPP(c_Set_Oinsert(_1110943), _1110947), _1110945)) = _1110947)], (17382 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1110943, tc_HOL_Obool)), _1110945), hAPP(hAPP(c_Set_Oinsert(_1110943), _1110947), c_Orderings_Obot__class_Obot(tc_fun(_1110943, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1110943, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1110943, hAPP(hAPP(c_Set_Oinsert(_1110943), _1110947), _1110945)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1110943), _1110947), c_Big__Operators_Olinorder__class_OMax(_1110943, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1110943, tc_HOL_Obool)), _1110945), hAPP(hAPP(c_Set_Oinsert(_1110943), _1110947), c_Orderings_Obot__class_Obot(tc_fun(_1110943, tc_HOL_Obool)))))))]]], (17388 ^ _782652) ^ [_1111413, _1111415, _1111417] : [class_Orderings_Olinorder(_1111413), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111413), _1111415)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111413), _1111417)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111413, tc_HOL_Obool)), _1111415), _1111417) = c_Orderings_Obot__class_Obot(tc_fun(_1111413, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1111413), c_Big__Operators_Olinorder__class_OMax(_1111413, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1111413, tc_HOL_Obool)), _1111415), _1111417))), c_Big__Operators_Olinorder__class_OMax(_1111413, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111413, tc_HOL_Obool)), _1111415), _1111417))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1111413), c_Big__Operators_Olinorder__class_OMax(_1111413, _1111415)), c_Big__Operators_Olinorder__class_OMax(_1111413, _1111417)))], (17406 ^ _782652) ^ [_1111761, _1111763, _1111765] : [class_Orderings_Olinorder(_1111761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111761), _1111763)), -(_1111763 = c_Orderings_Obot__class_Obot(tc_fun(_1111761, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111761), _1111765)), -(_1111765 = c_Orderings_Obot__class_Obot(tc_fun(_1111761, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111761, tc_HOL_Obool)), _1111763), _1111765) = c_Orderings_Obot__class_Obot(tc_fun(_1111761, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1111761, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1111761, tc_HOL_Obool)), _1111763), _1111765)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1111761), c_Big__Operators_Olinorder__class_OMax(_1111761, _1111763)), c_Big__Operators_Olinorder__class_OMax(_1111761, _1111765)))], (17432 ^ _782652) ^ [_1112238, _1112240, _1112242] : [class_Orderings_Olinorder(_1112238), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112238), _1112240)), 17439 ^ _782652 : [(17440 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1112238, tc_HOL_Obool)), _1112240), hAPP(hAPP(c_Set_Oinsert(_1112238), _1112242), c_Orderings_Obot__class_Obot(tc_fun(_1112238, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1112238, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1112238, hAPP(hAPP(c_Set_Oinsert(_1112238), _1112242), _1112240)) = _1112242)], (17446 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1112238, tc_HOL_Obool)), _1112240), hAPP(hAPP(c_Set_Oinsert(_1112238), _1112242), c_Orderings_Obot__class_Obot(tc_fun(_1112238, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1112238, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1112238, hAPP(hAPP(c_Set_Oinsert(_1112238), _1112242), _1112240)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1112238), _1112242), c_Big__Operators_Olinorder__class_OMin(_1112238, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1112238, tc_HOL_Obool)), _1112240), hAPP(hAPP(c_Set_Oinsert(_1112238), _1112242), c_Orderings_Obot__class_Obot(tc_fun(_1112238, tc_HOL_Obool)))))))]]], (17452 ^ _782652) ^ [_1112708, _1112710, _1112712] : [class_Orderings_Olinorder(_1112708), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112708), _1112710)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112708), _1112712)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112708, tc_HOL_Obool)), _1112710), _1112712) = c_Orderings_Obot__class_Obot(tc_fun(_1112708, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1112708), c_Big__Operators_Olinorder__class_OMin(_1112708, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1112708, tc_HOL_Obool)), _1112710), _1112712))), c_Big__Operators_Olinorder__class_OMin(_1112708, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112708, tc_HOL_Obool)), _1112710), _1112712))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1112708), c_Big__Operators_Olinorder__class_OMin(_1112708, _1112710)), c_Big__Operators_Olinorder__class_OMin(_1112708, _1112712)))], (17470 ^ _782652) ^ [_1113056, _1113058, _1113060] : [class_Orderings_Olinorder(_1113056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113056), _1113058)), -(_1113058 = c_Orderings_Obot__class_Obot(tc_fun(_1113056, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113056), _1113060)), -(_1113060 = c_Orderings_Obot__class_Obot(tc_fun(_1113056, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1113056, tc_HOL_Obool)), _1113058), _1113060) = c_Orderings_Obot__class_Obot(tc_fun(_1113056, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1113056, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1113056, tc_HOL_Obool)), _1113058), _1113060)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1113056), c_Big__Operators_Olinorder__class_OMin(_1113056, _1113058)), c_Big__Operators_Olinorder__class_OMin(_1113056, _1113060)))], (17496 ^ _782652) ^ [_1113533] : [class_Orderings_Olinorder(_1113533), -(c_Orderings_Oord_Omin(_1113533, hAPP(c_COMBC(_1113533, _1113533, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1113533))) = c_Orderings_Oord__class_Omax(_1113533))], (17502 ^ _782652) ^ [_1113634] : [class_Orderings_Olinorder(_1113634), -(c_Orderings_Oord_Omax(_1113634, hAPP(c_COMBC(_1113634, _1113634, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1113634))) = c_Orderings_Oord__class_Omin(_1113634))], (17508 ^ _782652) ^ [_1113735] : [class_Orderings_Oord(_1113735), -(c_Orderings_Oord__class_Omax(_1113735) = c_Orderings_Oord_Omax(_1113735, c_Orderings_Oord__class_Oless__eq(_1113735)))], (17514 ^ _782652) ^ [_1113822] : [class_Orderings_Oord(_1113822), -(c_Orderings_Oord__class_Omin(_1113822) = c_Orderings_Oord_Omin(_1113822, c_Orderings_Oord__class_Oless__eq(_1113822)))], (17520 ^ _782652) ^ [_1113909, _1113911, _1113913] : [class_Orderings_Olinorder(_1113909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113909), _1113911)), -(_1113911 = c_Orderings_Obot__class_Obot(tc_fun(_1113909, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113909), _1113913)), -(_1113913 = c_Orderings_Obot__class_Obot(tc_fun(_1113909, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1113909), c_Big__Operators_Olattice_OSup__fin(_1113909, c_Orderings_Oord__class_Omax(_1113909), _1113911)), c_Big__Operators_Olattice_OSup__fin(_1113909, c_Orderings_Oord__class_Omax(_1113909), _1113913)) = c_Big__Operators_Olattice_OSup__fin(_1113909, c_Orderings_Oord__class_Omax(_1113909), hAPP(c_Set_OCollect(_1113909), hAPP(hAPP(c_COMBB(tc_fun(_1113909, tc_HOL_Obool), tc_HOL_Obool, _1113909), c_HOL_OEx(_1113909)), hAPP(hAPP(c_COMBB(tc_fun(_1113909, tc_fun(_1113909, tc_HOL_Obool)), tc_fun(_1113909, tc_HOL_Obool), _1113909), hAPP(c_COMBB(tc_fun(_1113909, tc_HOL_Obool), tc_HOL_Obool, _1113909), c_HOL_OEx(_1113909))), hAPP(hAPP(c_COMBC(_1113909, tc_fun(_1113909, tc_fun(_1113909, tc_HOL_Obool)), tc_fun(_1113909, tc_fun(_1113909, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1113909, tc_fun(tc_fun(_1113909, tc_HOL_Obool), tc_fun(_1113909, tc_HOL_Obool))), tc_fun(tc_fun(_1113909, tc_fun(_1113909, tc_HOL_Obool)), tc_fun(_1113909, tc_fun(_1113909, tc_HOL_Obool))), _1113909), c_COMBS(_1113909, tc_fun(_1113909, tc_HOL_Obool), tc_fun(_1113909, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1113909, tc_fun(_1113909, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1113909, tc_fun(tc_fun(_1113909, tc_HOL_Obool), tc_fun(_1113909, tc_HOL_Obool))), _1113909), hAPP(c_COMBB(tc_fun(_1113909, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1113909, tc_HOL_Obool), tc_fun(_1113909, tc_HOL_Obool)), _1113909), c_COMBS(_1113909, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1113909, tc_fun(_1113909, tc_HOL_Obool)), tc_fun(_1113909, tc_fun(_1113909, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1113909), hAPP(c_COMBB(tc_fun(_1113909, tc_HOL_Obool), tc_fun(_1113909, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1113909), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1113909), c_fconj))), hAPP(hAPP(c_COMBC(_1113909, tc_fun(_1113909, tc_fun(_1113909, _1113909)), tc_fun(_1113909, tc_fun(_1113909, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1113909, _1113909), tc_fun(_1113909, tc_HOL_Obool)), tc_fun(tc_fun(_1113909, tc_fun(_1113909, _1113909)), tc_fun(_1113909, tc_fun(_1113909, tc_HOL_Obool))), _1113909), c_COMBB(tc_fun(_1113909, _1113909), tc_fun(_1113909, tc_HOL_Obool), _1113909)), hAPP(hAPP(c_COMBB(tc_fun(_1113909, tc_HOL_Obool), tc_fun(tc_fun(_1113909, _1113909), tc_fun(_1113909, tc_HOL_Obool)), _1113909), c_COMBB(_1113909, tc_HOL_Obool, _1113909)), c_fequal))), c_Orderings_Oord__class_Omin(_1113909)))))), hAPP(hAPP(c_COMBC(_1113909, tc_fun(_1113909, tc_HOL_Obool), tc_fun(_1113909, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1113909, tc_HOL_Obool), tc_fun(_1113909, tc_HOL_Obool)), _1113909), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1113909)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1113909), c_fconj), hAPP(hAPP(c_COMBC(_1113909, tc_fun(_1113909, tc_HOL_Obool), tc_HOL_Obool), c_member(_1113909)), _1113911)))), hAPP(hAPP(c_COMBC(_1113909, tc_fun(_1113909, tc_HOL_Obool), tc_HOL_Obool), c_member(_1113909)), _1113913))))))))], (17542 ^ _782652) ^ [_1115026, _1115028, _1115030] : [class_Orderings_Olinorder(_1115026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115026), _1115028)), -(_1115028 = c_Orderings_Obot__class_Obot(tc_fun(_1115026, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115026), _1115030)), -(_1115030 = c_Orderings_Obot__class_Obot(tc_fun(_1115026, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1115026), c_Big__Operators_Olattice_OInf__fin(_1115026, c_Orderings_Oord__class_Omin(_1115026), _1115028)), c_Big__Operators_Olattice_OInf__fin(_1115026, c_Orderings_Oord__class_Omin(_1115026), _1115030)) = c_Big__Operators_Olattice_OInf__fin(_1115026, c_Orderings_Oord__class_Omin(_1115026), hAPP(c_Set_OCollect(_1115026), hAPP(hAPP(c_COMBB(tc_fun(_1115026, tc_HOL_Obool), tc_HOL_Obool, _1115026), c_HOL_OEx(_1115026)), hAPP(hAPP(c_COMBB(tc_fun(_1115026, tc_fun(_1115026, tc_HOL_Obool)), tc_fun(_1115026, tc_HOL_Obool), _1115026), hAPP(c_COMBB(tc_fun(_1115026, tc_HOL_Obool), tc_HOL_Obool, _1115026), c_HOL_OEx(_1115026))), hAPP(hAPP(c_COMBC(_1115026, tc_fun(_1115026, tc_fun(_1115026, tc_HOL_Obool)), tc_fun(_1115026, tc_fun(_1115026, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1115026, tc_fun(tc_fun(_1115026, tc_HOL_Obool), tc_fun(_1115026, tc_HOL_Obool))), tc_fun(tc_fun(_1115026, tc_fun(_1115026, tc_HOL_Obool)), tc_fun(_1115026, tc_fun(_1115026, tc_HOL_Obool))), _1115026), c_COMBS(_1115026, tc_fun(_1115026, tc_HOL_Obool), tc_fun(_1115026, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1115026, tc_fun(_1115026, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1115026, tc_fun(tc_fun(_1115026, tc_HOL_Obool), tc_fun(_1115026, tc_HOL_Obool))), _1115026), hAPP(c_COMBB(tc_fun(_1115026, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1115026, tc_HOL_Obool), tc_fun(_1115026, tc_HOL_Obool)), _1115026), c_COMBS(_1115026, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1115026, tc_fun(_1115026, tc_HOL_Obool)), tc_fun(_1115026, tc_fun(_1115026, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1115026), hAPP(c_COMBB(tc_fun(_1115026, tc_HOL_Obool), tc_fun(_1115026, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1115026), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1115026), c_fconj))), hAPP(hAPP(c_COMBC(_1115026, tc_fun(_1115026, tc_fun(_1115026, _1115026)), tc_fun(_1115026, tc_fun(_1115026, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1115026, _1115026), tc_fun(_1115026, tc_HOL_Obool)), tc_fun(tc_fun(_1115026, tc_fun(_1115026, _1115026)), tc_fun(_1115026, tc_fun(_1115026, tc_HOL_Obool))), _1115026), c_COMBB(tc_fun(_1115026, _1115026), tc_fun(_1115026, tc_HOL_Obool), _1115026)), hAPP(hAPP(c_COMBB(tc_fun(_1115026, tc_HOL_Obool), tc_fun(tc_fun(_1115026, _1115026), tc_fun(_1115026, tc_HOL_Obool)), _1115026), c_COMBB(_1115026, tc_HOL_Obool, _1115026)), c_fequal))), c_Orderings_Oord__class_Omax(_1115026)))))), hAPP(hAPP(c_COMBC(_1115026, tc_fun(_1115026, tc_HOL_Obool), tc_fun(_1115026, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1115026, tc_HOL_Obool), tc_fun(_1115026, tc_HOL_Obool)), _1115026), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1115026)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1115026), c_fconj), hAPP(hAPP(c_COMBC(_1115026, tc_fun(_1115026, tc_HOL_Obool), tc_HOL_Obool), c_member(_1115026)), _1115028)))), hAPP(hAPP(c_COMBC(_1115026, tc_fun(_1115026, tc_HOL_Obool), tc_HOL_Obool), c_member(_1115026)), _1115030))))))))], (17564 ^ _782652) ^ [_1116143, _1116145, _1116147] : [class_Orderings_Olinorder(_1116143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116143), _1116145)), -(_1116145 = c_Orderings_Obot__class_Obot(tc_fun(_1116143, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1116143), _1116147), c_Big__Operators_Olattice_OSup__fin(_1116143, c_Orderings_Oord__class_Omax(_1116143), _1116145)) = c_Big__Operators_Olattice_OSup__fin(_1116143, c_Orderings_Oord__class_Omax(_1116143), hAPP(c_Set_OCollect(_1116143), hAPP(hAPP(c_COMBB(tc_fun(_1116143, tc_HOL_Obool), tc_HOL_Obool, _1116143), c_HOL_OEx(_1116143)), hAPP(hAPP(c_COMBC(_1116143, tc_fun(_1116143, tc_HOL_Obool), tc_fun(_1116143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1116143, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1116143, tc_HOL_Obool), tc_fun(_1116143, tc_HOL_Obool)), _1116143), c_COMBS(_1116143, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1116143, tc_HOL_Obool), tc_fun(_1116143, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1116143), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1116143), c_fconj)), hAPP(hAPP(c_COMBC(_1116143, tc_fun(_1116143, _1116143), tc_fun(_1116143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1116143, tc_HOL_Obool), tc_fun(tc_fun(_1116143, _1116143), tc_fun(_1116143, tc_HOL_Obool)), _1116143), c_COMBB(_1116143, tc_HOL_Obool, _1116143)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1116143), _1116147))))), hAPP(hAPP(c_COMBC(_1116143, tc_fun(_1116143, tc_HOL_Obool), tc_HOL_Obool), c_member(_1116143)), _1116145))))))], (17578 ^ _782652) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (17580 ^ _782652) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (17582 ^ _782652) ^ [_1116677, _1116679] : [class_Orderings_Olinorder(_1116677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116677), _1116679)), -(_1116679 = c_Orderings_Obot__class_Obot(tc_fun(_1116677, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116677), c_Big__Operators_Olattice_OInf__fin(_1116677, c_Orderings_Oord__class_Omin(_1116677), _1116679)), c_Big__Operators_Olattice_OSup__fin(_1116677, c_Orderings_Oord__class_Omax(_1116677), _1116679))))], (17596 ^ _782652) ^ [_1116875, _1116877, _1116879] : [class_Orderings_Olinorder(_1116875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116875), _1116877)), hBOOL(hAPP(hAPP(c_member(_1116875), _1116879), _1116877)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1116875), _1116879), c_Big__Operators_Olattice_OInf__fin(_1116875, c_Orderings_Oord__class_Omin(_1116875), _1116877)) = c_Big__Operators_Olattice_OInf__fin(_1116875, c_Orderings_Oord__class_Omin(_1116875), _1116877))], (17610 ^ _782652) ^ [_1117122, _1117124, _1117126] : [class_Orderings_Olinorder(_1117122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1117122), _1117124)), hBOOL(hAPP(hAPP(c_member(_1117122), _1117126), _1117124)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1117122), _1117126), c_Big__Operators_Olattice_OSup__fin(_1117122, c_Orderings_Oord__class_Omax(_1117122), _1117124)) = c_Big__Operators_Olattice_OSup__fin(_1117122, c_Orderings_Oord__class_Omax(_1117122), _1117124))], (17624 ^ _782652) ^ [_1117369, _1117371] : [class_Orderings_Olinorder(_1117369), -(c_Big__Operators_Olattice_OInf__fin(_1117369, c_Orderings_Oord__class_Omin(_1117369), hAPP(hAPP(c_Set_Oinsert(_1117369), _1117371), c_Orderings_Obot__class_Obot(tc_fun(_1117369, tc_HOL_Obool)))) = _1117371)], (17630 ^ _782652) ^ [_1117482, _1117484] : [class_Orderings_Olinorder(_1117482), -(c_Big__Operators_Olattice_OSup__fin(_1117482, c_Orderings_Oord__class_Omax(_1117482), hAPP(hAPP(c_Set_Oinsert(_1117482), _1117484), c_Orderings_Obot__class_Obot(tc_fun(_1117482, tc_HOL_Obool)))) = _1117484)], (17636 ^ _782652) ^ [_1117595, _1117597] : [class_Orderings_Olinorder(_1117595), hBOOL(hAPP(c_Finite__Set_Ofinite(_1117595), _1117597)), -(c_Big__Operators_Olattice_OInf__fin(_1117595, c_Orderings_Oord__class_Omin(_1117595), _1117597) = hAPP(c_Finite__Set_Ofold1(_1117595, c_Orderings_Oord__class_Omin(_1117595)), _1117597))], (17646 ^ _782652) ^ [_1117758, _1117760] : [class_Orderings_Olinorder(_1117758), hBOOL(hAPP(c_Finite__Set_Ofinite(_1117758), _1117760)), -(c_Big__Operators_Olattice_OSup__fin(_1117758, c_Orderings_Oord__class_Omax(_1117758), _1117760) = hAPP(c_Finite__Set_Ofold1(_1117758, c_Orderings_Oord__class_Omax(_1117758)), _1117760))], (17656 ^ _782652) ^ [_1117921, _1117923, _1117925] : [class_Orderings_Olinorder(_1117921), hBOOL(hAPP(c_Finite__Set_Ofinite(_1117921), _1117923)), -(_1117923 = c_Orderings_Obot__class_Obot(tc_fun(_1117921, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1117921, c_Orderings_Oord__class_Omin(_1117921), hAPP(hAPP(c_Set_Oinsert(_1117921), _1117925), _1117923)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1117921), _1117925), c_Big__Operators_Olattice_OInf__fin(_1117921, c_Orderings_Oord__class_Omin(_1117921), _1117923)))], (17670 ^ _782652) ^ [_1118141, _1118143, _1118145] : [class_Orderings_Olinorder(_1118141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118141), _1118143)), -(_1118143 = c_Orderings_Obot__class_Obot(tc_fun(_1118141, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1118141, c_Orderings_Oord__class_Omax(_1118141), hAPP(hAPP(c_Set_Oinsert(_1118141), _1118145), _1118143)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118141), _1118145), c_Big__Operators_Olattice_OSup__fin(_1118141, c_Orderings_Oord__class_Omax(_1118141), _1118143)))], (17684 ^ _782652) ^ [_1118361, _1118363, _1118365] : [class_Orderings_Olinorder(_1118361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118361), _1118363)), -(_1118365 = c_Orderings_Obot__class_Obot(tc_fun(_1118361, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1118361, tc_HOL_Obool)), _1118365), _1118363)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1118361), c_Big__Operators_Olattice_OInf__fin(_1118361, c_Orderings_Oord__class_Omin(_1118361), _1118365)), c_Big__Operators_Olattice_OInf__fin(_1118361, c_Orderings_Oord__class_Omin(_1118361), _1118363)) = c_Big__Operators_Olattice_OInf__fin(_1118361, c_Orderings_Oord__class_Omin(_1118361), _1118363))], (17702 ^ _782652) ^ [_1118693, _1118695, _1118697] : [class_Orderings_Olinorder(_1118693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118693), _1118695)), -(_1118697 = c_Orderings_Obot__class_Obot(tc_fun(_1118693, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1118693, tc_HOL_Obool)), _1118697), _1118695)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1118693), c_Big__Operators_Olattice_OSup__fin(_1118693, c_Orderings_Oord__class_Omax(_1118693), _1118697)), c_Big__Operators_Olattice_OSup__fin(_1118693, c_Orderings_Oord__class_Omax(_1118693), _1118695)) = c_Big__Operators_Olattice_OSup__fin(_1118693, c_Orderings_Oord__class_Omax(_1118693), _1118695))], (17720 ^ _782652) ^ [_1119025, _1119027, _1119029] : [class_Orderings_Olinorder(_1119025), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119025), _1119027)), hBOOL(hAPP(hAPP(c_member(_1119025), _1119029), _1119027)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1119025), _1119029), c_Big__Operators_Olattice_OSup__fin(_1119025, c_Orderings_Oord__class_Omax(_1119025), _1119027)) = _1119029)], (17734 ^ _782652) ^ [_1119260, _1119262, _1119264] : [class_Orderings_Olinorder(_1119260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119260), _1119262)), hBOOL(hAPP(hAPP(c_member(_1119260), _1119264), _1119262)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119260), _1119264), c_Big__Operators_Olattice_OInf__fin(_1119260, c_Orderings_Oord__class_Omin(_1119260), _1119262)) = _1119264)], (17748 ^ _782652) ^ [_1119495, _1119497, _1119499] : [class_Orderings_Olinorder(_1119495), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119495), _1119497)), -(_1119497 = c_Orderings_Obot__class_Obot(tc_fun(_1119495, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119495), _1119499)), -(_1119499 = c_Orderings_Obot__class_Obot(tc_fun(_1119495, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1119495, c_Orderings_Oord__class_Omin(_1119495), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119495, tc_HOL_Obool)), _1119497), _1119499)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1119495), c_Big__Operators_Olattice_OInf__fin(_1119495, c_Orderings_Oord__class_Omin(_1119495), _1119497)), c_Big__Operators_Olattice_OInf__fin(_1119495, c_Orderings_Oord__class_Omin(_1119495), _1119499)))], (17770 ^ _782652) ^ [_1119862, _1119864, _1119866] : [class_Orderings_Olinorder(_1119862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119862), _1119864)), -(_1119864 = c_Orderings_Obot__class_Obot(tc_fun(_1119862, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119862), _1119866)), -(_1119866 = c_Orderings_Obot__class_Obot(tc_fun(_1119862, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1119862, c_Orderings_Oord__class_Omax(_1119862), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119862, tc_HOL_Obool)), _1119864), _1119866)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119862), c_Big__Operators_Olattice_OSup__fin(_1119862, c_Orderings_Oord__class_Omax(_1119862), _1119864)), c_Big__Operators_Olattice_OSup__fin(_1119862, c_Orderings_Oord__class_Omax(_1119862), _1119866)))], (17792 ^ _782652) ^ [_1120229, _1120231, _1120233] : [class_Orderings_Olinorder(_1120229), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120229), _1120231)), -(hBOOL(hAPP(hAPP(c_member(_1120229), _1120233), _1120231))), -(_1120231 = c_Orderings_Obot__class_Obot(tc_fun(_1120229, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1120229, c_Orderings_Oord__class_Omin(_1120229), hAPP(hAPP(c_Set_Oinsert(_1120229), _1120233), _1120231)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1120229), _1120233), c_Big__Operators_Olattice_OInf__fin(_1120229, c_Orderings_Oord__class_Omin(_1120229), _1120231)))], (17810 ^ _782652) ^ [_1120478, _1120480, _1120482] : [class_Orderings_Olinorder(_1120478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120478), _1120480)), -(hBOOL(hAPP(hAPP(c_member(_1120478), _1120482), _1120480))), -(_1120480 = c_Orderings_Obot__class_Obot(tc_fun(_1120478, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1120478, c_Orderings_Oord__class_Omax(_1120478), hAPP(hAPP(c_Set_Oinsert(_1120478), _1120482), _1120480)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1120478), _1120482), c_Big__Operators_Olattice_OSup__fin(_1120478, c_Orderings_Oord__class_Omax(_1120478), _1120480)))], (17828 ^ _782652) ^ [_1120727, _1120729, _1120731] : [class_Orderings_Olinorder(_1120727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120727), _1120729)), 17835 ^ _782652 : [(17836 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1120727, tc_HOL_Obool)), _1120729), hAPP(hAPP(c_Set_Oinsert(_1120727), _1120731), c_Orderings_Obot__class_Obot(tc_fun(_1120727, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1120727, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1120727, c_Orderings_Oord__class_Omin(_1120727), hAPP(hAPP(c_Set_Oinsert(_1120727), _1120731), _1120729)) = _1120731)], (17842 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1120727, tc_HOL_Obool)), _1120729), hAPP(hAPP(c_Set_Oinsert(_1120727), _1120731), c_Orderings_Obot__class_Obot(tc_fun(_1120727, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1120727, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1120727, c_Orderings_Oord__class_Omin(_1120727), hAPP(hAPP(c_Set_Oinsert(_1120727), _1120731), _1120729)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1120727), _1120731), c_Big__Operators_Olattice_OInf__fin(_1120727, c_Orderings_Oord__class_Omin(_1120727), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1120727, tc_HOL_Obool)), _1120729), hAPP(hAPP(c_Set_Oinsert(_1120727), _1120731), c_Orderings_Obot__class_Obot(tc_fun(_1120727, tc_HOL_Obool)))))))]]], (17848 ^ _782652) ^ [_1121215, _1121217, _1121219] : [class_Orderings_Olinorder(_1121215), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121215), _1121217)), 17855 ^ _782652 : [(17856 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1121215, tc_HOL_Obool)), _1121217), hAPP(hAPP(c_Set_Oinsert(_1121215), _1121219), c_Orderings_Obot__class_Obot(tc_fun(_1121215, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1121215, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1121215, c_Orderings_Oord__class_Omax(_1121215), hAPP(hAPP(c_Set_Oinsert(_1121215), _1121219), _1121217)) = _1121219)], (17862 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1121215, tc_HOL_Obool)), _1121217), hAPP(hAPP(c_Set_Oinsert(_1121215), _1121219), c_Orderings_Obot__class_Obot(tc_fun(_1121215, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1121215, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1121215, c_Orderings_Oord__class_Omax(_1121215), hAPP(hAPP(c_Set_Oinsert(_1121215), _1121219), _1121217)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1121215), _1121219), c_Big__Operators_Olattice_OSup__fin(_1121215, c_Orderings_Oord__class_Omax(_1121215), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1121215, tc_HOL_Obool)), _1121217), hAPP(hAPP(c_Set_Oinsert(_1121215), _1121219), c_Orderings_Obot__class_Obot(tc_fun(_1121215, tc_HOL_Obool)))))))]]], (17868 ^ _782652) ^ [_1121703, _1121705, _1121707] : [class_Orderings_Olinorder(_1121703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121703), _1121705)), -(_1121705 = c_Orderings_Obot__class_Obot(tc_fun(_1121703, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121703), _1121707)), -(_1121707 = c_Orderings_Obot__class_Obot(tc_fun(_1121703, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1121703, tc_HOL_Obool)), _1121705), _1121707) = c_Orderings_Obot__class_Obot(tc_fun(_1121703, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1121703, c_Orderings_Oord__class_Omin(_1121703), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1121703, tc_HOL_Obool)), _1121705), _1121707)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1121703), c_Big__Operators_Olattice_OInf__fin(_1121703, c_Orderings_Oord__class_Omin(_1121703), _1121705)), c_Big__Operators_Olattice_OInf__fin(_1121703, c_Orderings_Oord__class_Omin(_1121703), _1121707)))], (17894 ^ _782652) ^ [_1122198, _1122200, _1122202] : [class_Orderings_Olinorder(_1122198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122198), _1122200)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122198), _1122202)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1122198, tc_HOL_Obool)), _1122200), _1122202) = c_Orderings_Obot__class_Obot(tc_fun(_1122198, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1122198), c_Big__Operators_Olattice_OInf__fin(_1122198, c_Orderings_Oord__class_Omin(_1122198), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1122198, tc_HOL_Obool)), _1122200), _1122202))), c_Big__Operators_Olattice_OInf__fin(_1122198, c_Orderings_Oord__class_Omin(_1122198), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1122198, tc_HOL_Obool)), _1122200), _1122202))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1122198), c_Big__Operators_Olattice_OInf__fin(_1122198, c_Orderings_Oord__class_Omin(_1122198), _1122200)), c_Big__Operators_Olattice_OInf__fin(_1122198, c_Orderings_Oord__class_Omin(_1122198), _1122202)))], (17912 ^ _782652) ^ [_1122570, _1122572, _1122574] : [class_Orderings_Olinorder(_1122570), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122570), _1122572)), -(_1122572 = c_Orderings_Obot__class_Obot(tc_fun(_1122570, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122570), _1122574)), -(_1122574 = c_Orderings_Obot__class_Obot(tc_fun(_1122570, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1122570, tc_HOL_Obool)), _1122572), _1122574) = c_Orderings_Obot__class_Obot(tc_fun(_1122570, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1122570, c_Orderings_Oord__class_Omax(_1122570), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1122570, tc_HOL_Obool)), _1122572), _1122574)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122570), c_Big__Operators_Olattice_OSup__fin(_1122570, c_Orderings_Oord__class_Omax(_1122570), _1122572)), c_Big__Operators_Olattice_OSup__fin(_1122570, c_Orderings_Oord__class_Omax(_1122570), _1122574)))], (17938 ^ _782652) ^ [_1123065, _1123067, _1123069] : [class_Orderings_Olinorder(_1123065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123065), _1123067)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123065), _1123069)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1123065, tc_HOL_Obool)), _1123067), _1123069) = c_Orderings_Obot__class_Obot(tc_fun(_1123065, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123065), c_Big__Operators_Olattice_OSup__fin(_1123065, c_Orderings_Oord__class_Omax(_1123065), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1123065, tc_HOL_Obool)), _1123067), _1123069))), c_Big__Operators_Olattice_OSup__fin(_1123065, c_Orderings_Oord__class_Omax(_1123065), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1123065, tc_HOL_Obool)), _1123067), _1123069))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123065), c_Big__Operators_Olattice_OSup__fin(_1123065, c_Orderings_Oord__class_Omax(_1123065), _1123067)), c_Big__Operators_Olattice_OSup__fin(_1123065, c_Orderings_Oord__class_Omax(_1123065), _1123069)))], (17956 ^ _782652) ^ [_1123437, _1123439, _1123441] : [class_Orderings_Olinorder(_1123437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123437), _1123439)), hBOOL(hAPP(hAPP(c_member(_1123437), _1123441), _1123439)), 17967 ^ _782652 : [(17968 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123437, tc_HOL_Obool)), _1123439), hAPP(hAPP(c_Set_Oinsert(_1123437), _1123441), c_Orderings_Obot__class_Obot(tc_fun(_1123437, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1123437, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1123437, c_Orderings_Oord__class_Omin(_1123437), _1123439) = _1123441)], (17974 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123437, tc_HOL_Obool)), _1123439), hAPP(hAPP(c_Set_Oinsert(_1123437), _1123441), c_Orderings_Obot__class_Obot(tc_fun(_1123437, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1123437, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1123437, c_Orderings_Oord__class_Omin(_1123437), _1123439) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123437), _1123441), c_Big__Operators_Olattice_OInf__fin(_1123437, c_Orderings_Oord__class_Omin(_1123437), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123437, tc_HOL_Obool)), _1123439), hAPP(hAPP(c_Set_Oinsert(_1123437), _1123441), c_Orderings_Obot__class_Obot(tc_fun(_1123437, tc_HOL_Obool)))))))]]], (17980 ^ _782652) ^ [_1123961, _1123963, _1123965] : [class_Orderings_Olinorder(_1123961), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123961), _1123963)), hBOOL(hAPP(hAPP(c_member(_1123961), _1123965), _1123963)), 17991 ^ _782652 : [(17992 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123961, tc_HOL_Obool)), _1123963), hAPP(hAPP(c_Set_Oinsert(_1123961), _1123965), c_Orderings_Obot__class_Obot(tc_fun(_1123961, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1123961, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1123961, c_Orderings_Oord__class_Omax(_1123961), _1123963) = _1123965)], (17998 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123961, tc_HOL_Obool)), _1123963), hAPP(hAPP(c_Set_Oinsert(_1123961), _1123965), c_Orderings_Obot__class_Obot(tc_fun(_1123961, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1123961, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1123961, c_Orderings_Oord__class_Omax(_1123961), _1123963) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123961), _1123965), c_Big__Operators_Olattice_OSup__fin(_1123961, c_Orderings_Oord__class_Omax(_1123961), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123961, tc_HOL_Obool)), _1123963), hAPP(hAPP(c_Set_Oinsert(_1123961), _1123965), c_Orderings_Obot__class_Obot(tc_fun(_1123961, tc_HOL_Obool)))))))]]], (18004 ^ _782652) ^ [_1124485, _1124487, _1124489] : [class_Orderings_Olinorder(_1124485), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124485), _1124487)), -(_1124487 = c_Orderings_Obot__class_Obot(tc_fun(_1124485, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124485), _1124489), c_Big__Operators_Olattice_OInf__fin(_1124485, c_Orderings_Oord__class_Omin(_1124485), _1124487)) = c_Big__Operators_Olattice_OInf__fin(_1124485, c_Orderings_Oord__class_Omin(_1124485), hAPP(c_Set_OCollect(_1124485), hAPP(hAPP(c_COMBB(tc_fun(_1124485, tc_HOL_Obool), tc_HOL_Obool, _1124485), c_HOL_OEx(_1124485)), hAPP(hAPP(c_COMBC(_1124485, tc_fun(_1124485, tc_HOL_Obool), tc_fun(_1124485, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1124485, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1124485, tc_HOL_Obool), tc_fun(_1124485, tc_HOL_Obool)), _1124485), c_COMBS(_1124485, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1124485, tc_HOL_Obool), tc_fun(_1124485, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1124485), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1124485), c_fconj)), hAPP(hAPP(c_COMBC(_1124485, tc_fun(_1124485, _1124485), tc_fun(_1124485, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1124485, tc_HOL_Obool), tc_fun(tc_fun(_1124485, _1124485), tc_fun(_1124485, tc_HOL_Obool)), _1124485), c_COMBB(_1124485, tc_HOL_Obool, _1124485)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1124485), _1124489))))), hAPP(hAPP(c_COMBC(_1124485, tc_fun(_1124485, tc_HOL_Obool), tc_HOL_Obool), c_member(_1124485)), _1124487))))))], (18018 ^ _782652) ^ [_1124983, _1124985] : [class_Orderings_Olinorder(_1124983), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124983), _1124985)), -(_1124985 = c_Orderings_Obot__class_Obot(tc_fun(_1124983, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1124983), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124983), 18031 ^ [_1124983, _1124985]), 18032 ^ [_1124983, _1124985])), hAPP(hAPP(c_Set_Oinsert(_1124983), 18031 ^ [_1124983, _1124985]), hAPP(hAPP(c_Set_Oinsert(_1124983), 18032 ^ [_1124983, _1124985]), c_Orderings_Obot__class_Obot(tc_fun(_1124983, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1124983), c_Big__Operators_Olattice_OSup__fin(_1124983, c_Orderings_Oord__class_Omax(_1124983), _1124985)), _1124985)))], (18038 ^ _782652) ^ [_1125433, _1125435] : [class_Orderings_Olinorder(_1125433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125433), _1125435)), -(_1125435 = c_Orderings_Obot__class_Obot(tc_fun(_1125433, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1125433), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1125433), 18051 ^ [_1125433, _1125435]), 18052 ^ [_1125433, _1125435])), hAPP(hAPP(c_Set_Oinsert(_1125433), 18051 ^ [_1125433, _1125435]), hAPP(hAPP(c_Set_Oinsert(_1125433), 18052 ^ [_1125433, _1125435]), c_Orderings_Obot__class_Obot(tc_fun(_1125433, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1125433), c_Big__Operators_Olattice_OInf__fin(_1125433, c_Orderings_Oord__class_Omin(_1125433), _1125435)), _1125435)))], (18058 ^ _782652) ^ [_1125883, _1125885] : [class_Orderings_Olinorder(_1125883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125883), _1125885)), -(_1125885 = c_Orderings_Obot__class_Obot(tc_fun(_1125883, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1125883), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1125883), 18071 ^ [_1125883, _1125885]), 18072 ^ [_1125883, _1125885])), hAPP(hAPP(c_Set_Oinsert(_1125883), 18071 ^ [_1125883, _1125885]), hAPP(hAPP(c_Set_Oinsert(_1125883), 18072 ^ [_1125883, _1125885]), c_Orderings_Obot__class_Obot(tc_fun(_1125883, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1125883), c_Big__Operators_Olinorder__class_OMax(_1125883, _1125885)), _1125885)))], (18078 ^ _782652) ^ [_1126327, _1126329] : [class_Orderings_Olinorder(_1126327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126327), _1126329)), -(_1126329 = c_Orderings_Obot__class_Obot(tc_fun(_1126327, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1126327), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1126327), 18091 ^ [_1126327, _1126329]), 18092 ^ [_1126327, _1126329])), hAPP(hAPP(c_Set_Oinsert(_1126327), 18091 ^ [_1126327, _1126329]), hAPP(hAPP(c_Set_Oinsert(_1126327), 18092 ^ [_1126327, _1126329]), c_Orderings_Obot__class_Obot(tc_fun(_1126327, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1126327), c_Big__Operators_Olinorder__class_OMin(_1126327, _1126329)), _1126329)))], (18098 ^ _782652) ^ [_1126771, _1126773] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1126771, _1126773)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1126771, _1126773), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1126773), c_Orderings_Otop__class_Otop(tc_fun(_1126773, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1126771), c_Orderings_Otop__class_Otop(tc_fun(_1126771, tc_HOL_Obool)))))], (18108 ^ _782652) ^ [_1126931, _1126933] : [-(hBOOL(hAPP(hAPP(c_member(_1126931), _1126933), c_Orderings_Otop__class_Otop(tc_fun(_1126931, tc_HOL_Obool)))))], (18110 ^ _782652) ^ [_1126968, _1126970, _1126972] : [class_Orderings_Olinorder(_1126968), hAPP(_1126970, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1126968), 18115 ^ [_1126968, _1126970, _1126972]), 18116 ^ [_1126968, _1126970, _1126972])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1126968), hAPP(_1126970, 18115 ^ [_1126968, _1126970, _1126972])), hAPP(_1126970, 18116 ^ [_1126968, _1126970, _1126972])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126968), _1126972)), -(_1126972 = c_Orderings_Obot__class_Obot(tc_fun(_1126968, tc_HOL_Obool))), -(hAPP(_1126970, c_Big__Operators_Olattice_OSup__fin(_1126968, c_Orderings_Oord__class_Omax(_1126968), _1126972)) = c_Big__Operators_Olattice_OSup__fin(_1126968, c_Orderings_Oord__class_Omax(_1126968), hAPP(c_Set_Oimage(_1126968, _1126968, _1126970), _1126972)))], (18130 ^ _782652) ^ [_1127392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127392), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18132 ^ _782652) ^ [_1127420] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1127420)))], (18134 ^ _782652) ^ [_1127445] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1127445))))], (18136 ^ _782652) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18138 ^ _782652) ^ [_1127491, _1127493] : [class_Groups_Ozero(_1127491), 18141 ^ _782652 : [(18142 ^ _782652) ^ [] : [c_Groups_Ozero__class_Ozero(_1127491) = _1127493, -(_1127493 = c_Groups_Ozero__class_Ozero(_1127491))], (18148 ^ _782652) ^ [] : [_1127493 = c_Groups_Ozero__class_Ozero(_1127491), -(c_Groups_Ozero__class_Ozero(_1127491) = _1127493)]]], (18154 ^ _782652) ^ [_1127708, _1127710, _1127712] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1127708), 18157 ^ _782652 : [(18158 ^ _782652) ^ [] : [_1127710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127708), _1127710), _1127712), -(_1127712 = c_Groups_Ozero__class_Ozero(_1127708))], (18164 ^ _782652) ^ [] : [_1127712 = c_Groups_Ozero__class_Ozero(_1127708), -(_1127710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127708), _1127710), _1127712))]]], (18170 ^ _782652) ^ [_1127949, _1127951] : [class_Rings_Ocomm__semiring__1(_1127949), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127949), _1127951), c_Groups_Ozero__class_Ozero(_1127949)) = _1127951)], (18176 ^ _782652) ^ [_1128044, _1128046] : [class_Rings_Ocomm__semiring__1(_1128044), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128044), c_Groups_Ozero__class_Ozero(_1128044)), _1128046) = _1128046)], (18182 ^ _782652) ^ [_1128139, _1128141] : [class_Groups_Omonoid__add(_1128139), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128139), c_Groups_Ozero__class_Ozero(_1128139)), _1128141) = _1128141)], (18188 ^ _782652) ^ [_1128234, _1128236] : [class_Groups_Ocomm__monoid__add(_1128234), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128234), c_Groups_Ozero__class_Ozero(_1128234)), _1128236) = _1128236)], (18194 ^ _782652) ^ [_1128329, _1128331] : [class_Groups_Olinordered__ab__group__add(_1128329), 18197 ^ _782652 : [(18198 ^ _782652) ^ [] : [c_Groups_Ozero__class_Ozero(_1128329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128329), _1128331), _1128331), -(_1128331 = c_Groups_Ozero__class_Ozero(_1128329))], (18204 ^ _782652) ^ [] : [_1128331 = c_Groups_Ozero__class_Ozero(_1128329), -(c_Groups_Ozero__class_Ozero(_1128329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128329), _1128331), _1128331))]]], (18210 ^ _782652) ^ [_1128570, _1128572] : [class_Groups_Omonoid__add(_1128570), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128570), _1128572), c_Groups_Ozero__class_Ozero(_1128570)) = _1128572)], (18216 ^ _782652) ^ [_1128665, _1128667] : [class_Groups_Ocomm__monoid__add(_1128665), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128665), _1128667), c_Groups_Ozero__class_Ozero(_1128665)) = _1128667)], (18222 ^ _782652) ^ [_1128760, _1128762] : [class_Rings_Omult__zero(_1128760), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128760), c_Groups_Ozero__class_Ozero(_1128760)), _1128762) = c_Groups_Ozero__class_Ozero(_1128760))], (18228 ^ _782652) ^ [_1128859, _1128861] : [class_Rings_Ocomm__semiring__1(_1128859), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128859), c_Groups_Ozero__class_Ozero(_1128859)), _1128861) = c_Groups_Ozero__class_Ozero(_1128859))], (18234 ^ _782652) ^ [_1128958, _1128960] : [class_Rings_Omult__zero(_1128958), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128958), _1128960), c_Groups_Ozero__class_Ozero(_1128958)) = c_Groups_Ozero__class_Ozero(_1128958))], (18240 ^ _782652) ^ [_1129057, _1129059] : [class_Rings_Ocomm__semiring__1(_1129057), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129057), _1129059), c_Groups_Ozero__class_Ozero(_1129057)) = c_Groups_Ozero__class_Ozero(_1129057))], (18246 ^ _782652) ^ [_1129156, _1129158, _1129160] : [class_Rings_Oring__no__zero__divisors(_1129156), 18249 ^ _782652 : [(18260 ^ _782652) ^ [] : [18261 ^ _782652 : [(18262 ^ _782652) ^ [] : [_1129158 = c_Groups_Ozero__class_Ozero(_1129156)], (18264 ^ _782652) ^ [] : [_1129160 = c_Groups_Ozero__class_Ozero(_1129156)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129156), _1129158), _1129160) = c_Groups_Ozero__class_Ozero(_1129156))], (18250 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129156), _1129158), _1129160) = c_Groups_Ozero__class_Ozero(_1129156), -(_1129158 = c_Groups_Ozero__class_Ozero(_1129156)), -(_1129160 = c_Groups_Ozero__class_Ozero(_1129156))]]], (18268 ^ _782652) ^ [_1129454, _1129456, _1129458] : [class_Rings_Ono__zero__divisors(_1129454), -(_1129456 = c_Groups_Ozero__class_Ozero(_1129454)), -(_1129458 = c_Groups_Ozero__class_Ozero(_1129454)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129454), _1129456), _1129458) = c_Groups_Ozero__class_Ozero(_1129454)], (18282 ^ _782652) ^ [_1129674, _1129676, _1129678] : [class_Rings_Ono__zero__divisors(_1129674), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129674), _1129676), _1129678) = c_Groups_Ozero__class_Ozero(_1129674), -(_1129676 = c_Groups_Ozero__class_Ozero(_1129674)), -(_1129678 = c_Groups_Ozero__class_Ozero(_1129674))], (18296 ^ _782652) ^ [_1129846, _1129848, _1129850] : [class_Groups_Ogroup__add(_1129846), 18299 ^ _782652 : [(18300 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1129846), _1129848), _1129850) = c_Groups_Ozero__class_Ozero(_1129846), -(_1129848 = _1129850)], (18306 ^ _782652) ^ [] : [_1129848 = _1129850, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1129846), _1129848), _1129850) = c_Groups_Ozero__class_Ozero(_1129846))]]], (18312 ^ _782652) ^ [_1130087, _1130089, _1130091] : [class_Groups_Oab__group__add(_1130087), 18315 ^ _782652 : [(18316 ^ _782652) ^ [] : [_1130089 = _1130091, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130087), _1130089), _1130091) = c_Groups_Ozero__class_Ozero(_1130087))], (18322 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130087), _1130089), _1130091) = c_Groups_Ozero__class_Ozero(_1130087), -(_1130089 = _1130091)]]], (18328 ^ _782652) ^ [_1130328, _1130330] : [class_Groups_Ogroup__add(_1130328), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130328), _1130330), _1130330) = c_Groups_Ozero__class_Ozero(_1130328))], (18334 ^ _782652) ^ [_1130423, _1130425] : [class_Groups_Ogroup__add(_1130423), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130423), _1130425), c_Groups_Ozero__class_Ozero(_1130423)) = _1130425)], (18340 ^ _782652) ^ [_1130518] : [class_Rings_Ozero__neq__one(_1130518), c_Groups_Oone__class_Oone(_1130518) = c_Groups_Ozero__class_Ozero(_1130518)], (18346 ^ _782652) ^ [_1130600] : [class_Rings_Ozero__neq__one(_1130600), c_Groups_Ozero__class_Ozero(_1130600) = c_Groups_Oone__class_Oone(_1130600)], (18352 ^ _782652) ^ [_1130682] : [class_Groups_Ogroup__add(_1130682), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130682), c_Groups_Ozero__class_Ozero(_1130682)) = c_Groups_Ozero__class_Ozero(_1130682))], (18358 ^ _782652) ^ [_1130773, _1130775] : [class_Groups_Ogroup__add(_1130773), 18361 ^ _782652 : [(18362 ^ _782652) ^ [] : [c_Groups_Ozero__class_Ozero(_1130773) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130773), _1130775), -(c_Groups_Ozero__class_Ozero(_1130773) = _1130775)], (18368 ^ _782652) ^ [] : [c_Groups_Ozero__class_Ozero(_1130773) = _1130775, -(c_Groups_Ozero__class_Ozero(_1130773) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130773), _1130775))]]], (18374 ^ _782652) ^ [_1131005, _1131007] : [class_Groups_Olinordered__ab__group__add(_1131005), 18377 ^ _782652 : [(18378 ^ _782652) ^ [] : [_1131007 = hAPP(c_Groups_Ouminus__class_Ouminus(_1131005), _1131007), -(_1131007 = c_Groups_Ozero__class_Ozero(_1131005))], (18384 ^ _782652) ^ [] : [_1131007 = c_Groups_Ozero__class_Ozero(_1131005), -(_1131007 = hAPP(c_Groups_Ouminus__class_Ouminus(_1131005), _1131007))]]], (18390 ^ _782652) ^ [_1131231, _1131233] : [class_Groups_Ogroup__add(_1131231), 18393 ^ _782652 : [(18394 ^ _782652) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1131231), _1131233) = c_Groups_Ozero__class_Ozero(_1131231), -(_1131233 = c_Groups_Ozero__class_Ozero(_1131231))], (18400 ^ _782652) ^ [] : [_1131233 = c_Groups_Ozero__class_Ozero(_1131231), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1131231), _1131233) = c_Groups_Ozero__class_Ozero(_1131231))]]], (18406 ^ _782652) ^ [_1131463, _1131465] : [class_Groups_Olinordered__ab__group__add(_1131463), 18409 ^ _782652 : [(18410 ^ _782652) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1131463), _1131465) = _1131465, -(_1131465 = c_Groups_Ozero__class_Ozero(_1131463))], (18416 ^ _782652) ^ [] : [_1131465 = c_Groups_Ozero__class_Ozero(_1131463), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1131463), _1131465) = _1131465)]]], (18422 ^ _782652) ^ [_1131698] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1131698)], (18424 ^ _782652) ^ [_1131733] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1131733)], (18426 ^ _782652) ^ [_1131768] : [hAPP(c_Nat_OSuc, _1131768) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18428 ^ _782652) ^ [_1131803] : [hAPP(c_Nat_OSuc, _1131803) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18430 ^ _782652) ^ [_1131838] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1131838)], (18432 ^ _782652) ^ [_1131873] : [hAPP(c_Nat_OSuc, _1131873) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18434 ^ _782652) ^ [_1131895] : [-(_1131895 = 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)), _1131895)))], (18440 ^ _782652) ^ [_1131931, _1131933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1131931), _1131933)), _1131933 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18446 ^ _782652) ^ [_1132028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1132028), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18448 ^ _782652) ^ [_1132062] : [-(_1132062 = 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)), _1132062)))], (18454 ^ _782652) ^ [_1132094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1132094)), _1132094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18460 ^ _782652) ^ [_1132185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1132185), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18462 ^ _782652) ^ [_1132213] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1132213) = _1132213)], (18464 ^ _782652) ^ [_1132239] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1132239), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1132239)], (18466 ^ _782652) ^ [_1132283, _1132285] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1132283), _1132285) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18469 ^ _782652 : [(18470 ^ _782652) ^ [] : [-(_1132283 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18472 ^ _782652) ^ [] : [-(_1132285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18474 ^ _782652) ^ [_1132394, _1132396] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1132394), _1132396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1132394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1132396 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18484 ^ _782652) ^ [_1132537, _1132539] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1132537), _1132539) = _1132537, -(_1132539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18490 ^ _782652) ^ [_1132638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1132638), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1132638 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18496 ^ _782652) ^ [_1132719] : [_1132719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1132719), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18502 ^ _782652) ^ [_1132806] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1132806)))], (18504 ^ _782652) ^ [_1132831, _1132833] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1132831), _1132833) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1132833), _1132831) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1132831 = _1132833)], (18514 ^ _782652) ^ [_1132984] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1132984), _1132984) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18516 ^ _782652) ^ [_1133013] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1133013), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1133013)], (18518 ^ _782652) ^ [_1133042] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1133042) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18530 ^ _782652) ^ [_1133198, _1133200, _1133202] : [18531 ^ _782652 : [(18532 ^ _782652) ^ [] : [_1133198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18534 ^ _782652) ^ [] : [_1133200 = _1133202]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133198), _1133200) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133198), _1133202))], (18520 ^ _782652) ^ [_1133086, _1133088, _1133090] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133086), _1133088) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133086), _1133090), -(_1133086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1133088 = _1133090)], (18548 ^ _782652) ^ [_1133471, _1133473, _1133475] : [18549 ^ _782652 : [(18550 ^ _782652) ^ [] : [_1133471 = _1133475], (18552 ^ _782652) ^ [] : [_1133473 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133471), _1133473) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133475), _1133473))], (18538 ^ _782652) ^ [_1133359, _1133361, _1133363] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133359), _1133361) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133363), _1133361), -(_1133359 = _1133363), -(_1133361 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18566 ^ _782652) ^ [_1133744, _1133746, _1133748] : [18567 ^ _782652 : [(18568 ^ _782652) ^ [] : [_1133746 = _1133748], (18570 ^ _782652) ^ [] : [_1133744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133744), _1133746) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133744), _1133748))], (18556 ^ _782652) ^ [_1133632, _1133634, _1133636] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133632), _1133634) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133632), _1133636), -(_1133634 = _1133636), -(_1133632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18584 ^ _782652) ^ [_1134000, _1134002] : [18585 ^ _782652 : [(18586 ^ _782652) ^ [] : [_1134000 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18588 ^ _782652) ^ [] : [_1134002 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1134000), _1134002) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18574 ^ _782652) ^ [_1133902, _1133904] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1133902), _1133904) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1133902 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1133904 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18592 ^ _782652) ^ [_1134129] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1134129), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18594 ^ _782652) ^ [_1134158] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1134158) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18596 ^ _782652) ^ [_1134184] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1134184), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18598 ^ _782652) ^ [_1134213] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1134213) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18600 ^ _782652) ^ [_1134239] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1134239), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1134239)], (18602 ^ _782652) ^ [_1134268] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1134268) = _1134268)], (18604 ^ _782652) ^ [_1134294, _1134296, _1134298] : [class_Groups_Ocomm__monoid__add(_1134294), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1134296, _1134294), hAPP(c_COMBK(_1134294, _1134296), c_Groups_Ozero__class_Ozero(_1134294))), _1134298) = c_Groups_Ozero__class_Ozero(_1134294))], (18610 ^ _782652) ^ [_1134409, _1134411, _1134413] : [class_Groups_Oordered__comm__monoid__add(_1134409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134409), _1134411), c_Groups_Ozero__class_Ozero(_1134409))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134409), _1134413), c_Groups_Ozero__class_Ozero(_1134409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134409), _1134411), _1134413)), c_Groups_Ozero__class_Ozero(_1134409))))], (18624 ^ _782652) ^ [_1134664, _1134666, _1134668, _1134670] : [class_Groups_Oordered__comm__monoid__add(_1134664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134664), c_Groups_Ozero__class_Ozero(_1134664)), _1134666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134664), _1134668), _1134670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134664), _1134668), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134664), _1134670), _1134666))))], (18638 ^ _782652) ^ [_1134917, _1134919, _1134921, _1134923] : [class_Groups_Oordered__comm__monoid__add(_1134917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134917), c_Groups_Ozero__class_Ozero(_1134917)), _1134919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134917), _1134921), _1134923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134917), _1134921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134917), _1134919), _1134923))))], (18652 ^ _782652) ^ [_1135170, _1135172, _1135174] : [class_Groups_Oordered__comm__monoid__add(_1135170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135170), c_Groups_Ozero__class_Ozero(_1135170)), _1135172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135170), c_Groups_Ozero__class_Ozero(_1135170)), _1135174)), 18663 ^ _782652 : [(18664 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135170), _1135172), _1135174) = c_Groups_Ozero__class_Ozero(_1135170), 18667 ^ _782652 : [(18668 ^ _782652) ^ [] : [-(_1135172 = c_Groups_Ozero__class_Ozero(_1135170))], (18670 ^ _782652) ^ [] : [-(_1135174 = c_Groups_Ozero__class_Ozero(_1135170))]]], (18672 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135170), _1135172), _1135174) = c_Groups_Ozero__class_Ozero(_1135170)), _1135172 = c_Groups_Ozero__class_Ozero(_1135170), _1135174 = c_Groups_Ozero__class_Ozero(_1135170)]]], (18682 ^ _782652) ^ [_1135641, _1135643, _1135645] : [class_Groups_Oordered__comm__monoid__add(_1135641), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135641), c_Groups_Ozero__class_Ozero(_1135641)), _1135643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135641), c_Groups_Ozero__class_Ozero(_1135641)), _1135645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135641), c_Groups_Ozero__class_Ozero(_1135641)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135641), _1135643), _1135645))))], (18696 ^ _782652) ^ [_1135896, _1135898] : [class_Groups_Olinordered__ab__group__add(_1135896), 18699 ^ _782652 : [(18700 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135896), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135896), _1135898), _1135898)), c_Groups_Ozero__class_Ozero(_1135896))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135896), _1135898), c_Groups_Ozero__class_Ozero(_1135896))))], (18706 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135896), _1135898), c_Groups_Ozero__class_Ozero(_1135896))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135896), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1135896), _1135898), _1135898)), c_Groups_Ozero__class_Ozero(_1135896))))]]], (18712 ^ _782652) ^ [_1136179, _1136181] : [class_Groups_Olinordered__ab__group__add(_1136179), 18715 ^ _782652 : [(18716 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136179), c_Groups_Ozero__class_Ozero(_1136179)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136179), _1136181), _1136181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136179), c_Groups_Ozero__class_Ozero(_1136179)), _1136181)))], (18722 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136179), c_Groups_Ozero__class_Ozero(_1136179)), _1136181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136179), c_Groups_Ozero__class_Ozero(_1136179)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136179), _1136181), _1136181))))]]], (18728 ^ _782652) ^ [_1136462, _1136464] : [class_Rings_Olinordered__ring(_1136462), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136462), c_Groups_Ozero__class_Ozero(_1136462)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136462), _1136464), _1136464))))], (18734 ^ _782652) ^ [_1136571, _1136573, _1136575] : [class_Rings_Olinordered__ring__strict(_1136571), 18737 ^ _782652 : [(18738 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), c_Groups_Ozero__class_Ozero(_1136571)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136571), _1136573), _1136575))), 18743 ^ _782652 : [(18744 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), c_Groups_Ozero__class_Ozero(_1136571)), _1136573)))], (18746 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), c_Groups_Ozero__class_Ozero(_1136571)), _1136575)))]], 18747 ^ _782652 : [(18748 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), _1136573), c_Groups_Ozero__class_Ozero(_1136571))))], (18750 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), _1136575), c_Groups_Ozero__class_Ozero(_1136571))))]]], (18752 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), c_Groups_Ozero__class_Ozero(_1136571)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136571), _1136573), _1136575)))), 18753 ^ _782652 : [(18754 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), c_Groups_Ozero__class_Ozero(_1136571)), _1136573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), c_Groups_Ozero__class_Ozero(_1136571)), _1136575))], (18760 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), _1136573), c_Groups_Ozero__class_Ozero(_1136571))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136571), _1136575), c_Groups_Ozero__class_Ozero(_1136571)))]]]]], (18768 ^ _782652) ^ [_1137161, _1137163, _1137165] : [class_Rings_Olinordered__ring__strict(_1137161), 18771 ^ _782652 : [(18772 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137161), _1137163), _1137165)), c_Groups_Ozero__class_Ozero(_1137161))), 18777 ^ _782652 : [(18778 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), c_Groups_Ozero__class_Ozero(_1137161)), _1137163)))], (18780 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), _1137165), c_Groups_Ozero__class_Ozero(_1137161))))]], 18781 ^ _782652 : [(18782 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), _1137163), c_Groups_Ozero__class_Ozero(_1137161))))], (18784 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), c_Groups_Ozero__class_Ozero(_1137161)), _1137165)))]]], (18786 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137161), _1137163), _1137165)), c_Groups_Ozero__class_Ozero(_1137161)))), 18787 ^ _782652 : [(18788 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), c_Groups_Ozero__class_Ozero(_1137161)), _1137163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), _1137165), c_Groups_Ozero__class_Ozero(_1137161)))], (18794 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), _1137163), c_Groups_Ozero__class_Ozero(_1137161))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137161), c_Groups_Ozero__class_Ozero(_1137161)), _1137165))]]]]], (18802 ^ _782652) ^ [_1137751, _1137753, _1137755] : [class_Rings_Oordered__cancel__semiring(_1137751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137751), c_Groups_Ozero__class_Ozero(_1137751)), _1137753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137751), c_Groups_Ozero__class_Ozero(_1137751)), _1137755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137751), c_Groups_Ozero__class_Ozero(_1137751)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137751), _1137753), _1137755))))], (18816 ^ _782652) ^ [_1138006, _1138008, _1138010] : [class_Rings_Oordered__cancel__semiring(_1138006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138006), c_Groups_Ozero__class_Ozero(_1138006)), _1138008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138006), _1138010), c_Groups_Ozero__class_Ozero(_1138006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138006), _1138008), _1138010)), c_Groups_Ozero__class_Ozero(_1138006))))], (18830 ^ _782652) ^ [_1138261, _1138263, _1138265] : [class_Rings_Oordered__cancel__semiring(_1138261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138261), c_Groups_Ozero__class_Ozero(_1138261)), _1138263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138261), _1138265), c_Groups_Ozero__class_Ozero(_1138261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138261), _1138265), _1138263)), c_Groups_Ozero__class_Ozero(_1138261))))], (18844 ^ _782652) ^ [_1138516, _1138518, _1138520] : [class_Rings_Oordered__cancel__semiring(_1138516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138516), _1138518), c_Groups_Ozero__class_Ozero(_1138516))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138516), c_Groups_Ozero__class_Ozero(_1138516)), _1138520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138516), _1138518), _1138520)), c_Groups_Ozero__class_Ozero(_1138516))))], (18858 ^ _782652) ^ [_1138771, _1138773, _1138775] : [class_Rings_Oordered__ring(_1138771), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138771), _1138773), c_Groups_Ozero__class_Ozero(_1138771))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138771), _1138775), c_Groups_Ozero__class_Ozero(_1138771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138771), c_Groups_Ozero__class_Ozero(_1138771)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138771), _1138773), _1138775))))], (18872 ^ _782652) ^ [_1139026, _1139028, _1139030, _1139032] : [class_Rings_Oordered__semiring(_1139026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139026), _1139028), _1139030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139026), c_Groups_Ozero__class_Ozero(_1139026)), _1139032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139026), _1139028), _1139032)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139026), _1139030), _1139032))))], (18886 ^ _782652) ^ [_1139295, _1139297, _1139299, _1139301] : [class_Rings_Oordered__semiring(_1139295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139295), _1139297), _1139299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139295), c_Groups_Ozero__class_Ozero(_1139295)), _1139301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139295), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139295), _1139301), _1139297)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139295), _1139301), _1139299))))], (18900 ^ _782652) ^ [_1139564, _1139566, _1139568, _1139570] : [class_Rings_Oordered__comm__semiring(_1139564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139564), _1139566), _1139568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139564), c_Groups_Ozero__class_Ozero(_1139564)), _1139570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139564), _1139570), _1139566)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139564), _1139570), _1139568))))], (18914 ^ _782652) ^ [_1139833, _1139835, _1139837, _1139839] : [class_Rings_Oordered__ring(_1139833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139833), _1139835), _1139837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139833), _1139839), c_Groups_Ozero__class_Ozero(_1139833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139833), _1139837), _1139839)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139833), _1139835), _1139839))))], (18928 ^ _782652) ^ [_1140102, _1140104, _1140106, _1140108] : [class_Rings_Oordered__ring(_1140102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140102), _1140104), _1140106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140102), _1140108), c_Groups_Ozero__class_Ozero(_1140102))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140102), _1140108), _1140106)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140102), _1140108), _1140104))))], (18942 ^ _782652) ^ [_1140371, _1140373, _1140375, _1140377, _1140379] : [class_Rings_Oordered__semiring(_1140371), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140371), _1140373), _1140375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140371), _1140377), _1140379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140371), c_Groups_Ozero__class_Ozero(_1140371)), _1140373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140371), c_Groups_Ozero__class_Ozero(_1140371)), _1140377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140371), _1140373), _1140377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140371), _1140375), _1140379))))], (18964 ^ _782652) ^ [_1140794, _1140796, _1140798, _1140800, _1140802] : [class_Rings_Oordered__semiring(_1140794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140794), _1140796), _1140798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140794), _1140800), _1140802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140794), c_Groups_Ozero__class_Ozero(_1140794)), _1140798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140794), c_Groups_Ozero__class_Ozero(_1140794)), _1140800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140794), _1140796), _1140800)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140794), _1140798), _1140802))))], (18986 ^ _782652) ^ [_1141217, _1141219, _1141221] : [class_Rings_Oordered__ring(_1141217), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141217), c_Groups_Ozero__class_Ozero(_1141217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141217), _1141219), _1141221)))), 18991 ^ _782652 : [(18992 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141217), c_Groups_Ozero__class_Ozero(_1141217)), _1141219)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141217), c_Groups_Ozero__class_Ozero(_1141217)), _1141221))], (18998 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141217), _1141219), c_Groups_Ozero__class_Ozero(_1141217))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141217), _1141221), c_Groups_Ozero__class_Ozero(_1141217)))]]], (19006 ^ _782652) ^ [_1141593, _1141595, _1141597] : [class_Rings_Oordered__cancel__semiring(_1141593), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141593), _1141595), _1141597)), c_Groups_Ozero__class_Ozero(_1141593)))), 19011 ^ _782652 : [(19012 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141593), c_Groups_Ozero__class_Ozero(_1141593)), _1141595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141593), _1141597), c_Groups_Ozero__class_Ozero(_1141593)))], (19018 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141593), _1141595), c_Groups_Ozero__class_Ozero(_1141593))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141593), c_Groups_Ozero__class_Ozero(_1141593)), _1141597))]]], (19026 ^ _782652) ^ [_1141969, _1141971] : [class_Groups_Olinordered__ab__group__add(_1141969), 19029 ^ _782652 : [(19030 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141969), c_Groups_Ozero__class_Ozero(_1141969)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141969), _1141971), _1141971))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141969), c_Groups_Ozero__class_Ozero(_1141969)), _1141971)))], (19036 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141969), c_Groups_Ozero__class_Ozero(_1141969)), _1141971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141969), c_Groups_Ozero__class_Ozero(_1141969)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141969), _1141971), _1141971))))]]], (19042 ^ _782652) ^ [_1142252, _1142254] : [class_Groups_Olinordered__ab__group__add(_1142252), 19045 ^ _782652 : [(19046 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142252), _1142254), _1142254)), c_Groups_Ozero__class_Ozero(_1142252))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142252), _1142254), c_Groups_Ozero__class_Ozero(_1142252))))], (19052 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142252), _1142254), c_Groups_Ozero__class_Ozero(_1142252))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142252), _1142254), _1142254)), c_Groups_Ozero__class_Ozero(_1142252))))]]], (19058 ^ _782652) ^ [_1142535, _1142537, _1142539] : [class_Groups_Oordered__comm__monoid__add(_1142535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142535), c_Groups_Ozero__class_Ozero(_1142535)), _1142537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142535), c_Groups_Ozero__class_Ozero(_1142535)), _1142539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142535), c_Groups_Ozero__class_Ozero(_1142535)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142535), _1142537), _1142539))))], (19072 ^ _782652) ^ [_1142790, _1142792, _1142794, _1142796] : [class_Rings_Olinordered__semidom(_1142790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142790), c_Groups_Ozero__class_Ozero(_1142790)), _1142792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142790), _1142794), _1142796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142790), _1142794), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142790), _1142792), _1142796))))], (19086 ^ _782652) ^ [_1143043, _1143045, _1143047] : [class_Groups_Oordered__comm__monoid__add(_1143043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143043), _1143045), c_Groups_Ozero__class_Ozero(_1143043))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143043), _1143047), c_Groups_Ozero__class_Ozero(_1143043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1143043), _1143045), _1143047)), c_Groups_Ozero__class_Ozero(_1143043))))], (19100 ^ _782652) ^ [_1143298, _1143300] : [class_Rings_Olinordered__ring(_1143298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143298), _1143300), _1143300)), c_Groups_Ozero__class_Ozero(_1143298)))], (19106 ^ _782652) ^ [_1143408, _1143410, _1143412, _1143414] : [class_Rings_Olinordered__ring__strict(_1143408), 19109 ^ _782652 : [(19110 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143408), _1143410), _1143412)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143408), _1143414), _1143412))), 19115 ^ _782652 : [(19116 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), c_Groups_Ozero__class_Ozero(_1143408)), _1143412)))], (19118 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), _1143410), _1143414)))]], 19119 ^ _782652 : [(19120 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), _1143412), c_Groups_Ozero__class_Ozero(_1143408))))], (19122 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), _1143414), _1143410)))]]], (19124 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143408), _1143410), _1143412)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143408), _1143414), _1143412)))), 19125 ^ _782652 : [(19126 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), c_Groups_Ozero__class_Ozero(_1143408)), _1143412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), _1143410), _1143414))], (19132 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), _1143412), c_Groups_Ozero__class_Ozero(_1143408))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143408), _1143414), _1143410))]]]]], (19140 ^ _782652) ^ [_1144014, _1144016, _1144018, _1144020] : [class_Rings_Olinordered__ring__strict(_1144014), 19143 ^ _782652 : [(19144 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144014), _1144016), _1144018)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144014), _1144016), _1144020))), 19149 ^ _782652 : [(19150 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), c_Groups_Ozero__class_Ozero(_1144014)), _1144016)))], (19152 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), _1144018), _1144020)))]], 19153 ^ _782652 : [(19154 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), _1144016), c_Groups_Ozero__class_Ozero(_1144014))))], (19156 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), _1144020), _1144018)))]]], (19158 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144014), _1144016), _1144018)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144014), _1144016), _1144020)))), 19159 ^ _782652 : [(19160 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), c_Groups_Ozero__class_Ozero(_1144014)), _1144016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), _1144018), _1144020))], (19166 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), _1144016), c_Groups_Ozero__class_Ozero(_1144014))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144014), _1144020), _1144018))]]]]], (19174 ^ _782652) ^ [_1144620, _1144622, _1144624, _1144626] : [class_Rings_Olinordered__ring__strict(_1144620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144620), c_Groups_Ozero__class_Ozero(_1144620)), _1144622)), 19181 ^ _782652 : [(19182 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144620), _1144622), _1144624)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144620), _1144622), _1144626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144620), _1144624), _1144626)))], (19188 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144620), _1144624), _1144626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144620), _1144622), _1144624)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144620), _1144622), _1144626))))]]], (19194 ^ _782652) ^ [_1145001, _1145003, _1145005] : [class_Rings_Olinordered__semiring__strict(_1145001), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145001), c_Groups_Ozero__class_Ozero(_1145001)), _1145003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145001), c_Groups_Ozero__class_Ozero(_1145001)), _1145005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145001), c_Groups_Ozero__class_Ozero(_1145001)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145001), _1145003), _1145005))))], (19208 ^ _782652) ^ [_1145256, _1145258, _1145260] : [class_Rings_Olinordered__semiring__strict(_1145256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145256), c_Groups_Ozero__class_Ozero(_1145256)), _1145258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145256), _1145260), c_Groups_Ozero__class_Ozero(_1145256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145256), _1145258), _1145260)), c_Groups_Ozero__class_Ozero(_1145256))))], (19222 ^ _782652) ^ [_1145511, _1145513, _1145515] : [class_Rings_Olinordered__semiring__strict(_1145511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145511), c_Groups_Ozero__class_Ozero(_1145511)), _1145513)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145511), _1145515), c_Groups_Ozero__class_Ozero(_1145511))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145511), _1145515), _1145513)), c_Groups_Ozero__class_Ozero(_1145511))))], (19236 ^ _782652) ^ [_1145766, _1145768, _1145770] : [class_Rings_Olinordered__semiring__strict(_1145766), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145766), c_Groups_Ozero__class_Ozero(_1145766)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145766), _1145768), _1145770))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145766), c_Groups_Ozero__class_Ozero(_1145766)), _1145768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145766), c_Groups_Ozero__class_Ozero(_1145766)), _1145770)))], (19250 ^ _782652) ^ [_1146021, _1146023, _1146025] : [class_Rings_Olinordered__semiring__strict(_1146021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146021), c_Groups_Ozero__class_Ozero(_1146021)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146021), _1146023), _1146025))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146021), c_Groups_Ozero__class_Ozero(_1146021)), _1146025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146021), c_Groups_Ozero__class_Ozero(_1146021)), _1146023)))], (19264 ^ _782652) ^ [_1146276, _1146278, _1146280, _1146282] : [class_Rings_Olinordered__ring__strict(_1146276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146276), _1146278), c_Groups_Ozero__class_Ozero(_1146276))), 19271 ^ _782652 : [(19272 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146276), _1146278), _1146280)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146276), _1146278), _1146282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146276), _1146282), _1146280)))], (19278 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146276), _1146282), _1146280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146276), _1146278), _1146280)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146276), _1146278), _1146282))))]]], (19284 ^ _782652) ^ [_1146657, _1146659, _1146661] : [class_Rings_Olinordered__semiring__strict(_1146657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146657), _1146659), c_Groups_Ozero__class_Ozero(_1146657))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146657), c_Groups_Ozero__class_Ozero(_1146657)), _1146661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146657), _1146659), _1146661)), c_Groups_Ozero__class_Ozero(_1146657))))], (19298 ^ _782652) ^ [_1146912, _1146914, _1146916] : [class_Rings_Olinordered__ring__strict(_1146912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146912), _1146914), c_Groups_Ozero__class_Ozero(_1146912))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146912), _1146916), c_Groups_Ozero__class_Ozero(_1146912))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146912), c_Groups_Ozero__class_Ozero(_1146912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146912), _1146914), _1146916))))], (19312 ^ _782652) ^ [_1147167, _1147169, _1147171, _1147173] : [class_Rings_Olinordered__semiring__strict(_1147167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147167), _1147169), _1147171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147167), c_Groups_Ozero__class_Ozero(_1147167)), _1147173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147167), _1147169), _1147173)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147167), _1147171), _1147173))))], (19326 ^ _782652) ^ [_1147436, _1147438, _1147440, _1147442] : [class_Rings_Olinordered__semiring__strict(_1147436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147436), _1147438), _1147440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147436), c_Groups_Ozero__class_Ozero(_1147436)), _1147442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147436), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147436), _1147442), _1147438)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147436), _1147442), _1147440))))], (19340 ^ _782652) ^ [_1147705, _1147707, _1147709, _1147711] : [class_Rings_Olinordered__comm__semiring__strict(_1147705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147705), _1147707), _1147709)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147705), c_Groups_Ozero__class_Ozero(_1147705)), _1147711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147705), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147705), _1147711), _1147707)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147705), _1147711), _1147709))))], (19354 ^ _782652) ^ [_1147974, _1147976, _1147978, _1147980] : [class_Rings_Olinordered__ring__strict(_1147974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147974), _1147976), _1147978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147974), _1147980), c_Groups_Ozero__class_Ozero(_1147974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147974), _1147978), _1147980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147974), _1147976), _1147980))))], (19368 ^ _782652) ^ [_1148243, _1148245, _1148247, _1148249] : [class_Rings_Olinordered__ring__strict(_1148243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148243), _1148245), _1148247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148243), _1148249), c_Groups_Ozero__class_Ozero(_1148243))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148243), _1148249), _1148247)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148243), _1148249), _1148245))))], (19382 ^ _782652) ^ [_1148512, _1148514, _1148516] : [class_Groups_Oordered__ab__group__add(_1148512), 19385 ^ _782652 : [(19386 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148512), _1148514), _1148516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148512), _1148514), _1148516)), c_Groups_Ozero__class_Ozero(_1148512))))], (19392 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148512), _1148514), _1148516)), c_Groups_Ozero__class_Ozero(_1148512))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148512), _1148514), _1148516)))]]], (19398 ^ _782652) ^ [_1148795, _1148797, _1148799] : [class_Groups_Oordered__ab__group__add(_1148795), 19401 ^ _782652 : [(19402 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148795), _1148797), _1148799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148795), _1148797), _1148799)), c_Groups_Ozero__class_Ozero(_1148795))))], (19408 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148795), _1148797), _1148799)), c_Groups_Ozero__class_Ozero(_1148795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148795), _1148797), _1148799)))]]], (19414 ^ _782652) ^ [_1149078, _1149080, _1149082] : [class_Rings_Olinordered__ring__strict(_1149078), 19417 ^ _782652 : [(19418 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149078), _1149080), _1149080)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149078), _1149082), _1149082)) = c_Groups_Ozero__class_Ozero(_1149078), 19421 ^ _782652 : [(19422 ^ _782652) ^ [] : [-(_1149080 = c_Groups_Ozero__class_Ozero(_1149078))], (19424 ^ _782652) ^ [] : [-(_1149082 = c_Groups_Ozero__class_Ozero(_1149078))]]], (19426 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149078), _1149080), _1149080)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149078), _1149082), _1149082)) = c_Groups_Ozero__class_Ozero(_1149078)), _1149080 = c_Groups_Ozero__class_Ozero(_1149078), _1149082 = c_Groups_Ozero__class_Ozero(_1149078)]]], (19436 ^ _782652) ^ [_1149453, _1149455, _1149457, _1149459, _1149461, _1149463] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1149453), -(_1149455 = c_Groups_Ozero__class_Ozero(_1149453)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149453), _1149457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149453), _1149455), _1149461)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149453), _1149459), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149453), _1149455), _1149463)), _1149457 = _1149459, -(_1149461 = _1149463)], (19454 ^ _782652) ^ [_1149791] : [class_Rings_Olinordered__semidom(_1149791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149791), c_Groups_Oone__class_Oone(_1149791)), c_Groups_Ozero__class_Ozero(_1149791)))], (19460 ^ _782652) ^ [_1149887] : [class_Rings_Olinordered__semidom(_1149887), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149887), c_Groups_Ozero__class_Ozero(_1149887)), c_Groups_Oone__class_Oone(_1149887))))], (19466 ^ _782652) ^ [_1149982] : [class_Rings_Olinordered__semidom(_1149982), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149982), c_Groups_Oone__class_Oone(_1149982)), c_Groups_Ozero__class_Ozero(_1149982)))], (19472 ^ _782652) ^ [_1150078] : [class_Rings_Olinordered__semidom(_1150078), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150078), c_Groups_Ozero__class_Ozero(_1150078)), c_Groups_Oone__class_Oone(_1150078))))], (19478 ^ _782652) ^ [_1150173, _1150175] : [class_Groups_Olinordered__ab__group__add(_1150173), 19481 ^ _782652 : [(19482 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150173), hAPP(c_Groups_Ouminus__class_Ouminus(_1150173), _1150175)), _1150175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150173), c_Groups_Ozero__class_Ozero(_1150173)), _1150175)))], (19488 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150173), c_Groups_Ozero__class_Ozero(_1150173)), _1150175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150173), hAPP(c_Groups_Ouminus__class_Ouminus(_1150173), _1150175)), _1150175)))]]], (19494 ^ _782652) ^ [_1150441, _1150443] : [class_Groups_Oordered__ab__group__add(_1150441), 19497 ^ _782652 : [(19498 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150441), hAPP(c_Groups_Ouminus__class_Ouminus(_1150441), _1150443)), c_Groups_Ozero__class_Ozero(_1150441))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150441), c_Groups_Ozero__class_Ozero(_1150441)), _1150443)))], (19504 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150441), c_Groups_Ozero__class_Ozero(_1150441)), _1150443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150441), hAPP(c_Groups_Ouminus__class_Ouminus(_1150441), _1150443)), c_Groups_Ozero__class_Ozero(_1150441))))]]], (19510 ^ _782652) ^ [_1150715, _1150717] : [class_Groups_Olinordered__ab__group__add(_1150715), 19513 ^ _782652 : [(19514 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150715), _1150717), hAPP(c_Groups_Ouminus__class_Ouminus(_1150715), _1150717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150715), _1150717), c_Groups_Ozero__class_Ozero(_1150715))))], (19520 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150715), _1150717), c_Groups_Ozero__class_Ozero(_1150715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150715), _1150717), hAPP(c_Groups_Ouminus__class_Ouminus(_1150715), _1150717))))]]], (19526 ^ _782652) ^ [_1150983, _1150985] : [class_Groups_Oordered__ab__group__add(_1150983), 19529 ^ _782652 : [(19530 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150983), c_Groups_Ozero__class_Ozero(_1150983)), hAPP(c_Groups_Ouminus__class_Ouminus(_1150983), _1150985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150983), _1150985), c_Groups_Ozero__class_Ozero(_1150983))))], (19536 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150983), _1150985), c_Groups_Ozero__class_Ozero(_1150983))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150983), c_Groups_Ozero__class_Ozero(_1150983)), hAPP(c_Groups_Ouminus__class_Ouminus(_1150983), _1150985))))]]], (19542 ^ _782652) ^ [_1151257, _1151259] : [class_Groups_Oordered__ab__group__add(_1151257), 19545 ^ _782652 : [(19546 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151257), c_Groups_Ozero__class_Ozero(_1151257)), hAPP(c_Groups_Ouminus__class_Ouminus(_1151257), _1151259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151257), _1151259), c_Groups_Ozero__class_Ozero(_1151257))))], (19552 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151257), _1151259), c_Groups_Ozero__class_Ozero(_1151257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151257), c_Groups_Ozero__class_Ozero(_1151257)), hAPP(c_Groups_Ouminus__class_Ouminus(_1151257), _1151259))))]]], (19558 ^ _782652) ^ [_1151531, _1151533] : [class_Groups_Oordered__ab__group__add(_1151531), 19561 ^ _782652 : [(19562 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151531), hAPP(c_Groups_Ouminus__class_Ouminus(_1151531), _1151533)), c_Groups_Ozero__class_Ozero(_1151531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151531), c_Groups_Ozero__class_Ozero(_1151531)), _1151533)))], (19568 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151531), c_Groups_Ozero__class_Ozero(_1151531)), _1151533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151531), hAPP(c_Groups_Ouminus__class_Ouminus(_1151531), _1151533)), c_Groups_Ozero__class_Ozero(_1151531))))]]], (19574 ^ _782652) ^ [_1151805, _1151807] : [class_Groups_Olinordered__ab__group__add(_1151805), 19577 ^ _782652 : [(19578 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151805), hAPP(c_Groups_Ouminus__class_Ouminus(_1151805), _1151807)), _1151807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151805), c_Groups_Ozero__class_Ozero(_1151805)), _1151807)))], (19584 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151805), c_Groups_Ozero__class_Ozero(_1151805)), _1151807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151805), hAPP(c_Groups_Ouminus__class_Ouminus(_1151805), _1151807)), _1151807)))]]], (19590 ^ _782652) ^ [_1152073, _1152075] : [class_Rings_Olinordered__idom(_1152073), 19593 ^ _782652 : [(19594 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152073), _1152075), hAPP(c_Groups_Ouminus__class_Ouminus(_1152073), _1152075))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152073), _1152075), c_Groups_Ozero__class_Ozero(_1152073))))], (19600 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152073), _1152075), c_Groups_Ozero__class_Ozero(_1152073))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152073), _1152075), hAPP(c_Groups_Ouminus__class_Ouminus(_1152073), _1152075))))]]], (19606 ^ _782652) ^ [_1152341, _1152343, _1152345] : [class_Groups_Ogroup__add(_1152341), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152341), _1152343), _1152345) = c_Groups_Ozero__class_Ozero(_1152341), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1152341), _1152343) = _1152345)], (19616 ^ _782652) ^ [_1152502, _1152504] : [class_Groups_Oab__group__add(_1152502), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152502), hAPP(c_Groups_Ouminus__class_Ouminus(_1152502), _1152504)), _1152504) = c_Groups_Ozero__class_Ozero(_1152502))], (19622 ^ _782652) ^ [_1152607, _1152609] : [class_Groups_Ogroup__add(_1152607), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152607), hAPP(c_Groups_Ouminus__class_Ouminus(_1152607), _1152609)), _1152609) = c_Groups_Ozero__class_Ozero(_1152607))], (19628 ^ _782652) ^ [_1152712, _1152714, _1152716] : [class_Groups_Ogroup__add(_1152712), 19631 ^ _782652 : [(19632 ^ _782652) ^ [] : [_1152714 = hAPP(c_Groups_Ouminus__class_Ouminus(_1152712), _1152716), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152712), _1152714), _1152716) = c_Groups_Ozero__class_Ozero(_1152712))], (19638 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152712), _1152714), _1152716) = c_Groups_Ozero__class_Ozero(_1152712), -(_1152714 = hAPP(c_Groups_Ouminus__class_Ouminus(_1152712), _1152716))]]], (19644 ^ _782652) ^ [_1152968, _1152970] : [class_Groups_Ogroup__add(_1152968), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152968), _1152970), hAPP(c_Groups_Ouminus__class_Ouminus(_1152968), _1152970)) = c_Groups_Ozero__class_Ozero(_1152968))], (19650 ^ _782652) ^ [_1153073, _1153075] : [class_Groups_Ogroup__add(_1153073), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1153073), c_Groups_Ozero__class_Ozero(_1153073)), _1153075) = hAPP(c_Groups_Ouminus__class_Ouminus(_1153073), _1153075))], (19656 ^ _782652) ^ [_1153178, _1153180, _1153182] : [class_Groups_Ocomm__monoid__add(_1153178), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153180, _1153178), _1153182), c_Orderings_Obot__class_Obot(tc_fun(_1153180, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1153178))], (19662 ^ _782652) ^ [_1153287, _1153289, _1153291] : [class_Groups_Ocomm__monoid__add(_1153287), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153289, _1153287), _1153291), c_Orderings_Obot__class_Obot(tc_fun(_1153289, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1153287))], (19668 ^ _782652) ^ [_1153396, _1153398, _1153400, _1153402] : [class_Groups_Ocomm__monoid__add(_1153396), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1153398), _1153400))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153398, _1153396), _1153402), _1153400) = c_Groups_Ozero__class_Ozero(_1153396))], (19678 ^ _782652) ^ [_1153520, _1153522, _1153524, _1153526] : [class_Groups_Ocomm__monoid__add(_1153520), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1153522), _1153524))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153522, _1153520), _1153526), _1153524) = c_Groups_Ozero__class_Ozero(_1153520))], (19688 ^ _782652) ^ [_1153659, _1153661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1153659), hAPP(c_Nat_OSuc, _1153661))), -(_1153659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 19696 ^ _782652 : [(19697 ^ _782652) ^ [] : [-(_1153659 = hAPP(c_Nat_OSuc, 19695 ^ [_1153659, _1153661]))], (19699 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19695 ^ [_1153659, _1153661]), _1153661)))]]], (19701 ^ _782652) ^ [_1153839, _1153841] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1153839), hAPP(c_Nat_OSuc, _1153841)))), 19702 ^ _782652 : [(19703 ^ _782652) ^ [] : [_1153839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19705 ^ _782652) ^ [_1153927] : [_1153839 = hAPP(c_Nat_OSuc, _1153927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1153927), _1153841))]]], (19713 ^ _782652) ^ [_1154073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1154073), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1154073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19719 ^ _782652) ^ [_1154154] : [_1154154 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1154154), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (19725 ^ _782652) ^ [_1154253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1154253)), -(_1154253 = hAPP(c_Nat_OSuc, 19728 ^ [_1154253]))], (19732 ^ _782652) ^ [_1154344] : [19733 ^ _782652 : [(19734 ^ _782652) ^ [_1154386] : [_1154344 = hAPP(c_Nat_OSuc, _1154386)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1154344)))], (19738 ^ _782652) ^ [_1154459, _1154461] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1154459), _1154461) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 19743 ^ _782652 : [(19744 ^ _782652) ^ [] : [-(_1154459 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19746 ^ _782652) ^ [] : [-(_1154461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 19747 ^ _782652 : [(19748 ^ _782652) ^ [] : [-(_1154459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19750 ^ _782652) ^ [] : [-(_1154461 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (19752 ^ _782652) ^ [_1154643, _1154645] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1154643), _1154645) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 19753 ^ _782652 : [(19754 ^ _782652) ^ [] : [_1154643 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1154645 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19760 ^ _782652) ^ [] : [_1154643 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1154645 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19768 ^ _782652) ^ [_1154884, _1154886] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1154884), _1154886), 19773 ^ _782652 : [(19774 ^ _782652) ^ [] : [-(_1154884 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19776 ^ _782652) ^ [] : [-(_1154886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 19777 ^ _782652 : [(19778 ^ _782652) ^ [] : [-(_1154884 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19780 ^ _782652) ^ [] : [-(_1154886 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (19782 ^ _782652) ^ [_1155068, _1155070] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1155068), _1155070)), 19783 ^ _782652 : [(19784 ^ _782652) ^ [] : [_1155068 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19790 ^ _782652) ^ [] : [_1155068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1155070 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19808 ^ _782652) ^ [_1155419, _1155421] : [19809 ^ _782652 : [(19810 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155419))], (19812 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155421))]], -(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), _1155419), _1155421))))], (19798 ^ _782652) ^ [_1155309, _1155311] : [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), _1155309), _1155311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155309))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155311)))], (19816 ^ _782652) ^ [_1155560] : [-(hAPP(c_Finite__Set_Ocard(_1155560), c_Orderings_Obot__class_Obot(tc_fun(_1155560, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19818 ^ _782652) ^ [_1155589, _1155591] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1155589), _1155591))), -(hAPP(c_Finite__Set_Ocard(_1155589), _1155591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19824 ^ _782652) ^ [_1155649, _1155651] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155649), _1155651) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 19827 ^ _782652 : [(19828 ^ _782652) ^ [] : [-(_1155649 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19830 ^ _782652) ^ [] : [-(_1155651 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (19832 ^ _782652) ^ [_1155760, _1155762] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1155760), _1155762) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1155760 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155762 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19842 ^ _782652) ^ [_1155903, _1155905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1155905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1155905), _1155903)), _1155905)))], (19852 ^ _782652) ^ [_1156077, _1156079] : [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), _1156077), _1156079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156079), _1156077)))], (19858 ^ _782652) ^ [_1156176, _1156178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156178), _1156176)), -(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), _1156176), _1156178))))], (19864 ^ _782652) ^ [_1156281, _1156283, _1156285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1156281)), 19867 ^ _782652 : [(19868 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156281), _1156283) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156281), _1156285), -(_1156283 = _1156285)], (19874 ^ _782652) ^ [] : [_1156283 = _1156285, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156281), _1156283) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156281), _1156285))]]], (19880 ^ _782652) ^ [_1156534, _1156536, _1156538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1156534)), 19883 ^ _782652 : [(19884 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156534), _1156536)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156534), _1156538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156536), _1156538)))], (19890 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156536), _1156538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156534), _1156536)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156534), _1156538))))]]], (19896 ^ _782652) ^ [_1156817, _1156819, _1156821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156817), _1156819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1156821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156821), _1156817)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156821), _1156819))))], (19906 ^ _782652) ^ [_1156998, _1157000, _1157002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156998), _1157000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1156998), _1157002)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157000), _1157002))))], (19916 ^ _782652) ^ [_1157197, _1157199, _1157201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157197), _1157199)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157201), _1157199))), 19919 ^ _782652 : [(19920 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157199)))], (19922 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157197), _1157201)))]]], (19924 ^ _782652) ^ [_1157346, _1157348, _1157350] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157346), _1157348)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157350), _1157348)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157346), _1157350))], (19934 ^ _782652) ^ [_1157547, _1157549, _1157551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157547), _1157549)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157547), _1157551))), 19937 ^ _782652 : [(19938 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157547)))], (19940 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157549), _1157551)))]]], (19942 ^ _782652) ^ [_1157696, _1157698, _1157700] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157696), _1157698)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1157696), _1157700)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1157698), _1157700))], (19952 ^ _782652) ^ [_1157894, _1157896] : [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), _1157894), _1157896))), 19955 ^ _782652 : [(19956 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157894)))], (19958 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157896)))]]], (19960 ^ _782652) ^ [_1158017, _1158019] : [-(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), _1158017), _1158019)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1158019))], (19970 ^ _782652) ^ [_1158172, _1158174] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158172), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1158172), _1158174)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19972 ^ _782652) ^ [_1158209, _1158211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158209), _1158211)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158209), _1158211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19978 ^ _782652) ^ [_1158323, _1158325] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158323), _1158325) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158323), _1158325)))], (19984 ^ _782652) ^ [_1158418, _1158420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1158418), _1158420)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1158418), _1158420) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19990 ^ _782652) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19992 ^ _782652) ^ [_1158537, _1158539] : [_1158537 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1158537), _1158539), -(_1158539 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1158537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20002 ^ _782652) ^ [_1158639, _1158641, _1158643] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1158639), _1158641)), 20005 ^ _782652 : [(20016 ^ _782652) ^ [] : [20018 ^ _782652 : [(20019 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1158639), 20017 ^ [_1158639, _1158641, _1158643]), _1158641)))], (20021 ^ _782652) ^ [] : [hAPP(_1158643, 20017 ^ [_1158639, _1158641, _1158643]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1158639, tc_Nat_Onat), _1158643), _1158641) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20006 ^ _782652) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1158639, tc_Nat_Onat), _1158643), _1158641) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 20009 ^ _782652 : [(20010 ^ _782652) ^ [_1158801] : [hBOOL(hAPP(hAPP(c_member(_1158639), _1158801), _1158641)), -(hAPP(_1158643, _1158801) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (20025 ^ _782652) ^ [_1159059, _1159061, _1159063] : [class_Groups_Oordered__comm__monoid__add(_1159059), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159059), _1159061), c_Groups_Ozero__class_Ozero(_1159059))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159059), _1159063), c_Groups_Ozero__class_Ozero(_1159059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1159059), _1159061), _1159063)), c_Groups_Ozero__class_Ozero(_1159059))))], (20039 ^ _782652) ^ [_1159314, _1159316, _1159318] : [class_Groups_Oordered__comm__monoid__add(_1159314), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159314), _1159316), c_Groups_Ozero__class_Ozero(_1159314))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159314), _1159318), c_Groups_Ozero__class_Ozero(_1159314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159314), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1159314), _1159316), _1159318)), c_Groups_Ozero__class_Ozero(_1159314))))], (20053 ^ _782652) ^ [_1159569, _1159571, _1159573, _1159575] : [class_Groups_Oordered__comm__monoid__add(_1159569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159569), c_Groups_Ozero__class_Ozero(_1159569)), _1159571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159569), _1159573), _1159575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159569), _1159573), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1159569), _1159571), _1159575))))], (20067 ^ _782652) ^ [_1159822, _1159824, _1159826, _1159828] : [class_Groups_Oordered__comm__monoid__add(_1159822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159822), c_Groups_Ozero__class_Ozero(_1159822)), _1159824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159822), _1159826), _1159828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159822), _1159826), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1159822), _1159824), _1159828))))], (20081 ^ _782652) ^ [_1160075, _1160077, _1160079] : [class_Groups_Oordered__comm__monoid__add(_1160075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160075), c_Groups_Ozero__class_Ozero(_1160075)), _1160077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160075), c_Groups_Ozero__class_Ozero(_1160075)), _1160079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160075), c_Groups_Ozero__class_Ozero(_1160075)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160075), _1160077), _1160079))))], (20095 ^ _782652) ^ [_1160330, _1160332, _1160334] : [class_Groups_Oordered__comm__monoid__add(_1160330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160330), c_Groups_Ozero__class_Ozero(_1160330)), _1160332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160330), c_Groups_Ozero__class_Ozero(_1160330)), _1160334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160330), c_Groups_Ozero__class_Ozero(_1160330)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160330), _1160332), _1160334))))], (20109 ^ _782652) ^ [_1160585, _1160587, _1160589, _1160591] : [class_Rings_Olinordered__semiring__strict(_1160585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160585), _1160587), _1160589)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160585), _1160587), _1160591))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160585), c_Groups_Ozero__class_Ozero(_1160585)), _1160587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160585), _1160589), _1160591)))], (20123 ^ _782652) ^ [_1160854, _1160856, _1160858, _1160860] : [class_Rings_Olinordered__semiring__strict(_1160854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160854), _1160856), _1160858)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160854), _1160860), _1160858))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160854), c_Groups_Ozero__class_Ozero(_1160854)), _1160858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160854), _1160856), _1160860)))], (20137 ^ _782652) ^ [_1161123, _1161125, _1161127, _1161129] : [class_Rings_Olinordered__semiring__strict(_1161123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161123), _1161125), _1161127)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161123), _1161125), _1161129))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161123), c_Groups_Ozero__class_Ozero(_1161123)), _1161125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161123), _1161127), _1161129)))], (20151 ^ _782652) ^ [_1161392, _1161394, _1161396, _1161398] : [class_Rings_Olinordered__semiring(_1161392), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161392), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161392), _1161394), _1161396)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161392), _1161394), _1161398))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161392), c_Groups_Ozero__class_Ozero(_1161392)), _1161394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161392), _1161396), _1161398)))], (20165 ^ _782652) ^ [_1161661, _1161663, _1161665, _1161667] : [class_Rings_Olinordered__semiring__strict(_1161661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161661), _1161663), _1161665)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161661), _1161667), _1161665))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161661), c_Groups_Ozero__class_Ozero(_1161661)), _1161665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161661), _1161663), _1161667)))], (20179 ^ _782652) ^ [_1161930, _1161932, _1161934, _1161936] : [class_Rings_Olinordered__semiring(_1161930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161930), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161930), _1161932), _1161934)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161930), _1161936), _1161934))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161930), c_Groups_Ozero__class_Ozero(_1161930)), _1161934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161930), _1161932), _1161936)))], (20193 ^ _782652) ^ [_1162199, _1162201, _1162203, _1162205, _1162207] : [class_Rings_Olinordered__semiring__strict(_1162199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162199), _1162201), _1162203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162199), _1162205), _1162207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162199), c_Groups_Ozero__class_Ozero(_1162199)), _1162201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162199), c_Groups_Ozero__class_Ozero(_1162199)), _1162205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162199), _1162201), _1162205)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162199), _1162203), _1162207))))], (20215 ^ _782652) ^ [_1162622, _1162624, _1162626, _1162628, _1162630] : [class_Rings_Olinordered__semiring__strict(_1162622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162622), _1162624), _1162626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162622), _1162628), _1162630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162622), c_Groups_Ozero__class_Ozero(_1162622)), _1162624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162622), c_Groups_Ozero__class_Ozero(_1162622)), _1162628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162622), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162622), _1162624), _1162628)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162622), _1162626), _1162630))))], (20237 ^ _782652) ^ [_1163045, _1163047, _1163049, _1163051, _1163053] : [class_Rings_Olinordered__semiring__strict(_1163045), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163045), _1163047), _1163049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163045), _1163051), _1163053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163045), c_Groups_Ozero__class_Ozero(_1163045)), _1163047)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163045), c_Groups_Ozero__class_Ozero(_1163045)), _1163051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163045), _1163047), _1163051)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163045), _1163049), _1163053))))], (20259 ^ _782652) ^ [_1163468, _1163470, _1163472, _1163474, _1163476] : [class_Rings_Olinordered__semiring__strict(_1163468), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163468), _1163470), _1163472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163468), _1163474), _1163476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163468), c_Groups_Ozero__class_Ozero(_1163468)), _1163472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163468), c_Groups_Ozero__class_Ozero(_1163468)), _1163474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163468), _1163470), _1163474)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163468), _1163472), _1163476))))], (20281 ^ _782652) ^ [_1163891, _1163893, _1163895, _1163897] : [class_Rings_Olinordered__ring__strict(_1163891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163891), _1163893), c_Groups_Ozero__class_Ozero(_1163891))), 20288 ^ _782652 : [(20289 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163891), _1163893), _1163895)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163891), _1163893), _1163897))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163891), _1163897), _1163895)))], (20295 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163891), _1163897), _1163895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163891), _1163893), _1163895)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163891), _1163893), _1163897))))]]], (20301 ^ _782652) ^ [_1164272, _1164274, _1164276, _1164278] : [class_Rings_Olinordered__ring__strict(_1164272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164272), c_Groups_Ozero__class_Ozero(_1164272)), _1164274)), 20308 ^ _782652 : [(20309 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164272), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164272), _1164274), _1164276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164272), _1164274), _1164278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164272), _1164276), _1164278)))], (20315 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164272), _1164276), _1164278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164272), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164272), _1164274), _1164276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164272), _1164274), _1164278))))]]], (20321 ^ _782652) ^ [_1164653, _1164655, _1164657] : [class_Rings_Olinordered__ring(_1164653), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164653), c_Groups_Ozero__class_Ozero(_1164653)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164653), _1164655), _1164655)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164653), _1164657), _1164657)))))], (20327 ^ _782652) ^ [_1164796, _1164798, _1164800] : [class_Rings_Olinordered__ring__strict(_1164796), 20330 ^ _782652 : [(20331 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164796), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164796), _1164798), _1164798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164796), _1164800), _1164800))), c_Groups_Ozero__class_Ozero(_1164796))), 20334 ^ _782652 : [(20335 ^ _782652) ^ [] : [-(_1164798 = c_Groups_Ozero__class_Ozero(_1164796))], (20337 ^ _782652) ^ [] : [-(_1164800 = c_Groups_Ozero__class_Ozero(_1164796))]]], (20339 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164796), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164796), _1164798), _1164798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164796), _1164800), _1164800))), c_Groups_Ozero__class_Ozero(_1164796)))), _1164798 = c_Groups_Ozero__class_Ozero(_1164796), _1164800 = c_Groups_Ozero__class_Ozero(_1164796)]]], (20349 ^ _782652) ^ [_1165192, _1165194, _1165196] : [class_Rings_Olinordered__ring(_1165192), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165192), _1165194), _1165194)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165192), _1165196), _1165196))), c_Groups_Ozero__class_Ozero(_1165192)))], (20355 ^ _782652) ^ [_1165336, _1165338, _1165340] : [class_Rings_Olinordered__ring__strict(_1165336), 20358 ^ _782652 : [(20369 ^ _782652) ^ [] : [20370 ^ _782652 : [(20371 ^ _782652) ^ [] : [-(_1165338 = c_Groups_Ozero__class_Ozero(_1165336))], (20373 ^ _782652) ^ [] : [-(_1165340 = c_Groups_Ozero__class_Ozero(_1165336))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165336), c_Groups_Ozero__class_Ozero(_1165336)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165336), _1165338), _1165338)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165336), _1165340), _1165340)))))], (20359 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165336), c_Groups_Ozero__class_Ozero(_1165336)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165336), _1165338), _1165338)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165336), _1165340), _1165340)))), _1165338 = c_Groups_Ozero__class_Ozero(_1165336), _1165340 = c_Groups_Ozero__class_Ozero(_1165336)]]], (20377 ^ _782652) ^ [_1165711, _1165713, _1165715] : [class_Rings_Olinordered__idom(_1165711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165711), c_Groups_Ozero__class_Ozero(_1165711)), _1165713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165711), c_Groups_Ozero__class_Ozero(_1165711)), _1165715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165711), _1165715), c_Groups_Oone__class_Oone(_1165711))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165711), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165711), _1165713), _1165715)), _1165713)))], (20395 ^ _782652) ^ [_1166034, _1166036, _1166038] : [class_Rings_Olinordered__idom(_1166034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166034), c_Groups_Ozero__class_Ozero(_1166034)), _1166036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166034), c_Groups_Ozero__class_Ozero(_1166034)), _1166038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166034), _1166038), c_Groups_Oone__class_Oone(_1166034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166034), _1166038), _1166036)), _1166036)))], (20413 ^ _782652) ^ [_1166357] : [class_Rings_Olinordered__semidom(_1166357), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166357), c_Groups_Ozero__class_Ozero(_1166357)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166357), c_Groups_Oone__class_Oone(_1166357)), c_Groups_Oone__class_Oone(_1166357)))))], (20429 ^ _782652) ^ [_1166642, _1166644] : [20430 ^ _782652 : [(20431 ^ _782652) ^ [] : [_1166644 = c_Orderings_Obot__class_Obot(tc_fun(_1166642, tc_HOL_Obool))], (20433 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1166642), _1166644)))]], -(hAPP(c_Finite__Set_Ocard(_1166642), _1166644) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20419 ^ _782652) ^ [_1166487, _1166489] : [hAPP(c_Finite__Set_Ocard(_1166487), _1166489) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1166489 = c_Orderings_Obot__class_Obot(tc_fun(_1166487, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166487), _1166489))], (20437 ^ _782652) ^ [_1166786, _1166788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1166786), _1166788))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1166786), _1166788)))], (20443 ^ _782652) ^ [_1166885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1166885)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166885), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1166885)], (20449 ^ _782652) ^ [_1166982, _1166984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1166982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166982), hAPP(c_Nat_OSuc, _1166984))), _1166982)))], (20455 ^ _782652) ^ [_1167091, _1167093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167093)), -(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), _1167093), _1167091))))], (20465 ^ _782652) ^ [_1167244, _1167246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1167244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167244), _1167246))))], (20475 ^ _782652) ^ [_1167403, _1167405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1167405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1167403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167405), _1167403))))], (20501 ^ _782652) ^ [_1167872, _1167874, _1167876] : [-(hBOOL(hAPP(_1167872, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167874), _1167876)))), 20504 ^ _782652 : [(20505 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1167874), _1167876)))], (20507 ^ _782652) ^ [] : [hBOOL(hAPP(_1167872, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20509 ^ _782652 : [(20510 ^ _782652) ^ [] : [-(_1167874 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1167876), 20508 ^ [_1167872, _1167874, _1167876]))], (20512 ^ _782652) ^ [] : [hBOOL(hAPP(_1167872, 20508 ^ [_1167872, _1167874, _1167876]))]]], (20485 ^ _782652) ^ [_1167580, _1167582, _1167584] : [hBOOL(hAPP(_1167580, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167582), _1167584))), 20488 ^ _782652 : [(20489 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1167582), _1167584)), -(hBOOL(hAPP(_1167580, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20495 ^ _782652) ^ [_1167771] : [_1167582 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1167584), _1167771), -(hBOOL(hAPP(_1167580, _1167771)))]]], (20532 ^ _782652) ^ [_1168467, _1168469, _1168471] : [-(hBOOL(hAPP(_1168467, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1168469), _1168471)))), 20535 ^ _782652 : [(20536 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1168469), _1168471)))], (20538 ^ _782652) ^ [] : [hBOOL(hAPP(_1168467, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20540 ^ _782652 : [(20541 ^ _782652) ^ [] : [-(_1168469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1168471), 20539 ^ [_1168467, _1168469, _1168471]))], (20543 ^ _782652) ^ [] : [hBOOL(hAPP(_1168467, 20539 ^ [_1168467, _1168469, _1168471]))]]], (20516 ^ _782652) ^ [_1168183, _1168185, _1168187] : [hBOOL(hAPP(_1168183, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1168185), _1168187))), 20519 ^ _782652 : [(20520 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1168185), _1168187)), -(hBOOL(hAPP(_1168183, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20526 ^ _782652) ^ [_1168368] : [_1168185 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1168187), _1168368), -(hBOOL(hAPP(_1168183, _1168368)))]]], (20547 ^ _782652) ^ [_1168767, _1168769] : [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), _1168767), _1168769))), 20550 ^ _782652 : [(20551 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168767)))], (20553 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168769)))]]], (20555 ^ _782652) ^ [_1168890, _1168892] : [-(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), _1168890), _1168892)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1168892))], (20565 ^ _782652) ^ [_1169045, _1169047, _1169049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169045)), 20568 ^ _782652 : [(20569 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169045), _1169047)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169045), _1169049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169047), _1169049)))], (20575 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169047), _1169049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169045), _1169047)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169045), _1169049))))]]], (20591 ^ _782652) ^ [_1169523, _1169525, _1169527] : [20592 ^ _782652 : [(20593 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169523)))], (20595 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169525), _1169527))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169523), _1169525)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169523), _1169527))))], (20581 ^ _782652) ^ [_1169346, _1169348, _1169350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169346), _1169348)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169346), _1169350))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169348), _1169350)))], (20609 ^ _782652) ^ [_1169880, _1169882, _1169884] : [20610 ^ _782652 : [(20611 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169882)))], (20613 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169880), _1169884))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169880), _1169882)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169884), _1169882))))], (20599 ^ _782652) ^ [_1169703, _1169705, _1169707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169703), _1169705)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1169707), _1169705))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169703), _1169707)))], (20617 ^ _782652) ^ [_1170042, _1170044, _1170046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1170042), _1170044)), 20620 ^ _782652 : [(20621 ^ _782652) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170042, tc_Nat_Onat), _1170046), _1170044) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20625 ^ _782652 : [(20626 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1170042), 20624 ^ [_1170042, _1170044, _1170046]), _1170044)))], (20628 ^ _782652) ^ [] : [-(hAPP(_1170046, 20624 ^ [_1170042, _1170044, _1170046]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20630 ^ _782652) ^ [_1170362] : [hBOOL(hAPP(hAPP(c_member(_1170042), _1170362), _1170044)), -(20624 ^ [_1170042, _1170044, _1170046] = _1170362), -(hAPP(_1170046, _1170362) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20640 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170042, tc_Nat_Onat), _1170046), _1170044) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 20641 ^ _782652 : [(20642 ^ _782652) ^ [_1170523] : [hBOOL(hAPP(hAPP(c_member(_1170042), _1170523), _1170044)), hAPP(_1170046, _1170523) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20650 ^ _782652 : [(20651 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1170042), 20649 ^ [_1170042, _1170044, _1170046, _1170523]), _1170044)))], (20653 ^ _782652) ^ [] : [_1170523 = 20649 ^ [_1170042, _1170044, _1170046, _1170523]], (20655 ^ _782652) ^ [] : [hAPP(_1170046, 20649 ^ [_1170042, _1170044, _1170046, _1170523]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (20659 ^ _782652) ^ [_1170876, _1170878, _1170880] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1170876), _1170878)), 20662 ^ _782652 : [(20663 ^ _782652) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170876, tc_Nat_Onat), _1170880), _1170878) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 20667 ^ _782652 : [(20668 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1170876), 20666 ^ [_1170876, _1170878, _1170880]), _1170878)))], (20670 ^ _782652) ^ [] : [-(hAPP(_1170880, 20666 ^ [_1170876, _1170878, _1170880]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20672 ^ _782652) ^ [_1171196] : [hBOOL(hAPP(hAPP(c_member(_1170876), _1171196), _1170878)), -(20666 ^ [_1170876, _1170878, _1170880] = _1171196), -(hAPP(_1170880, _1171196) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20682 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170876, tc_Nat_Onat), _1170880), _1170878) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 20683 ^ _782652 : [(20684 ^ _782652) ^ [_1171357] : [hBOOL(hAPP(hAPP(c_member(_1170876), _1171357), _1170878)), hAPP(_1170880, _1171357) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 20692 ^ _782652 : [(20693 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1170876), 20691 ^ [_1170876, _1170878, _1170880, _1171357]), _1170878)))], (20695 ^ _782652) ^ [] : [_1171357 = 20691 ^ [_1170876, _1170878, _1170880, _1171357]], (20697 ^ _782652) ^ [] : [hAPP(_1170880, 20691 ^ [_1170876, _1170878, _1170880, _1171357]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (20701 ^ _782652) ^ [_1171710, _1171712, _1171714, _1171716, _1171718] : [class_Groups_Ocomm__monoid__add(_1171710), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171712), _1171714)), 20708 ^ _782652 : [(20709 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1171712), _1171716), _1171714)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1171712, _1171710), hAPP(hAPP(c_COMBC(_1171712, _1171710, _1171710), hAPP(hAPP(c_COMBS(_1171712, _1171710, tc_fun(_1171710, _1171710)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1171710, tc_fun(_1171710, _1171710)), _1171712), c_If(_1171710)), hAPP(c_fequal, _1171716))), _1171718)), c_Groups_Ozero__class_Ozero(_1171710))), _1171714) = hAPP(_1171718, _1171716))], (20715 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1171712), _1171716), _1171714))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1171712, _1171710), hAPP(hAPP(c_COMBC(_1171712, _1171710, _1171710), hAPP(hAPP(c_COMBS(_1171712, _1171710, tc_fun(_1171710, _1171710)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1171710, tc_fun(_1171710, _1171710)), _1171712), c_If(_1171710)), hAPP(c_fequal, _1171716))), _1171718)), c_Groups_Ozero__class_Ozero(_1171710))), _1171714) = c_Groups_Ozero__class_Ozero(_1171710))]]], (20721 ^ _782652) ^ [_1172220, _1172222, _1172224, _1172226, _1172228] : [class_Groups_Ocomm__monoid__add(_1172220), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172222), _1172224)), 20728 ^ _782652 : [(20729 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1172222), _1172226), _1172224)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1172222, _1172220), hAPP(hAPP(c_COMBC(_1172222, _1172220, _1172220), hAPP(hAPP(c_COMBS(_1172222, _1172220, tc_fun(_1172220, _1172220)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1172220, tc_fun(_1172220, _1172220)), _1172222), c_If(_1172220)), hAPP(hAPP(c_COMBC(_1172222, _1172222, tc_HOL_Obool), c_fequal), _1172226))), _1172228)), c_Groups_Ozero__class_Ozero(_1172220))), _1172224) = hAPP(_1172228, _1172226))], (20735 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1172222), _1172226), _1172224))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1172222, _1172220), hAPP(hAPP(c_COMBC(_1172222, _1172220, _1172220), hAPP(hAPP(c_COMBS(_1172222, _1172220, tc_fun(_1172220, _1172220)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1172220, tc_fun(_1172220, _1172220)), _1172222), c_If(_1172220)), hAPP(hAPP(c_COMBC(_1172222, _1172222, tc_HOL_Obool), c_fequal), _1172226))), _1172228)), c_Groups_Ozero__class_Ozero(_1172220))), _1172224) = c_Groups_Ozero__class_Ozero(_1172220))]]], (20741 ^ _782652) ^ [_1172758, _1172760, _1172762, _1172764] : [-(c_Hoare__Mirabelle_Otriple__valid(_1172758, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1172758), _1172760), hAPP(c_Com_Ocom_OBODY, _1172762)), _1172764)))], (20743 ^ _782652) ^ [_1172802, _1172804] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172802)), -(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)), _1172802))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1172804))))) = 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)), _1172802))), 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, _1172804))))))], (20749 ^ _782652) ^ [_1172979, _1172981] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172979)), 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)), _1172979))), 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, _1172981))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20755 ^ _782652) ^ [_1173105, _1173107] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173105))), -(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)), _1173105))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1173107)))) = 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)), _1173105))), 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, _1173107))))))], (20761 ^ _782652) ^ [_1173188, _1173190, _1173192, _1173194, _1173196, _1173198] : [class_Rings_Olinordered__semiring__1(_1173188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173188), _1173190), _1173192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173188), _1173194), _1173192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173188), c_Groups_Ozero__class_Ozero(_1173188)), _1173196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173188), c_Groups_Ozero__class_Ozero(_1173188)), _1173198)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173188), _1173196), _1173198) = c_Groups_Oone__class_Oone(_1173188), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1173188), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173188), _1173196), _1173190)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173188), _1173198), _1173194))), _1173192)))], (20787 ^ _782652) ^ [_1173732, _1173734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1173732), _1173734))), 20790 ^ _782652 : [(20791 ^ _782652) ^ [] : [_1173734 = c_Orderings_Obot__class_Obot(tc_fun(_1173732, tc_HOL_Obool))], (20793 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1173732), _1173734)))]]], (20795 ^ _782652) ^ [_1173873, _1173875] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1173873), _1173875)))), -(_1173875 = c_Orderings_Obot__class_Obot(tc_fun(_1173873, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173873), _1173875))], (20805 ^ _782652) ^ [_1174039] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1174039), c_Orderings_Otop__class_Otop(tc_fun(_1174039, 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(_1174039), c_Orderings_Otop__class_Otop(tc_fun(_1174039, tc_HOL_Obool))))))], (20811 ^ _782652) ^ [_1174156, _1174158, _1174160, _1174162] : [class_Groups_Ocomm__monoid__add(_1174156), 20814 ^ _782652 : [(20815 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1174158), _1174160)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1174158, _1174156), _1174162), _1174160) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1174156, _1174158, c_Groups_Oplus__class_Oplus(_1174156)), _1174162), c_Groups_Ozero__class_Ozero(_1174156)), _1174160))], (20821 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1174158), _1174160))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1174158, _1174156), _1174162), _1174160) = c_Groups_Ozero__class_Ozero(_1174156))]]], (20827 ^ _782652) ^ [_1174428, _1174430, _1174432, _1174434] : [class_Groups_Ocomm__monoid__add(_1174428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174430), _1174432)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1174430, _1174428), _1174434), _1174432) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1174428, _1174430, c_Groups_Oplus__class_Oplus(_1174428)), _1174434), c_Groups_Ozero__class_Ozero(_1174428)), _1174432))], (20837 ^ _782652) ^ [_1174623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174623)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174623), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1174623)], (20843 ^ _782652) ^ [_1174720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174720)), -(_1174720 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174720), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (20849 ^ _782652) ^ [_1174826, _1174828] : [_1174826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1174826), _1174828) = _1174828)], (20855 ^ _782652) ^ [_1174909, _1174911] : [-(_1174909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1174909), _1174911) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174909), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1174911)))], (20861 ^ _782652) ^ [_1174977, _1174979] : [_1174977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174977), _1174979) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20867 ^ _782652) ^ [_1175060, _1175062] : [-(_1175060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175060), _1175062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175060), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1175062)))], (20873 ^ _782652) ^ [_1175122, _1175124, _1175126, _1175128, _1175130] : [class_Groups_Ocomm__monoid__add(_1175122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175124), _1175126)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1175124, _1175122), _1175128), hAPP(c_Set_OCollect(_1175124), hAPP(hAPP(c_COMBS(_1175124, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1175124), c_fconj), hAPP(hAPP(c_COMBC(_1175124, tc_fun(_1175124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1175124)), _1175126))), hAPP(hAPP(c_COMBC(_1175124, tc_fun(_1175124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1175124)), _1175130)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1175124, _1175122), hAPP(hAPP(c_COMBC(_1175124, _1175122, _1175122), hAPP(hAPP(c_COMBS(_1175124, _1175122, tc_fun(_1175122, _1175122)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1175122, tc_fun(_1175122, _1175122)), _1175124), c_If(_1175122)), hAPP(hAPP(c_COMBC(_1175124, tc_fun(_1175124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1175124)), _1175130))), _1175128)), c_Groups_Ozero__class_Ozero(_1175122))), _1175126))], (20883 ^ _782652) ^ [_1175531, _1175533, _1175535, _1175537, _1175539] : [class_Groups_Ocomm__monoid__add(_1175531), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175533), _1175535)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1175533, _1175531), _1175537), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1175533, tc_HOL_Obool)), _1175535), _1175539)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1175533, _1175531), hAPP(hAPP(c_COMBC(_1175533, _1175531, _1175531), hAPP(hAPP(c_COMBS(_1175533, _1175531, tc_fun(_1175531, _1175531)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1175531, tc_fun(_1175531, _1175531)), _1175533), c_If(_1175531)), hAPP(hAPP(c_COMBC(_1175533, tc_fun(_1175533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1175533)), _1175539))), _1175537)), c_Groups_Ozero__class_Ozero(_1175531))), _1175535))], (20893 ^ _782652) ^ [_1175861, _1175863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1175861), _1175863)), -(hAPP(c_Finite__Set_Ocard(_1175861), _1175863) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1175861, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1175861), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175863))], (20899 ^ _782652) ^ [_1175988, _1175990] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1175988), _1175990))), -(hAPP(c_Finite__Set_Ocard(_1175988), _1175990) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20905 ^ _782652) ^ [_1176035, _1176037] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1176035), _1176037)), -(hAPP(c_Finite__Set_Ocard(_1176035), _1176037) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1176035, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1176035), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176037))], (20911 ^ _782652) ^ [_1176168, _1176170, _1176172, _1176174, _1176176, _1176178] : [class_Rings_Olinordered__semiring__1__strict(_1176168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176168), _1176170), _1176172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176168), _1176174), _1176172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176168), c_Groups_Ozero__class_Ozero(_1176168)), _1176176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176168), c_Groups_Ozero__class_Ozero(_1176168)), _1176178)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176168), _1176176), _1176178) = c_Groups_Oone__class_Oone(_1176168), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176168), _1176176), _1176170)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176168), _1176178), _1176174))), _1176172)))], (20937 ^ _782652) ^ [_1176697, _1176699, _1176701, _1176703, _1176705] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1176697, _1176699, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1176697), _1176701), _1176703), _1176705)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20939 ^ _782652) ^ [_1176743, _1176745] : [class_Rings_Olinordered__idom(_1176743), 20942 ^ _782652 : [(20943 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176743), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176743), _1176745), _1176745)), c_Groups_Ozero__class_Ozero(_1176743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176743), _1176745), c_Groups_Ozero__class_Ozero(_1176743))))], (20949 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176743), _1176745), c_Groups_Ozero__class_Ozero(_1176743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176743), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176743), _1176745), _1176745)), c_Groups_Ozero__class_Ozero(_1176743))))]]], (20955 ^ _782652) ^ [_1177026, _1177028, _1177030, _1177032] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1177026)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1177026), _1177028), _1177030), _1177032)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20957 ^ _782652) ^ [_1177073, _1177075, _1177077] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1177073), _1177075)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177073), _1177077)), 20967 ^ _782652 : [(20968 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1177073), 20966 ^ [_1177073, _1177075, _1177077]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1177073, tc_HOL_Obool)), _1177075), _1177077))))], (20970 ^ _782652) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1177073), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1177073, tc_HOL_Obool)), _1177075), _1177077)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1177073), _1177075)), hAPP(c_Finite__Set_Ocard(_1177073), _1177077)))], (20974 ^ _782652) ^ [_1177417, _1177419, _1177421, _1177423, _1177425] : [class_Groups_Oordered__comm__monoid__add(_1177417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177419), _1177421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1177419, tc_HOL_Obool)), _1177423), _1177421)), 20988 ^ _782652 : [(20989 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1177419), 20987 ^ [_1177417, _1177419, _1177421, _1177423, _1177425]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1177419, tc_HOL_Obool)), _1177421), _1177423))))], (20991 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177417), c_Groups_Ozero__class_Ozero(_1177417)), hAPP(_1177425, 20987 ^ [_1177417, _1177419, _1177421, _1177423, _1177425])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177417), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177419, _1177417), _1177425), _1177423)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177419, _1177417), _1177425), _1177421))))], (20995 ^ _782652) ^ [_1177903, _1177905, _1177907] : [-(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), _1177903)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1177905))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1177907))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177907), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1177903), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1177903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1177907), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1177905)))))], (20997 ^ _782652) ^ [_1177984, _1177986, _1177988, _1177990, _1177992] : [class_Groups_Ocomm__monoid__add(_1177984), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177986), _1177988)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177986), _1177990)), 21011 ^ _782652 : [(21012 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1177986), 21010 ^ [_1177984, _1177986, _1177988, _1177990, _1177992]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1177986, tc_HOL_Obool)), _1177988), _1177990))))], (21014 ^ _782652) ^ [] : [hAPP(_1177992, 21010 ^ [_1177984, _1177986, _1177988, _1177990, _1177992]) = c_Groups_Ozero__class_Ozero(_1177984)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177986, _1177984), _1177992), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1177986, tc_HOL_Obool)), _1177988), _1177990)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177984), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177986, _1177984), _1177992), _1177988)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1177986, _1177984), _1177992), _1177990)))], (21018 ^ _782652) ^ [_1178479] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1178479))))], (21020 ^ _782652) ^ [_1178507] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1178507)) = _1178507)], (21022 ^ _782652) ^ [_1178536, _1178538, _1178540] : [class_Orderings_Olinorder(_1178536), 21025 ^ _782652 : [(21026 ^ _782652) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1178536), _1178538) = hAPP(c_SetInterval_Oord__class_OlessThan(_1178536), _1178540), -(_1178538 = _1178540)], (21032 ^ _782652) ^ [] : [_1178538 = _1178540, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1178536), _1178538) = hAPP(c_SetInterval_Oord__class_OlessThan(_1178536), _1178540))]]], (21038 ^ _782652) ^ [] : [-(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)))], (21040 ^ _782652) ^ [_1178795] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1178795)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1178795), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1178795)))], (21042 ^ _782652) ^ [_1178833] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1178833)) = 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), _1178833))))], (21044 ^ _782652) ^ [_1178871, _1178873, _1178875] : [class_Groups_Ocomm__monoid__add(_1178871), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1178871), _1178873), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1178875))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178871), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1178871), _1178873), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1178875))), hAPP(_1178873, _1178875)))], (21050 ^ _782652) ^ [_1179024, _1179026, _1179028] : [class_Orderings_Oord(_1179024), 21053 ^ _782652 : [(21054 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1179024), _1179026), hAPP(c_SetInterval_Oord__class_OlessThan(_1179024), _1179028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179024), _1179026), _1179028)))], (21060 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179024), _1179026), _1179028)), -(hBOOL(hAPP(hAPP(c_member(_1179024), _1179026), hAPP(c_SetInterval_Oord__class_OlessThan(_1179024), _1179028))))]]], (21066 ^ _782652) ^ [_1179292, _1179294, _1179296] : [class_Orderings_Olinorder(_1179292), 21069 ^ _782652 : [(21070 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179292, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1179292), _1179294)), hAPP(c_SetInterval_Oord__class_OlessThan(_1179292), _1179296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179292), _1179294), _1179296)))], (21076 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179292), _1179294), _1179296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1179292, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1179292), _1179294)), hAPP(c_SetInterval_Oord__class_OlessThan(_1179292), _1179296))))]]], (21082 ^ _782652) ^ [_1179584, _1179586, _1179588] : [class_Orderings_Olinorder(_1179584), 21085 ^ _782652 : [(21086 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1179584, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1179584), _1179586)), hAPP(c_SetInterval_Oord__class_OlessThan(_1179584), _1179588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179584), _1179586), _1179588)))], (21092 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179584), _1179586), _1179588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1179584, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1179584), _1179586)), hAPP(c_SetInterval_Oord__class_OlessThan(_1179584), _1179588))))]]], (21098 ^ _782652) ^ [_1179876, _1179878] : [class_Orderings_Oorder(_1179876), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1179876, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1179876), _1179878), c_Orderings_Obot__class_Obot(tc_fun(_1179876, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1179876), _1179878)) = hAPP(hAPP(c_Set_Oinsert(_1179876), _1179878), c_Orderings_Obot__class_Obot(tc_fun(_1179876, tc_HOL_Obool))))], (21104 ^ _782652) ^ [_1180035, _1180037] : [class_Groups_Olinordered__ab__group__add(_1180035), 21107 ^ _782652 : [(21108 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180035), _1180037), _1180037) = c_Groups_Ozero__class_Ozero(_1180035), -(_1180037 = c_Groups_Ozero__class_Ozero(_1180035))], (21114 ^ _782652) ^ [] : [_1180037 = c_Groups_Ozero__class_Ozero(_1180035), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180035), _1180037), _1180037) = c_Groups_Ozero__class_Ozero(_1180035))]]], (21120 ^ _782652) ^ [_1180276, _1180278, _1180280, _1180282] : [class_Rings_Ocomm__semiring__1(_1180276), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180276), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180276), c_Groups_Oone__class_Oone(_1180276)), c_Groups_Oone__class_Oone(_1180276))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1180276), hAPP(hAPP(c_COMBB(_1180276, _1180276, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1180276), _1180278)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1180276, _1180276), hAPP(hAPP(c_COMBB(_1180276, tc_fun(_1180276, _1180276), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1180276)), c_Nat_Osemiring__1__class_Oof__nat(_1180276))), _1180280))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1180282))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180276), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1180276), _1180282)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180276), _1180278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180276), _1180278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180276), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1180276), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1180282), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1180280)))))], (21126 ^ _782652) ^ [_1180599, _1180601, _1180603, _1180605, _1180607] : [class_Groups_Ocomm__monoid__add(_1180599), hBOOL(hAPP(c_Finite__Set_Ofinite(_1180601), _1180603)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1180601), _1180605)), 21140 ^ _782652 : [(21141 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1180601), 21139 ^ [_1180599, _1180601, _1180603, _1180605, _1180607]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1180601, tc_HOL_Obool)), _1180603), _1180605))))], (21143 ^ _782652) ^ [] : [hAPP(_1180607, 21139 ^ [_1180599, _1180601, _1180603, _1180605, _1180607]) = c_Groups_Ozero__class_Ozero(_1180599)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1180601, _1180599), _1180607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1180601, tc_HOL_Obool)), _1180603), _1180605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180599), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1180601, _1180599), _1180607), _1180603)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1180601, _1180599), _1180607), _1180605)))], (21147 ^ _782652) ^ [_1181112, _1181114, _1181116] : [hAPP(c_Finite__Set_Ocard(_1181112), _1181114) = hAPP(c_Nat_OSuc, _1181116), 21152 ^ _782652 : [(21153 ^ _782652) ^ [] : [-(_1181114 = hAPP(hAPP(c_Set_Oinsert(_1181112), 21150 ^ [_1181112, _1181114, _1181116]), 21151 ^ [_1181112, _1181114, _1181116]))], (21155 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1181112), 21150 ^ [_1181112, _1181114, _1181116]), 21151 ^ [_1181112, _1181114, _1181116]))], (21157 ^ _782652) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1181112), 21151 ^ [_1181112, _1181114, _1181116]) = _1181116)], (21159 ^ _782652) ^ [] : [_1181116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(21151 ^ [_1181112, _1181114, _1181116] = c_Orderings_Obot__class_Obot(tc_fun(_1181112, tc_HOL_Obool)))]]], (21165 ^ _782652) ^ [_1181530, _1181532, _1181534] : [-(hAPP(c_Finite__Set_Ocard(_1181530), _1181532) = hAPP(c_Nat_OSuc, _1181534)), 21166 ^ _782652 : [(21167 ^ _782652) ^ [_1181630, _1181632] : [_1181532 = hAPP(hAPP(c_Set_Oinsert(_1181530), _1181632), _1181630), -(hBOOL(hAPP(hAPP(c_member(_1181530), _1181632), _1181630))), hAPP(c_Finite__Set_Ocard(_1181530), _1181630) = _1181534, 21178 ^ _782652 : [(21179 ^ _782652) ^ [] : [-(_1181534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21181 ^ _782652) ^ [] : [_1181630 = c_Orderings_Obot__class_Obot(tc_fun(_1181530, tc_HOL_Obool))]]]]], (21185 ^ _782652) ^ [_1181952, _1181954, _1181956, _1181958, _1181960] : [class_Groups_Ocomm__monoid__add(_1181952), class_Groups_Oordered__ab__semigroup__add(_1181952), hBOOL(hAPP(c_Finite__Set_Ofinite(_1181954), _1181956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1181954, tc_HOL_Obool)), _1181958), _1181956)), 21203 ^ _782652 : [(21204 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1181954), 21202 ^ [_1181952, _1181954, _1181956, _1181958, _1181960]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1181954, tc_HOL_Obool)), _1181956), _1181958))))], (21206 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181952), c_Groups_Ozero__class_Ozero(_1181952)), hAPP(_1181960, 21202 ^ [_1181952, _1181954, _1181956, _1181958, _1181960])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181952), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1181954, _1181952), _1181960), _1181958)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1181954, _1181952), _1181960), _1181956))))], (21210 ^ _782652) ^ [_1182496, _1182498, _1182500] : [-(c_Option_Ooption_Ooption__size(_1182496, _1182498, hAPP(c_Option_Ooption_OSome(_1182496), _1182500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1182498, _1182500)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21212 ^ _782652) ^ [_1182541, _1182543] : [class_Rings_Olinordered__idom(_1182541), hBOOL(hAPP(hAPP(c_member(_1182541), _1182543), c_Int_Oring__1__class_OInts(_1182541))), 21219 ^ _782652 : [(21220 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182541), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182541), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182541), c_Groups_Oone__class_Oone(_1182541)), _1182543)), _1182543)), c_Groups_Ozero__class_Ozero(_1182541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182541), _1182543), c_Groups_Ozero__class_Ozero(_1182541))))], (21226 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182541), _1182543), c_Groups_Ozero__class_Ozero(_1182541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182541), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182541), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182541), c_Groups_Oone__class_Oone(_1182541)), _1182543)), _1182543)), c_Groups_Ozero__class_Ozero(_1182541))))]]], (21232 ^ _782652) ^ [_1182924, _1182926] : [-(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, _1182924)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1182926))))], (21234 ^ _782652) ^ [_1182966, _1182968] : [class_Rings_Oring__1(_1182966), -(hBOOL(hAPP(hAPP(c_member(_1182966), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1182966), _1182968)), c_Int_Oring__1__class_OInts(_1182966))))], (21240 ^ _782652) ^ [_1183069, _1183071, _1183073] : [class_Nat_Osemiring__char__0(_1183069), 21243 ^ _782652 : [(21244 ^ _782652) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1183069), _1183071) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1183069), _1183073), -(_1183071 = _1183073)], (21250 ^ _782652) ^ [] : [_1183071 = _1183073, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1183069), _1183071) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1183069), _1183073))]]], (21256 ^ _782652) ^ [] : [-(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))], (21258 ^ _782652) ^ [_1183340] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183340) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1183340 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21264 ^ _782652) ^ [_1183417] : [_1183417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183417) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21270 ^ _782652) ^ [_1183512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183512)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1183512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21276 ^ _782652) ^ [_1183599] : [_1183599 = 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), _1183599)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21282 ^ _782652) ^ [_1183707, _1183709] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183707)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183709), 21285 ^ _782652 : [(21286 ^ _782652) ^ [] : [-(_1183707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21288 ^ _782652) ^ [] : [-(_1183709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21290 ^ _782652) ^ [_1183824, _1183826] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183824)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183826)), _1183824 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1183826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21300 ^ _782652) ^ [_1183988, _1183990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183988)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183990)))), 21303 ^ _782652 : [(21304 ^ _782652) ^ [] : [-(_1183988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21306 ^ _782652) ^ [] : [-(_1183990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21308 ^ _782652) ^ [_1184115, _1184117] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184115)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184117))))), _1184115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1184117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21318 ^ _782652) ^ [_1184289, _1184291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184289), _1184291)), -(_1184291 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1184289), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 21321 ^ [_1184289, _1184291]))))], (21325 ^ _782652) ^ [_1184408, _1184410] : [21326 ^ _782652 : [(21327 ^ _782652) ^ [_1184464] : [_1184410 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1184408), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1184464)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184408), _1184410)))], (21331 ^ _782652) ^ [_1184534] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1184534)) = 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), _1184534)))], (21333 ^ _782652) ^ [_1184569] : [-(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, _1184569)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21335 ^ _782652) ^ [_1184615] : [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, _1184615)))))], (21337 ^ _782652) ^ [_1184664, _1184666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184664)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184664), _1184666)))], (21343 ^ _782652) ^ [_1184769, _1184771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184769), _1184771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184769)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184771))))], (21349 ^ _782652) ^ [_1184880, _1184882, _1184884] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184880)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184882)), _1184884)) = 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), _1184880), _1184882))), _1184884))], (21351 ^ _782652) ^ [_1184940, _1184942] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184940)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184942)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1184940), _1184942)))], (21353 ^ _782652) ^ [_1185001, _1185003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185001)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1185001), _1185003)))], (21359 ^ _782652) ^ [_1185106, _1185108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1185106), _1185108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185106)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185108))))], (21365 ^ _782652) ^ [_1185217, _1185219] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185217)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185219)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185217), _1185219)))], (21367 ^ _782652) ^ [_1185263, _1185265] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185263), _1185265)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185263)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185265)))], (21369 ^ _782652) ^ [] : [-(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))], (21371 ^ _782652) ^ [] : [-(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))))], (21373 ^ _782652) ^ [_1185345, _1185347, _1185349] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1185345, tc_Nat_Onat), _1185347), _1185349)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1185345, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1185345), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1185347)), _1185349))], (21375 ^ _782652) ^ [] : [-(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))], (21377 ^ _782652) ^ [_1185421, _1185423, _1185425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185421), _1185423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185425)), -(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), _1185425)), _1185421)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185425)), _1185423))))], (21387 ^ _782652) ^ [_1185626] : [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), _1185626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185626)))], (21393 ^ _782652) ^ [_1185711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185711)), -(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), _1185711))))], (21399 ^ _782652) ^ [_1185802, _1185804] : [class_Rings_Olinordered__semidom(_1185802), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185802), c_Groups_Ozero__class_Ozero(_1185802)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1185802), _1185804))))], (21405 ^ _782652) ^ [_1185905, _1185907] : [class_Rings_Olinordered__semidom(_1185905), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185905), c_Groups_Ozero__class_Ozero(_1185905)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1185905), _1185907))))], (21411 ^ _782652) ^ [_1186008, _1186010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186008), _1186010)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186010)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186008)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186010), _1186008)))], (21417 ^ _782652) ^ [_1186137, _1186139] : [class_Rings_Olinordered__semidom(_1186137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186137), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186137), _1186139)), c_Groups_Ozero__class_Ozero(_1186137)))], (21423 ^ _782652) ^ [_1186241] : [class_Rings_Osemiring__1(_1186241), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186241), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1186241))], (21429 ^ _782652) ^ [_1186328, _1186330, _1186332] : [class_Rings_Olinordered__semidom(_1186328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186328), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186328), _1186330)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186328), _1186332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186330), _1186332)))], (21439 ^ _782652) ^ [_1186503, _1186505, _1186507] : [class_Rings_Olinordered__semidom(_1186503), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186505), _1186507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186503), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186503), _1186505)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186503), _1186507))))], (21449 ^ _782652) ^ [_1186678, _1186680, _1186682] : [class_Rings_Olinordered__semidom(_1186678), 21452 ^ _782652 : [(21453 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186678), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186678), _1186680)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186678), _1186682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186680), _1186682)))], (21459 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1186680), _1186682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186678), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186678), _1186680)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186678), _1186682))))]]], (21465 ^ _782652) ^ [_1186955, _1186957, _1186959] : [class_Rings_Olinordered__semidom(_1186955), 21468 ^ _782652 : [(21469 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186955), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186955), _1186957)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186955), _1186959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186957), _1186959)))], (21475 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186957), _1186959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186955), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186955), _1186957)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1186955), _1186959))))]]], (21481 ^ _782652) ^ [_1187232, _1187234, _1187236] : [class_Rings_Osemiring__1(_1187232), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1187234), _1187236)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187232), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187232), _1187234)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187232), _1187236)))], (21487 ^ _782652) ^ [_1187367, _1187369, _1187371] : [class_Rings_Osemiring__1(_1187367), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187367), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1187369), _1187371)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187367), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187367), _1187369)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187367), _1187371)))], (21493 ^ _782652) ^ [_1187502] : [class_Rings_Osemiring__1(_1187502), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187502), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1187502))], (21499 ^ _782652) ^ [_1187589, _1187591, _1187593, _1187595] : [class_Rings_Osemiring__1(_1187589), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1187589), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187591, tc_Nat_Onat), _1187593), _1187595)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187591, _1187589), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1187589, _1187591), c_Nat_Osemiring__1__class_Oof__nat(_1187589)), _1187593)), _1187595))], (21505 ^ _782652) ^ [_1187738] : [class_Nat_Osemiring__char__0(_1187738), -(c_Fun_Oinj__on(tc_Nat_Onat, _1187738, c_Nat_Osemiring__1__class_Oof__nat(_1187738), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (21511 ^ _782652) ^ [_1187819] : [class_Rings_Oring__1(_1187819), -(hBOOL(hAPP(hAPP(c_member(_1187819), c_Groups_Ozero__class_Ozero(_1187819)), c_Int_Oring__1__class_OInts(_1187819))))], (21517 ^ _782652) ^ [_1187914, _1187916, _1187918] : [class_Rings_Oring__1(_1187914), hBOOL(hAPP(hAPP(c_member(_1187914), _1187916), c_Int_Oring__1__class_OInts(_1187914))), hBOOL(hAPP(hAPP(c_member(_1187914), _1187918), c_Int_Oring__1__class_OInts(_1187914))), -(hBOOL(hAPP(hAPP(c_member(_1187914), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187914), _1187916), _1187918)), c_Int_Oring__1__class_OInts(_1187914))))], (21531 ^ _782652) ^ [_1188169, _1188171, _1188173] : [class_Rings_Oring__1(_1188169), hBOOL(hAPP(hAPP(c_member(_1188169), _1188171), c_Int_Oring__1__class_OInts(_1188169))), hBOOL(hAPP(hAPP(c_member(_1188169), _1188173), c_Int_Oring__1__class_OInts(_1188169))), -(hBOOL(hAPP(hAPP(c_member(_1188169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188169), _1188171), _1188173)), c_Int_Oring__1__class_OInts(_1188169))))], (21545 ^ _782652) ^ [_1188424, _1188426, _1188428] : [class_Rings_Oring__1(_1188424), hBOOL(hAPP(hAPP(c_member(_1188424), _1188426), c_Int_Oring__1__class_OInts(_1188424))), hBOOL(hAPP(hAPP(c_member(_1188424), _1188428), c_Int_Oring__1__class_OInts(_1188424))), -(hBOOL(hAPP(hAPP(c_member(_1188424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1188424), _1188426), _1188428)), c_Int_Oring__1__class_OInts(_1188424))))], (21559 ^ _782652) ^ [_1188679] : [class_Rings_Oring__1(_1188679), -(hBOOL(hAPP(hAPP(c_member(_1188679), c_Groups_Oone__class_Oone(_1188679)), c_Int_Oring__1__class_OInts(_1188679))))], (21565 ^ _782652) ^ [_1188774, _1188776] : [class_Rings_Oring__1(_1188774), hBOOL(hAPP(hAPP(c_member(_1188774), _1188776), c_Int_Oring__1__class_OInts(_1188774))), -(hBOOL(hAPP(hAPP(c_member(_1188774), hAPP(c_Groups_Ouminus__class_Ouminus(_1188774), _1188776)), c_Int_Oring__1__class_OInts(_1188774))))], (21575 ^ _782652) ^ [_1188947, _1188949] : [class_Rings_Osemiring__1(_1188947), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188947), hAPP(c_Nat_OSuc, _1188949)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1188947), c_Groups_Oone__class_Oone(_1188947)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188947), _1188949)))], (21581 ^ _782652) ^ [_1189068, _1189070, _1189072] : [class_Rings_Oring__1(_1189068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1189070), _1189072)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1189072), _1189070)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1189068), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189068), _1189072)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189068), _1189070)))], (21591 ^ _782652) ^ [_1189267, _1189269] : [-(c_Option_Ooption_Ooption__size(_1189267, _1189269, c_Option_Ooption_ONone(_1189267)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21593 ^ _782652) ^ [_1189298, _1189300, _1189302, _1189304] : [class_Rings_Osemiring__1(_1189298), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1189300, _1189298), hAPP(c_COMBK(_1189298, _1189300), _1189302)), _1189304) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189298), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189298), hAPP(c_Finite__Set_Ocard(_1189300), _1189304))), _1189302))], (21599 ^ _782652) ^ [_1189443, _1189445] : [class_Rings_Olinordered__semidom(_1189443), 21602 ^ _782652 : [(21603 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189443), c_Groups_Ozero__class_Ozero(_1189443)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189443), _1189445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189445)))], (21609 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1189445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189443), c_Groups_Ozero__class_Ozero(_1189443)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1189443), _1189445))))]]], (21615 ^ _782652) ^ [_1189696, _1189698] : [class_Int_Oring__char__0(_1189696), hBOOL(hAPP(hAPP(c_member(_1189696), _1189698), c_Int_Oring__1__class_OInts(_1189696))), 21622 ^ _782652 : [(21623 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1189696), _1189698), _1189698) = c_Groups_Ozero__class_Ozero(_1189696), -(_1189698 = c_Groups_Ozero__class_Ozero(_1189696))], (21629 ^ _782652) ^ [] : [_1189698 = c_Groups_Ozero__class_Ozero(_1189696), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1189696), _1189698), _1189698) = c_Groups_Ozero__class_Ozero(_1189696))]]], (21635 ^ _782652) ^ [_1190007, _1190009] : [class_Int_Oring__char__0(_1190007), hBOOL(hAPP(hAPP(c_member(_1190007), _1190009), c_Int_Oring__1__class_OInts(_1190007))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190007), c_Groups_Oone__class_Oone(_1190007)), _1190009)), _1190009) = c_Groups_Ozero__class_Ozero(_1190007)], (21645 ^ _782652) ^ [_1190193, _1190195] : [class_Rings_Osemiring__1(_1190193), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1190193), _1190195) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1190193, hAPP(hAPP(c_COMBC(_1190193, _1190193, _1190193), c_Groups_Oplus__class_Oplus(_1190193)), c_Groups_Oone__class_Oone(_1190193)), _1190195, c_Groups_Ozero__class_Ozero(_1190193)))], (21667 ^ _782652) ^ [_1190627, _1190629, _1190631] : [-(hBOOL(hAPP(_1190627, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1190629), _1190631))))), 21670 ^ _782652 : [(21671 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1190631), _1190629)))], (21673 ^ _782652) ^ [] : [hBOOL(hAPP(_1190627, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190629)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190631))))]], 21674 ^ _782652 : [(21675 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190629), _1190631)))], (21677 ^ _782652) ^ [] : [hBOOL(hAPP(_1190627, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (21651 ^ _782652) ^ [_1190338, _1190340, _1190342] : [hBOOL(hAPP(_1190338, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1190340), _1190342)))), 21654 ^ _782652 : [(21655 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1190342), _1190340)), -(hBOOL(hAPP(_1190338, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190340)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1190342)))))], (21661 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190340), _1190342)), -(hBOOL(hAPP(_1190338, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (21681 ^ _782652) ^ [_1190902] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1190902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1190902)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21683 ^ _782652) ^ [_1190938] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1190938)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1190938)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21685 ^ _782652) ^ [_1190976, _1190978, _1190980, _1190982, _1190984] : [class_Groups_Oordered__ab__semigroup__add(_1190976), class_Rings_Osemiring__1(_1190976), 21695 ^ _782652 : [(21696 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1190978), 21694 ^ [_1190976, _1190978, _1190980, _1190982, _1190984]), _1190980)))], (21698 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190976), hAPP(_1190982, 21694 ^ [_1190976, _1190978, _1190980, _1190982, _1190984])), _1190984))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190976), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1190978, _1190976), _1190982), _1190980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190976), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1190976), hAPP(c_Finite__Set_Ocard(_1190978), _1190980))), _1190984))))], (21702 ^ _782652) ^ [_1191366, _1191368] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1191366)), hAPP(c_Option_Ooption_OSome(_1191366), _1191368)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21704 ^ _782652) ^ [_1191403, _1191405] : [-(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), _1191403))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191405))))], (21706 ^ _782652) ^ [_1191442] : [-(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), _1191442))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21708 ^ _782652) ^ [_1191476] : [-(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), _1191476))))], (21710 ^ _782652) ^ [_1191513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191513)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21712 ^ _782652) ^ [_1191559, _1191561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1191559), _1191561)), -(_1191561 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191559), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21715 ^ [_1191559, _1191561])))], (21719 ^ _782652) ^ [_1191672, _1191674] : [21720 ^ _782652 : [(21721 ^ _782652) ^ [_1191725] : [_1191674 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191672), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191725))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1191672), _1191674)))], (21725 ^ _782652) ^ [_1191792] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1191792) = _1191792)], (21727 ^ _782652) ^ [_1191833, _1191835] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191833) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191835), -(_1191833 = _1191835)], (21733 ^ _782652) ^ [_1191918, _1191920] : [_1191918 = _1191920, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191918) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191920))], (21739 ^ _782652) ^ [_1192021, _1192023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1192021)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1192023))))], (21741 ^ _782652) ^ [_1192060, _1192062, _1192064] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1192062), _1192064)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192060), _1192062)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192060), _1192064)))], (21743 ^ _782652) ^ [_1192117, _1192119, _1192121] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1192117), _1192119)), _1192121) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192117), _1192121)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192119), _1192121)))], (21745 ^ _782652) ^ [_1192189, _1192191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192189), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1192191), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192189), _1192191)))], (21751 ^ _782652) ^ [_1192294, _1192296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192294), _1192296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192294), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1192296), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21757 ^ _782652) ^ [_1192405, _1192407, _1192409] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192405), _1192407)), _1192409) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192407), _1192409)))], (21759 ^ _782652) ^ [_1192456, _1192458] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1192456)), _1192458) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192456), _1192458)))], (21761 ^ _782652) ^ [_1192499, _1192501] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192499), _1192501) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192501), _1192499))], (21763 ^ _782652) ^ [_1192536] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192536), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1192536)], (21765 ^ _782652) ^ [_1192565] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1192565) = _1192565)], (21767 ^ _782652) ^ [_1192591] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1192591)) = _1192591)], (21769 ^ _782652) ^ [_1192635, _1192637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192635), _1192637)), 21772 ^ _782652 : [(21773 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192635), _1192637)))], (21775 ^ _782652) ^ [] : [_1192635 = _1192637]]], (21777 ^ _782652) ^ [_1192762, _1192764] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192762), _1192764))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192762), _1192764)), -(_1192762 = _1192764)], (21787 ^ _782652) ^ [_1192916] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192916), _1192916)))], (21789 ^ _782652) ^ [_1192940, _1192942] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192940), _1192942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192942), _1192940)))], (21795 ^ _782652) ^ [_1192986, _1192988, _1192990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192986), _1192988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192988), _1192990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192986), _1192990)))], (21805 ^ _782652) ^ [_1193149, _1193151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193149), _1193151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193151), _1193149)), -(_1193149 = _1193151)], (21815 ^ _782652) ^ [_1193294, _1193296] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193294), _1193296))), -(_1193294 = _1193296), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193296), _1193294)))], (21825 ^ _782652) ^ [_1193347, _1193349, _1193351, _1193353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193347), _1193349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193351), _1193353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193347), _1193351)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193349), _1193353))))], (21835 ^ _782652) ^ [_1193538, _1193540, _1193542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193538), _1193540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193542), _1193538)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193542), _1193540))))], (21841 ^ _782652) ^ [_1193661, _1193663, _1193665] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193661), _1193663)), _1193665) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193663), _1193665)))], (21843 ^ _782652) ^ [_1193712, _1193714, _1193716] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193712), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193714), _1193716)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193712), _1193716)))], (21845 ^ _782652) ^ [_1193763, _1193765] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193763), _1193765) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193765), _1193763))], (21847 ^ _782652) ^ [_1193800, _1193802, _1193804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193800), _1193802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193800), _1193804)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193802), _1193804))))], (21863 ^ _782652) ^ [_1194056, _1194058] : [21864 ^ _782652 : [(21865 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194056), _1194058))], (21867 ^ _782652) ^ [] : [_1194056 = _1194058]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194058), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21853 ^ _782652) ^ [_1193938, _1193940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193938), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193940), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193938), _1193940))), -(_1193938 = _1193940)], (21871 ^ _782652) ^ [_1194205, _1194207] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194205), _1194207)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1194205)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1194207)))], (21873 ^ _782652) ^ [_1194251, _1194253, _1194255] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194253), _1194255)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194251), _1194253)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194251), _1194255)))], (21875 ^ _782652) ^ [_1194308, _1194310, _1194312] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194308), _1194310)), _1194312) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194308), _1194312)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194310), _1194312)))], (21877 ^ _782652) ^ [_1194380, _1194382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194382), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194380), _1194382)))], (21883 ^ _782652) ^ [_1194485, _1194487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194485), _1194487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194487), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21889 ^ _782652) ^ [_1194611, _1194613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194611), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1194613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194611), _1194613)))], (21895 ^ _782652) ^ [_1194716, _1194718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194716), _1194718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194716), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1194718)))], (21901 ^ _782652) ^ [_1194827, _1194829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194827), _1194829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194827), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1194829)))], (21907 ^ _782652) ^ [_1194936, _1194938] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194936), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1194938)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1194936), _1194938))], (21909 ^ _782652) ^ [_1194976, _1194978] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1194976), _1194978) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194976), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1194978)))], (21911 ^ _782652) ^ [_1195016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195016)), -(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)), _1195016))))], (21917 ^ _782652) ^ [_1195105] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195105)), _1195105) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21919 ^ _782652) ^ [_1195146] : [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)), _1195146)), _1195146) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (21921 ^ _782652) ^ [_1195190] : [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)), _1195190)), _1195190)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195190), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21927 ^ _782652) ^ [_1195299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195299), 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)), _1195299)), _1195299)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21933 ^ _782652) ^ [_1195414] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195414) = _1195414)], (21935 ^ _782652) ^ [_1195440] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1195440), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1195440)], (21937 ^ _782652) ^ [_1195484, _1195486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195484), _1195486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195484), _1195486)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21943 ^ _782652) ^ [_1195589, _1195591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195589), _1195591)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195589), _1195591)))], (21949 ^ _782652) ^ [_1195700, _1195702, _1195704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1195700), _1195702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195704), _1195700)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195704), _1195702))))], (21959 ^ _782652) ^ [_1195881, _1195883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195881)), 21962 ^ _782652 : [(21963 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195881), _1195883) = c_Groups_Oone__class_Oone(tc_Int_Oint), 21966 ^ _782652 : [(21967 ^ _782652) ^ [] : [-(_1195881 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21969 ^ _782652) ^ [] : [-(_1195883 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (21971 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1195881), _1195883) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1195881 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1195883 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (21981 ^ _782652) ^ [] : [-(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))))], (21983 ^ _782652) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (21985 ^ _782652) ^ [] : [-(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))], (21987 ^ _782652) ^ [_1196254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1196254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196254)))], (21993 ^ _782652) ^ [_1196333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1196333)))], (21999 ^ _782652) ^ [] : [-(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))], (22001 ^ _782652) ^ [_1196436, _1196438, _1196440] : [class_Rings_Osemiring__1(_1196436), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1196436, _1196438, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1196440) = _1196440)], (22007 ^ _782652) ^ [_1196523, _1196525, _1196527, _1196529] : [class_Rings_Osemiring__1(_1196523), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1196523, _1196525, hAPP(c_Nat_OSuc, _1196527), _1196529) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1196523, _1196525, _1196527, hAPP(_1196525, _1196529)))], (22013 ^ _782652) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22015 ^ _782652) ^ [_1196652] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1196652)), c_Option_Ooption_ONone(_1196652)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22017 ^ _782652) ^ [_1196684, _1196686, _1196688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196684)), _1196684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1196686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196684), _1196688)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196686), _1196684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1196688)))], (22031 ^ _782652) ^ [_1196913, _1196915, _1196917] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196913)), _1196913 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1196915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1196913), _1196917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1196915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196917), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (22045 ^ _782652) ^ [_1197142, _1197144, _1197146, _1197148, _1197150, _1197152] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1197142), _1197144)), _1197146) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1197148), _1197150)), _1197152), 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), _1197148), _1197150)), _1197152)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197146), _1197142)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197148), _1197142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197150), _1197144)))], (22071 ^ _782652) ^ [_1197647, _1197649, _1197651, _1197653, _1197655] : [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), _1197647), _1197649)), _1197651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1197647), _1197653)), _1197655))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197655), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197647), _1197655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197647), _1197651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197653), _1197649)))], (22089 ^ _782652) ^ [_1198002, _1198004, _1198006, _1198008, _1198010, _1198012] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1198002), _1198004)), _1198006) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1198008), _1198010)), _1198012), 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), _1198008), _1198010)), _1198012))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198012), _1198008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198008), _1198002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198004), _1198010)))], (22115 ^ _782652) ^ [_1198501, _1198503, _1198505, _1198507, _1198509] : [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), _1198501), _1198503)), _1198505)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1198501), _1198507)), _1198509))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198505)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198505), _1198501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198509), _1198501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198503), _1198507)))], (22133 ^ _782652) ^ [_1198850, _1198852, _1198854] : [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), _1198850), _1198852)), _1198854))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198854), _1198850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198852)))], (22147 ^ _782652) ^ [_1199083, _1199085, _1199087] : [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), _1199083), _1199085)), _1199087)), 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)), _1199087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1199085), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22161 ^ _782652) ^ [_1199322] : [-(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)))), _1199322)) = 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), _1199322), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (22163 ^ _782652) ^ [] : [-(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)))], (22165 ^ _782652) ^ [_1199381, _1199383] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199381)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199383)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1199381), _1199383)))], (22167 ^ _782652) ^ [_1199427, _1199429] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199427)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199429)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1199427), _1199429)))], (22169 ^ _782652) ^ [_1199488, _1199490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199488)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199488), _1199490)))], (22175 ^ _782652) ^ [_1199593, _1199595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199593), _1199595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199593)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199595))))], (22181 ^ _782652) ^ [_1199719, _1199721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199719)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1199719), _1199721)))], (22187 ^ _782652) ^ [_1199824, _1199826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1199824), _1199826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199824)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1199826))))], (22193 ^ _782652) ^ [_1199950, _1199952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1199950), _1199952)), -(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)), _1199950)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1199952))))], (22199 ^ _782652) ^ [_1200055, _1200057] : [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)), _1200055)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1200055), _1200057)))], (22205 ^ _782652) ^ [_1200181, _1200183] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200181) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200183), -(_1200181 = _1200183)], (22211 ^ _782652) ^ [_1200266, _1200268] : [_1200266 = _1200268, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200266) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200268))], (22217 ^ _782652) ^ [_1200372, _1200374] : [_1200372 = _1200374, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200372) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200374))], (22223 ^ _782652) ^ [_1200457, _1200459] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200457) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200459), -(_1200457 = _1200459)], (22229 ^ _782652) ^ [_1200563, _1200565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1200563), _1200565)), -(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)), _1200563)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200565))))], (22235 ^ _782652) ^ [_1200668, _1200670] : [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)), _1200668)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1200668), _1200670)))], (22241 ^ _782652) ^ [] : [-(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))))], (22243 ^ _782652) ^ [_1200812, _1200814] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1200812), _1200814)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200812)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200814))))], (22249 ^ _782652) ^ [_1200917, _1200919] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200917)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1200919))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1200917), _1200919)))], (22255 ^ _782652) ^ [] : [-(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))))], (22257 ^ _782652) ^ [_1201046] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1201046) = 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)), _1201046)))], (22259 ^ _782652) ^ [_1201090] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1201090)), -(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)), _1201090))))], (22265 ^ _782652) ^ [_1201175] : [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)), _1201175))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1201175)))], (22271 ^ _782652) ^ [] : [-(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)))], (22273 ^ _782652) ^ [_1201284, _1201286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201286)), -(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), _1201284), _1201286))))], (22283 ^ _782652) ^ [_1201437] : [-(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), _1201437))))], (22296 ^ _782652) ^ [_1201647] : [22297 ^ _782652 : [(22298 ^ _782652) ^ [_1201704] : [hBOOL(hAPP(_1201647, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201704)))]], 22300 ^ _782652 : [(22301 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22299 ^ [_1201647])))], (22303 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1201647, 22299 ^ [_1201647])))]]], (22285 ^ _782652) ^ [_1201477] : [-(hBOOL(hAPP(_1201477, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 22292 ^ [_1201477])))), 22286 ^ _782652 : [(22287 ^ _782652) ^ [_1201529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201529)), hBOOL(hAPP(_1201477, _1201529))]]], (22305 ^ _782652) ^ [_1201808] : [22307 ^ _782652 : [(22308 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22306 ^ [_1201808])))], (22310 ^ _782652) ^ [] : [hBOOL(hAPP(_1201808, 22306 ^ [_1201808]))]], 22311 ^ _782652 : [(22312 ^ _782652) ^ [_1201935] : [-(hBOOL(hAPP(_1201808, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1201935))))]]], (22314 ^ _782652) ^ [_1201965] : [hBOOL(hAPP(_1201965, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 22315 ^ [_1201965]))), 22318 ^ _782652 : [(22319 ^ _782652) ^ [_1202065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202065)), -(hBOOL(hAPP(_1201965, _1202065)))]]], (22325 ^ _782652) ^ [] : [-(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))))], (22327 ^ _782652) ^ [_1202174, _1202176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202176)), -(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), _1202174), _1202176))))], (22337 ^ _782652) ^ [_1202336, _1202338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202336), _1202338)), -(c_Nat__Transfer_Otsub(_1202338, _1202336) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202338), _1202336))], (22343 ^ _782652) ^ [_1202435, _1202437] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202435), _1202437))), -(c_Nat__Transfer_Otsub(_1202437, _1202435) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22349 ^ _782652) ^ [_1202493, _1202495, _1202497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202493), _1202495)), -(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)), _1202493)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1202497), _1202495)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1202497), _1202493)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1202495), _1202493)))], (22355 ^ _782652) ^ [_1202645, _1202647, _1202649] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202645), _1202647))), 22358 ^ _782652 : [(22359 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202649), _1202647)), -(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)), _1202645)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1202649), _1202647)) = 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))))], (22365 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202649), _1202647))), -(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)), _1202645)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1202649), _1202647)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (22371 ^ _782652) ^ [_1202914, _1202916] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1202914, _1202916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1202914)), c_Com_Ocom_Ocom__size(_1202916))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22383 ^ _782652) ^ [_1203180, _1203182, _1203184, _1203186] : [22384 ^ _782652 : [(22385 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1203180), _1203182)))], (22387 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1203184), _1203186)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1203180, _1203184)), c_Sum__Type_OPlus(_1203180, _1203184, _1203182, _1203186)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22373 ^ _782652) ^ [_1202975, _1202977, _1202979, _1202981] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1202975, _1202979)), c_Sum__Type_OPlus(_1202975, _1202979, _1202977, _1202981)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1202975), _1202977)), hAPP(c_Finite__Set_Ocard(_1202979), _1202981))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1202975), _1202977)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1202979), _1202981))], (22391 ^ _782652) ^ [_1203280, _1203282] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1203280, _1203282)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1203282)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22393 ^ _782652) ^ [_1203318, _1203320] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1203318, _1203320)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1203318)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1203320))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22395 ^ _782652) ^ [_1203367, _1203369] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1203367), _1203369))))], (22397 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (22399 ^ _782652) ^ [_1203424, _1203426, _1203428, _1203430, _1203432] : [class_Orderings_Olinorder(_1203424), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203424, _1203426), _1203428) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203424, _1203430), _1203432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203424), _1203426), _1203428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203424), _1203430), _1203432)), -(_1203428 = _1203432)], (22417 ^ _782652) ^ [_1203731, _1203733, _1203735, _1203737, _1203739] : [class_Orderings_Olinorder(_1203731), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203731, _1203733), _1203735) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1203731, _1203737), _1203739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203731), _1203733), _1203735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1203731), _1203737), _1203739)), -(_1203733 = _1203737)], (22435 ^ _782652) ^ [_1204038, _1204040, _1204042, _1204044, _1204046] : [class_Orderings_Olinorder(_1204038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204038), _1204040), _1204042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1204038), _1204044), _1204046)), 22446 ^ _782652 : [(22447 ^ _782652) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204038, _1204040), _1204042) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204038, _1204044), _1204046), 22450 ^ _782652 : [(22451 ^ _782652) ^ [] : [-(_1204040 = _1204044)], (22453 ^ _782652) ^ [] : [-(_1204042 = _1204046)]]], (22455 ^ _782652) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204038, _1204040), _1204042) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204038, _1204044), _1204046)), _1204040 = _1204044, _1204042 = _1204046]]], (22465 ^ _782652) ^ [_1204519, _1204521, _1204523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204519), _1204521)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1204519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204521), _1204523)) = 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, _1204519), _1204521)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1204521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204521), _1204523))))], (22471 ^ _782652) ^ [_1204680] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1204680), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (22473 ^ _782652) ^ [_1204709] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204709) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1204709))], (22475 ^ _782652) ^ [_1204738, _1204740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1204738), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1204740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204740), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1204738))))), -(_1204738 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1204740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204740), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1204738))))], (22481 ^ _782652) ^ [_1204885, _1204887] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1204885), _1204887)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204887), _1204885))], (22483 ^ _782652) ^ [_1204925, _1204927] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1204925), _1204927)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1204925)), hAPP(c_Nat_OSuc, _1204927)))], (22485 ^ _782652) ^ [_1204971, _1204973, _1204975] : [class_Orderings_Oorder(_1204971), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204971), _1204973), _1204975)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1204971, _1204975), _1204973) = c_Orderings_Obot__class_Obot(tc_fun(_1204971, tc_HOL_Obool)))], (22495 ^ _782652) ^ [_1205138, _1205140, _1205142] : [class_Orderings_Oorder(_1205138), 22498 ^ _782652 : [(22499 ^ _782652) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1205138, _1205140), _1205142) = c_Orderings_Obot__class_Obot(tc_fun(_1205138, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205138), _1205140), _1205142))], (22505 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205138), _1205140), _1205142))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1205138, _1205140), _1205142) = c_Orderings_Obot__class_Obot(tc_fun(_1205138, tc_HOL_Obool)))]]], (22511 ^ _782652) ^ [_1205363, _1205365, _1205367] : [class_Orderings_Oorder(_1205363), 22514 ^ _782652 : [(22515 ^ _782652) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1205363, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1205363, _1205365), _1205367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205363), _1205365), _1205367))], (22521 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205363), _1205365), _1205367))), -(c_Orderings_Obot__class_Obot(tc_fun(_1205363, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1205363, _1205365), _1205367))]]], (22527 ^ _782652) ^ [_1205588, _1205590, _1205592, _1205594, _1205596] : [class_Orderings_Olinorder(_1205588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1205588, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1205588, _1205590), _1205592)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1205588, _1205594), _1205596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205588), _1205592), _1205590))), 22538 ^ _782652 : [(22539 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205588), _1205594), _1205590)))], (22541 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205588), _1205592), _1205596)))]]], (22543 ^ _782652) ^ [_1205869, _1205871, _1205873, _1205875] : [class_Groups_Ocomm__monoid__add(_1205869), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1205869), _1205871), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1205873)), hAPP(c_Nat_OSuc, _1205875))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1205869), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1205869, tc_Nat_Onat), _1205871), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1205873), _1205875)))], (22549 ^ _782652) ^ [_1206040, _1206042, _1206044, _1206046] : [class_Orderings_Olinorder(_1206040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206040), _1206042), _1206044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206040), _1206044), _1206046)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1206040, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1206040, _1206042), _1206044)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1206040, _1206044), _1206046)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1206040, _1206042), _1206046))], (22563 ^ _782652) ^ [_1206317, _1206319, _1206321, _1206323, _1206325] : [class_Groups_Ocomm__monoid__add(_1206317), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206317), _1206319), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206321), _1206323)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206325), _1206323))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206317), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1206317, tc_Nat_Onat), _1206319), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1206323))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206321), _1206325)))], (22569 ^ _782652) ^ [_1206508, _1206510, _1206512, _1206514] : [class_Orderings_Olinorder(_1206508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1206508), _1206510), _1206512)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206508, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1206508, _1206510), _1206514)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1206508, _1206510), _1206512)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1206508, _1206512), _1206514))], (22579 ^ _782652) ^ [_1206715, _1206717, _1206719, _1206721] : [class_Orderings_Oorder(_1206715), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1206715, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1206715, _1206717), _1206719)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1206715, _1206719), _1206721)) = c_Orderings_Obot__class_Obot(tc_fun(_1206715, tc_HOL_Obool)))], (22585 ^ _782652) ^ [_1206850, _1206852, _1206854] : [-(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)), _1206850)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206852), _1206854)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206852), _1206850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206854), _1206850)))], (22587 ^ _782652) ^ [_1206911, _1206913, _1206915, _1206917, _1206919] : [class_Groups_Ocomm__monoid__add(_1206911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206913), _1206915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206915), _1206917)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206911), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206911), _1206919), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206913), _1206915))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206911), _1206919), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206915), _1206917))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206911), _1206919), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206913), _1206917)))], (22601 ^ _782652) ^ [_1207234, _1207236, _1207238, _1207240, _1207242] : [class_Groups_Oab__group__add(_1207234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207236), _1207238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207238), _1207240)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207234), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207234), _1207242), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207236), _1207240))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207234), _1207242), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207236), _1207238))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207234), _1207242), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207238), _1207240)))], (22615 ^ _782652) ^ [_1207557] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207557), hAPP(c_Nat_OSuc, _1207557)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1207557), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (22617 ^ _782652) ^ [_1207595] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _1207595)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22619 ^ _782652) ^ [_1207624] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _1207624)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22621 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22623 ^ _782652) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22625 ^ _782652) ^ [_1207688, _1207690, _1207692, _1207694, _1207696] : [class_Orderings_Olinorder(_1207688), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1207688, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207688, _1207690), _1207692)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207688, _1207694), _1207696)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207688, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207688), _1207690), _1207694)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1207688), _1207692), _1207696)))], (22631 ^ _782652) ^ [_1207859, _1207861, _1207863] : [class_Orderings_Olinorder(_1207859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207859), _1207861), _1207863)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1207859, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207859), _1207861)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1207859, _1207861), _1207863)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1207859), _1207863))], (22641 ^ _782652) ^ [_1208058, _1208060, _1208062] : [class_Orderings_Oorder(_1208058), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1208058, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1208058), _1208060)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1208058, _1208060), _1208062)) = c_Orderings_Obot__class_Obot(tc_fun(_1208058, tc_HOL_Obool)))], (22647 ^ _782652) ^ [_1208189, _1208191, _1208193] : [class_Groups_Ocomm__monoid__add(_1208189), hAPP(_1208191, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1208189), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208189), _1208191), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1208193)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208189), _1208191), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208193)))], (22657 ^ _782652) ^ [_1208378, _1208380, _1208382, _1208384] : [class_Groups_Ocomm__monoid__add(_1208378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1208380), _1208382)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208378), _1208384), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1208380), _1208382)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208378), hAPP(_1208384, _1208380)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1208378), _1208384), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1208380)), _1208382))))], (22667 ^ _782652) ^ [_1208620, _1208622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1208620), _1208622)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1208620), hAPP(c_Nat_OSuc, _1208622)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1208622), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1208620), _1208622)))], (22673 ^ _782652) ^ [_1208743, _1208745] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1208743), _1208745))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1208743), hAPP(c_Nat_OSuc, _1208745)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (22679 ^ _782652) ^ [_1208816, _1208818, _1208820, _1208822] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1208816, _1208818)), c_Sum__Type_OPlus(_1208816, _1208818, _1208820, _1208822))), 22682 ^ _782652 : [(22683 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1208816), _1208820)))], (22685 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1208818), _1208822)))]]], (22687 ^ _782652) ^ [_1208959, _1208961, _1208963, _1208965] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1208959, _1208961)), c_Sum__Type_OPlus(_1208959, _1208961, _1208963, _1208965)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1208959), _1208963)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1208961), _1208965))], (22697 ^ _782652) ^ [_1209138, _1209140, _1209142, _1209144] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1209138), _1209140)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209142), _1209144)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1209138, _1209142)), c_Sum__Type_OPlus(_1209138, _1209142, _1209140, _1209144))))], (22707 ^ _782652) ^ [_1209315, _1209317, _1209319, _1209321] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1209315, _1209317)), c_Sum__Type_OPlus(_1209315, _1209317, _1209319, _1209321))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1209315), _1209319)))], (22713 ^ _782652) ^ [_1209428, _1209430, _1209432, _1209434] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1209428, _1209430)), c_Sum__Type_OPlus(_1209428, _1209430, _1209432, _1209434))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1209430), _1209434)))], (22719 ^ _782652) ^ [_1209541, _1209543, _1209545, _1209547] : [class_Groups_Ocomm__monoid__add(_1209541), 22722 ^ _782652 : [(22723 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209543), _1209545)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1209541), _1209547), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209545), hAPP(c_Nat_OSuc, _1209543))) = c_Groups_Ozero__class_Ozero(_1209541))], (22729 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209543), _1209545))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1209541), _1209547), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209545), hAPP(c_Nat_OSuc, _1209543))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209541), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1209541), _1209547), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1209545), _1209543))), hAPP(_1209547, _1209543)))]]], (22735 ^ _782652) ^ [_1209871, _1209873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1209871, _1209873))))], (22745 ^ _782652) ^ [_1210018, _1210020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210018), _1210020)), -(c_Nat__Transfer_Otsub(_1210020, _1210018) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1210020), _1210018))], (22751 ^ _782652) ^ [_1210123, _1210125] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210123), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210125)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210123), _1210125)))], (22753 ^ _782652) ^ [_1210166, _1210168, _1210170, _1210172] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1210166), _1210168)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1210170), _1210172)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1210166, _1210170)), c_Sum__Type_OPlus(_1210166, _1210170, _1210168, _1210172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1210166), _1210168)), hAPP(c_Finite__Set_Ocard(_1210170), _1210172)))], (22763 ^ _782652) ^ [_1210377, _1210379] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1210377, _1210379)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1210379)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22765 ^ _782652) ^ [_1210417, _1210419] : [-(c_Sum__Type_OPlus(_1210417, _1210419, c_Orderings_Otop__class_Otop(tc_fun(_1210417, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1210419, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1210417, _1210419), tc_HOL_Obool)))], (22767 ^ _782652) ^ [_1210480, _1210482] : [22775 ^ _782652 : [(22776 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 22774 ^ [_1210480, _1210482]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210480))))], (22778 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1210482, 22774 ^ [_1210480, _1210482])))]], 22768 ^ _782652 : [(22769 ^ _782652) ^ [_1210548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210548), _1210480)), hBOOL(hAPP(_1210482, _1210548))]]], (22780 ^ _782652) ^ [_1210708, _1210710] : [22788 ^ _782652 : [(22789 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 22787 ^ [_1210708, _1210710]), _1210708)))], (22791 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1210710, 22787 ^ [_1210708, _1210710])))]], 22781 ^ _782652 : [(22782 ^ _782652) ^ [_1210776] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1210776), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210708))), hBOOL(hAPP(_1210710, _1210776))]]], (22793 ^ _782652) ^ [_1210960, _1210962] : [22795 ^ _782652 : [(22796 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 22794 ^ [_1210960, _1210962]), _1210960)))], (22798 ^ _782652) ^ [] : [hBOOL(hAPP(_1210962, 22794 ^ [_1210960, _1210962]))]], 22799 ^ _782652 : [(22800 ^ _782652) ^ [_1211110] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1211110), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1210960))), -(hBOOL(hAPP(_1210962, _1211110)))]]], (22806 ^ _782652) ^ [_1211211, _1211213] : [22808 ^ _782652 : [(22809 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 22807 ^ [_1211211, _1211213]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211211))))], (22811 ^ _782652) ^ [] : [hBOOL(hAPP(_1211213, 22807 ^ [_1211211, _1211213]))]], 22812 ^ _782652 : [(22813 ^ _782652) ^ [_1211364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211364), _1211211)), -(hBOOL(hAPP(_1211213, _1211364)))]]], (22819 ^ _782652) ^ [_1211486, _1211488, _1211490, _1211492] : [c_Sum__Type_OPlus(_1211486, _1211488, _1211490, _1211492) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1211486, _1211488), tc_HOL_Obool)), 22822 ^ _782652 : [(22823 ^ _782652) ^ [] : [-(_1211490 = c_Orderings_Obot__class_Obot(tc_fun(_1211486, tc_HOL_Obool)))], (22825 ^ _782652) ^ [] : [-(_1211492 = c_Orderings_Obot__class_Obot(tc_fun(_1211488, tc_HOL_Obool)))]]], (22827 ^ _782652) ^ [_1211635, _1211637, _1211639, _1211641] : [-(c_Sum__Type_OPlus(_1211635, _1211637, _1211639, _1211641) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1211635, _1211637), tc_HOL_Obool))), _1211639 = c_Orderings_Obot__class_Obot(tc_fun(_1211635, tc_HOL_Obool)), _1211641 = c_Orderings_Obot__class_Obot(tc_fun(_1211637, tc_HOL_Obool))], (22837 ^ _782652) ^ [_1211820, _1211822, _1211824] : [class_Orderings_Olinorder(_1211820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211820), _1211822), _1211824)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1211820, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1211820), _1211822), c_Orderings_Obot__class_Obot(tc_fun(_1211820, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1211820, _1211822, _1211824)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1211820, _1211822), _1211824))], (22847 ^ _782652) ^ [_1212033, _1212035, _1212037, _1212039, _1212041] : [class_Groups_Oordered__ab__group__add(_1212033), hBOOL(hAPP(c_Finite__Set_Ofinite(_1212035), _1212037)), 22857 ^ _782652 : [(22858 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1212035), 22856 ^ [_1212033, _1212035, _1212037, _1212039, _1212041]), _1212037)))], (22860 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212033), c_Groups_Ozero__class_Ozero(_1212033)), hAPP(_1212039, 22856 ^ [_1212033, _1212035, _1212037, _1212039, _1212041])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212035, _1212033), _1212039), _1212037) = c_Groups_Ozero__class_Ozero(_1212033), hBOOL(hAPP(hAPP(c_member(_1212035), _1212041), _1212037)), -(hAPP(_1212039, _1212041) = c_Groups_Ozero__class_Ozero(_1212033))], (22872 ^ _782652) ^ [_1212531, _1212533] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1212531, _1212533))))], (22874 ^ _782652) ^ [_1212562, _1212564] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1212562), _1212564))))], (22876 ^ _782652) ^ [_1212595, _1212597] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1212595, _1212597))))], (22878 ^ _782652) ^ [_1212626, _1212628] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1212626), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1212628) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1212626, _1212628))], (22880 ^ _782652) ^ [_1212667] : [-(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)), _1212667))))], (22882 ^ _782652) ^ [_1212695, _1212697, _1212699] : [class_Orderings_Oorder(_1212695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212695), _1212697), _1212699)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1212695, _1212699, _1212697) = c_Orderings_Obot__class_Obot(tc_fun(_1212695, tc_HOL_Obool)))], (22892 ^ _782652) ^ [_1212858, _1212860] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1212858)), _1212860) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1212858, _1212860))], (22894 ^ _782652) ^ [_1212896, _1212898, _1212900] : [class_Groups_Oordered__ab__group__add(_1212896), -(hAPP(c_Set_Oimage(_1212896, _1212896, c_Groups_Ouminus__class_Ouminus(_1212896)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1212896, _1212898, _1212900)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1212896, hAPP(c_Groups_Ouminus__class_Ouminus(_1212896), _1212900), hAPP(c_Groups_Ouminus__class_Ouminus(_1212896), _1212898)))], (22900 ^ _782652) ^ [_1213027, _1213029] : [-(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)), _1213027)), 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), _1213029), _1213027))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1213027), _1213029))], (22902 ^ _782652) ^ [_1213077, _1213079, _1213081, _1213083] : [class_Orderings_Oorder(_1213077), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1213077, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1213077, _1213079, _1213081)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1213077, _1213081), _1213083)) = c_Orderings_Obot__class_Obot(tc_fun(_1213077, tc_HOL_Obool)))], (22908 ^ _782652) ^ [_1213208, _1213210, _1213212, _1213214, _1213216] : [class_Orderings_Olinorder(_1213208), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1213208, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1213208, _1213210, _1213212)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1213208, _1213214, _1213216)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1213208, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213208), _1213210), _1213214), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1213208), _1213212), _1213216)))], (22914 ^ _782652) ^ [_1213367, _1213369] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1213367, _1213369)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1213369), hAPP(c_Nat_OSuc, _1213367)))], (22916 ^ _782652) ^ [_1213408, _1213410, _1213412, _1213414] : [class_Orderings_Olinorder(_1213408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213408), _1213410), _1213412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213408), _1213412), _1213414)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1213408, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1213408, _1213410, _1213412)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1213408, _1213412), _1213414)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1213408, _1213410, _1213414))], (22930 ^ _782652) ^ [_1213677, _1213679, _1213681] : [class_Orderings_Olinorder(_1213677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213677), _1213679), _1213681)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1213677, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1213677, _1213679, _1213681)), hAPP(hAPP(c_Set_Oinsert(_1213677), _1213681), c_Orderings_Obot__class_Obot(tc_fun(_1213677, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1213677, _1213679, _1213681))], (22940 ^ _782652) ^ [_1213886, _1213888, _1213890, _1213892, _1213894, _1213896] : [class_Groups_Oordered__ab__group__add(_1213886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1213888), _1213890)), 22950 ^ _782652 : [(22951 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1213888), 22949 ^ [_1213886, _1213888, _1213890, _1213892, _1213894, _1213896]), _1213890)))], (22953 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213886), c_Groups_Ozero__class_Ozero(_1213886)), hAPP(_1213892, 22949 ^ [_1213886, _1213888, _1213890, _1213892, _1213894, _1213896])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1213888, _1213886), _1213892), _1213890) = _1213894, hBOOL(hAPP(hAPP(c_member(_1213888), _1213896), _1213890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213886), hAPP(_1213892, _1213896)), _1213894)))], (22965 ^ _782652) ^ [] : [-(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))))], (22967 ^ _782652) ^ [_1214424, _1214426, _1214428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1214424, 22968 ^ [_1214424, _1214426, _1214428])), hAPP(_1214426, 22968 ^ [_1214424, _1214426, _1214428]))), -(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), _1214426), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214428))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1214424), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214428))) = 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)), _1214426)), _1214424)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214428)))], (22974 ^ _782652) ^ [_1214657, _1214659, _1214661, _1214663] : [class_Groups_Oab__group__add(_1214657), 22977 ^ _782652 : [(22978 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1214659), _1214661)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214657), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1214657, _1214657), hAPP(hAPP(c_COMBB(_1214657, tc_fun(_1214657, _1214657), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1214657)), _1214663)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1214657, tc_Nat_Onat), _1214663), 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, _1214659, _1214661)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1214657), hAPP(_1214663, _1214659)), hAPP(_1214663, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1214661), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (22984 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1214659), _1214661))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214657), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1214657, _1214657), hAPP(hAPP(c_COMBB(_1214657, tc_fun(_1214657, _1214657), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1214657)), _1214663)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1214657, tc_Nat_Onat), _1214663), 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, _1214659, _1214661)) = c_Groups_Ozero__class_Ozero(_1214657))]]], (22990 ^ _782652) ^ [_1215095, _1215097] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1215095, _1215097))))], (22992 ^ _782652) ^ [_1215126, _1215128] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1215126, _1215128))))], (22994 ^ _782652) ^ [_1215157, _1215159] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1215157, _1215159))))], (22996 ^ _782652) ^ [_1215188, _1215190, _1215192] : [class_Orderings_Olinorder(_1215188), 22999 ^ _782652 : [(23000 ^ _782652) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1215188), _1215190) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1215188), _1215192), -(_1215190 = _1215192)], (23006 ^ _782652) ^ [] : [_1215190 = _1215192, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1215188), _1215190) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1215188), _1215192))]]], (23012 ^ _782652) ^ [_1215429, _1215431] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1215429), _1215431) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1215429, _1215431))], (23014 ^ _782652) ^ [_1215465, _1215467, _1215469, _1215471] : [class_Orderings_Olinorder(_1215465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215465), _1215467), _1215469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215465), _1215469), _1215471)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1215465, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1215465, _1215467, _1215469)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1215465, _1215469, _1215471)) = c_SetInterval_Oord__class_OatLeastAtMost(_1215465, _1215467, _1215471))], (23028 ^ _782652) ^ [_1215730, _1215732, _1215734, _1215736] : [class_Orderings_Oorder(_1215730), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1215730, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1215730, _1215732, _1215734)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1215730, _1215734, _1215736)) = c_Orderings_Obot__class_Obot(tc_fun(_1215730, tc_HOL_Obool)))], (23034 ^ _782652) ^ [_1215857, _1215859, _1215861] : [class_Orderings_Oorder(_1215857), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1215857, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1215857, _1215859, _1215861)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1215857), _1215861)) = c_Orderings_Obot__class_Obot(tc_fun(_1215857, tc_HOL_Obool)))], (23040 ^ _782652) ^ [_1215984, _1215986, _1215988] : [class_Orderings_Olinorder(_1215984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215984), _1215986), _1215988)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1215984, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1215984, _1215986, _1215988)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1215984), _1215988)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1215984), _1215986))], (23050 ^ _782652) ^ [_1216179, _1216181, _1216183] : [class_Orderings_Oorder(_1216179), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1216179, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1216179, _1216181, _1216183)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1216179), _1216183)) = c_Orderings_Obot__class_Obot(tc_fun(_1216179, tc_HOL_Obool)))], (23056 ^ _782652) ^ [_1216306, _1216308, _1216310, _1216312] : [class_Groups_Ocomm__monoid__add(_1216306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216308), _1216310)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1216306), _1216312), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1216308, _1216310)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216306), hAPP(_1216312, _1216308)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1216306), _1216312), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1216308, _1216310))))], (23066 ^ _782652) ^ [_1216540, _1216542] : [23074 ^ _782652 : [(23075 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 23073 ^ [_1216540, _1216542]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1216540))))], (23077 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1216542, 23073 ^ [_1216540, _1216542])))]], 23067 ^ _782652 : [(23068 ^ _782652) ^ [_1216609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216609), _1216540)), hBOOL(hAPP(_1216542, _1216609))]]], (23079 ^ _782652) ^ [_1216770, _1216772] : [23087 ^ _782652 : [(23088 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 23086 ^ [_1216770, _1216772]), _1216770)))], (23090 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1216772, 23086 ^ [_1216770, _1216772])))]], 23080 ^ _782652 : [(23081 ^ _782652) ^ [_1216839] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1216839), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1216770))), hBOOL(hAPP(_1216772, _1216839))]]], (23092 ^ _782652) ^ [_1217025, _1217027] : [23094 ^ _782652 : [(23095 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 23093 ^ [_1217025, _1217027]), _1217025)))], (23097 ^ _782652) ^ [] : [hBOOL(hAPP(_1217027, 23093 ^ [_1217025, _1217027]))]], 23098 ^ _782652 : [(23099 ^ _782652) ^ [_1217176] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1217176), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1217025))), -(hBOOL(hAPP(_1217027, _1217176)))]]], (23105 ^ _782652) ^ [_1217279, _1217281] : [23107 ^ _782652 : [(23108 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 23106 ^ [_1217279, _1217281]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1217279))))], (23110 ^ _782652) ^ [] : [hBOOL(hAPP(_1217281, 23106 ^ [_1217279, _1217281]))]], 23111 ^ _782652 : [(23112 ^ _782652) ^ [_1217434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1217434), _1217279)), -(hBOOL(hAPP(_1217281, _1217434)))]]], (23118 ^ _782652) ^ [_1217535, _1217537] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1217535), hAPP(c_Nat_OSuc, _1217537)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1217535, _1217537))], (23120 ^ _782652) ^ [_1217573, _1217575, _1217577] : [class_Orderings_Olinorder(_1217573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217573), _1217575), _1217577)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1217573, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1217573), _1217575), c_Orderings_Obot__class_Obot(tc_fun(_1217573, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1217573, _1217575, _1217577)) = c_SetInterval_Oord__class_OatLeastAtMost(_1217573, _1217575, _1217577))], (23130 ^ _782652) ^ [_1217782, _1217784, _1217786] : [class_Orderings_Oorder(_1217782), 23133 ^ _782652 : [(23134 ^ _782652) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1217782, _1217784, _1217786) = c_Orderings_Obot__class_Obot(tc_fun(_1217782, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217782), _1217784), _1217786))], (23140 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217782), _1217784), _1217786))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1217782, _1217784, _1217786) = c_Orderings_Obot__class_Obot(tc_fun(_1217782, tc_HOL_Obool)))]]], (23146 ^ _782652) ^ [_1218001, _1218003, _1218005] : [class_Orderings_Oorder(_1218001), 23149 ^ _782652 : [(23150 ^ _782652) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1218001, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1218001, _1218003, _1218005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218001), _1218003), _1218005))], (23156 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218001), _1218003), _1218005))), -(c_Orderings_Obot__class_Obot(tc_fun(_1218001, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1218001, _1218003, _1218005))]]], (23162 ^ _782652) ^ [_1218220, _1218222, _1218224] : [class_Orderings_Oorder(_1218220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218220), _1218222), _1218224)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1218220, _1218224, _1218222) = c_Orderings_Obot__class_Obot(tc_fun(_1218220, tc_HOL_Obool)))], (23172 ^ _782652) ^ [_1218383, _1218385, _1218387, _1218389, _1218391] : [class_Orderings_Oorder(_1218383), 23175 ^ _782652 : [(23176 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218383, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1218383, _1218385, _1218387)), c_SetInterval_Oord__class_OatLeastAtMost(_1218383, _1218389, _1218391))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218383), _1218385), _1218387)), 23183 ^ _782652 : [(23184 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218383), _1218389), _1218385)))], (23186 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218383), _1218387), _1218391)))]]], (23188 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1218383, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1218383, _1218385, _1218387)), c_SetInterval_Oord__class_OatLeastAtMost(_1218383, _1218389, _1218391)))), 23189 ^ _782652 : [(23190 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218383), _1218385), _1218387)))], (23192 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218383), _1218389), _1218385)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218383), _1218387), _1218391))]]]]], (23200 ^ _782652) ^ [_1218886, _1218888, _1218890] : [class_Orderings_Oorder(_1218886), _1218888 = _1218890, -(c_SetInterval_Oord__class_OatLeastAtMost(_1218886, _1218888, _1218890) = hAPP(hAPP(c_Set_Oinsert(_1218886), _1218888), c_Orderings_Obot__class_Obot(tc_fun(_1218886, tc_HOL_Obool))))], (23210 ^ _782652) ^ [_1219051, _1219053, _1219055, _1219057] : [class_Orderings_Oorder(_1219051), 23213 ^ _782652 : [(23214 ^ _782652) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1219051, _1219053, _1219055) = hAPP(hAPP(c_Set_Oinsert(_1219051), _1219057), c_Orderings_Obot__class_Obot(tc_fun(_1219051, tc_HOL_Obool))), 23217 ^ _782652 : [(23218 ^ _782652) ^ [] : [-(_1219053 = _1219055)], (23220 ^ _782652) ^ [] : [-(_1219055 = _1219057)]]], (23222 ^ _782652) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1219051, _1219053, _1219055) = hAPP(hAPP(c_Set_Oinsert(_1219051), _1219057), c_Orderings_Obot__class_Obot(tc_fun(_1219051, tc_HOL_Obool)))), _1219053 = _1219055, _1219055 = _1219057]]], (23232 ^ _782652) ^ [_1219395, _1219397] : [class_Orderings_Oorder(_1219395), -(c_SetInterval_Oord__class_OatLeastAtMost(_1219395, _1219397, _1219397) = hAPP(hAPP(c_Set_Oinsert(_1219395), _1219397), c_Orderings_Obot__class_Obot(tc_fun(_1219395, tc_HOL_Obool))))], (23238 ^ _782652) ^ [_1219504, _1219506, _1219508] : [class_Groups_Oordered__ab__group__add(_1219504), -(hAPP(c_Set_Oimage(_1219504, _1219504, c_Groups_Ouminus__class_Ouminus(_1219504)), c_SetInterval_Oord__class_OatLeastAtMost(_1219504, _1219506, _1219508)) = c_SetInterval_Oord__class_OatLeastAtMost(_1219504, hAPP(c_Groups_Ouminus__class_Ouminus(_1219504), _1219508), hAPP(c_Groups_Ouminus__class_Ouminus(_1219504), _1219506)))], (23244 ^ _782652) ^ [_1219635, _1219637, _1219639, _1219641] : [class_Orderings_Olinorder(_1219635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219635), _1219637), _1219639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219635), _1219639), _1219641)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1219635, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1219635, _1219637, _1219639)), c_SetInterval_Oord__class_OatLeastAtMost(_1219635, _1219639, _1219641)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1219635, _1219637, _1219641))], (23258 ^ _782652) ^ [_1219900, _1219902] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1219900, _1219902)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1219900), hAPP(c_Nat_OSuc, _1219902)))], (23260 ^ _782652) ^ [_1219942, _1219944, _1219946, _1219948] : [class_Groups_Ocomm__monoid__add(_1219942), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219942), _1219944), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1219946), hAPP(c_Nat_OSuc, _1219948))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219942), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1219942, tc_Nat_Onat), _1219944), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1219946, _1219948)))], (23266 ^ _782652) ^ [_1220105, _1220107, _1220109, _1220111, _1220113] : [class_Groups_Ocomm__monoid__add(_1220105), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220105), _1220107), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220109), _1220111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220113), _1220111))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220105), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1220105, tc_Nat_Onat), _1220107), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1220111))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220109, _1220113)))], (23272 ^ _782652) ^ [_1220288, _1220290, _1220292] : [class_Orderings_Oorder(_1220288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220288), _1220290), _1220292)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1220288, _1220292, _1220290) = c_Orderings_Obot__class_Obot(tc_fun(_1220288, tc_HOL_Obool)))], (23282 ^ _782652) ^ [_1220451, _1220453, _1220455] : [class_Orderings_Oorder(_1220451), 23285 ^ _782652 : [(23286 ^ _782652) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1220451, _1220453, _1220455) = c_Orderings_Obot__class_Obot(tc_fun(_1220451, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220451), _1220453), _1220455))], (23292 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220451), _1220453), _1220455))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1220451, _1220453, _1220455) = c_Orderings_Obot__class_Obot(tc_fun(_1220451, tc_HOL_Obool)))]]], (23298 ^ _782652) ^ [_1220670, _1220672, _1220674] : [class_Orderings_Oorder(_1220670), 23301 ^ _782652 : [(23302 ^ _782652) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1220670, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1220670, _1220672, _1220674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220670), _1220672), _1220674))], (23308 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220670), _1220672), _1220674))), -(c_Orderings_Obot__class_Obot(tc_fun(_1220670, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1220670, _1220672, _1220674))]]], (23314 ^ _782652) ^ [_1220889, _1220891, _1220893, _1220895] : [class_Orderings_Olinorder(_1220889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220889), _1220891), _1220893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220889), _1220893), _1220895)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1220889, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1220889, _1220891, _1220893)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1220889, _1220893, _1220895)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1220889, _1220891, _1220895))], (23328 ^ _782652) ^ [_1221154, _1221156, _1221158, _1221160] : [class_Orderings_Oorder(_1221154), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1221154, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1221154, _1221156, _1221158)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1221154, _1221158, _1221160)) = c_Orderings_Obot__class_Obot(tc_fun(_1221154, tc_HOL_Obool)))], (23334 ^ _782652) ^ [_1221281, _1221283, _1221285] : [-(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)), _1221281)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1221283, _1221285)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1221283), _1221281), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1221285), _1221281)))], (23336 ^ _782652) ^ [_1221338, _1221340] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1221338, _1221340)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1221340), _1221338))], (23338 ^ _782652) ^ [_1221376, _1221378, _1221380] : [class_Orderings_Oord(_1221376), 23341 ^ _782652 : [(23342 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1221376), _1221378), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1221376), _1221380))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221376), _1221380), _1221378)))], (23348 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221376), _1221380), _1221378)), -(hBOOL(hAPP(hAPP(c_member(_1221376), _1221378), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1221376), _1221380))))]]], (23354 ^ _782652) ^ [_1221644, _1221646, _1221648] : [class_Orderings_Olinorder(_1221644), 23357 ^ _782652 : [(23358 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1221644, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1221644), _1221646)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1221644), _1221648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221644), _1221648), _1221646)))], (23364 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221644), _1221648), _1221646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1221644, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1221644), _1221646)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1221644), _1221648))))]]], (23370 ^ _782652) ^ [_1221936, _1221938] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1221936, _1221938)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1221938)), _1221936))], (23372 ^ _782652) ^ [_1221977, _1221979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221977), hAPP(c_Nat_OSuc, _1221979))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1221977, hAPP(c_Nat_OSuc, _1221979)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1221979)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1221977, _1221979)))], (23378 ^ _782652) ^ [_1222110, _1222112] : [hAPP(_1222110, 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), _1222110), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1222112)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1222110), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1222112)))], (23384 ^ _782652) ^ [_1222233, _1222235, _1222237, _1222239] : [class_Orderings_Olinorder(_1222233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222233), _1222235), _1222237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222233), _1222237), _1222239)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222233, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222233, _1222235), _1222237)), c_SetInterval_Oord__class_OatLeastAtMost(_1222233, _1222237, _1222239)) = c_SetInterval_Oord__class_OatLeastAtMost(_1222233, _1222235, _1222239))], (23398 ^ _782652) ^ [_1222502, _1222504, _1222506, _1222508] : [class_Orderings_Oorder(_1222502), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222502, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222502, _1222504), _1222506)), c_SetInterval_Oord__class_OatLeastAtMost(_1222502, _1222506, _1222508)) = c_Orderings_Obot__class_Obot(tc_fun(_1222502, tc_HOL_Obool)))], (23404 ^ _782652) ^ [_1222633, _1222635, _1222637, _1222639, _1222641] : [class_Orderings_Olinorder(_1222633), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222633, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1222633, _1222635, _1222637)), c_SetInterval_Oord__class_OatLeastAtMost(_1222633, _1222639, _1222641)) = c_SetInterval_Oord__class_OatLeastAtMost(_1222633, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222633), _1222635), _1222639), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1222633), _1222637), _1222641)))], (23410 ^ _782652) ^ [_1222792, _1222794, _1222796, _1222798, _1222800] : [class_Orderings_Oorder(_1222792), 23413 ^ _782652 : [(23414 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1222792, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1222792, _1222794, _1222796)), c_SetInterval_Oord__class_OatLeastAtMost(_1222792, _1222798, _1222800))), 23417 ^ _782652 : [(23432 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222792), _1222798), _1222800)))], (23418 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222792), _1222794), _1222796)), 23421 ^ _782652 : [(23422 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222792), _1222798), _1222794)))], (23424 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222792), _1222796), _1222800)))], (23426 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222792), _1222798), _1222794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222792), _1222796), _1222800)))]]]]], (23434 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1222792, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1222792, _1222794, _1222796)), c_SetInterval_Oord__class_OatLeastAtMost(_1222792, _1222798, _1222800)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222792), _1222798), _1222800)), 23437 ^ _782652 : [(23438 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222792), _1222794), _1222796)))], (23440 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222792), _1222798), _1222794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222792), _1222796), _1222800)), 23447 ^ _782652 : [(23448 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222792), _1222798), _1222794))], (23450 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222792), _1222796), _1222800))]]]]]]], (23456 ^ _782652) ^ [_1223563, _1223565, _1223567] : [class_Orderings_Oorder(_1223563), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1223563, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1223563), _1223565)), c_SetInterval_Oord__class_OatLeastAtMost(_1223563, _1223565, _1223567)) = c_Orderings_Obot__class_Obot(tc_fun(_1223563, tc_HOL_Obool)))], (23462 ^ _782652) ^ [_1223690, _1223692, _1223694, _1223696] : [class_Orderings_Oorder(_1223690), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1223690, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1223690, _1223692, _1223694)), c_SetInterval_Oord__class_OatLeastAtMost(_1223690, _1223694, _1223696)) = c_Orderings_Obot__class_Obot(tc_fun(_1223690, tc_HOL_Obool)))], (23468 ^ _782652) ^ [_1223817, _1223819, _1223821, _1223823] : [class_Orderings_Oorder(_1223817), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1223817, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1223817, _1223819, _1223821)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1223817, _1223821, _1223823)) = c_Orderings_Obot__class_Obot(tc_fun(_1223817, tc_HOL_Obool)))], (23474 ^ _782652) ^ [_1223944, _1223946, _1223948, _1223950] : [class_Groups_Ocomm__monoid__add(_1223944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223946), _1223948)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223944), _1223950), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1223946, _1223948)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223944), hAPP(_1223950, _1223946)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223944), _1223950), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1223946), _1223948))))], (23484 ^ _782652) ^ [_1224169, _1224171, _1224173, _1224175, _1224177] : [class_Orderings_Olinorder(_1224169), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1224169, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1224169, _1224171, _1224173)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1224169, _1224175, _1224177)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1224169, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224169), _1224171), _1224175), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1224169), _1224173), _1224177)))], (23490 ^ _782652) ^ [_1224328, _1224330, _1224332] : [class_Groups_Oordered__ab__group__add(_1224328), -(hAPP(c_Set_Oimage(_1224328, _1224328, c_Groups_Ouminus__class_Ouminus(_1224328)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1224328, _1224330, _1224332)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1224328, hAPP(c_Groups_Ouminus__class_Ouminus(_1224328), _1224332)), hAPP(c_Groups_Ouminus__class_Ouminus(_1224328), _1224330)))], (23496 ^ _782652) ^ [_1224463, _1224465, _1224467] : [class_Groups_Oordered__ab__group__add(_1224463), -(hAPP(c_Set_Oimage(_1224463, _1224463, c_Groups_Ouminus__class_Ouminus(_1224463)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1224463, _1224465), _1224467)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1224463, hAPP(c_Groups_Ouminus__class_Ouminus(_1224463), _1224467), hAPP(c_Groups_Ouminus__class_Ouminus(_1224463), _1224465)))], (23502 ^ _782652) ^ [_1224598, _1224600, _1224602, _1224604] : [class_Orderings_Oorder(_1224598), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1224598, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1224598, _1224600, _1224602)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1224598, _1224602, _1224604)) = c_Orderings_Obot__class_Obot(tc_fun(_1224598, tc_HOL_Obool)))], (23508 ^ _782652) ^ [_1224725, _1224727] : [class_Groups_Oordered__ab__group__add(_1224725), -(hAPP(c_Set_Oimage(_1224725, _1224725, c_Groups_Ouminus__class_Ouminus(_1224725)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1224725), _1224727)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1224725), hAPP(c_Groups_Ouminus__class_Ouminus(_1224725), _1224727)))], (23514 ^ _782652) ^ [_1224848, _1224850] : [class_Groups_Oordered__ab__group__add(_1224848), -(hAPP(c_Set_Oimage(_1224848, _1224848, c_Groups_Ouminus__class_Ouminus(_1224848)), hAPP(c_SetInterval_Oord__class_OlessThan(_1224848), _1224850)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1224848), hAPP(c_Groups_Ouminus__class_Ouminus(_1224848), _1224850)))], (23520 ^ _782652) ^ [_1224971] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1224971)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1224971)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1224971)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (23522 ^ _782652) ^ [_1225018, _1225020, _1225022, _1225024] : [class_Groups_Ocomm__monoid__add(_1225018), 23525 ^ _782652 : [(23526 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1225020)), _1225022)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1225018), _1225024), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1225022, hAPP(c_Nat_OSuc, _1225020))) = c_Groups_Ozero__class_Ozero(_1225018))], (23532 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1225020)), _1225022))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1225018), _1225024), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1225022, hAPP(c_Nat_OSuc, _1225020))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225018), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1225018), _1225024), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1225022, _1225020))), hAPP(_1225024, hAPP(c_Nat_OSuc, _1225020))))]]], (23538 ^ _782652) ^ [_1225354, _1225356, _1225358, _1225360, _1225362] : [class_Groups_Ocomm__monoid__add(_1225354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1225356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1225358), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1225354), _1225360), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1225356, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1225358), _1225362))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1225354), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1225354), _1225360), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1225356, _1225358))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1225354), _1225360), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1225358), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1225358), _1225362)))))], (23548 ^ _782652) ^ [_1225645, _1225647, _1225649, _1225651] : [class_Orderings_Olinorder(_1225645), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225645), _1225647), _1225649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225645), _1225649), _1225651)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1225645, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1225645, _1225647, _1225649)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1225645, _1225649, _1225651)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1225645, _1225647, _1225651))], (23562 ^ _782652) ^ [_1225910, _1225912, _1225914] : [class_Orderings_Olinorder(_1225910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225910), _1225912), _1225914)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1225910, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1225910, _1225912), _1225914)), hAPP(hAPP(c_Set_Oinsert(_1225910), _1225914), c_Orderings_Obot__class_Obot(tc_fun(_1225910, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1225910, _1225912, _1225914))], (23572 ^ _782652) ^ [_1226123, _1226125, _1226127, _1226129] : [class_Orderings_Olinorder(_1226123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1226123), _1226125), _1226127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226123), _1226127), _1226129)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1226123, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1226123, _1226125, _1226127)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1226123, _1226127, _1226129)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1226123, _1226125), _1226129))], (23586 ^ _782652) ^ [_1226392, _1226394] : [class_Rings_Ocomm__semiring__1(_1226392), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226392), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226392), c_Groups_Oone__class_Oone(_1226392)), c_Groups_Oone__class_Oone(_1226392))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1226392), c_Nat_Osemiring__1__class_Oof__nat(_1226392)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1226394))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226392), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1226392), _1226394)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1226392), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1226392), _1226394)), c_Groups_Oone__class_Oone(_1226392))))], (23592 ^ _782652) ^ [_1226593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226593)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226593) = 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, _1226593))))], (23598 ^ _782652) ^ [_1226696, _1226698, _1226700] : [class_Orderings_Olinorder(_1226696), hAPP(_1226698, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1226696), 23603 ^ [_1226696, _1226698, _1226700]), 23604 ^ [_1226696, _1226698, _1226700])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1226696), hAPP(_1226698, 23603 ^ [_1226696, _1226698, _1226700])), hAPP(_1226698, 23604 ^ [_1226696, _1226698, _1226700])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1226696), _1226700)), -(_1226700 = c_Orderings_Obot__class_Obot(tc_fun(_1226696, tc_HOL_Obool))), -(hAPP(_1226698, c_Big__Operators_Olattice_OInf__fin(_1226696, c_Orderings_Oord__class_Omin(_1226696), _1226700)) = c_Big__Operators_Olattice_OInf__fin(_1226696, c_Orderings_Oord__class_Omin(_1226696), hAPP(c_Set_Oimage(_1226696, _1226696, _1226698), _1226700)))], (23618 ^ _782652) ^ [_1227111, _1227113, _1227115] : [class_Orderings_Olinorder(_1227111), hAPP(_1227113, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1227111), 23623 ^ [_1227111, _1227113, _1227115]), 23624 ^ [_1227111, _1227113, _1227115])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1227111), hAPP(_1227113, 23623 ^ [_1227111, _1227113, _1227115])), hAPP(_1227113, 23624 ^ [_1227111, _1227113, _1227115])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1227111), _1227115)), -(_1227115 = c_Orderings_Obot__class_Obot(tc_fun(_1227111, tc_HOL_Obool))), -(hAPP(_1227113, c_Big__Operators_Olinorder__class_OMax(_1227111, _1227115)) = c_Big__Operators_Olinorder__class_OMax(_1227111, hAPP(c_Set_Oimage(_1227111, _1227111, _1227113), _1227115)))], (23638 ^ _782652) ^ [_1227514, _1227516, _1227518] : [class_Orderings_Olinorder(_1227514), hAPP(_1227516, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1227514), 23643 ^ [_1227514, _1227516, _1227518]), 23644 ^ [_1227514, _1227516, _1227518])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1227514), hAPP(_1227516, 23643 ^ [_1227514, _1227516, _1227518])), hAPP(_1227516, 23644 ^ [_1227514, _1227516, _1227518])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1227514), _1227518)), -(_1227518 = c_Orderings_Obot__class_Obot(tc_fun(_1227514, tc_HOL_Obool))), -(hAPP(_1227516, c_Big__Operators_Olinorder__class_OMin(_1227514, _1227518)) = c_Big__Operators_Olinorder__class_OMin(_1227514, hAPP(c_Set_Oimage(_1227514, _1227514, _1227516), _1227518)))], (23658 ^ _782652) ^ [_1227917, _1227919, _1227921] : [class_Orderings_Olinorder(_1227917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1227917), _1227919), _1227921)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1227917, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1227917, _1227919, _1227921)), hAPP(c_SetInterval_Oord__class_OatLeast(_1227917), _1227921)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1227917), _1227919))], (23668 ^ _782652) ^ [_1228112, _1228114] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1228112, _1228114))))], (23670 ^ _782652) ^ [_1228143, _1228145] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1228143, _1228145) = 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), _1228143), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228145))))], (23672 ^ _782652) ^ [_1228185, _1228187, _1228189] : [class_Orderings_Olinorder(_1228185), 23675 ^ _782652 : [(23676 ^ _782652) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1228185), _1228187) = hAPP(c_SetInterval_Oord__class_OatLeast(_1228185), _1228189), -(_1228187 = _1228189)], (23682 ^ _782652) ^ [] : [_1228187 = _1228189, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1228185), _1228187) = hAPP(c_SetInterval_Oord__class_OatLeast(_1228185), _1228189))]]], (23688 ^ _782652) ^ [_1228426] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228426)) = _1228426)], (23690 ^ _782652) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23692 ^ _782652) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23694 ^ _782652) ^ [_1228491, _1228493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228493)), 23701 ^ _782652 : [(23702 ^ _782652) ^ [] : [hAPP(c_Int_Onat, _1228491) = hAPP(c_Int_Onat, _1228493), -(_1228491 = _1228493)], (23708 ^ _782652) ^ [] : [_1228491 = _1228493, -(hAPP(c_Int_Onat, _1228491) = hAPP(c_Int_Onat, _1228493))]]], (23725 ^ _782652) ^ [_1228973] : [23727 ^ _782652 : [(23728 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23726 ^ [_1228973])))], (23730 ^ _782652) ^ [] : [hBOOL(hAPP(_1228973, hAPP(c_Int_Onat, 23726 ^ [_1228973])))]], 23731 ^ _782652 : [(23732 ^ _782652) ^ [_1229106] : [-(hBOOL(hAPP(_1228973, _1229106)))]]], (23714 ^ _782652) ^ [_1228788] : [hBOOL(hAPP(_1228788, 23715 ^ [_1228788])), 23718 ^ _782652 : [(23719 ^ _782652) ^ [_1228882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228882)), -(hBOOL(hAPP(_1228788, hAPP(c_Int_Onat, _1228882))))]]], (23734 ^ _782652) ^ [_1229151] : [23735 ^ _782652 : [(23736 ^ _782652) ^ [_1229208] : [hBOOL(hAPP(_1229151, _1229208))]], 23738 ^ _782652 : [(23739 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23737 ^ [_1229151])))], (23741 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1229151, hAPP(c_Int_Onat, 23737 ^ [_1229151]))))]]], (23743 ^ _782652) ^ [_1229294] : [-(hBOOL(hAPP(_1229294, 23750 ^ [_1229294]))), 23744 ^ _782652 : [(23745 ^ _782652) ^ [_1229346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229346)), hBOOL(hAPP(_1229294, hAPP(c_Int_Onat, _1229346)))]]], (23754 ^ _782652) ^ [_1229473, _1229475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229475)), 23761 ^ _782652 : [(23762 ^ _782652) ^ [] : [hAPP(c_Int_Onat, _1229473) = hAPP(c_Int_Onat, _1229475), -(_1229473 = _1229475)], (23768 ^ _782652) ^ [] : [_1229473 = _1229475, -(hAPP(c_Int_Onat, _1229473) = hAPP(c_Int_Onat, _1229475))]]], (23774 ^ _782652) ^ [_1229758, _1229760] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1229758), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1229760) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1229758, _1229760))], (23776 ^ _782652) ^ [_1229797, _1229799] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1229797, _1229799)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1229799), _1229797)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (23778 ^ _782652) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23780 ^ _782652) ^ [_1229862, _1229864] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1229862), _1229864) = 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)), _1229862)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1229864))))], (23782 ^ _782652) ^ [_1229908] : [-(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)), _1229908)) = _1229908)], (23784 ^ _782652) ^ [_1229937, _1229939] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1229937, _1229939)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1229939), _1229937)))], (23786 ^ _782652) ^ [] : [-(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))))], (23788 ^ _782652) ^ [_1230008] : [hAPP(c_Int_Onat, _1230008) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230008), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23794 ^ _782652) ^ [_1230095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230095), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1230095) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23800 ^ _782652) ^ [_1230188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230188), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1230188) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23806 ^ _782652) ^ [_1230294, _1230296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1230294)), hAPP(c_Int_Onat, _1230296))), 23809 ^ _782652 : [(23810 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230296)))], (23812 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230294), _1230296)))]]], (23814 ^ _782652) ^ [_1230429, _1230431] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1230429)), hAPP(c_Int_Onat, _1230431)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230429), _1230431))], (23824 ^ _782652) ^ [_1230596, _1230598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230596)), 23827 ^ _782652 : [(23828 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1230598)), hAPP(c_Int_Onat, _1230596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230598), _1230596)))], (23834 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230598), _1230596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1230598)), hAPP(c_Int_Onat, _1230596))))]]], (23840 ^ _782652) ^ [_1230855, _1230857, _1230859] : [class_Orderings_Oord(_1230855), 23843 ^ _782652 : [(23844 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1230855), _1230857), hAPP(c_SetInterval_Oord__class_OatLeast(_1230855), _1230859))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230855), _1230859), _1230857)))], (23850 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230855), _1230859), _1230857)), -(hBOOL(hAPP(hAPP(c_member(_1230855), _1230857), hAPP(c_SetInterval_Oord__class_OatLeast(_1230855), _1230859))))]]], (23856 ^ _782652) ^ [_1231123, _1231125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231125)), 23863 ^ _782652 : [(23864 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1231123)), hAPP(c_Int_Onat, _1231125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231123), _1231125)))], (23870 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231123), _1231125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1231123)), hAPP(c_Int_Onat, _1231125))))]]], (23876 ^ _782652) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23878 ^ _782652) ^ [_1231462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231462)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1231462)) = _1231462)], (23884 ^ _782652) ^ [_1231547] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231547))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1231547)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23890 ^ _782652) ^ [_1231606, _1231608] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231606) = _1231608, 23893 ^ _782652 : [(23894 ^ _782652) ^ [] : [-(_1231606 = hAPP(c_Int_Onat, _1231608))], (23896 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231608)))]]], (23898 ^ _782652) ^ [_1231721, _1231723] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231721) = _1231723), _1231721 = hAPP(c_Int_Onat, _1231723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231723))], (23908 ^ _782652) ^ [_1231868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231868)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1231868)) = _1231868)], (23914 ^ _782652) ^ [_1231974, _1231976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1231974), hAPP(c_Int_Onat, _1231976))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231974)), _1231976)))], (23920 ^ _782652) ^ [_1232079, _1232081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232079)), _1232081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232079), hAPP(c_Int_Onat, _1232081))))], (23926 ^ _782652) ^ [_1232190, _1232192, _1232194] : [class_Orderings_Oorder(_1232190), 23929 ^ _782652 : [(23930 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1232190, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232190), _1232192)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232190), _1232194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232190), _1232194), _1232192)))], (23936 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232190), _1232194), _1232192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1232190, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232190), _1232192)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232190), _1232194))))]]], (23942 ^ _782652) ^ [_1232482] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1232482))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23944 ^ _782652) ^ [] : [-(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)))], (23946 ^ _782652) ^ [_1232532, _1232534] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1232532), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1232534), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1232532, _1232534))], (23948 ^ _782652) ^ [_1232573, _1232575] : [class_Orderings_Olinorder(_1232573), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1232573, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1232573), _1232575)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1232573), _1232575))], (23954 ^ _782652) ^ [_1232684, _1232686] : [class_Orderings_Olinorder(_1232684), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1232684, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1232684), _1232686)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1232684), _1232686))], (23960 ^ _782652) ^ [_1232795] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1232795)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1232795))], (23962 ^ _782652) ^ [_1232827, _1232829, _1232831] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1232827), _1232829), _1232831) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1232827), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1232827, tc_Int_Oint), _1232829), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1232831))), class_Groups_Ocomm__monoid__add(_1232827), class_Groups_Ocomm__monoid__mult(_1232827)], (23972 ^ _782652) ^ [_1233018] : [-(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)), _1233018)) = hAPP(c_Int_Onat, _1233018))], (23974 ^ _782652) ^ [_1233050, _1233052] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1233050), _1233052)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1233052), _1233050)))], (23976 ^ _782652) ^ [_1233105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1233105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233105)))], (23982 ^ _782652) ^ [_1233190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1233190))))], (23988 ^ _782652) ^ [_1233281, _1233283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233283)), 23995 ^ _782652 : [(23996 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233281)), hAPP(c_Int_Onat, _1233283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233281), _1233283)))], (24002 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233281), _1233283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233281)), hAPP(c_Int_Onat, _1233283))))]]], (24008 ^ _782652) ^ [_1233596, _1233598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233596)), 24011 ^ _782652 : [(24012 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233596)), hAPP(c_Int_Onat, _1233598))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233596), _1233598)))], (24018 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233596), _1233598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1233596)), hAPP(c_Int_Onat, _1233598))))]]], (24040 ^ _782652) ^ [_1234062, _1234064] : [-(hAPP(c_Int_Onat, _1234062) = _1234064), 24043 ^ _782652 : [(24044 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234062)))], (24046 ^ _782652) ^ [] : [_1234062 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234064)]], 24047 ^ _782652 : [(24048 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234062))], (24050 ^ _782652) ^ [] : [_1234064 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (24024 ^ _782652) ^ [_1233870, _1233872] : [hAPP(c_Int_Onat, _1233870) = _1233872, 24027 ^ _782652 : [(24028 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233870)), -(_1233870 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233872))], (24034 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233870))), -(_1233872 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (24070 ^ _782652) ^ [_1234493, _1234495] : [-(_1234493 = hAPP(c_Int_Onat, _1234495)), 24073 ^ _782652 : [(24074 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234495)))], (24076 ^ _782652) ^ [] : [_1234495 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234493)]], 24077 ^ _782652 : [(24078 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234495))], (24080 ^ _782652) ^ [] : [_1234493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (24054 ^ _782652) ^ [_1234301, _1234303] : [_1234301 = hAPP(c_Int_Onat, _1234303), 24057 ^ _782652 : [(24058 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234303)), -(_1234303 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234301))], (24064 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234303))), -(_1234301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (24084 ^ _782652) ^ [_1234717, _1234719] : [24085 ^ _782652 : [(24086 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234717))], (24088 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234719))]], 24089 ^ _782652 : [(24090 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1234717)), hAPP(c_Int_Onat, _1234719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234717), _1234719)))], (24096 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234717), _1234719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1234717)), hAPP(c_Int_Onat, _1234719))))]]], (24118 ^ _782652) ^ [_1235296, _1235298] : [-(hBOOL(hAPP(_1235296, hAPP(c_Int_Onat, _1235298)))), 24122 ^ _782652 : [(24123 ^ _782652) ^ [] : [-(_1235298 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 24121 ^ [_1235296, _1235298]))], (24125 ^ _782652) ^ [] : [hBOOL(hAPP(_1235296, 24121 ^ [_1235296, _1235298]))]], 24126 ^ _782652 : [(24127 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235298), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24129 ^ _782652) ^ [] : [hBOOL(hAPP(_1235296, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (24102 ^ _782652) ^ [_1235033, _1235035] : [hBOOL(hAPP(_1235033, hAPP(c_Int_Onat, _1235035))), 24105 ^ _782652 : [(24106 ^ _782652) ^ [_1235133] : [_1235035 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235133), -(hBOOL(hAPP(_1235033, _1235133)))], (24112 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235035), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1235033, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (24133 ^ _782652) ^ [_1235559, _1235561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235561)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1235559)), hAPP(c_Int_Onat, _1235561)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235559), _1235561)))], (24143 ^ _782652) ^ [_1235738, _1235740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235740)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235738), _1235740)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1235738)), hAPP(c_Int_Onat, _1235740)))], (24153 ^ _782652) ^ [_1235917, _1235919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235919)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1235917)), hAPP(c_Int_Onat, _1235919)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235917), _1235919)))], (24163 ^ _782652) ^ [_1236096, _1236098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236096)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236096), _1236098)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1236096)), hAPP(c_Int_Onat, _1236098)))], (24169 ^ _782652) ^ [_1236219, _1236221] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1236219), _1236221) = 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)), _1236219)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1236221))))], (24171 ^ _782652) ^ [_1236265, _1236267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236265), _1236267)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1236267), _1236265)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1236267)), hAPP(c_Int_Onat, _1236265)))], (24181 ^ _782652) ^ [_1236450, _1236452, _1236454] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236450, tc_Nat_Onat), _1236452), _1236454) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236450, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1236450), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1236452)), _1236454)))], (24183 ^ _782652) ^ [_1236508, _1236510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236510)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1236508)), hAPP(c_Int_Onat, _1236510)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1236508, _1236510)))], (24193 ^ _782652) ^ [_1236681, _1236683, _1236685] : [class_Orderings_Olinorder(_1236681), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236681), _1236683), _1236685)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1236681, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1236681, _1236683), _1236685)), hAPP(c_SetInterval_Oord__class_OatLeast(_1236681), _1236685)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1236681), _1236683))], (24203 ^ _782652) ^ [_1236889, _1236891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236889), _1236891)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1236891, _1236889) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (24209 ^ _782652) ^ [_1236978, _1236980] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236978), _1236980))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1236980, _1236978) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1236980), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236980), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1236978)))], (24215 ^ _782652) ^ [_1237041, _1237043, _1237045] : [class_Orderings_Oorder(_1237041), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1237041, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1237041, _1237043), _1237045)), hAPP(c_SetInterval_Oord__class_OatLeast(_1237041), _1237045)) = c_Orderings_Obot__class_Obot(tc_fun(_1237041, tc_HOL_Obool)))], (24221 ^ _782652) ^ [_1237172, _1237174, _1237176, _1237178] : [class_Orderings_Olinorder(_1237172), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1237172, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1237172, _1237174, _1237176)), hAPP(c_SetInterval_Oord__class_OatLeast(_1237172), _1237178)) = c_SetInterval_Oord__class_OatLeastAtMost(_1237172, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1237172), _1237174), _1237178), _1237176))], (24227 ^ _782652) ^ [_1237315, _1237317, _1237319, _1237321] : [class_Orderings_Olinorder(_1237315), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1237315, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1237315), _1237317)), c_SetInterval_Oord__class_OatLeastAtMost(_1237315, _1237319, _1237321)) = c_SetInterval_Oord__class_OatLeastAtMost(_1237315, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1237315), _1237317), _1237319), _1237321))], (24233 ^ _782652) ^ [_1237458, _1237460, _1237462] : [class_Orderings_Oorder(_1237458), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1237458, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1237458, _1237460, _1237462)), hAPP(c_SetInterval_Oord__class_OatLeast(_1237458), _1237462)) = c_Orderings_Obot__class_Obot(tc_fun(_1237458, tc_HOL_Obool)))], (24239 ^ _782652) ^ [_1237585] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1237585)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1237585)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1237585), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (24241 ^ _782652) ^ [_1237641] : [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, _1237641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1237641)))], (24247 ^ _782652) ^ [_1237726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1237726)), -(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, _1237726))))], (24253 ^ _782652) ^ [_1237817, _1237819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237817)), 24256 ^ _782652 : [(24257 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1237817)), _1237819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237817), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237819))))], (24263 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237817), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1237817)), _1237819)))]]], (24269 ^ _782652) ^ [_1238076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238076)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1238076)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1238076)))], (24275 ^ _782652) ^ [_1238179, _1238181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1238179), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1238179), _1238181)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1238179))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1238181))))], (24281 ^ _782652) ^ [_1238320] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1238320) = 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), _1238320), c_Int_Onat)))))], (24283 ^ _782652) ^ [_1238361, _1238363] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1238361, _1238363)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1238363), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1238361), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (24285 ^ _782652) ^ [_1238408, _1238410] : [class_Orderings_Olinorder(_1238408), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1238408, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1238408), _1238410), c_Orderings_Obot__class_Obot(tc_fun(_1238408, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1238408), _1238410)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1238408), _1238410))], (24291 ^ _782652) ^ [_1238551, _1238553, _1238555] : [class_Orderings_Olinorder(_1238551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238551), _1238553), _1238555)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1238551, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1238551, _1238553, _1238555)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1238551), _1238555)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1238551), _1238553))], (24301 ^ _782652) ^ [_1238746, _1238748] : [-(c_Int_Onat__aux(_1238746, _1238748) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1238746)), _1238748))], (24303 ^ _782652) ^ [] : [-(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))))], (24305 ^ _782652) ^ [_1238801, _1238803, _1238805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238801)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1238803), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1238805)), 24312 ^ _782652 : [(24313 ^ _782652) ^ [_1239009] : [24315 ^ _782652 : [(24316 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24314 ^ [_1238801, _1238803, _1238805, _1239009]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1238801))))], (24319 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24317 ^ [_1238801, _1238803, _1238805, _1239009]), _1238805)))], (24321 ^ _782652) ^ [] : [-(_1239009 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24317 ^ [_1238801, _1238803, _1238805, _1239009]), 24314 ^ [_1238801, _1238803, _1238805, _1239009]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239009), _1238803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1239009), _1238801)), _1238803)))]]], (24329 ^ _782652) ^ [_1239285, _1239287, _1239289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239285)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1239287), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1239289)), 24336 ^ _782652 : [(24337 ^ _782652) ^ [_1239493] : [24339 ^ _782652 : [(24340 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24338 ^ [_1239285, _1239287, _1239289, _1239493]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1239285))))], (24343 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24341 ^ [_1239285, _1239287, _1239289, _1239493]), _1239289)))], (24345 ^ _782652) ^ [] : [-(_1239493 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24341 ^ [_1239285, _1239287, _1239289, _1239493]), 24338 ^ [_1239285, _1239287, _1239289, _1239493]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239287), _1239493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239287), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1239493), _1239285))))]]], (24353 ^ _782652) ^ [_1239769, _1239771, _1239773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239769)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1239771), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1239773)), 24363 ^ _782652 : [(24364 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24362 ^ [_1239769, _1239771, _1239773]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1239769))))], (24367 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24365 ^ [_1239769, _1239771, _1239773]), _1239773)))], (24369 ^ _782652) ^ [] : [-(_1239771 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24365 ^ [_1239769, _1239771, _1239773]), 24362 ^ [_1239769, _1239771, _1239773]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1239771), _1239769) = _1239771)], (24373 ^ _782652) ^ [_1240108, _1240110] : [c_Nat__Transfer_Onat__set(_1240108), c_Nat__Transfer_Onat__set(_1240110), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1240108), _1240110) = 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), _1240108)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1240110))))], (24383 ^ _782652) ^ [_1240275, _1240277] : [c_Nat__Transfer_Onat__set(_1240275), c_Nat__Transfer_Onat__set(_1240277), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1240275), _1240277) = 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), _1240275)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1240277))))], (24393 ^ _782652) ^ [_1240442, _1240444, _1240446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240442)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1240444), _1240446)), 24400 ^ _782652 : [(24401 ^ _782652) ^ [_1240632] : [24403 ^ _782652 : [(24404 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24402 ^ [_1240442, _1240444, _1240446, _1240632]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1240442))))], (24407 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24405 ^ [_1240442, _1240444, _1240446, _1240632]), _1240446)))], (24409 ^ _782652) ^ [] : [-(_1240632 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24405 ^ [_1240442, _1240444, _1240446, _1240632]), 24402 ^ [_1240442, _1240444, _1240446, _1240632]))]], -(_1240632 = _1240444), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1240632), _1240442) = _1240444]]], (24417 ^ _782652) ^ [_1240892, _1240894, _1240896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240892)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1240894), _1240896)), 24424 ^ _782652 : [(24425 ^ _782652) ^ [_1241082] : [24427 ^ _782652 : [(24428 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24426 ^ [_1240892, _1240894, _1240896, _1241082]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1240892))))], (24431 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24429 ^ [_1240892, _1240894, _1240896, _1241082]), _1240896)))], (24433 ^ _782652) ^ [] : [-(_1241082 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24429 ^ [_1240892, _1240894, _1240896, _1241082]), 24426 ^ [_1240892, _1240894, _1240896, _1241082]))]], -(_1241082 = _1240894), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1241082), _1240892) = _1240894]]], (24441 ^ _782652) ^ [_1241342, _1241344, _1241346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241342)), 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-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246622)))], (24774 ^ _782652) ^ [_1246695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246695)), -(c_Nat__Transfer_Ois__nat(_1246695))], (24780 ^ _782652) ^ [_1246774, _1246776] : [c_Nat__Transfer_Ois__nat(_1246774), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1246774, _1246776)))], (24786 ^ _782652) ^ [_1246855, _1246857] : [c_Nat__Transfer_Onat__set(_1246855), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1246857), _1246855)), -(c_Nat__Transfer_Ois__nat(_1246857))], (24796 ^ _782652) ^ [_1246990, _1246992] : [c_Nat__Transfer_Ois__nat(_1246990), c_Nat__Transfer_Ois__nat(_1246992), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1246990, _1246992) = 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, _1246990), hAPP(c_Int_Onat, _1246992))))], (24806 ^ _782652) ^ [_1247149, _1247151, _1247153] : [24808 ^ _782652 : [(24809 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1247149), 24807 ^ [_1247149, _1247151, _1247153]), _1247151)))], (24811 ^ _782652) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1247153, 24807 ^ [_1247149, _1247151, _1247153]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247149, tc_Int_Oint), _1247153), _1247151) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247149, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1247149), c_Int_Onat), _1247153)), _1247151)))], (24815 ^ _782652) ^ [_1247379, _1247381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247379)), 24824 ^ _782652 : [(24825 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1247381, 24820 ^ [_1247379, _1247381])))], (24827 ^ _782652) ^ [] : [hBOOL(hAPP(_1247381, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24820 ^ [_1247379, _1247381]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 24821 ^ [_1247379, _1247381]), _1247379))))]], 24828 ^ _782652 : [(24829 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1247381, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24820 ^ [_1247379, _1247381]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 24821 ^ [_1247379, _1247381]), _1247379)))))], (24831 ^ _782652) ^ [] : [hBOOL(hAPP(_1247381, 24820 ^ [_1247379, _1247381]))]], 24832 ^ _782652 : [(24833 ^ _782652) ^ [] : [24834 ^ _782652 : [(24835 ^ _782652) ^ [_1247811] : [hBOOL(hAPP(_1247381, _1247811))]], 24837 ^ _782652 : [(24838 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24836 ^ [_1247379, _1247381]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1247379))))], (24840 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1247381, 24836 ^ [_1247379, _1247381])))]]], (24842 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1247381, 24849 ^ [_1247379, _1247381]))), 24843 ^ _782652 : [(24844 ^ _782652) ^ [_1247926] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1247926), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1247379))), hBOOL(hAPP(_1247381, _1247926))]]]]], (24853 ^ _782652) ^ [_1248073, _1248075, _1248077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248073)), 24856 ^ _782652 : [(24857 ^ _782652) ^ [_1248207] : [24859 ^ _782652 : [(24860 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24858 ^ [_1248073, _1248075, _1248077, _1248207]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1248073))))], (24863 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24861 ^ [_1248073, _1248075, _1248077, _1248207]), _1248075)))], (24865 ^ _782652) ^ [] : [-(_1248207 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24861 ^ [_1248073, _1248075, _1248077, _1248207]), 24858 ^ [_1248073, _1248075, _1248077, _1248207]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248077), _1248207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248077), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1248207), _1248073))))]]], (24873 ^ _782652) ^ [_1248481, _1248483, _1248485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248481)), 24876 ^ _782652 : [(24877 ^ _782652) ^ [_1248615] : [24879 ^ _782652 : [(24880 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24878 ^ [_1248481, _1248483, _1248485, _1248615]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1248481))))], (24883 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24881 ^ [_1248481, _1248483, _1248485, _1248615]), _1248483)))], (24885 ^ _782652) ^ [] : [-(_1248615 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24881 ^ [_1248481, _1248483, _1248485, _1248615]), 24878 ^ [_1248481, _1248483, _1248485, _1248615]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248615), _1248485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1248615), _1248481)), _1248485)))]]], (24893 ^ _782652) ^ [_1248889, _1248891] : [class_Rings_Oring__1(_1248889), 24896 ^ _782652 : [(24897 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248891), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1248889), _1248891) = hAPP(c_Groups_Ouminus__class_Ouminus(_1248889), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1248889), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1248891)))))], (24903 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248891), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1248889), _1248891) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1248889), hAPP(c_Int_Onat, _1248891)))]]], (24909 ^ _782652) ^ [_1249151, _1249153, _1249155] : [class_Int_Oring__char__0(_1249151), 24912 ^ _782652 : [(24913 ^ _782652) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1249151), _1249153) = hAPP(c_Int_Oring__1__class_Oof__int(_1249151), _1249155), -(_1249153 = _1249155)], (24919 ^ _782652) ^ [] : [_1249153 = _1249155, -(hAPP(c_Int_Oring__1__class_Oof__int(_1249151), _1249153) = hAPP(c_Int_Oring__1__class_Oof__int(_1249151), _1249155))]]], (24925 ^ _782652) ^ [_1249392] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249392)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249392))], (24927 ^ _782652) ^ [_1249424, _1249426] : [class_Int_Oring__char__0(_1249424), 24930 ^ _782652 : [(24931 ^ _782652) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1249424), _1249426) = c_Groups_Ozero__class_Ozero(_1249424), -(_1249426 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24937 ^ _782652) ^ [] : [_1249426 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1249424), _1249426) = c_Groups_Ozero__class_Ozero(_1249424))]]], (24943 ^ _782652) ^ [_1249650, _1249652] : [class_Int_Oring__char__0(_1249650), 24946 ^ _782652 : [(24947 ^ _782652) ^ [] : [c_Groups_Ozero__class_Ozero(_1249650) = hAPP(c_Int_Oring__1__class_Oof__int(_1249650), _1249652), -(_1249652 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24953 ^ _782652) ^ [] : [_1249652 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1249650) = hAPP(c_Int_Oring__1__class_Oof__int(_1249650), _1249652))]]], (24959 ^ _782652) ^ [_1249876] : [class_Rings_Oring__1(_1249876), -(hAPP(c_Int_Oring__1__class_Oof__int(_1249876), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1249876))], (24965 ^ _782652) ^ [_1249963, _1249965, _1249967] : [class_Rings_Olinordered__idom(_1249963), 24968 ^ _782652 : [(24969 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249963), hAPP(c_Int_Oring__1__class_Oof__int(_1249963), _1249965)), hAPP(c_Int_Oring__1__class_Oof__int(_1249963), _1249967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249965), _1249967)))], (24975 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249965), _1249967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249963), hAPP(c_Int_Oring__1__class_Oof__int(_1249963), _1249965)), hAPP(c_Int_Oring__1__class_Oof__int(_1249963), _1249967))))]]], (24981 ^ _782652) ^ [_1250240, _1250242, _1250244] : [class_Rings_Olinordered__idom(_1250240), 24984 ^ _782652 : [(24985 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250240), hAPP(c_Int_Oring__1__class_Oof__int(_1250240), _1250242)), hAPP(c_Int_Oring__1__class_Oof__int(_1250240), _1250244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250242), _1250244)))], (24991 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250242), _1250244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250240), hAPP(c_Int_Oring__1__class_Oof__int(_1250240), _1250242)), hAPP(c_Int_Oring__1__class_Oof__int(_1250240), _1250244))))]]], (24997 ^ _782652) ^ [_1250517, _1250519, _1250521] : [class_Rings_Oring__1(_1250517), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250517), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1250519), _1250521)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1250517), hAPP(c_Int_Oring__1__class_Oof__int(_1250517), _1250519)), hAPP(c_Int_Oring__1__class_Oof__int(_1250517), _1250521)))], (25003 ^ _782652) ^ [_1250652, _1250654, _1250656] : [class_Rings_Oring__1(_1250652), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250652), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1250654), _1250656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250652), hAPP(c_Int_Oring__1__class_Oof__int(_1250652), _1250654)), hAPP(c_Int_Oring__1__class_Oof__int(_1250652), _1250656)))], (25009 ^ _782652) ^ [_1250787] : [class_Rings_Oring__1(_1250787), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250787), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1250787))], (25015 ^ _782652) ^ [_1250874, _1250876, _1250878] : [class_Rings_Oring__1(_1250874), -(hAPP(c_Int_Oring__1__class_Oof__int(_1250874), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1250876), _1250878)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1250874), hAPP(c_Int_Oring__1__class_Oof__int(_1250874), _1250876)), hAPP(c_Int_Oring__1__class_Oof__int(_1250874), _1250878)))], (25021 ^ _782652) ^ [_1251009, _1251011] : [class_Rings_Oring__1(_1251009), -(hAPP(c_Int_Oring__1__class_Oof__int(_1251009), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1251011)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1251009), _1251011))], (25027 ^ _782652) ^ [_1251110, _1251112] : [class_Rings_Oring__1(_1251110), -(hAPP(c_Int_Oring__1__class_Oof__int(_1251110), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1251112)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1251110), hAPP(c_Int_Oring__1__class_Oof__int(_1251110), _1251112)))], (25033 ^ _782652) ^ [_1251221, _1251223] : [class_Rings_Oring__1(_1251221), -(hBOOL(hAPP(hAPP(c_member(_1251221), hAPP(c_Int_Oring__1__class_Oof__int(_1251221), _1251223)), c_Int_Oring__1__class_OInts(_1251221))))], (25039 ^ _782652) ^ [_1251324, _1251326, _1251328, _1251330] : [class_Rings_Oring__1(_1251324), -(hAPP(c_Int_Oring__1__class_Oof__int(_1251324), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1251326, tc_Int_Oint), _1251328), _1251330)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1251326, _1251324), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1251324, _1251326), c_Int_Oring__1__class_Oof__int(_1251324)), _1251328)), _1251330))], (25045 ^ _782652) ^ [_1251473, _1251475] : [class_Rings_Olinordered__idom(_1251473), 25048 ^ _782652 : [(25049 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251473), hAPP(c_Int_Oring__1__class_Oof__int(_1251473), _1251475)), c_Groups_Ozero__class_Ozero(_1251473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251475), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25055 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251475), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251473), hAPP(c_Int_Oring__1__class_Oof__int(_1251473), _1251475)), c_Groups_Ozero__class_Ozero(_1251473))))]]], (25061 ^ _782652) ^ [_1251735, _1251737] : [class_Rings_Olinordered__idom(_1251735), 25064 ^ _782652 : [(25065 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251735), c_Groups_Ozero__class_Ozero(_1251735)), hAPP(c_Int_Oring__1__class_Oof__int(_1251735), _1251737))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251737)))], (25071 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251735), c_Groups_Ozero__class_Ozero(_1251735)), hAPP(c_Int_Oring__1__class_Oof__int(_1251735), _1251737))))]]], (25077 ^ _782652) ^ [_1251988, _1251990] : [class_Rings_Olinordered__idom(_1251988), 25080 ^ _782652 : [(25081 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251988), hAPP(c_Int_Oring__1__class_Oof__int(_1251988), _1251990)), c_Groups_Ozero__class_Ozero(_1251988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251990), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25087 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251990), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251988), hAPP(c_Int_Oring__1__class_Oof__int(_1251988), _1251990)), c_Groups_Ozero__class_Ozero(_1251988))))]]], (25093 ^ _782652) ^ [_1252250, _1252252] : [class_Rings_Olinordered__idom(_1252250), 25096 ^ _782652 : [(25097 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252250), c_Groups_Ozero__class_Ozero(_1252250)), hAPP(c_Int_Oring__1__class_Oof__int(_1252250), _1252252))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252252)))], (25103 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252250), c_Groups_Ozero__class_Ozero(_1252250)), hAPP(c_Int_Oring__1__class_Oof__int(_1252250), _1252252))))]]], (25109 ^ _782652) ^ [_1252503, _1252505] : [class_Rings_Oring__1(_1252503), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252505)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1252503), hAPP(c_Int_Onat, _1252505)) = hAPP(c_Int_Oring__1__class_Oof__int(_1252503), _1252505))], (25119 ^ _782652) ^ [_1252660] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1252660) = 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), _1252660))))], (25121 ^ _782652) ^ [_1252696, _1252698, _1252700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252696)), 25127 ^ _782652 : [(25128 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1252698, 25126 ^ [_1252696, _1252698, _1252700])))], (25130 ^ _782652) ^ [] : [hBOOL(hAPP(_1252698, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 25126 ^ [_1252696, _1252698, _1252700]), _1252696)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252700)), 25135 ^ _782652 : [(25136 ^ _782652) ^ [_1252985] : [hBOOL(hAPP(_1252698, _1252985)), -(hBOOL(hAPP(_1252698, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1252985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1252700), _1252696)))))]]], (25142 ^ _782652) ^ [_1253108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253108), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1253108 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 25145 ^ [_1253108]))))], (25149 ^ _782652) ^ [_1253221, _1253223, _1253225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253221)), 25155 ^ _782652 : [(25156 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1253223, 25154 ^ [_1253221, _1253223, _1253225])))], (25158 ^ _782652) ^ [] : [hBOOL(hAPP(_1253223, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 25154 ^ [_1253221, _1253223, _1253225]), _1253221)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253225)), 25163 ^ _782652 : [(25164 ^ _782652) ^ [_1253510] : [hBOOL(hAPP(_1253223, _1253510)), -(hBOOL(hAPP(_1253223, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1253510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1253225), _1253221)))))]]], (25170 ^ _782652) ^ [_1253632, _1253634] : [-(hBOOL(hAPP(_1253632, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1253632, _1253634)), 25178 ^ _782652 : [(25179 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25177 ^ [_1253632, _1253634]), _1253634)))], (25187 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1253632, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 25177 ^ [_1253632, _1253634]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (25181 ^ _782652) ^ [_1253870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253870), 25177 ^ [_1253632, _1253634])), hBOOL(hAPP(_1253632, _1253870))]]], (25189 ^ _782652) ^ [_1254022] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1254022))))], (25191 ^ _782652) ^ [_1254050, _1254052, _1254054] : [class_Orderings_Olinorder(_1254050), 25194 ^ _782652 : [(25195 ^ _782652) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1254050), _1254052) = hAPP(c_SetInterval_Oord__class_OatMost(_1254050), _1254054), -(_1254052 = _1254054)], (25201 ^ _782652) ^ [] : [_1254052 = _1254054, -(hAPP(c_SetInterval_Oord__class_OatMost(_1254050), _1254052) = hAPP(c_SetInterval_Oord__class_OatMost(_1254050), _1254054))]]], (25207 ^ _782652) ^ [_1254291] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1254291) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1254291))], (25209 ^ _782652) ^ [_1254321] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1254321)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1254321))], (25211 ^ _782652) ^ [_1254353] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1254353)) = hAPP(c_Nat_OSuc, _1254353))], (25213 ^ _782652) ^ [_1254385] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1254385)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1254385)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1254385)))], (25215 ^ _782652) ^ [_1254426, _1254428, _1254430] : [class_Orderings_Oord(_1254426), 25218 ^ _782652 : [(25219 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254426), _1254428), hAPP(c_SetInterval_Oord__class_OatMost(_1254426), _1254430))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254426), _1254428), _1254430)))], (25225 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254426), _1254428), _1254430)), -(hBOOL(hAPP(hAPP(c_member(_1254426), _1254428), hAPP(c_SetInterval_Oord__class_OatMost(_1254426), _1254430))))]]], (25231 ^ _782652) ^ [_1254694, _1254696, _1254698] : [class_Orderings_Oorder(_1254694), 25234 ^ _782652 : [(25235 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254694, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1254694), _1254696)), hAPP(c_SetInterval_Oord__class_OatMost(_1254694), _1254698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254694), _1254696), _1254698)))], (25241 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254694), _1254696), _1254698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1254694, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1254694), _1254696)), hAPP(c_SetInterval_Oord__class_OatMost(_1254694), _1254698))))]]], (25247 ^ _782652) ^ [_1254986, _1254988] : [class_Orderings_Olinorder(_1254986), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1254986, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1254986), _1254988)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1254986), _1254988))], (25253 ^ _782652) ^ [_1255097, _1255099] : [class_Orderings_Olinorder(_1255097), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1255097, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1255097), _1255099)) = hAPP(c_SetInterval_Oord__class_OatMost(_1255097), _1255099))], (25259 ^ _782652) ^ [_1255208, _1255210, _1255212] : [class_Groups_Ocomm__monoid__add(_1255208), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1255208), _1255210), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1255212))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255208), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1255208), _1255210), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1255212))), hAPP(_1255210, hAPP(c_Nat_OSuc, _1255212))))], (25265 ^ _782652) ^ [] : [-(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))))], (25267 ^ _782652) ^ [_1255385, _1255387, _1255389, _1255391] : [class_Orderings_Olinorder(_1255385), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1255385, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1255385), _1255387)), c_SetInterval_Oord__class_OatLeastAtMost(_1255385, _1255389, _1255391)) = c_SetInterval_Oord__class_OatLeastAtMost(_1255385, _1255389, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1255385), _1255387), _1255391)))], (25273 ^ _782652) ^ [_1255528, _1255530, _1255532, _1255534] : [class_Orderings_Olinorder(_1255528), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1255528, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1255528, _1255530, _1255532)), hAPP(c_SetInterval_Oord__class_OatMost(_1255528), _1255534)) = c_SetInterval_Oord__class_OatLeastAtMost(_1255528, _1255530, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1255528), _1255532), _1255534)))], (25279 ^ _782652) ^ [_1255671, _1255673, _1255675] : [class_Orderings_Olinorder(_1255671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1255671), _1255673), _1255675)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255671, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1255671), _1255673)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1255671, _1255673, _1255675)) = hAPP(c_SetInterval_Oord__class_OatMost(_1255671), _1255675))], (25289 ^ _782652) ^ [_1255866, _1255868, _1255870] : [class_Orderings_Oorder(_1255866), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1255866, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1255866), _1255868)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1255866, _1255868, _1255870)) = c_Orderings_Obot__class_Obot(tc_fun(_1255866, tc_HOL_Obool)))], (25295 ^ _782652) ^ [_1255993, _1255995, _1255997] : [class_Orderings_Oorder(_1255993), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1255993, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1255993), _1255995)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1255993, _1255995, _1255997)) = c_Orderings_Obot__class_Obot(tc_fun(_1255993, tc_HOL_Obool)))], (25301 ^ _782652) ^ [_1256120, _1256122] : [class_Groups_Oordered__ab__group__add(_1256120), -(hAPP(c_Set_Oimage(_1256120, _1256120, c_Groups_Ouminus__class_Ouminus(_1256120)), hAPP(c_SetInterval_Oord__class_OatLeast(_1256120), _1256122)) = hAPP(c_SetInterval_Oord__class_OatMost(_1256120), hAPP(c_Groups_Ouminus__class_Ouminus(_1256120), _1256122)))], (25307 ^ _782652) ^ [_1256243, _1256245] : [class_Groups_Oordered__ab__group__add(_1256243), -(hAPP(c_Set_Oimage(_1256243, _1256243, c_Groups_Ouminus__class_Ouminus(_1256243)), hAPP(c_SetInterval_Oord__class_OatMost(_1256243), _1256245)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1256243), hAPP(c_Groups_Ouminus__class_Ouminus(_1256243), _1256245)))], (25313 ^ _782652) ^ [_1256366, _1256368] : [class_Orderings_Olinorder(_1256366), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256366, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1256366), _1256368)), hAPP(hAPP(c_Set_Oinsert(_1256366), _1256368), c_Orderings_Obot__class_Obot(tc_fun(_1256366, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1256366), _1256368))], (25319 ^ _782652) ^ [_1256509, _1256511, _1256513] : [class_Orderings_Olinorder(_1256509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256509), _1256511), _1256513)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256509, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1256509), _1256511)), c_SetInterval_Oord__class_OatLeastAtMost(_1256509, _1256511, _1256513)) = hAPP(c_SetInterval_Oord__class_OatMost(_1256509), _1256513))], (25329 ^ _782652) ^ [_1256704, _1256706] : [class_Orderings_Oorder(_1256704), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1256704, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1256704), _1256706)), hAPP(c_SetInterval_Oord__class_OatLeast(_1256704), _1256706)) = hAPP(hAPP(c_Set_Oinsert(_1256704), _1256706), c_Orderings_Obot__class_Obot(tc_fun(_1256704, tc_HOL_Obool))))], (25335 ^ _782652) ^ [_1256847, _1256849, _1256851] : [class_Orderings_Olinorder(_1256847), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256847), _1256849), _1256851)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1256847, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1256847), _1256849)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1256847, _1256849, _1256851)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1256847), _1256851))], (25345 ^ _782652) ^ [_1257042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257042)), 25349 ^ _782652 : [(25350 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25348 ^ [_1257042])))], (25352 ^ _782652) ^ [] : [-(_1257042 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 25348 ^ [_1257042]))]]], (25354 ^ _782652) ^ [_1257172, _1257174, _1257176, _1257178, _1257180] : [class_Groups_Ocomm__monoid__add(_1257172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257174), _1257176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257174, tc_HOL_Obool)), _1257178), _1257176)), 25368 ^ _782652 : [(25369 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1257174), 25367 ^ [_1257172, _1257174, _1257176, _1257178, _1257180]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1257174, tc_HOL_Obool)), _1257176), _1257178))))], (25371 ^ _782652) ^ [] : [hAPP(_1257180, 25367 ^ [_1257172, _1257174, _1257176, _1257178, _1257180]) = c_Groups_Ozero__class_Ozero(_1257172)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1257174, _1257172), _1257180), _1257176) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1257174, _1257172), _1257180), _1257178))], (25375 ^ _782652) ^ [_1257623, _1257625, _1257627, _1257629, _1257631] : [class_Groups_Ocomm__monoid__add(_1257623), hBOOL(hAPP(c_Finite__Set_Ofinite(_1257625), _1257627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257625, tc_HOL_Obool)), _1257629), _1257627)), 25389 ^ _782652 : [(25390 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1257625), 25388 ^ [_1257623, _1257625, _1257627, _1257629, _1257631]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1257625, tc_HOL_Obool)), _1257627), _1257629))))], (25392 ^ _782652) ^ [] : [hAPP(_1257631, 25388 ^ [_1257623, _1257625, _1257627, _1257629, _1257631]) = c_Groups_Ozero__class_Ozero(_1257623)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1257625, _1257623), _1257631), _1257629) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1257625, _1257623), _1257631), _1257627))], (25396 ^ _782652) ^ [_1258074, _1258076] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1258074)), _1258076) = 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), _1258074)), _1258076))], (25398 ^ _782652) ^ [_1258119, _1258121] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1258119), hAPP(c_Nat_OSuc, _1258121)) = 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)), _1258121)), _1258119))], (25400 ^ _782652) ^ [_1258164, _1258166, _1258168] : [-(c_Nat_Onat_Onat__case(_1258164, _1258166, _1258168, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1258166)], (25402 ^ _782652) ^ [_1258196, _1258198, _1258200, _1258202] : [-(c_Nat_Onat_Onat__case(_1258196, _1258198, _1258200, hAPP(c_Nat_OSuc, _1258202)) = hAPP(_1258200, _1258202))], (25404 ^ _782652) ^ [_1258236, _1258238] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1258236)), _1258238) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1258236), 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), _1258236)), _1258238))], (25406 ^ _782652) ^ [_1258284, _1258286] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1258284), hAPP(c_Nat_OSuc, _1258286)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1258286), 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)), _1258286)), _1258284))], (25408 ^ _782652) ^ [_1258332, _1258334] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1258332), hAPP(c_Nat_OSuc, _1258334)) = 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), _1258332), _1258334)))], (25410 ^ _782652) ^ [_1258377, _1258379] : [class_Rings_Olinordered__idom(_1258377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258377), _1258379), c_Groups_Ozero__class_Ozero(_1258377))), -(c_Groups_Osgn__class_Osgn(_1258377, _1258379) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258377), c_Groups_Oone__class_Oone(_1258377)))], (25420 ^ _782652) ^ [_1258542, _1258544] : [class_Rings_Olinordered__idom(_1258542), 25423 ^ _782652 : [(25424 ^ _782652) ^ [] : [c_Groups_Osgn__class_Osgn(_1258542, _1258544) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258542), c_Groups_Oone__class_Oone(_1258542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258542), _1258544), c_Groups_Ozero__class_Ozero(_1258542))))], (25430 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258542), _1258544), c_Groups_Ozero__class_Ozero(_1258542))), -(c_Groups_Osgn__class_Osgn(_1258542, _1258544) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258542), c_Groups_Oone__class_Oone(_1258542)))]]], (25436 ^ _782652) ^ [_1258804, _1258806] : [class_Groups_Osgn__if(_1258804), 25439 ^ _782652 : [(25440 ^ _782652) ^ [] : [_1258806 = c_Groups_Ozero__class_Ozero(_1258804), -(c_Groups_Osgn__class_Osgn(_1258804, _1258806) = c_Groups_Ozero__class_Ozero(_1258804))], (25446 ^ _782652) ^ [] : [-(_1258806 = c_Groups_Ozero__class_Ozero(_1258804)), 25449 ^ _782652 : [(25450 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258804), c_Groups_Ozero__class_Ozero(_1258804)), _1258806)), -(c_Groups_Osgn__class_Osgn(_1258804, _1258806) = c_Groups_Oone__class_Oone(_1258804))], (25456 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258804), c_Groups_Ozero__class_Ozero(_1258804)), _1258806))), -(c_Groups_Osgn__class_Osgn(_1258804, _1258806) = hAPP(c_Groups_Ouminus__class_Ouminus(_1258804), c_Groups_Oone__class_Oone(_1258804)))]]]]], (25462 ^ _782652) ^ [_1259201, _1259203, _1259205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1259203), 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), _1259203), _1259205))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1259201))), _1259205)))], (25468 ^ _782652) ^ [_1259348, _1259350, _1259352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1259350), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1259352), 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), _1259352), _1259350))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1259348)))))], (25474 ^ _782652) ^ [_1259495, _1259497, _1259499, _1259501] : [class_Groups_Oordered__ab__group__add__abs(_1259495), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259495), hAPP(c_Groups_Oabs__class_Oabs(_1259495), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1259497, _1259495), _1259499), _1259501))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1259497, _1259495), hAPP(hAPP(c_COMBB(_1259495, _1259495, _1259497), c_Groups_Oabs__class_Oabs(_1259495)), _1259499)), _1259501))))], (25480 ^ _782652) ^ [_1259658, _1259660, _1259662, _1259664] : [class_Groups_Oordered__ab__group__add__abs(_1259658), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259658), c_Groups_Ozero__class_Ozero(_1259658)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1259660, _1259658), hAPP(hAPP(c_COMBB(_1259658, _1259658, _1259660), c_Groups_Oabs__class_Oabs(_1259658)), _1259662)), _1259664))))], (25486 ^ _782652) ^ [_1259797, _1259799, _1259801] : [class_Groups_Oordered__ab__group__add__abs(_1259797), -(hAPP(c_Groups_Oabs__class_Oabs(_1259797), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1259797), _1259799), _1259801)) = hAPP(c_Groups_Oabs__class_Oabs(_1259797), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1259797), _1259801), _1259799)))], (25492 ^ _782652) ^ [_1259926, _1259928] : [class_Rings_Olinordered__idom(_1259926), -(hAPP(c_Groups_Oabs__class_Oabs(_1259926), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1259926), _1259928)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1259926), _1259928))], (25498 ^ _782652) ^ [_1260031] : [class_Rings_Olinordered__idom(_1260031), -(hAPP(c_Groups_Oabs__class_Oabs(_1260031), c_Groups_Oone__class_Oone(_1260031)) = c_Groups_Oone__class_Oone(_1260031))], (25504 ^ _782652) ^ [_1260122, _1260124] : [class_Groups_Oordered__ab__group__add__abs(_1260122), -(hAPP(c_Groups_Oabs__class_Oabs(_1260122), hAPP(c_Groups_Ouminus__class_Ouminus(_1260122), _1260124)) = hAPP(c_Groups_Oabs__class_Oabs(_1260122), _1260124))], (25510 ^ _782652) ^ [_1260227, _1260229] : [class_Rings_Olinordered__idom(_1260227), -(hAPP(c_Groups_Oabs__class_Oabs(_1260227), _1260229) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1260227), _1260229), c_Groups_Osgn__class_Osgn(_1260227, _1260229)))], (25516 ^ _782652) ^ [_1260334, _1260336] : [class_Rings_Olinordered__idom(_1260334), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1260334), c_Groups_Osgn__class_Osgn(_1260334, _1260336)), hAPP(c_Groups_Oabs__class_Oabs(_1260334), _1260336)) = _1260336)], (25522 ^ _782652) ^ [_1260441, _1260443] : [class_Rings_Olinordered__idom(_1260441), -(c_Groups_Osgn__class_Osgn(_1260441, c_Groups_Osgn__class_Osgn(_1260441, _1260443)) = c_Groups_Osgn__class_Osgn(_1260441, _1260443))], (25528 ^ _782652) ^ [_1260534, _1260536] : [class_Groups_Oordered__ab__group__add__abs(_1260534), -(hAPP(c_Groups_Oabs__class_Oabs(_1260534), hAPP(c_Groups_Oabs__class_Oabs(_1260534), _1260536)) = hAPP(c_Groups_Oabs__class_Oabs(_1260534), _1260536))], (25534 ^ _782652) ^ [_1260639, _1260641] : [class_Rings_Olinordered__idom(_1260639), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1260639), hAPP(c_Groups_Oabs__class_Oabs(_1260639), _1260641)), hAPP(c_Groups_Oabs__class_Oabs(_1260639), _1260641)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1260639), _1260641), _1260641))], (25540 ^ _782652) ^ [_1260766, _1260768, _1260770] : [class_Rings_Olinordered__idom(_1260766), -(hAPP(c_Groups_Oabs__class_Oabs(_1260766), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1260766), _1260768), _1260770)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1260766), hAPP(c_Groups_Oabs__class_Oabs(_1260766), _1260768)), hAPP(c_Groups_Oabs__class_Oabs(_1260766), _1260770)))], (25546 ^ _782652) ^ [_1260905, _1260907, _1260909] : [class_Groups_Oordered__ab__group__add__abs(_1260905), -(hAPP(c_Groups_Oabs__class_Oabs(_1260905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1260905), hAPP(c_Groups_Oabs__class_Oabs(_1260905), _1260907)), hAPP(c_Groups_Oabs__class_Oabs(_1260905), _1260909))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1260905), hAPP(c_Groups_Oabs__class_Oabs(_1260905), _1260907)), hAPP(c_Groups_Oabs__class_Oabs(_1260905), _1260909)))], (25552 ^ _782652) ^ [_1261064, _1261066] : [class_Groups_Oordered__ab__group__add__abs(_1261064), 25555 ^ _782652 : [(25556 ^ _782652) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1261064), _1261066) = c_Groups_Ozero__class_Ozero(_1261064), -(_1261066 = c_Groups_Ozero__class_Ozero(_1261064))], (25562 ^ _782652) ^ [] : [_1261066 = c_Groups_Ozero__class_Ozero(_1261064), -(hAPP(c_Groups_Oabs__class_Oabs(_1261064), _1261066) = c_Groups_Ozero__class_Ozero(_1261064))]]], (25568 ^ _782652) ^ [_1261296] : [class_Groups_Oordered__ab__group__add__abs(_1261296), -(hAPP(c_Groups_Oabs__class_Oabs(_1261296), c_Groups_Ozero__class_Ozero(_1261296)) = c_Groups_Ozero__class_Ozero(_1261296))], (25574 ^ _782652) ^ [_1261387, _1261389, _1261391] : [class_Groups_Oordered__ab__group__add__abs(_1261387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261387), hAPP(c_Groups_Oabs__class_Oabs(_1261387), _1261389)), _1261391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261387), _1261389), _1261391)))], (25584 ^ _782652) ^ [_1261556, _1261558] : [class_Groups_Oordered__ab__group__add__abs(_1261556), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261556), _1261558), hAPP(c_Groups_Oabs__class_Oabs(_1261556), _1261558))))], (25590 ^ _782652) ^ [_1261655] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1261655)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1261655))], (25592 ^ _782652) ^ [_1261687, _1261689, _1261691, _1261693] : [class_Groups_Oordered__ab__group__add__abs(_1261687), -(hAPP(c_Groups_Oabs__class_Oabs(_1261687), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1261689, _1261687), hAPP(hAPP(c_COMBB(_1261687, _1261687, _1261689), c_Groups_Oabs__class_Oabs(_1261687)), _1261691)), _1261693)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1261689, _1261687), hAPP(hAPP(c_COMBB(_1261687, _1261687, _1261689), c_Groups_Oabs__class_Oabs(_1261687)), _1261691)), _1261693))], (25598 ^ _782652) ^ [_1261860, _1261862] : [class_Rings_Olinordered__idom(_1261860), 25601 ^ _782652 : [(25602 ^ _782652) ^ [] : [c_Groups_Osgn__class_Osgn(_1261860, _1261862) = c_Groups_Ozero__class_Ozero(_1261860), -(_1261862 = c_Groups_Ozero__class_Ozero(_1261860))], (25608 ^ _782652) ^ [] : [_1261862 = c_Groups_Ozero__class_Ozero(_1261860), -(c_Groups_Osgn__class_Osgn(_1261860, _1261862) = c_Groups_Ozero__class_Ozero(_1261860))]]], (25614 ^ _782652) ^ [_1262086] : [class_Groups_Osgn__if(_1262086), -(c_Groups_Osgn__class_Osgn(_1262086, c_Groups_Ozero__class_Ozero(_1262086)) = c_Groups_Ozero__class_Ozero(_1262086))], (25620 ^ _782652) ^ [_1262173, _1262175, _1262177] : [class_Rings_Olinordered__idom(_1262173), -(c_Groups_Osgn__class_Osgn(_1262173, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262173), _1262175), _1262177)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262173), c_Groups_Osgn__class_Osgn(_1262173, _1262175)), c_Groups_Osgn__class_Osgn(_1262173, _1262177)))], (25626 ^ _782652) ^ [_1262300, _1262302] : [class_Groups_Oordered__ab__group__add__abs(_1262300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262300), c_Groups_Ozero__class_Ozero(_1262300)), _1262302)), -(hAPP(c_Groups_Oabs__class_Oabs(_1262300), _1262302) = _1262302)], (25636 ^ _782652) ^ [_1262455, _1262457] : [class_Groups_Oordered__ab__group__add__abs(_1262455), 25639 ^ _782652 : [(25640 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262455), hAPP(c_Groups_Oabs__class_Oabs(_1262455), _1262457)), c_Groups_Ozero__class_Ozero(_1262455))), -(_1262457 = c_Groups_Ozero__class_Ozero(_1262455))], (25646 ^ _782652) ^ [] : [_1262457 = c_Groups_Ozero__class_Ozero(_1262455), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262455), hAPP(c_Groups_Oabs__class_Oabs(_1262455), _1262457)), c_Groups_Ozero__class_Ozero(_1262455))))]]], (25652 ^ _782652) ^ [_1262708, _1262710] : [class_Groups_Oordered__ab__group__add__abs(_1262708), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262708), c_Groups_Ozero__class_Ozero(_1262708)), hAPP(c_Groups_Oabs__class_Oabs(_1262708), _1262710))))], (25658 ^ _782652) ^ [_1262811, _1262813] : [class_Groups_Oordered__ab__group__add__abs(_1262811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262811), hAPP(c_Groups_Oabs__class_Oabs(_1262811), _1262813)), c_Groups_Ozero__class_Ozero(_1262811)))], (25664 ^ _782652) ^ [_1262915, _1262917] : [class_Groups_Oordered__ab__group__add__abs(_1262915), 25667 ^ _782652 : [(25668 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262915), c_Groups_Ozero__class_Ozero(_1262915)), hAPP(c_Groups_Oabs__class_Oabs(_1262915), _1262917))), _1262917 = c_Groups_Ozero__class_Ozero(_1262915)], (25674 ^ _782652) ^ [] : [-(_1262917 = c_Groups_Ozero__class_Ozero(_1262915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262915), c_Groups_Ozero__class_Ozero(_1262915)), hAPP(c_Groups_Oabs__class_Oabs(_1262915), _1262917))))]]], (25680 ^ _782652) ^ [_1263130, _1263132] : [class_Groups_Oordered__ab__group__add__abs(_1263130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263130), c_Groups_Ozero__class_Ozero(_1263130)), _1263132)), -(hAPP(c_Groups_Oabs__class_Oabs(_1263130), _1263132) = _1263132)], (25690 ^ _782652) ^ [_1263285, _1263287, _1263289] : [class_Groups_Oordered__ab__group__add__abs(_1263285), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263285), hAPP(c_Groups_Oabs__class_Oabs(_1263285), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1263285), _1263287), _1263289))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1263285), hAPP(c_Groups_Oabs__class_Oabs(_1263285), _1263287)), hAPP(c_Groups_Oabs__class_Oabs(_1263285), _1263289)))))], (25696 ^ _782652) ^ [_1263438, _1263440, _1263442, _1263444, _1263446] : [class_Rings_Olinordered__idom(_1263438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263438), hAPP(c_Groups_Oabs__class_Oabs(_1263438), _1263440)), _1263442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263438), hAPP(c_Groups_Oabs__class_Oabs(_1263438), _1263444)), _1263446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263438), hAPP(c_Groups_Oabs__class_Oabs(_1263438), _1263440)), hAPP(c_Groups_Oabs__class_Oabs(_1263438), _1263444))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263438), _1263442), _1263446))))], (25710 ^ _782652) ^ [_1263749, _1263751, _1263753] : [class_Groups_Oordered__ab__group__add__abs(_1263749), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263749), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1263749), hAPP(c_Groups_Oabs__class_Oabs(_1263749), _1263751)), hAPP(c_Groups_Oabs__class_Oabs(_1263749), _1263753))), hAPP(c_Groups_Oabs__class_Oabs(_1263749), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1263749), _1263753), _1263751)))))], (25716 ^ _782652) ^ [_1263902, _1263904, _1263906] : [class_Groups_Oordered__ab__group__add__abs(_1263902), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263902), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1263902), hAPP(c_Groups_Oabs__class_Oabs(_1263902), _1263904)), hAPP(c_Groups_Oabs__class_Oabs(_1263902), _1263906))), hAPP(c_Groups_Oabs__class_Oabs(_1263902), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1263902), _1263904), _1263906)))))], (25722 ^ _782652) ^ [_1264055, _1264057, _1264059] : [class_Groups_Oordered__ab__group__add__abs(_1264055), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264055), hAPP(c_Groups_Oabs__class_Oabs(_1264055), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1264055), hAPP(c_Groups_Oabs__class_Oabs(_1264055), _1264057)), hAPP(c_Groups_Oabs__class_Oabs(_1264055), _1264059)))), hAPP(c_Groups_Oabs__class_Oabs(_1264055), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1264055), _1264057), _1264059)))))], (25728 ^ _782652) ^ [_1264218, _1264220, _1264222] : [class_Groups_Oordered__ab__group__add__abs(_1264218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264218), hAPP(c_Groups_Oabs__class_Oabs(_1264218), _1264220)), _1264222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264218), hAPP(c_Groups_Ouminus__class_Ouminus(_1264218), _1264220)), _1264222)))], (25738 ^ _782652) ^ [_1264397, _1264399, _1264401] : [class_Groups_Oordered__ab__group__add__abs(_1264397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264397), _1264399), _1264401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264397), hAPP(c_Groups_Ouminus__class_Ouminus(_1264397), _1264399)), _1264401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264397), hAPP(c_Groups_Oabs__class_Oabs(_1264397), _1264399)), _1264401)))], (25752 ^ _782652) ^ [_1264644, _1264646, _1264648] : [class_Groups_Oordered__ab__group__add__abs(_1264644), 25755 ^ _782652 : [(25756 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264644), hAPP(c_Groups_Oabs__class_Oabs(_1264644), _1264646)), _1264648)), 25759 ^ _782652 : [(25760 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264644), _1264646), _1264648)))], (25762 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264644), hAPP(c_Groups_Ouminus__class_Ouminus(_1264644), _1264646)), _1264648)))]]], (25764 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264644), hAPP(c_Groups_Oabs__class_Oabs(_1264644), _1264646)), _1264648))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264644), _1264646), _1264648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264644), hAPP(c_Groups_Ouminus__class_Ouminus(_1264644), _1264646)), _1264648))]]], (25774 ^ _782652) ^ [_1265022, _1265024] : [class_Groups_Oordered__ab__group__add__abs(_1265022), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265022), hAPP(c_Groups_Ouminus__class_Ouminus(_1265022), _1265024)), hAPP(c_Groups_Oabs__class_Oabs(_1265022), _1265024))))], (25780 ^ _782652) ^ [_1265131, _1265133, _1265135] : [class_Rings_Olinordered__idom(_1265131), 25783 ^ _782652 : [(25784 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265131), hAPP(c_Groups_Oabs__class_Oabs(_1265131), _1265133)), _1265135)), 25787 ^ _782652 : [(25788 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265131), _1265133), _1265135)))], (25790 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265131), hAPP(c_Groups_Ouminus__class_Ouminus(_1265131), _1265133)), _1265135)))]]], (25792 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265131), hAPP(c_Groups_Oabs__class_Oabs(_1265131), _1265133)), _1265135))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265131), _1265133), _1265135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265131), hAPP(c_Groups_Ouminus__class_Ouminus(_1265131), _1265133)), _1265135))]]], (25802 ^ _782652) ^ [_1265509, _1265511] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1265509), _1265511)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1265509) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25808 ^ _782652) ^ [_1265610, _1265612, _1265614] : [class_Rings_Olinordered__idom(_1265610), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265610), c_Groups_Ozero__class_Ozero(_1265610)), _1265612)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265610), hAPP(c_Groups_Oabs__class_Oabs(_1265610), _1265614)), _1265612) = hAPP(c_Groups_Oabs__class_Oabs(_1265610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265610), _1265614), _1265612)))], (25818 ^ _782652) ^ [_1265811, _1265813, _1265815] : [class_Rings_Oordered__ring__abs(_1265811), -(hAPP(c_Groups_Oabs__class_Oabs(_1265811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265811), _1265813), _1265815)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265811), hAPP(c_Groups_Oabs__class_Oabs(_1265811), _1265813)), hAPP(c_Groups_Oabs__class_Oabs(_1265811), _1265815))), 25825 ^ _782652 : [(25826 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265811), c_Groups_Ozero__class_Ozero(_1265811)), _1265813))], (25828 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265811), _1265813), c_Groups_Ozero__class_Ozero(_1265811)))]], 25829 ^ _782652 : [(25830 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265811), c_Groups_Ozero__class_Ozero(_1265811)), _1265815))], (25832 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265811), _1265815), c_Groups_Ozero__class_Ozero(_1265811)))]]], (25836 ^ _782652) ^ [_1266206, _1266208, _1266210, _1266212, _1266214] : [class_Groups_Oordered__ab__group__add__abs(_1266206), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266206), hAPP(c_Groups_Oabs__class_Oabs(_1266206), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266206), _1266208), _1266210)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266206), _1266212), _1266214)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266206), hAPP(c_Groups_Oabs__class_Oabs(_1266206), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266206), _1266208), _1266212))), hAPP(c_Groups_Oabs__class_Oabs(_1266206), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266206), _1266210), _1266214))))))], (25842 ^ _782652) ^ [_1266427, _1266429, _1266431] : [class_Groups_Oordered__ab__group__add__abs(_1266427), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266427), hAPP(c_Groups_Oabs__class_Oabs(_1266427), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1266427), _1266429), _1266431))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266427), hAPP(c_Groups_Oabs__class_Oabs(_1266427), _1266429)), hAPP(c_Groups_Oabs__class_Oabs(_1266427), _1266431)))))], (25848 ^ _782652) ^ [_1266580, _1266582] : [class_Groups_Oordered__ab__group__add__abs(_1266580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266580), _1266582), c_Groups_Ozero__class_Ozero(_1266580))), -(hAPP(c_Groups_Oabs__class_Oabs(_1266580), _1266582) = hAPP(c_Groups_Ouminus__class_Ouminus(_1266580), _1266582))], (25858 ^ _782652) ^ [_1266745, _1266747] : [class_Groups_Oordered__ab__group__add__abs(_1266745), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266745), hAPP(c_Groups_Ouminus__class_Ouminus(_1266745), hAPP(c_Groups_Oabs__class_Oabs(_1266745), _1266747))), c_Groups_Ozero__class_Ozero(_1266745))))], (25864 ^ _782652) ^ [_1266858, _1266860] : [class_Groups_Oabs__if(_1266858), 25867 ^ _782652 : [(25868 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266858), _1266860), c_Groups_Ozero__class_Ozero(_1266858))), -(hAPP(c_Groups_Oabs__class_Oabs(_1266858), _1266860) = hAPP(c_Groups_Ouminus__class_Ouminus(_1266858), _1266860))], (25874 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1266858), _1266860), c_Groups_Ozero__class_Ozero(_1266858)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1266858), _1266860) = _1266860)]]], (25880 ^ _782652) ^ [_1267098, _1267100] : [class_Groups_Oordered__ab__group__add__abs(_1267098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267098), _1267100), c_Groups_Ozero__class_Ozero(_1267098))), -(hAPP(c_Groups_Oabs__class_Oabs(_1267098), _1267100) = hAPP(c_Groups_Ouminus__class_Ouminus(_1267098), _1267100))], (25890 ^ _782652) ^ [_1267275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1267275)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1267275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25896 ^ _782652) ^ [_1267362] : [_1267362 = 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), _1267362)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (25902 ^ _782652) ^ [_1267461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1267461), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1267461) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1267461))], (25908 ^ _782652) ^ [_1267552] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1267552), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1267552) = _1267552)], (25914 ^ _782652) ^ [_1267596, _1267598] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1267596), _1267598))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1267596))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1267598))))], (25916 ^ _782652) ^ [_1267651, _1267653] : [class_Rings_Olinordered__idom(_1267651), 25919 ^ _782652 : [(25920 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267651), c_Groups_Osgn__class_Osgn(_1267651, _1267653)), c_Groups_Ozero__class_Ozero(_1267651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267651), _1267653), c_Groups_Ozero__class_Ozero(_1267651))))], (25926 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267651), _1267653), c_Groups_Ozero__class_Ozero(_1267651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267651), c_Groups_Osgn__class_Osgn(_1267651, _1267653)), c_Groups_Ozero__class_Ozero(_1267651))))]]], (25932 ^ _782652) ^ [_1267919, _1267921] : [class_Rings_Olinordered__idom(_1267919), 25935 ^ _782652 : [(25936 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267919), c_Groups_Ozero__class_Ozero(_1267919)), c_Groups_Osgn__class_Osgn(_1267919, _1267921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267919), c_Groups_Ozero__class_Ozero(_1267919)), _1267921)))], (25942 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267919), c_Groups_Ozero__class_Ozero(_1267919)), _1267921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267919), c_Groups_Ozero__class_Ozero(_1267919)), c_Groups_Osgn__class_Osgn(_1267919, _1267921))))]]], (25948 ^ _782652) ^ [_1268187, _1268189] : [class_Rings_Olinordered__idom(_1268187), 25951 ^ _782652 : [(25952 ^ _782652) ^ [] : [c_Groups_Osgn__class_Osgn(_1268187, _1268189) = c_Groups_Oone__class_Oone(_1268187), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268187), c_Groups_Ozero__class_Ozero(_1268187)), _1268189)))], (25958 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268187), c_Groups_Ozero__class_Ozero(_1268187)), _1268189)), -(c_Groups_Osgn__class_Osgn(_1268187, _1268189) = c_Groups_Oone__class_Oone(_1268187))]]], (25964 ^ _782652) ^ [_1268434, _1268436] : [class_Rings_Olinordered__idom(_1268434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268434), c_Groups_Ozero__class_Ozero(_1268434)), _1268436)), -(c_Groups_Osgn__class_Osgn(_1268434, _1268436) = c_Groups_Oone__class_Oone(_1268434))], (25974 ^ _782652) ^ [_1268604, _1268606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1268604)), _1268606)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1268604), _1268606)))], (25980 ^ _782652) ^ [_1268707, _1268709] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1268707), _1268709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1268707)), _1268709)))], (25986 ^ _782652) ^ [_1268822] : [_1268822 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1268822) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25992 ^ _782652) ^ [_1268898] : [-(_1268898 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25995 ^ _782652 : [(25996 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1268898)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1268898) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (26002 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1268898))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1268898) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (26008 ^ _782652) ^ [_1269090, _1269092] : [-(c_Nitpick_Oint__lcm(_1269090, _1269092) = 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), _1269090)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1269092)))))], (26010 ^ _782652) ^ [_1269136, _1269138, _1269140, _1269142, _1269144] : [class_Groups_Ocomm__monoid__add(_1269136), class_Groups_Ocomm__monoid__mult(_1269136), _1269138 = _1269140, c_Nat__Transfer_Onat__set(_1269140), 26028 ^ _782652 : [(26029 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26027 ^ [_1269136, _1269138, _1269140, _1269142, _1269144])))], (26031 ^ _782652) ^ [] : [hAPP(_1269142, 26027 ^ [_1269136, _1269138, _1269140, _1269142, _1269144]) = hAPP(_1269144, 26027 ^ [_1269136, _1269138, _1269140, _1269142, _1269144])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1269136), _1269142), _1269138) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1269136), _1269144), _1269140))], (26035 ^ _782652) ^ [_1269599, _1269601, _1269603] : [26037 ^ _782652 : [(26038 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26036 ^ [_1269599, _1269601, _1269603]), _1269599)))], (26040 ^ _782652) ^ [] : [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(_1269601, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 26036 ^ [_1269599, _1269601, _1269603]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1269601, 26036 ^ [_1269599, _1269601, _1269603])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1269601, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1269603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269603), hAPP(_1269601, _1269599))), 26050 ^ _782652 : [(26051 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26049 ^ [_1269599, _1269601, _1269603]), _1269599)))], (26053 ^ _782652) ^ [] : [-(hAPP(_1269601, 26049 ^ [_1269599, _1269601, _1269603]) = _1269603)]]], (26055 ^ _782652) ^ [_1270049, _1270051, _1270053] : [26057 ^ _782652 : [(26058 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26056 ^ [_1270049, _1270051, _1270053]), _1270049)))], (26060 ^ _782652) ^ [] : [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(_1270051, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 26056 ^ [_1270049, _1270051, _1270053]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1270051, 26056 ^ [_1270049, _1270051, _1270053])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1270051, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1270053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1270053), hAPP(_1270051, _1270049))), 26070 ^ _782652 : [(26071 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26069 ^ [_1270049, _1270051, _1270053]), _1270049)))], (26073 ^ _782652) ^ [] : [-(hAPP(_1270051, 26069 ^ [_1270049, _1270051, _1270053]) = _1270053)]]], (26075 ^ _782652) ^ [_1270499, _1270501, _1270503] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1270499, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1270501)), _1270503) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270499, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1270499, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1270501)), _1270503)), hAPP(_1270503, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26077 ^ _782652) ^ [_1270571, _1270573, _1270575, _1270577, _1270579, _1270581] : [hBOOL(hAPP(hAPP(c_member(_1270571), _1270573), _1270575)), hBOOL(hAPP(hAPP(_1270577, _1270573), _1270579)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270571, tc_fun(_1270581, tc_HOL_Obool)), _1270575), _1270577), _1270579)))], (26087 ^ _782652) ^ [_1270768, _1270770, _1270772, _1270774] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1270768), _1270770)), 26090 ^ _782652 : [(26101 ^ _782652) ^ [] : [26103 ^ _782652 : [(26104 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270768), 26102 ^ [_1270768, _1270770, _1270772, _1270774]), _1270770)))], (26106 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1270772), hAPP(_1270774, 26102 ^ [_1270768, _1270770, _1270772, _1270774])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1270772), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270768, tc_fun(_1270772, tc_HOL_Obool)), _1270770), _1270774))))], (26091 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1270772), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1270768, tc_fun(_1270772, tc_HOL_Obool)), _1270770), _1270774))), 26094 ^ _782652 : [(26095 ^ _782652) ^ [_1270952] : [hBOOL(hAPP(hAPP(c_member(_1270768), _1270952), _1270770)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1270772), hAPP(_1270774, _1270952))))]]]]], (26110 ^ _782652) ^ [_1271267, _1271269, _1271271, _1271273, _1271275] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271267, tc_fun(_1271269, tc_HOL_Obool)), _1271271), _1271273), _1271275)), 26114 ^ _782652 : [(26115 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1271267), 26113 ^ [_1271267, _1271269, _1271271, _1271273, _1271275]), _1271271)))], (26117 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1271273, 26113 ^ [_1271267, _1271269, _1271271, _1271273, _1271275]), _1271275)))]]], (26119 ^ _782652) ^ [_1271455, _1271457, _1271459, _1271461, _1271463] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271455, tc_fun(_1271457, tc_HOL_Obool)), _1271459), _1271461), _1271463))), 26120 ^ _782652 : [(26121 ^ _782652) ^ [_1271527] : [hBOOL(hAPP(hAPP(c_member(_1271455), _1271527), _1271459)), hBOOL(hAPP(hAPP(_1271461, _1271527), _1271463))]]], (26129 ^ _782652) ^ [_1271700, _1271702, _1271704, _1271706] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271700, tc_fun(_1271702, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1271700, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1271702, tc_HOL_Obool), tc_fun(_1271702, tc_HOL_Obool), _1271700), hAPP(c_COMBC(_1271702, tc_fun(_1271702, tc_HOL_Obool), tc_HOL_Obool), c_member(_1271702))), _1271704)), _1271706)), -(hBOOL(hAPP(hAPP(c_member(_1271702), _1271706), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271700, tc_fun(_1271702, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1271700, tc_HOL_Obool))), _1271704))))], (26135 ^ _782652) ^ [_1271919, _1271921, _1271923, _1271925] : [hBOOL(hAPP(hAPP(c_member(_1271921), _1271925), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271919, tc_fun(_1271921, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1271919, tc_HOL_Obool))), _1271923))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1271919, tc_fun(_1271921, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1271919, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1271921, tc_HOL_Obool), tc_fun(_1271921, tc_HOL_Obool), _1271919), hAPP(c_COMBC(_1271921, tc_fun(_1271921, tc_HOL_Obool), tc_HOL_Obool), c_member(_1271921))), _1271923)), _1271925)))], (26141 ^ _782652) ^ [] : [-(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)))], (26143 ^ _782652) ^ [] : [-(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)))], (26145 ^ _782652) ^ [] : [-(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)))], (26147 ^ _782652) ^ [_1272198, _1272200] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1272198, 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(_1272198, tc_HOL_Obool)), tc_fun(_1272198, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1272198, tc_HOL_Obool)), tc_fun(_1272198, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1272198, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1272200)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1272198, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1272200))], (26149 ^ _782652) ^ [_1272294, _1272296, _1272298, _1272300] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1272294, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1272296)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1272294, tc_HOL_Obool), tc_Nat_Onat), _1272298), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1272300))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1272294, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1272300, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1272296), _1272300))), _1272298))], (26151 ^ _782652) ^ [_1272376, _1272378, _1272380, _1272382, _1272384, _1272386] : [hBOOL(hAPP(hAPP(c_member(_1272376), _1272378), _1272380)), hBOOL(hAPP(hAPP(c_member(_1272382), _1272384), hAPP(_1272386, _1272378))), -(hBOOL(hAPP(hAPP(c_member(_1272382), _1272384), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272376, tc_fun(_1272382, tc_HOL_Obool)), _1272380), _1272386))))], (26161 ^ _782652) ^ [_1272593, _1272595, _1272597, _1272599] : [-(hAPP(c_Set_Ovimage(_1272593, _1272595, _1272597), _1272599) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272595, tc_fun(_1272593, tc_HOL_Obool)), _1272599), hAPP(hAPP(c_COMBB(tc_fun(_1272595, tc_HOL_Obool), tc_fun(_1272593, tc_HOL_Obool), _1272595), c_Set_Ovimage(_1272593, _1272595, _1272597)), hAPP(hAPP(c_COMBC(_1272595, tc_fun(_1272595, tc_HOL_Obool), tc_fun(_1272595, tc_HOL_Obool)), c_Set_Oinsert(_1272595)), c_Orderings_Obot__class_Obot(tc_fun(_1272595, tc_HOL_Obool))))))], (26163 ^ _782652) ^ [_1272684, _1272686, _1272688, _1272690] : [-(hAPP(c_Set_Oimage(_1272684, _1272686, _1272688), _1272690) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272684, tc_fun(_1272686, tc_HOL_Obool)), _1272690), hAPP(hAPP(c_COMBC(_1272684, tc_fun(_1272686, tc_HOL_Obool), tc_fun(_1272686, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1272686, tc_fun(tc_fun(_1272686, tc_HOL_Obool), tc_fun(_1272686, tc_HOL_Obool)), _1272684), c_Set_Oinsert(_1272686)), _1272688)), c_Orderings_Obot__class_Obot(tc_fun(_1272686, tc_HOL_Obool)))))], (26165 ^ _782652) ^ [_1272774, _1272776, _1272778, _1272780, _1272782] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272774, tc_fun(_1272776, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1272774), _1272778), _1272780)), _1272782) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272776, tc_HOL_Obool)), hAPP(_1272782, _1272778)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272774, tc_fun(_1272776, tc_HOL_Obool)), _1272780), _1272782)))], (26167 ^ _782652) ^ [_1272869, _1272871, _1272873, _1272875, _1272877] : [_1272869 = c_Orderings_Obot__class_Obot(tc_fun(_1272871, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272873, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1272871, tc_fun(_1272873, tc_HOL_Obool)), _1272869), _1272875)), _1272877) = _1272877)], (26173 ^ _782652) ^ [_1273002, _1273004, _1273006, _1273008, _1273010] : [-(_1273002 = c_Orderings_Obot__class_Obot(tc_fun(_1273004, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273006, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1273004, tc_fun(_1273006, tc_HOL_Obool)), _1273002), _1273008)), _1273010) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1273004, tc_fun(_1273006, tc_HOL_Obool)), _1273002), hAPP(hAPP(c_COMBC(_1273004, tc_fun(_1273006, tc_HOL_Obool), tc_fun(_1273006, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273006, tc_HOL_Obool), tc_fun(tc_fun(_1273006, tc_HOL_Obool), tc_fun(_1273006, tc_HOL_Obool)), _1273004), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273006, tc_HOL_Obool))), _1273008)), _1273010)))], (26196 ^ _782652) ^ [_1273589, _1273591, _1273593, _1273595, _1273597] : [26198 ^ _782652 : [(26199 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1273591), 26197 ^ [_1273589, _1273591, _1273593, _1273595, _1273597]), _1273593)))], (26202 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1273589), 26200 ^ [_1273589, _1273591, _1273593, _1273595, _1273597]), hAPP(_1273595, 26197 ^ [_1273589, _1273591, _1273593, _1273595, _1273597]))))], (26204 ^ _782652) ^ [] : [hBOOL(hAPP(_1273597, 26200 ^ [_1273589, _1273591, _1273593, _1273595, _1273597]))]], 26205 ^ _782652 : [(26206 ^ _782652) ^ [_1273899] : [hBOOL(hAPP(hAPP(c_member(_1273589), _1273899), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1273591, tc_fun(_1273589, tc_HOL_Obool)), _1273593), _1273595))), -(hBOOL(hAPP(_1273597, _1273899)))]]], (26179 ^ _782652) ^ [_1273153, _1273155, _1273157, _1273159, _1273161] : [26181 ^ _782652 : [(26182 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1273153), 26180 ^ [_1273153, _1273155, _1273157, _1273159, _1273161]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1273155, tc_fun(_1273153, tc_HOL_Obool)), _1273157), _1273159))))], (26184 ^ _782652) ^ [] : [hBOOL(hAPP(_1273161, 26180 ^ [_1273153, _1273155, _1273157, _1273159, _1273161]))]], 26185 ^ _782652 : [(26186 ^ _782652) ^ [_1273375] : [hBOOL(hAPP(hAPP(c_member(_1273155), _1273375), _1273157)), 26189 ^ _782652 : [(26190 ^ _782652) ^ [_1273472] : [hBOOL(hAPP(hAPP(c_member(_1273153), _1273472), hAPP(_1273159, _1273375))), -(hBOOL(hAPP(_1273161, _1273472)))]]]]], (26212 ^ _782652) ^ [_1274034, _1274036, _1274038, _1274040, _1274042, _1274044] : [class_Complete__Lattice_Ocomplete__lattice(_1274034), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274036, _1274034), _1274038), hAPP(hAPP(c_COMBB(tc_fun(_1274040, _1274034), _1274034, _1274036), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274040, _1274034), _1274042)), _1274044)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274040, _1274034), _1274042), hAPP(hAPP(c_COMBB(tc_fun(_1274036, _1274034), _1274034, _1274040), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274036, _1274034), _1274038)), hAPP(c_COMBC(_1274036, _1274040, _1274034), _1274044))))], (26218 ^ _782652) ^ [_1274243, _1274245, _1274247, _1274249, _1274251, _1274253] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274243, tc_fun(_1274245, tc_HOL_Obool)), _1274247), hAPP(hAPP(c_COMBC(_1274243, tc_fun(_1274249, tc_fun(_1274245, tc_HOL_Obool)), tc_fun(_1274245, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1274249, tc_HOL_Obool), tc_fun(tc_fun(_1274249, tc_fun(_1274245, tc_HOL_Obool)), tc_fun(_1274245, tc_HOL_Obool)), _1274243), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274249, tc_fun(_1274245, tc_HOL_Obool))), _1274251)), _1274253)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274249, tc_fun(_1274245, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274243, tc_fun(_1274249, tc_HOL_Obool)), _1274247), _1274251)), _1274253))], (26220 ^ _782652) ^ [_1274362, _1274364, _1274366, _1274368, _1274370, _1274372] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274362, tc_fun(_1274364, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274366, tc_fun(_1274362, tc_HOL_Obool)), _1274368), _1274370)), _1274372) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274366, tc_fun(_1274364, tc_HOL_Obool)), _1274368), hAPP(hAPP(c_COMBC(_1274366, tc_fun(_1274362, tc_fun(_1274364, tc_HOL_Obool)), tc_fun(_1274364, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1274362, tc_HOL_Obool), tc_fun(tc_fun(_1274362, tc_fun(_1274364, tc_HOL_Obool)), tc_fun(_1274364, tc_HOL_Obool)), _1274366), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274362, tc_fun(_1274364, tc_HOL_Obool))), _1274370)), _1274372)))], (26222 ^ _782652) ^ [_1274481, _1274483, _1274485, _1274487, _1274489, _1274491] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274481, tc_fun(_1274483, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274485, tc_fun(_1274481, tc_HOL_Obool)), _1274487), _1274489)), _1274491) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274485, tc_fun(_1274483, tc_HOL_Obool)), _1274487), hAPP(hAPP(c_COMBC(_1274485, tc_fun(_1274481, tc_fun(_1274483, tc_HOL_Obool)), tc_fun(_1274483, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1274481, tc_HOL_Obool), tc_fun(tc_fun(_1274481, tc_fun(_1274483, tc_HOL_Obool)), tc_fun(_1274483, tc_HOL_Obool)), _1274485), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274481, tc_fun(_1274483, tc_HOL_Obool))), _1274489)), _1274491)))], (26224 ^ _782652) ^ [_1274600, _1274602, _1274604, _1274606, _1274608] : [class_Complete__Lattice_Ocomplete__lattice(_1274600), 26227 ^ _782652 : [(26238 ^ _782652) ^ [] : [26240 ^ _782652 : [(26241 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1274602), 26239 ^ [_1274600, _1274602, _1274604, _1274606, _1274608]), _1274604)))], (26243 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274600), hAPP(_1274606, 26239 ^ [_1274600, _1274602, _1274604, _1274606, _1274608])), _1274608))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274600), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274602, _1274600), _1274604), _1274606)), _1274608)))], (26228 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274600), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1274602, _1274600), _1274604), _1274606)), _1274608)), 26231 ^ _782652 : [(26232 ^ _782652) ^ [_1274781] : [hBOOL(hAPP(hAPP(c_member(_1274602), _1274781), _1274604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274600), hAPP(_1274606, _1274781)), _1274608)))]]]]], (26247 ^ _782652) ^ [_1275094, _1275096, _1275098, _1275100, _1275102] : [class_Complete__Lattice_Ocomplete__lattice(_1275094), class_Orderings_Olinorder(_1275094), 26254 ^ _782652 : [(26255 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275094), _1275096), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1275098, _1275094), _1275100), _1275102))), 26259 ^ _782652 : [(26260 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1275098), 26258 ^ [_1275094, _1275096, _1275098, _1275100, _1275102]), _1275100)))], (26262 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275094), _1275096), hAPP(_1275102, 26258 ^ [_1275094, _1275096, _1275098, _1275100, _1275102]))))]]], (26264 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275094), _1275096), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1275098, _1275094), _1275100), _1275102)))), 26265 ^ _782652 : [(26266 ^ _782652) ^ [_1275442] : [hBOOL(hAPP(hAPP(c_member(_1275098), _1275442), _1275100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275094), _1275096), hAPP(_1275102, _1275442)))]]]]], (26274 ^ _782652) ^ [_1275636, _1275638, _1275640, _1275642, _1275644] : [hBOOL(hAPP(hAPP(c_member(_1275636), _1275638), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1275640, tc_fun(_1275636, tc_HOL_Obool)), _1275642), _1275644))), 26278 ^ _782652 : [(26279 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1275640), 26277 ^ [_1275636, _1275638, _1275640, _1275642, _1275644]), _1275642)))], (26281 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1275636), _1275638), hAPP(_1275644, 26277 ^ [_1275636, _1275638, _1275640, _1275642, _1275644]))))]]], (26283 ^ _782652) ^ [_1275844, _1275846, _1275848, _1275850, _1275852] : [-(hBOOL(hAPP(hAPP(c_member(_1275844), _1275846), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1275848, tc_fun(_1275844, tc_HOL_Obool)), _1275850), _1275852)))), 26284 ^ _782652 : [(26285 ^ _782652) ^ [_1275926] : [hBOOL(hAPP(hAPP(c_member(_1275848), _1275926), _1275850)), hBOOL(hAPP(hAPP(c_member(_1275844), _1275846), hAPP(_1275852, _1275926)))]]], (26293 ^ _782652) ^ [_1276093, _1276095, _1276097, _1276099] : [class_Complete__Lattice_Ocomplete__lattice(_1276093), -(_1276095 = c_Orderings_Obot__class_Obot(tc_fun(_1276097, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1276097, _1276093), _1276095), hAPP(c_COMBK(_1276093, _1276097), _1276099)) = _1276099)], (26313 ^ _782652) ^ [_1276477, _1276479, _1276481, _1276483] : [26315 ^ _782652 : [(26316 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276479), 26314 ^ [_1276477, _1276479, _1276481, _1276483]), _1276481)))], (26318 ^ _782652) ^ [] : [hAPP(_1276483, 26314 ^ [_1276477, _1276479, _1276481, _1276483]) = c_Orderings_Obot__class_Obot(tc_fun(_1276477, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1276477, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1276479, tc_fun(_1276477, tc_HOL_Obool)), _1276481), _1276483))], (26303 ^ _782652) ^ [_1276248, _1276250, _1276252, _1276254] : [c_Orderings_Obot__class_Obot(tc_fun(_1276248, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1276250, tc_fun(_1276248, tc_HOL_Obool)), _1276252), _1276254), 26306 ^ _782652 : [(26307 ^ _782652) ^ [_1276364] : [hBOOL(hAPP(hAPP(c_member(_1276250), _1276364), _1276252)), -(hAPP(_1276254, _1276364) = c_Orderings_Obot__class_Obot(tc_fun(_1276248, tc_HOL_Obool)))]]], (26322 ^ _782652) ^ [_1276707, _1276709, _1276711] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1276707, tc_fun(_1276709, tc_HOL_Obool)), _1276711), hAPP(c_COMBK(tc_fun(_1276709, tc_HOL_Obool), _1276707), c_Orderings_Obot__class_Obot(tc_fun(_1276709, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1276709, tc_HOL_Obool)))], (26324 ^ _782652) ^ [_1276780, _1276782, _1276784, _1276786] : [_1276780 = c_Orderings_Obot__class_Obot(tc_fun(_1276782, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1276782, tc_fun(_1276784, tc_HOL_Obool)), _1276780), hAPP(c_COMBK(tc_fun(_1276784, tc_HOL_Obool), _1276782), _1276786)) = c_Orderings_Obot__class_Obot(tc_fun(_1276784, tc_HOL_Obool)))], (26330 ^ _782652) ^ [_1276917, _1276919, _1276921, _1276923] : [-(_1276917 = c_Orderings_Obot__class_Obot(tc_fun(_1276919, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1276919, tc_fun(_1276921, tc_HOL_Obool)), _1276917), hAPP(c_COMBK(tc_fun(_1276921, tc_HOL_Obool), _1276919), _1276923)) = _1276923)], (26346 ^ _782652) ^ [_1277235, _1277237, _1277239, _1277241] : [26348 ^ _782652 : [(26349 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277235), 26347 ^ [_1277235, _1277237, _1277239, _1277241]), _1277239)))], (26351 ^ _782652) ^ [] : [hAPP(_1277241, 26347 ^ [_1277235, _1277237, _1277239, _1277241]) = c_Orderings_Obot__class_Obot(tc_fun(_1277237, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1277235, tc_fun(_1277237, tc_HOL_Obool)), _1277239), _1277241) = c_Orderings_Obot__class_Obot(tc_fun(_1277237, tc_HOL_Obool)))], (26336 ^ _782652) ^ [_1277006, _1277008, _1277010, _1277012] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1277006, tc_fun(_1277008, tc_HOL_Obool)), _1277010), _1277012) = c_Orderings_Obot__class_Obot(tc_fun(_1277008, tc_HOL_Obool)), 26339 ^ _782652 : [(26340 ^ _782652) ^ [_1277122] : [hBOOL(hAPP(hAPP(c_member(_1277006), _1277122), _1277010)), -(hAPP(_1277012, _1277122) = c_Orderings_Obot__class_Obot(tc_fun(_1277008, tc_HOL_Obool)))]]], (26365 ^ _782652) ^ [_1277747, _1277749, _1277751, _1277753, _1277755] : [26367 ^ _782652 : [(26368 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277749), 26366 ^ [_1277747, _1277749, _1277751, _1277753, _1277755]), _1277751)))], (26370 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277747, tc_HOL_Obool)), hAPP(_1277753, 26366 ^ [_1277747, _1277749, _1277751, _1277753, _1277755])), _1277755))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277747, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1277749, tc_fun(_1277747, tc_HOL_Obool)), _1277751), _1277753)), _1277755)))], (26355 ^ _782652) ^ [_1277489, _1277491, _1277493, _1277495, _1277497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277489, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1277491, tc_fun(_1277489, tc_HOL_Obool)), _1277493), _1277495)), _1277497)), 26358 ^ _782652 : [(26359 ^ _782652) ^ [_1277622] : [hBOOL(hAPP(hAPP(c_member(_1277491), _1277622), _1277493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277489, tc_HOL_Obool)), hAPP(_1277495, _1277622)), _1277497)))]]], (26374 ^ _782652) ^ [_1278010, _1278012, _1278014, _1278016, _1278018, _1278020] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278010, tc_fun(_1278012, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1278014, _1278010, _1278016), _1278018)), _1278020) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278014, tc_fun(_1278012, tc_HOL_Obool)), _1278018), hAPP(hAPP(c_COMBB(_1278010, tc_fun(_1278012, tc_HOL_Obool), _1278014), _1278020), _1278016)))], (26376 ^ _782652) ^ [_1278087, _1278089, _1278091, _1278093, _1278095, _1278097] : [-(hAPP(c_Set_Oimage(_1278087, _1278089, _1278091), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278093, tc_fun(_1278087, tc_HOL_Obool)), _1278095), _1278097)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278093, tc_fun(_1278089, tc_HOL_Obool)), _1278095), hAPP(hAPP(c_COMBB(tc_fun(_1278087, tc_HOL_Obool), tc_fun(_1278089, tc_HOL_Obool), _1278093), c_Set_Oimage(_1278087, _1278089, _1278091)), _1278097)))], (26378 ^ _782652) ^ [_1278171, _1278173, _1278175, _1278177, _1278179, _1278181] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278171, tc_fun(_1278173, tc_HOL_Obool)), _1278175), hAPP(hAPP(c_COMBB(_1278177, tc_fun(_1278173, tc_HOL_Obool), _1278171), _1278179), _1278181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278177, tc_fun(_1278173, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1278171, _1278177, _1278181), _1278175)), _1278179))], (26380 ^ _782652) ^ [_1278248, _1278250, _1278252, _1278254, _1278256] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278248, tc_fun(_1278250, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278248, tc_HOL_Obool)), _1278252), _1278254)), _1278256) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278250, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278248, tc_fun(_1278250, tc_HOL_Obool)), _1278252), _1278256)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278248, tc_fun(_1278250, tc_HOL_Obool)), _1278254), _1278256)))], (26382 ^ _782652) ^ [_1278337, _1278339, _1278341, _1278343, _1278345] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278337, tc_fun(_1278339, tc_HOL_Obool)), _1278341), hAPP(hAPP(c_COMBS(_1278337, tc_fun(_1278339, tc_HOL_Obool), tc_fun(_1278339, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278339, tc_HOL_Obool), tc_fun(tc_fun(_1278339, tc_HOL_Obool), tc_fun(_1278339, tc_HOL_Obool)), _1278337), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278339, tc_HOL_Obool))), _1278343)), _1278345)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278339, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278337, tc_fun(_1278339, tc_HOL_Obool)), _1278341), _1278343)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278337, tc_fun(_1278339, tc_HOL_Obool)), _1278341), _1278345)))], (26384 ^ _782652) ^ [_1278458, _1278460, _1278462, _1278464, _1278466] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278458, tc_fun(_1278460, tc_HOL_Obool)), _1278462), hAPP(hAPP(c_COMBB(tc_fun(_1278460, tc_HOL_Obool), tc_fun(_1278460, tc_HOL_Obool), _1278458), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278460, tc_HOL_Obool)), _1278464)), _1278466)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278460, tc_HOL_Obool)), _1278464), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278458, tc_fun(_1278460, tc_HOL_Obool)), _1278462), _1278466)))], (26386 ^ _782652) ^ [_1278548, _1278550, _1278552, _1278554, _1278556] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278548, tc_fun(_1278550, tc_HOL_Obool)), _1278552), hAPP(hAPP(c_COMBC(_1278548, tc_fun(_1278550, tc_HOL_Obool), tc_fun(_1278550, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278550, tc_HOL_Obool), tc_fun(tc_fun(_1278550, tc_HOL_Obool), tc_fun(_1278550, tc_HOL_Obool)), _1278548), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278550, tc_HOL_Obool))), _1278554)), _1278556)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278550, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278548, tc_fun(_1278550, tc_HOL_Obool)), _1278552), _1278554)), _1278556))], (26388 ^ _782652) ^ [_1278657, _1278659, _1278661, _1278663, _1278665] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278657, tc_HOL_Obool)), _1278659), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278661, tc_fun(_1278657, tc_HOL_Obool)), _1278663), _1278665)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278661, tc_fun(_1278657, tc_HOL_Obool)), _1278663), hAPP(hAPP(c_COMBB(tc_fun(_1278657, tc_HOL_Obool), tc_fun(_1278657, tc_HOL_Obool), _1278661), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278657, tc_HOL_Obool)), _1278659)), _1278665)))], (26390 ^ _782652) ^ [_1278747, _1278749, _1278751, _1278753, _1278755] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278747, tc_HOL_Obool)), _1278749), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278751, tc_fun(_1278747, tc_HOL_Obool)), _1278753), _1278755)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278751, tc_fun(_1278747, tc_HOL_Obool)), _1278753), hAPP(hAPP(c_COMBB(tc_fun(_1278747, tc_HOL_Obool), tc_fun(_1278747, tc_HOL_Obool), _1278751), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278747, tc_HOL_Obool)), _1278749)), _1278755)))], (26392 ^ _782652) ^ [_1278837, _1278839, _1278841, _1278843, _1278845] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278837, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278839, tc_fun(_1278837, tc_HOL_Obool)), _1278841), _1278843)), _1278845) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278839, tc_fun(_1278837, tc_HOL_Obool)), _1278841), hAPP(hAPP(c_COMBC(_1278839, tc_fun(_1278837, tc_HOL_Obool), tc_fun(_1278837, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278837, tc_HOL_Obool), tc_fun(tc_fun(_1278837, tc_HOL_Obool), tc_fun(_1278837, tc_HOL_Obool)), _1278839), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278837, tc_HOL_Obool))), _1278843)), _1278845)))], (26394 ^ _782652) ^ [_1278946, _1278948, _1278950, _1278952, _1278954, _1278956, _1278958] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278946, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278948, tc_fun(_1278946, tc_HOL_Obool)), _1278950), _1278952)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278954, tc_fun(_1278946, tc_HOL_Obool)), _1278956), _1278958)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278948, tc_fun(_1278946, tc_HOL_Obool)), _1278950), hAPP(hAPP(c_COMBB(tc_fun(_1278954, tc_fun(_1278946, tc_HOL_Obool)), tc_fun(_1278946, tc_HOL_Obool), _1278948), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1278954, tc_fun(_1278946, tc_HOL_Obool)), _1278956)), hAPP(hAPP(c_COMBC(_1278948, tc_fun(_1278954, tc_fun(_1278946, tc_HOL_Obool)), tc_fun(_1278954, tc_fun(_1278946, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1278946, tc_HOL_Obool), tc_fun(_1278946, tc_HOL_Obool)), tc_fun(tc_fun(_1278954, tc_fun(_1278946, tc_HOL_Obool)), tc_fun(_1278954, tc_fun(_1278946, tc_HOL_Obool))), _1278948), c_COMBB(tc_fun(_1278946, tc_HOL_Obool), tc_fun(_1278946, tc_HOL_Obool), _1278954)), hAPP(hAPP(c_COMBB(tc_fun(_1278946, tc_HOL_Obool), tc_fun(tc_fun(_1278946, tc_HOL_Obool), tc_fun(_1278946, tc_HOL_Obool)), _1278948), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1278946, tc_HOL_Obool))), _1278952))), _1278958))))], (26396 ^ _782652) ^ [_1279149, _1279151, _1279153, _1279155, _1279157, _1279159] : [class_Complete__Lattice_Ocomplete__lattice(_1279149), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279151, tc_fun(_1279153, _1279149)), _1279155), _1279157), _1279159) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279151, _1279149), _1279155), hAPP(hAPP(c_COMBC(_1279151, _1279153, _1279149), _1279157), _1279159)))], (26402 ^ _782652) ^ [_1279300, _1279302, _1279304, _1279306, _1279308] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279300, tc_fun(_1279302, tc_HOL_Obool)), _1279304), hAPP(hAPP(c_COMBC(_1279300, tc_fun(_1279302, tc_HOL_Obool), tc_fun(_1279302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279302, tc_HOL_Obool), tc_fun(tc_fun(_1279302, tc_HOL_Obool), tc_fun(_1279302, tc_HOL_Obool)), _1279300), c_Groups_Ominus__class_Ominus(tc_fun(_1279302, tc_HOL_Obool))), _1279306)), _1279308)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279302, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279300, tc_fun(_1279302, tc_HOL_Obool)), _1279304), _1279306)), _1279308))], (26404 ^ _782652) ^ [_1279409, _1279411, _1279413, _1279415, _1279417] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279409, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279411, tc_fun(_1279409, tc_HOL_Obool)), _1279413), _1279415)), _1279417) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279411, tc_fun(_1279409, tc_HOL_Obool)), _1279413), hAPP(hAPP(c_COMBC(_1279411, tc_fun(_1279409, tc_HOL_Obool), tc_fun(_1279409, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279409, tc_HOL_Obool), tc_fun(tc_fun(_1279409, tc_HOL_Obool), tc_fun(_1279409, tc_HOL_Obool)), _1279411), c_Groups_Ominus__class_Ominus(tc_fun(_1279409, tc_HOL_Obool))), _1279415)), _1279417)))], (26406 ^ _782652) ^ [_1279518, _1279520, _1279522, _1279524, _1279526, _1279528] : [-(hAPP(c_Set_Ovimage(_1279518, _1279520, _1279522), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279524, tc_fun(_1279520, tc_HOL_Obool)), _1279526), _1279528)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279524, tc_fun(_1279518, tc_HOL_Obool)), _1279526), hAPP(hAPP(c_COMBB(tc_fun(_1279520, tc_HOL_Obool), tc_fun(_1279518, tc_HOL_Obool), _1279524), c_Set_Ovimage(_1279518, _1279520, _1279522)), _1279528)))], (26408 ^ _782652) ^ [_1279602, _1279604, _1279606, _1279608, _1279610] : [class_Complete__Lattice_Ocomplete__lattice(_1279602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279604, tc_HOL_Obool)), _1279606), _1279608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279602), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279604, _1279602), _1279606), _1279610)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279604, _1279602), _1279608), _1279610))))], (26418 ^ _782652) ^ [_1279811, _1279813, _1279815, _1279817, _1279819] : [class_Complete__Lattice_Ocomplete__lattice(_1279811), hBOOL(hAPP(hAPP(c_member(_1279813), _1279815), _1279817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279811), hAPP(_1279819, _1279815)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1279813, _1279811), _1279817), _1279819))))], (26428 ^ _782652) ^ [_1280002, _1280004, _1280006, _1280008, _1280010, _1280012] : [hBOOL(hAPP(hAPP(c_member(_1280002), _1280004), _1280006)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280002, tc_fun(_1280008, tc_HOL_Obool)), _1280006), hAPP(hAPP(c_COMBB(tc_fun(_1280008, tc_HOL_Obool), tc_fun(_1280008, tc_HOL_Obool), _1280002), hAPP(c_Set_Oinsert(_1280008), _1280010)), _1280012)) = hAPP(hAPP(c_Set_Oinsert(_1280008), _1280010), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280002, tc_fun(_1280008, tc_HOL_Obool)), _1280006), _1280012)))], (26434 ^ _782652) ^ [_1280207, _1280209, _1280211, _1280213, _1280215] : [hBOOL(hAPP(hAPP(c_member(_1280207), _1280209), _1280211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280213, tc_HOL_Obool)), hAPP(_1280215, _1280209)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280207, tc_fun(_1280213, tc_HOL_Obool)), _1280211), _1280215))))], (26440 ^ _782652) ^ [_1280354, _1280356, _1280358, _1280360, _1280362] : [hBOOL(hAPP(hAPP(c_member(_1280354), _1280356), _1280358)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280360, tc_HOL_Obool)), hAPP(_1280362, _1280356)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280354, tc_fun(_1280360, tc_HOL_Obool)), _1280358), _1280362)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280354, tc_fun(_1280360, tc_HOL_Obool)), _1280358), _1280362))], (26446 ^ _782652) ^ [_1280545, _1280547, _1280549, _1280551, _1280553] : [_1280545 = c_Orderings_Obot__class_Obot(tc_fun(_1280547, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1280549), _1280551), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280547, tc_fun(_1280549, tc_HOL_Obool)), _1280545), _1280553)) = hAPP(hAPP(c_Set_Oinsert(_1280549), _1280551), c_Orderings_Obot__class_Obot(tc_fun(_1280549, tc_HOL_Obool))))], (26452 ^ _782652) ^ [_1280698, _1280700, _1280702, _1280704, _1280706] : [-(_1280698 = c_Orderings_Obot__class_Obot(tc_fun(_1280700, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1280702), _1280704), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280700, tc_fun(_1280702, tc_HOL_Obool)), _1280698), _1280706)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280700, tc_fun(_1280702, tc_HOL_Obool)), _1280698), hAPP(hAPP(c_COMBB(tc_fun(_1280702, tc_HOL_Obool), tc_fun(_1280702, tc_HOL_Obool), _1280700), hAPP(c_Set_Oinsert(_1280702), _1280704)), _1280706)))], (26458 ^ _782652) ^ [_1280800, _1280802] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280800, tc_fun(_1280800, tc_HOL_Obool)), _1280802), hAPP(hAPP(c_COMBC(_1280800, tc_fun(_1280800, tc_HOL_Obool), tc_fun(_1280800, tc_HOL_Obool)), c_Set_Oinsert(_1280800)), c_Orderings_Obot__class_Obot(tc_fun(_1280800, tc_HOL_Obool)))) = _1280802)], (26460 ^ _782652) ^ [_1280878, _1280880, _1280882, _1280884, _1280886] : [_1280878 = c_Orderings_Obot__class_Obot(tc_fun(_1280880, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1280880, tc_fun(_1280882, tc_HOL_Obool)), _1280878), hAPP(hAPP(c_COMBB(tc_fun(_1280882, tc_HOL_Obool), tc_fun(_1280882, tc_HOL_Obool), _1280880), hAPP(c_Set_Oinsert(_1280882), _1280884)), _1280886)) = c_Orderings_Obot__class_Obot(tc_fun(_1280882, tc_HOL_Obool)))], (26466 ^ _782652) ^ [_1281041, _1281043, _1281045, _1281047, _1281049] : [-(_1281041 = c_Orderings_Obot__class_Obot(tc_fun(_1281043, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281043, tc_fun(_1281045, tc_HOL_Obool)), _1281041), hAPP(hAPP(c_COMBB(tc_fun(_1281045, tc_HOL_Obool), tc_fun(_1281045, tc_HOL_Obool), _1281043), hAPP(c_Set_Oinsert(_1281045), _1281047)), _1281049)) = hAPP(hAPP(c_Set_Oinsert(_1281045), _1281047), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281043, tc_fun(_1281045, tc_HOL_Obool)), _1281041), _1281049)))], (26472 ^ _782652) ^ [_1281161, _1281163, _1281165, _1281167, _1281169] : [_1281161 = c_Orderings_Obot__class_Obot(tc_fun(_1281163, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281163, tc_fun(_1281165, tc_HOL_Obool)), _1281161), hAPP(hAPP(c_COMBB(tc_fun(_1281165, tc_HOL_Obool), tc_fun(_1281165, tc_HOL_Obool), _1281163), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281165, tc_HOL_Obool)), _1281167)), _1281169)) = c_Orderings_Obot__class_Obot(tc_fun(_1281165, tc_HOL_Obool)))], (26478 ^ _782652) ^ [_1281330, _1281332, _1281334, _1281336, _1281338] : [-(_1281330 = c_Orderings_Obot__class_Obot(tc_fun(_1281332, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281332, tc_fun(_1281334, tc_HOL_Obool)), _1281330), hAPP(hAPP(c_COMBB(tc_fun(_1281334, tc_HOL_Obool), tc_fun(_1281334, tc_HOL_Obool), _1281332), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281334, tc_HOL_Obool)), _1281336)), _1281338)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281334, tc_HOL_Obool)), _1281336), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281332, tc_fun(_1281334, tc_HOL_Obool)), _1281330), _1281338)))], (26484 ^ _782652) ^ [_1281456, _1281458, _1281460, _1281462, _1281464] : [_1281456 = c_Orderings_Obot__class_Obot(tc_fun(_1281458, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281458, tc_fun(_1281460, tc_HOL_Obool)), _1281456), hAPP(hAPP(c_COMBC(_1281458, tc_fun(_1281460, tc_HOL_Obool), tc_fun(_1281460, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1281460, tc_HOL_Obool), tc_fun(tc_fun(_1281460, tc_HOL_Obool), tc_fun(_1281460, tc_HOL_Obool)), _1281458), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281460, tc_HOL_Obool))), _1281462)), _1281464)) = c_Orderings_Obot__class_Obot(tc_fun(_1281460, tc_HOL_Obool)))], (26490 ^ _782652) ^ [_1281663, _1281665, _1281667, _1281669, _1281671] : [-(_1281663 = c_Orderings_Obot__class_Obot(tc_fun(_1281665, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281665, tc_fun(_1281667, tc_HOL_Obool)), _1281663), hAPP(hAPP(c_COMBC(_1281665, tc_fun(_1281667, tc_HOL_Obool), tc_fun(_1281667, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1281667, tc_HOL_Obool), tc_fun(tc_fun(_1281667, tc_HOL_Obool), tc_fun(_1281667, tc_HOL_Obool)), _1281665), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281667, tc_HOL_Obool))), _1281669)), _1281671)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281667, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281665, tc_fun(_1281667, tc_HOL_Obool)), _1281663), _1281669)), _1281671))], (26496 ^ _782652) ^ [_1281808, _1281810, _1281812, _1281814, _1281816] : [_1281808 = c_Orderings_Obot__class_Obot(tc_fun(_1281810, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281812, tc_HOL_Obool)), _1281814), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281810, tc_fun(_1281812, tc_HOL_Obool)), _1281808), _1281816)) = _1281814)], (26502 ^ _782652) ^ [_1281941, _1281943, _1281945, _1281947, _1281949] : [-(_1281941 = c_Orderings_Obot__class_Obot(tc_fun(_1281943, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281945, tc_HOL_Obool)), _1281947), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281943, tc_fun(_1281945, tc_HOL_Obool)), _1281941), _1281949)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1281943, tc_fun(_1281945, tc_HOL_Obool)), _1281941), hAPP(hAPP(c_COMBB(tc_fun(_1281945, tc_HOL_Obool), tc_fun(_1281945, tc_HOL_Obool), _1281943), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281945, tc_HOL_Obool)), _1281947)), _1281949)))], (26508 ^ _782652) ^ [_1282049, _1282051, _1282053, _1282055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282049, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282049, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26509 ^ [_1282049, _1282051, _1282053, _1282055])), _1282051)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282049, 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), 26509 ^ [_1282049, _1282051, _1282053, _1282055]), _1282053))), _1282055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282049, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282049, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1282051)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282049, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1282055))))], (26515 ^ _782652) ^ [_1282379, _1282381, _1282383, _1282385] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282379, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26516 ^ [_1282379, _1282381, _1282383, _1282385])), _1282381) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282379, 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), 26516 ^ [_1282379, _1282381, _1282383, _1282385]), _1282383))), _1282385), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282379, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1282381) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282379, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1282385))], (26522 ^ _782652) ^ [_1282659, _1282661, _1282663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282659, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282659, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26523 ^ [_1282659, _1282661, _1282663])), _1282661)), _1282663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282659, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1282659, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1282661)), _1282663)))], (26529 ^ _782652) ^ [_1282885, _1282887, _1282889, _1282891] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282885), _1282887)), 26535 ^ _782652 : [(26536 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1282885), 26534 ^ [_1282885, _1282887, _1282889, _1282891]), _1282887)))], (26538 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282889), hAPP(_1282891, 26534 ^ [_1282885, _1282887, _1282889, _1282891])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282889), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1282885, tc_fun(_1282889, tc_HOL_Obool)), _1282887), _1282891))))], (26542 ^ _782652) ^ [_1283172, _1283174] : [26544 ^ _782652 : [(26545 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26543 ^ [_1283172, _1283174]), _1283172)))], (26547 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1283174), 26543 ^ [_1283172, _1283174]))]], -(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)), _1283174), _1283172))], (26551 ^ _782652) ^ [_1283347, _1283349, _1283351, _1283353, _1283355, _1283357, _1283359, _1283361] : [hBOOL(hAPP(hAPP(c_member(_1283347), _1283349), _1283351)), hBOOL(hAPP(hAPP(hAPP(_1283353, _1283349), _1283355), _1283357)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1283347, tc_fun(_1283359, tc_fun(_1283361, tc_HOL_Obool))), _1283351), _1283353), _1283355), _1283357)))], (26561 ^ _782652) ^ [_1283570, _1283572, _1283574] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283570), c_Map_Odom(_1283570, _1283572, _1283574))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283570), c_Orderings_Otop__class_Otop(tc_fun(_1283570, tc_HOL_Obool))))), -(hAPP(_1283574, 26568 ^ [_1283570, _1283572, _1283574]) = c_Option_Ooption_ONone(_1283572))], (26572 ^ _782652) ^ [_1283731, _1283733] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1283731)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1283733)), hAPP(c_Int_Onat, _1283731)) = hAPP(c_Int_Onat, _1283733))], (26578 ^ _782652) ^ [_1283836, _1283838] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1283836))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1283838)), hAPP(c_Int_Onat, _1283836)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1283838), _1283836)), 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)))], (26584 ^ _782652) ^ [_1283900, _1283902, _1283904, _1283906] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1283900, tc_Nat_Onat), _1283902), _1283904) = hAPP(c_Nat_OSuc, _1283906), 26588 ^ _782652 : [(26589 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1283900), 26587 ^ [_1283900, _1283902, _1283904, _1283906]), _1283904)))], (26591 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1283902, 26587 ^ [_1283900, _1283902, _1283904, _1283906]))))]]], (26593 ^ _782652) ^ [_1284082, _1284084, _1284086, _1284088, _1284090] : [class_Groups_Ocomm__monoid__mult(_1284082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284084), _1284086)), hBOOL(hAPP(hAPP(c_member(_1284084), _1284088), _1284086)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284084, _1284082), _1284090), _1284086) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284082), hAPP(_1284090, _1284088)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284084, _1284082), _1284090), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284084, tc_HOL_Obool)), _1284086), hAPP(hAPP(c_Set_Oinsert(_1284084), _1284088), c_Orderings_Obot__class_Obot(tc_fun(_1284084, tc_HOL_Obool)))))))], (26607 ^ _782652) ^ [_1284407, _1284409, _1284411] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1284407, _1284409, _1284411)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1284409)), c_Com_Ocom_Ocom__size(_1284411))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26609 ^ _782652) ^ [_1284455, _1284457, _1284459, _1284461, _1284463, _1284465] : [-(hBOOL(hAPP(_1284455, _1284457))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1284459), _1284457), _1284461), _1284463)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1284455, _1284465, _1284459)), _1284457), _1284461), _1284463)))], (26619 ^ _782652) ^ [_1284652, _1284654, _1284656, _1284658, _1284660, _1284662] : [hBOOL(hAPP(_1284652, _1284654)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1284656), _1284654), _1284658), _1284660)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1284652, _1284656, _1284662)), _1284654), _1284658), _1284660)))], (26629 ^ _782652) ^ [_1284853, _1284855, _1284857, _1284859, _1284861, _1284863] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1284853, _1284855, _1284857)), _1284859), _1284861), _1284863)), 26634 ^ _782652 : [(26635 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1284853, _1284859)))], (26637 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1284855), _1284859), _1284861), _1284863)))]], 26638 ^ _782652 : [(26639 ^ _782652) ^ [] : [hBOOL(hAPP(_1284853, _1284859))], (26641 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1284857), _1284859), _1284861), _1284863)))]]], (26643 ^ _782652) ^ [_1285149, _1285151, _1285153, _1285155, _1285157] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1285149, _1285151, _1285153)), _1285155), _1285157)), 26648 ^ _782652 : [(26649 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1285149, _1285155)))], (26651 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1285151), _1285155), _1285157)))]], 26652 ^ _782652 : [(26653 ^ _782652) ^ [] : [hBOOL(hAPP(_1285149, _1285155))], (26655 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1285153), _1285155), _1285157)))]]], (26657 ^ _782652) ^ [_1285417, _1285419, _1285421, _1285423, _1285425] : [hBOOL(hAPP(_1285417, _1285419)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1285421), _1285419), _1285423)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1285417, _1285421, _1285425)), _1285419), _1285423)))], (26667 ^ _782652) ^ [_1285597, _1285599, _1285601, _1285603, _1285605] : [-(hBOOL(hAPP(_1285597, _1285599))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1285601), _1285599), _1285603)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1285597, _1285605, _1285601)), _1285599), _1285603)))], (26677 ^ _782652) ^ [_1285774, _1285776, _1285778] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1285774, _1285776, _1285778))), 26680 ^ _782652 : [(26681 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1285776)))], (26683 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1285778)))]]], (26685 ^ _782652) ^ [_1285933, _1285935, _1285937, _1285939, _1285941, _1285943, _1285945] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1285933, tc_fun(_1285935, tc_fun(_1285937, tc_HOL_Obool))), _1285939), _1285941), _1285943), _1285945)), 26689 ^ _782652 : [(26690 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285933), 26688 ^ [_1285933, _1285935, _1285937, _1285939, _1285941, _1285943, _1285945]), _1285939)))], (26692 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1285941, 26688 ^ [_1285933, _1285935, _1285937, _1285939, _1285941, _1285943, _1285945]), _1285943), _1285945)))]]], (26694 ^ _782652) ^ [_1286151, _1286153, _1286155, _1286157, _1286159, _1286161, _1286163] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1286151, tc_fun(_1286153, tc_fun(_1286155, tc_HOL_Obool))), _1286157), _1286159), _1286161), _1286163))), 26695 ^ _782652 : [(26696 ^ _782652) ^ [_1286236] : [hBOOL(hAPP(hAPP(c_member(_1286151), _1286236), _1286157)), hBOOL(hAPP(hAPP(hAPP(_1286159, _1286236), _1286161), _1286163))]]], (26704 ^ _782652) ^ [_1286404, _1286406, _1286408] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286404, tc_Nat_Onat), _1286406), _1286408) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286404, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1286404), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1286406)), _1286408)))], (26706 ^ _782652) ^ [_1286462, _1286464, _1286466] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286462, tc_Nat_Onat), _1286464), _1286466)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286462, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1286462), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1286464)), _1286466))], (26708 ^ _782652) ^ [_1286520, _1286522, _1286524, _1286526] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1286520), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286522, tc_Nat_Onat), _1286524), _1286526)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1286522, _1286520), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1286520, _1286522), c_Nat_Osemiring__1__class_Oof__nat(_1286520)), _1286524)), _1286526)), class_Groups_Ocomm__monoid__mult(_1286520), class_Rings_Osemiring__1(_1286520)], (26718 ^ _782652) ^ [_1286750, _1286752, _1286754, _1286756, _1286758, _1286760] : [c_Com_Ocom_OCond(_1286750, _1286752, _1286754) = c_Com_Ocom_OCond(_1286756, _1286758, _1286760), 26721 ^ _782652 : [(26722 ^ _782652) ^ [] : [-(_1286750 = _1286756)], (26724 ^ _782652) ^ [] : [-(_1286752 = _1286758)], (26726 ^ _782652) ^ [] : [-(_1286754 = _1286760)]]], (26728 ^ _782652) ^ [_1286897, _1286899, _1286901, _1286903, _1286905, _1286907] : [-(c_Com_Ocom_OCond(_1286897, _1286899, _1286901) = c_Com_Ocom_OCond(_1286903, _1286905, _1286907)), _1286897 = _1286903, _1286899 = _1286905, _1286901 = _1286907], (26742 ^ _782652) ^ [_1287120, _1287122, _1287124, _1287126] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1287120), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287122, tc_Int_Oint), _1287124), _1287126)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287122, _1287120), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1287120, _1287122), c_Int_Oring__1__class_Oof__int(_1287120)), _1287124)), _1287126)), class_Groups_Ocomm__monoid__mult(_1287120), class_Rings_Oring__1(_1287120)], (26752 ^ _782652) ^ [_1287323, _1287325, _1287327, _1287329, _1287331] : [class_Groups_Ocomm__monoid__mult(_1287323), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287325, _1287323), hAPP(hAPP(c_COMBS(_1287325, _1287323, _1287323), hAPP(hAPP(c_COMBB(_1287323, tc_fun(_1287323, _1287323), _1287325), c_Groups_Otimes__class_Otimes(_1287323)), _1287327)), _1287329)), _1287331) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287323), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287325, _1287323), _1287327), _1287331)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287325, _1287323), _1287329), _1287331)))], (26758 ^ _782652) ^ [_1287524, _1287526, _1287528] : [class_Groups_Ocomm__monoid__mult(_1287524), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287526, _1287524), hAPP(c_COMBK(_1287524, _1287526), c_Groups_Oone__class_Oone(_1287524))), _1287528) = c_Groups_Oone__class_Oone(_1287524))], (26764 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26766 ^ _782652) ^ [_1287663, _1287665, _1287667, _1287669] : [class_Fields_Olinordered__field(_1287663), -(hAPP(c_Groups_Oabs__class_Oabs(_1287663), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287665, _1287663), _1287667), _1287669)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1287665, _1287663), hAPP(hAPP(c_COMBB(_1287663, _1287663, _1287665), c_Groups_Oabs__class_Oabs(_1287663)), _1287667)), _1287669))], (26772 ^ _782652) ^ [_1287821] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287821)))], (26774 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (26776 ^ _782652) ^ [_1287900, _1287902, _1287904, _1287906, _1287908, _1287910] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1287900, _1287902, _1287904)), _1287906), _1287908), _1287910)), 26781 ^ _782652 : [(26782 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1287900, _1287906)))], (26784 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1287902), _1287906), _1287908), _1287910)))]], 26785 ^ _782652 : [(26786 ^ _782652) ^ [] : [hBOOL(hAPP(_1287900, _1287906))], (26788 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1287904), _1287906), _1287908), _1287910)))]]], (26790 ^ _782652) ^ [_1288186, _1288188, _1288190, _1288192, _1288194, _1288196] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1288186, _1288188, _1288190)), _1288192), _1288194), _1288196))), 26791 ^ _782652 : [(26792 ^ _782652) ^ [] : [hBOOL(hAPP(_1288186, _1288192)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1288188), _1288192), _1288194), _1288196))], (26798 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1288186, _1288192))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1288190), _1288192), _1288194), _1288196))]]], (26806 ^ _782652) ^ [_1288536, _1288538, _1288540, _1288542, _1288544, _1288546] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1288536, _1288538, _1288540)), _1288542), _1288544), _1288546)), 26811 ^ _782652 : [(26812 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1288536, _1288542)))], (26814 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1288538), _1288542), _1288544), _1288546)))]], 26815 ^ _782652 : [(26816 ^ _782652) ^ [] : [hBOOL(hAPP(_1288536, _1288542))], (26818 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1288540), _1288542), _1288544), _1288546)))]]], (26820 ^ _782652) ^ [_1288822, _1288824, _1288826, _1288828, _1288830, _1288832] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_1288822, _1288824, _1288826)), _1288828), _1288830), _1288832))), 26821 ^ _782652 : [(26822 ^ _782652) ^ [] : [hBOOL(hAPP(_1288822, _1288828)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1288824), _1288828), _1288830), _1288832))], (26828 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1288822, _1288828))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _1288826), _1288828), _1288830), _1288832))]]], (26836 ^ _782652) ^ [_1289169, _1289171, _1289173, _1289175, _1289177] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1289169, _1289171, _1289173)), _1289175), _1289177)), 26841 ^ _782652 : [(26842 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1289169, _1289175)))], (26844 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1289171), _1289175), _1289177)))]], 26845 ^ _782652 : [(26846 ^ _782652) ^ [] : [hBOOL(hAPP(_1289169, _1289175))], (26848 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1289173), _1289175), _1289177)))]]], (26850 ^ _782652) ^ [_1289427, _1289429, _1289431, _1289433, _1289435] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1289427, _1289429, _1289431)), _1289433), _1289435))), 26851 ^ _782652 : [(26852 ^ _782652) ^ [] : [hBOOL(hAPP(_1289427, _1289433)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1289429), _1289433), _1289435))], (26858 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1289427, _1289433))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1289431), _1289433), _1289435))]]], (26866 ^ _782652) ^ [_1289744, _1289746, _1289748, _1289750, _1289752] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1289744, _1289746, _1289748)), _1289750), _1289752)), 26871 ^ _782652 : [(26872 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1289744, _1289750)))], (26874 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1289746), _1289750), _1289752)))]], 26875 ^ _782652 : [(26876 ^ _782652) ^ [] : [hBOOL(hAPP(_1289744, _1289750))], (26878 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1289748), _1289750), _1289752)))]]], (26880 ^ _782652) ^ [_1290002, _1290004, _1290006, _1290008, _1290010] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_1290002, _1290004, _1290006)), _1290008), _1290010))), 26881 ^ _782652 : [(26882 ^ _782652) ^ [] : [hBOOL(hAPP(_1290002, _1290008)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1290004), _1290008), _1290010))], (26888 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1290002, _1290008))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_1290006), _1290008), _1290010))]]], (26896 ^ _782652) ^ [_1290313, _1290315, _1290317, _1290319] : [hAPP(c_Com_Ocom_OBODY, _1290313) = c_Com_Ocom_OCond(_1290315, _1290317, _1290319)], (26898 ^ _782652) ^ [_1290367, _1290369, _1290371, _1290373] : [c_Com_Ocom_OCond(_1290367, _1290369, _1290371) = hAPP(c_Com_Ocom_OBODY, _1290373)], (26900 ^ _782652) ^ [_1290421, _1290423, _1290425] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1290421, _1290423, _1290425))), 26903 ^ _782652 : [(26904 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1290423)))], (26906 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1290425)))]]], (26908 ^ _782652) ^ [_1290542, _1290544, _1290546] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1290542, _1290544, _1290546)))), hBOOL(hAPP(c_Com_OWT, _1290544)), hBOOL(hAPP(c_Com_OWT, _1290546))], (26918 ^ _782652) ^ [_1290697, _1290699, _1290701] : [hBOOL(hAPP(c_Com_OWT, _1290697)), hBOOL(hAPP(c_Com_OWT, _1290699)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1290701, _1290697, _1290699))))], (26928 ^ _782652) ^ [_1290871, _1290873, _1290875, _1290877, _1290879] : [c_Com_Ocom_OWhile(_1290871, _1290873) = c_Com_Ocom_OCond(_1290875, _1290877, _1290879)], (26930 ^ _782652) ^ [_1290930, _1290932, _1290934, _1290936, _1290938] : [c_Com_Ocom_OCond(_1290930, _1290932, _1290934) = c_Com_Ocom_OWhile(_1290936, _1290938)], (26932 ^ _782652) ^ [_1290968, _1290970, _1290972] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1290968), _1290970), _1290972) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1290968), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1290968, tc_Int_Oint), _1290970), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1290972))), class_Groups_Ocomm__monoid__add(_1290968), class_Groups_Ocomm__monoid__mult(_1290968)], (26942 ^ _782652) ^ [_1291180, _1291182, _1291184, _1291186, _1291188] : [c_Com_Ocom_OSemi(_1291180, _1291182) = c_Com_Ocom_OCond(_1291184, _1291186, _1291188)], (26944 ^ _782652) ^ [_1291239, _1291241, _1291243, _1291245, _1291247] : [c_Com_Ocom_OCond(_1291239, _1291241, _1291243) = c_Com_Ocom_OSemi(_1291245, _1291247)], (26946 ^ _782652) ^ [_1291292, _1291294, _1291296] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1291292, _1291294, _1291296)], (26948 ^ _782652) ^ [_1291338, _1291340, _1291342] : [c_Com_Ocom_OCond(_1291338, _1291340, _1291342) = c_Com_Ocom_OSKIP], (26950 ^ _782652) ^ [_1291369, _1291371, _1291373, _1291375] : [class_Rings_Ocomm__semiring__1(_1291369), class_Rings_Ono__zero__divisors(_1291369), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291371), _1291373)), 26961 ^ _782652 : [(26962 ^ _782652) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1291371, _1291369), _1291375), _1291373) = c_Groups_Ozero__class_Ozero(_1291369), 26966 ^ _782652 : [(26967 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1291371), 26965 ^ [_1291369, _1291371, _1291373, _1291375]), _1291373)))], (26969 ^ _782652) ^ [] : [-(hAPP(_1291375, 26965 ^ [_1291369, _1291371, _1291373, _1291375]) = c_Groups_Ozero__class_Ozero(_1291369))]]], (26971 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1291371, _1291369), _1291375), _1291373) = c_Groups_Ozero__class_Ozero(_1291369)), 26972 ^ _782652 : [(26973 ^ _782652) ^ [_1291747] : [hBOOL(hAPP(hAPP(c_member(_1291371), _1291747), _1291373)), hAPP(_1291375, _1291747) = c_Groups_Ozero__class_Ozero(_1291369)]]]]], (26981 ^ _782652) ^ [_1291902, _1291904, _1291906, _1291908] : [class_Rings_Ocomm__semiring__1(_1291902), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291904), _1291906)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1291904, _1291902), _1291908), _1291906) = c_Groups_Ozero__class_Ozero(_1291902)), 26990 ^ _782652 : [(26991 ^ _782652) ^ [_1292083] : [hBOOL(hAPP(hAPP(c_member(_1291904), _1292083), _1291906)), hAPP(_1291908, _1292083) = c_Groups_Ozero__class_Ozero(_1291902)]]], (26999 ^ _782652) ^ [_1292232, _1292234, _1292236] : [class_Groups_Ocomm__monoid__mult(_1292232), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292234, _1292232), _1292236), c_Orderings_Obot__class_Obot(tc_fun(_1292234, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1292232))], (27005 ^ _782652) ^ [_1292341, _1292343, _1292345] : [class_Groups_Ocomm__monoid__mult(_1292341), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292343, _1292341), _1292345), c_Orderings_Obot__class_Obot(tc_fun(_1292343, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1292341))], (27011 ^ _782652) ^ [_1292450, _1292452, _1292454, _1292456] : [class_Groups_Ocomm__monoid__mult(_1292450), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1292452), _1292454))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292452, _1292450), _1292456), _1292454) = c_Groups_Oone__class_Oone(_1292450))], (27021 ^ _782652) ^ [_1292574, _1292576, _1292578, _1292580] : [class_Groups_Ocomm__monoid__mult(_1292574), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1292576), _1292578))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292576, _1292574), _1292580), _1292578) = c_Groups_Oone__class_Oone(_1292574))], (27031 ^ _782652) ^ [_1292698, _1292700, _1292702] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1292698), _1292700)), 27034 ^ _782652 : [(27045 ^ _782652) ^ [] : [27047 ^ _782652 : [(27048 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1292698), 27046 ^ [_1292698, _1292700, _1292702]), _1292700)))], (27050 ^ _782652) ^ [] : [hAPP(_1292702, 27046 ^ [_1292698, _1292700, _1292702]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292698, tc_Nat_Onat), _1292702), _1292700) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27035 ^ _782652) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292698, tc_Nat_Onat), _1292702), _1292700) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 27038 ^ _782652 : [(27039 ^ _782652) ^ [_1292860] : [hBOOL(hAPP(hAPP(c_member(_1292698), _1292860), _1292700)), -(hAPP(_1292702, _1292860) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (27054 ^ _782652) ^ [_1293118, _1293120, _1293122] : [class_Groups_Ocomm__monoid__add(_1293118), class_Groups_Ocomm__monoid__mult(_1293118), c_Nat__Transfer_Onat__set(_1293120), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1293118), _1293122), _1293120) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1293118), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1293118, tc_Nat_Onat), _1293122), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1293120)))], (27068 ^ _782652) ^ [_1293363, _1293365, _1293367, _1293369, _1293371] : [class_Groups_Ocomm__monoid__mult(_1293363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1293365), _1293367)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293365, _1293363), hAPP(hAPP(c_COMBS(_1293365, _1293363, _1293363), hAPP(hAPP(c_COMBB(_1293363, tc_fun(_1293363, _1293363), _1293365), c_Groups_Otimes__class_Otimes(_1293363)), _1293369)), _1293371)), _1293367) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293363), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293365, _1293363), _1293369), _1293367)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293365, _1293363), _1293371), _1293367)))], (27078 ^ _782652) ^ [_1293636] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1293636))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293636)))], (27084 ^ _782652) ^ [_1293670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293670)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1293670))], (27090 ^ _782652) ^ [_1293768] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1293768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293768), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27096 ^ _782652) ^ [_1293853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1293853), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1293853)))], (27102 ^ _782652) ^ [_1293944] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1293944)), -(hAPP(c_Int_Onat, _1293944) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27108 ^ _782652) ^ [_1294025] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1294025))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1294025)) = _1294025)], (27114 ^ _782652) ^ [_1294067, _1294069, _1294071] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1294067), _1294069)), 27117 ^ _782652 : [(27128 ^ _782652) ^ [] : [27130 ^ _782652 : [(27131 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294067), 27129 ^ [_1294067, _1294069, _1294071]), _1294069)))], (27133 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1294071, 27129 ^ [_1294067, _1294069, _1294071])))]], -(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(_1294067, tc_Nat_Onat), _1294071), _1294069))))], (27118 ^ _782652) ^ [] : [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(_1294067, tc_Nat_Onat), _1294071), _1294069))), 27121 ^ _782652 : [(27122 ^ _782652) ^ [_1294235] : [hBOOL(hAPP(hAPP(c_member(_1294067), _1294235), _1294069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1294071, _1294235))))]]]]], (27137 ^ _782652) ^ [_1294503, _1294505, _1294507, _1294509, _1294511] : [class_Groups_Ocomm__monoid__mult(_1294503), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294505), _1294507)), 27144 ^ _782652 : [(27145 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1294505), _1294509), _1294507)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294505, _1294503), hAPP(hAPP(c_COMBC(_1294505, _1294503, _1294503), hAPP(hAPP(c_COMBS(_1294505, _1294503, tc_fun(_1294503, _1294503)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1294503, tc_fun(_1294503, _1294503)), _1294505), c_If(_1294503)), hAPP(c_fequal, _1294509))), _1294511)), c_Groups_Oone__class_Oone(_1294503))), _1294507) = hAPP(_1294511, _1294509))], (27151 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294505), _1294509), _1294507))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294505, _1294503), hAPP(hAPP(c_COMBC(_1294505, _1294503, _1294503), hAPP(hAPP(c_COMBS(_1294505, _1294503, tc_fun(_1294503, _1294503)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1294503, tc_fun(_1294503, _1294503)), _1294505), c_If(_1294503)), hAPP(c_fequal, _1294509))), _1294511)), c_Groups_Oone__class_Oone(_1294503))), _1294507) = c_Groups_Oone__class_Oone(_1294503))]]], (27157 ^ _782652) ^ [_1295013, _1295015, _1295017, _1295019, _1295021] : [class_Groups_Ocomm__monoid__mult(_1295013), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295015), _1295017)), 27164 ^ _782652 : [(27165 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1295015), _1295019), _1295017)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295015, _1295013), hAPP(hAPP(c_COMBC(_1295015, _1295013, _1295013), hAPP(hAPP(c_COMBS(_1295015, _1295013, tc_fun(_1295013, _1295013)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1295013, tc_fun(_1295013, _1295013)), _1295015), c_If(_1295013)), hAPP(hAPP(c_COMBC(_1295015, _1295015, tc_HOL_Obool), c_fequal), _1295019))), _1295021)), c_Groups_Oone__class_Oone(_1295013))), _1295017) = hAPP(_1295021, _1295019))], (27171 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1295015), _1295019), _1295017))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295015, _1295013), hAPP(hAPP(c_COMBC(_1295015, _1295013, _1295013), hAPP(hAPP(c_COMBS(_1295015, _1295013, tc_fun(_1295013, _1295013)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1295013, tc_fun(_1295013, _1295013)), _1295015), c_If(_1295013)), hAPP(hAPP(c_COMBC(_1295015, _1295015, tc_HOL_Obool), c_fequal), _1295019))), _1295021)), c_Groups_Oone__class_Oone(_1295013))), _1295017) = c_Groups_Oone__class_Oone(_1295013))]]], (27177 ^ _782652) ^ [_1295551, _1295553, _1295555, _1295557, _1295559] : [class_Groups_Ocomm__monoid__mult(_1295551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295553), _1295555)), -(hBOOL(hAPP(hAPP(c_member(_1295553), _1295557), _1295555))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295553, _1295551), _1295559), hAPP(hAPP(c_Set_Oinsert(_1295553), _1295557), _1295555)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295551), hAPP(_1295559, _1295557)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295553, _1295551), _1295559), _1295555)))], (27191 ^ _782652) ^ [_1295801, _1295803, _1295805, _1295807, _1295809] : [class_Groups_Ocomm__monoid__mult(_1295801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295803), _1295805)), -(hBOOL(hAPP(hAPP(c_member(_1295803), _1295807), _1295805))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295803, _1295801), _1295809), hAPP(hAPP(c_Set_Oinsert(_1295803), _1295807), _1295805)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295801), hAPP(_1295809, _1295807)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295803, _1295801), _1295809), _1295805)))], (27205 ^ _782652) ^ [_1296051, _1296053, _1296055, _1296057, _1296059] : [class_Groups_Ocomm__monoid__mult(_1296051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296053), _1296055)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296053), _1296057)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296051), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296053, _1296051), _1296059), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296053, tc_HOL_Obool)), _1296055), _1296057))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296053, _1296051), _1296059), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296053, tc_HOL_Obool)), _1296055), _1296057))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296051), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296053, _1296051), _1296059), _1296055)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296053, _1296051), _1296059), _1296057)))], (27219 ^ _782652) ^ [_1296412, _1296414, _1296416, _1296418, _1296420] : [class_Groups_Ocomm__monoid__mult(_1296412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296414), _1296416)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296414), _1296418)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296412), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296414, _1296412), _1296420), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296414, tc_HOL_Obool)), _1296416), _1296418))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296414, _1296412), _1296420), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296414, tc_HOL_Obool)), _1296416), _1296418))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296412), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296414, _1296412), _1296420), _1296416)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296414, _1296412), _1296420), _1296418)))], (27233 ^ _782652) ^ [_1296773, _1296775, _1296777, _1296779] : [class_Groups_Ocomm__monoid__mult(_1296773), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296775), _1296777)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296775, _1296773), _1296779), _1296777) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1296773, _1296775, c_Groups_Otimes__class_Otimes(_1296773)), _1296779), c_Groups_Oone__class_Oone(_1296773)), _1296777))], (27243 ^ _782652) ^ [_1296968, _1296970, _1296972, _1296974] : [class_Groups_Ocomm__monoid__mult(_1296968), 27246 ^ _782652 : [(27247 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1296970), _1296972)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296970, _1296968), _1296974), _1296972) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1296968, _1296970, c_Groups_Otimes__class_Otimes(_1296968)), _1296974), c_Groups_Oone__class_Oone(_1296968)), _1296972))], (27253 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1296970), _1296972))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296970, _1296968), _1296974), _1296972) = c_Groups_Oone__class_Oone(_1296968))]]], (27259 ^ _782652) ^ [_1297240] : [-(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, _1297240))))))], (27261 ^ _782652) ^ [_1297274, _1297276, _1297278, _1297280, _1297282] : [class_Groups_Ocomm__monoid__mult(_1297274), hBOOL(hAPP(c_Finite__Set_Ofinite(_1297276), _1297278)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297276, _1297274), _1297280), hAPP(hAPP(c_Set_Oinsert(_1297276), _1297282), _1297278)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297274), hAPP(_1297280, _1297282)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297276, _1297274), _1297280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1297276, tc_HOL_Obool)), _1297278), hAPP(hAPP(c_Set_Oinsert(_1297276), _1297282), c_Orderings_Obot__class_Obot(tc_fun(_1297276, tc_HOL_Obool)))))))], (27271 ^ _782652) ^ [_1297543, _1297545, _1297547, _1297549, _1297551] : [class_Groups_Ocomm__monoid__mult(_1297543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1297545), _1297547)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1297545), _1297549)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297545, tc_HOL_Obool)), _1297547), _1297549) = c_Orderings_Obot__class_Obot(tc_fun(_1297545, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297545, _1297543), _1297551), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297545, tc_HOL_Obool)), _1297547), _1297549)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297543), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297545, _1297543), _1297551), _1297547)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297545, _1297543), _1297551), _1297549)))], (27289 ^ _782652) ^ [_1297938, _1297940, _1297942, _1297944, _1297946] : [class_Groups_Ocomm__monoid__mult(_1297938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1297940), _1297942)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1297940), _1297944)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297940, tc_HOL_Obool)), _1297942), _1297944) = c_Orderings_Obot__class_Obot(tc_fun(_1297940, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297940, _1297938), _1297946), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297940, tc_HOL_Obool)), _1297942), _1297944)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1297938), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297940, _1297938), _1297946), _1297942)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297940, _1297938), _1297946), _1297944)))], (27307 ^ _782652) ^ [_1298333, _1298335, _1298337] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1298333, _1298335, _1298337)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1298335)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1298337))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27309 ^ _782652) ^ [_1298385, _1298387, _1298389, _1298391, _1298393] : [class_Groups_Ocomm__monoid__mult(_1298385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298387), _1298389)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298387), _1298391)), 27323 ^ _782652 : [(27324 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298387), 27322 ^ [_1298385, _1298387, _1298389, _1298391, _1298393]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298387, tc_HOL_Obool)), _1298389), _1298391))))], (27326 ^ _782652) ^ [] : [hAPP(_1298393, 27322 ^ [_1298385, _1298387, _1298389, _1298391, _1298393]) = c_Groups_Oone__class_Oone(_1298385)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298387, _1298385), _1298393), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298387, tc_HOL_Obool)), _1298389), _1298391)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1298385), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298387, _1298385), _1298393), _1298389)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298387, _1298385), _1298393), _1298391)))], (27330 ^ _782652) ^ [_1298880, _1298882, _1298884, _1298886, _1298888] : [class_Groups_Ocomm__monoid__mult(_1298880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298882), _1298884)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298882), _1298886)), 27344 ^ _782652 : [(27345 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298882), 27343 ^ [_1298880, _1298882, _1298884, _1298886, _1298888]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298882, tc_HOL_Obool)), _1298884), _1298886))))], (27347 ^ _782652) ^ [] : [hAPP(_1298888, 27343 ^ [_1298880, _1298882, _1298884, _1298886, _1298888]) = c_Groups_Oone__class_Oone(_1298880)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298882, _1298880), _1298888), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298882, tc_HOL_Obool)), _1298884), _1298886)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1298880), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298882, _1298880), _1298888), _1298884)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298882, _1298880), _1298888), _1298886)))], (27351 ^ _782652) ^ [_1299375, _1299377, _1299379, _1299381, _1299383, _1299385] : [class_Groups_Ocomm__monoid__mult(_1299375), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299377), _1299379)), 27358 ^ _782652 : [(27359 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1299377), _1299381), _1299379)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1299377, _1299375), hAPP(hAPP(c_COMBC(_1299377, _1299375, _1299375), hAPP(hAPP(c_COMBS(_1299377, _1299375, tc_fun(_1299375, _1299375)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1299375, tc_fun(_1299375, _1299375)), _1299377), c_If(_1299375)), hAPP(hAPP(c_COMBC(_1299377, _1299377, tc_HOL_Obool), c_fequal), _1299381))), _1299383)), _1299385)), _1299379) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1299375), hAPP(_1299383, _1299381)), hAPP(hAPP(c_Power_Opower__class_Opower(_1299375), _1299385), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1299377), _1299379)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (27365 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1299377), _1299381), _1299379))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1299377, _1299375), hAPP(hAPP(c_COMBC(_1299377, _1299375, _1299375), hAPP(hAPP(c_COMBS(_1299377, _1299375, tc_fun(_1299375, _1299375)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1299375, tc_fun(_1299375, _1299375)), _1299377), c_If(_1299375)), hAPP(hAPP(c_COMBC(_1299377, _1299377, tc_HOL_Obool), c_fequal), _1299381))), _1299383)), _1299385)), _1299379) = hAPP(hAPP(c_Power_Opower__class_Opower(_1299375), _1299385), hAPP(c_Finite__Set_Ocard(_1299377), _1299379)))]]], (27371 ^ _782652) ^ [_1299987, _1299989, _1299991, _1299993, _1299995] : [class_Fields_Ofield(_1299987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299989), _1299991)), -(hAPP(_1299993, _1299995) = c_Groups_Ozero__class_Ozero(_1299987)), 27382 ^ _782652 : [(27383 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1299989), _1299995), _1299991)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1299989, _1299987), _1299993), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1299989, tc_HOL_Obool)), _1299991), hAPP(hAPP(c_Set_Oinsert(_1299989), _1299995), c_Orderings_Obot__class_Obot(tc_fun(_1299989, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299987), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1299989, _1299987), _1299993), _1299991)), hAPP(_1299993, _1299995)))], (27389 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1299989), _1299995), _1299991))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1299989, _1299987), _1299993), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1299989, tc_HOL_Obool)), _1299991), hAPP(hAPP(c_Set_Oinsert(_1299989), _1299995), c_Orderings_Obot__class_Obot(tc_fun(_1299989, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1299989, _1299987), _1299993), _1299991))]]], (27395 ^ _782652) ^ [_1300528, _1300530, _1300532, _1300534, _1300536] : [class_Groups_Ocomm__monoid__mult(_1300528), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300530), _1300532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300530, tc_HOL_Obool)), _1300534), _1300532)), 27409 ^ _782652 : [(27410 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1300530), 27408 ^ [_1300528, _1300530, _1300532, _1300534, _1300536]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1300530, tc_HOL_Obool)), _1300532), _1300534))))], (27412 ^ _782652) ^ [] : [hAPP(_1300536, 27408 ^ [_1300528, _1300530, _1300532, _1300534, _1300536]) = c_Groups_Oone__class_Oone(_1300528)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1300530, _1300528), _1300536), _1300532) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1300530, _1300528), _1300536), _1300534))], (27416 ^ _782652) ^ [_1300979, _1300981, _1300983] : [class_Rings_Oring__1(_1300979), -(hAPP(c_Int_Oring__1__class_Oof__int(_1300979), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1300981), _1300983)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1300979), hAPP(c_Int_Oring__1__class_Oof__int(_1300979), _1300981)), _1300983))], (27422 ^ _782652) ^ [_1301104, _1301106, _1301108, _1301110] : [class_Rings_Ocomm__semiring__1(_1301104), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301104), hAPP(hAPP(c_Power_Opower__class_Opower(_1301104), _1301106), _1301108)), _1301110) = hAPP(hAPP(c_Power_Opower__class_Opower(_1301104), _1301106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1301108), _1301110)))], (27428 ^ _782652) ^ [_1301243, _1301245, _1301247] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1301243), _1301245)), _1301247) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1301243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1301245), _1301247)))], (27430 ^ _782652) ^ [_1301294, _1301296, _1301298, _1301300] : [class_Rings_Ocomm__semiring__1(_1301294), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1301294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301294), _1301296), _1301298)), _1301300) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301294), hAPP(hAPP(c_Power_Opower__class_Opower(_1301294), _1301296), _1301300)), hAPP(hAPP(c_Power_Opower__class_Opower(_1301294), _1301298), _1301300)))], (27436 ^ _782652) ^ [_1301453, _1301455] : [class_Rings_Odivision__ring(_1301453), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301453), c_Groups_Ozero__class_Ozero(_1301453)), _1301455) = c_Groups_Ozero__class_Ozero(_1301453))], (27442 ^ _782652) ^ [_1301552, _1301554] : [class_Rings_Odivision__ring__inverse__zero(_1301552), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301552), _1301554), c_Groups_Ozero__class_Ozero(_1301552)) = c_Groups_Ozero__class_Ozero(_1301552))], (27448 ^ _782652) ^ [_1301651, _1301653] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1301651)), _1301653) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1301651), _1301653)))], (27450 ^ _782652) ^ [_1301694, _1301696] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1301694), _1301696)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1301694)), _1301696))], (27452 ^ _782652) ^ [_1301737, _1301739] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1301737)), _1301739) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1301737), _1301739)))], (27454 ^ _782652) ^ [_1301780, _1301782, _1301784, _1301786] : [class_Rings_Odivision__ring(_1301780), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301780), _1301782), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301780), _1301784), _1301786)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301780), _1301782), _1301784)), _1301786))], (27460 ^ _782652) ^ [_1301923, _1301925, _1301927, _1301929] : [class_Rings_Odivision__ring(_1301923), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1301923), _1301925), _1301927)), _1301929) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1301923), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301923), _1301925), _1301929)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301923), _1301927), _1301929)))], (27466 ^ _782652) ^ [_1302082, _1302084, _1302086] : [class_Rings_Odivision__ring(_1302082), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1302082), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302082), _1302084), _1302086)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302082), hAPP(c_Groups_Ouminus__class_Ouminus(_1302082), _1302084)), _1302086))], (27472 ^ _782652) ^ [_1302211, _1302213] : [class_Rings_Odivision__ring(_1302211), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302211), _1302213), c_Groups_Oone__class_Oone(_1302211)) = _1302213)], (27478 ^ _782652) ^ [_1302306, _1302308, _1302310, _1302312] : [class_Rings_Odivision__ring(_1302306), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302306), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1302306), _1302308), _1302310)), _1302312) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1302306), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302306), _1302308), _1302312)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302306), _1302310), _1302312)))], (27484 ^ _782652) ^ [_1302465, _1302467] : [class_Rings_Ocomm__semiring__1(_1302465), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1302465), _1302467), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1302467)], (27490 ^ _782652) ^ [_1302556, _1302558] : [c_Nat__Transfer_Ois__nat(_1302556), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1302556), _1302558)))], (27496 ^ _782652) ^ [_1302641, _1302643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302641)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1302641)), _1302643) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1302641), _1302643)))], (27502 ^ _782652) ^ [_1302758, _1302760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302758)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1302758), _1302760)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1302758)), _1302760))], (27508 ^ _782652) ^ [_1302875, _1302877, _1302879, _1302881, _1302883] : [class_Fields_Ofield(_1302875), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302875), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1302877, _1302875), _1302879), _1302881)), _1302883) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1302877, _1302875), hAPP(hAPP(c_COMBC(_1302877, _1302875, _1302875), hAPP(hAPP(c_COMBB(_1302875, tc_fun(_1302875, _1302875), _1302877), c_Rings_Oinverse__class_Odivide(_1302875)), _1302879)), _1302883)), _1302881))], (27514 ^ _782652) ^ [_1303058, _1303060, _1303062, _1303064] : [class_Rings_Odivision__ring(_1303058), -(_1303060 = c_Groups_Ozero__class_Ozero(_1303058)), 27521 ^ _782652 : [(27522 ^ _782652) ^ [] : [_1303062 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303058), _1303064), _1303060), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303058), _1303062), _1303060) = _1303064)], (27528 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303058), _1303062), _1303060) = _1303064, -(_1303062 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303058), _1303064), _1303060))]]], (27534 ^ _782652) ^ [_1303386, _1303388, _1303390, _1303392] : [class_Rings_Odivision__ring(_1303386), -(_1303388 = c_Groups_Ozero__class_Ozero(_1303386)), 27541 ^ _782652 : [(27542 ^ _782652) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303386), _1303390), _1303388) = _1303392, -(_1303390 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303386), _1303392), _1303388))], (27548 ^ _782652) ^ [] : [_1303390 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303386), _1303392), _1303388), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303386), _1303390), _1303388) = _1303392)]]], (27554 ^ _782652) ^ [_1303714, _1303716, _1303718, _1303720] : [class_Rings_Odivision__ring(_1303714), -(_1303716 = c_Groups_Ozero__class_Ozero(_1303714)), _1303718 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303714), _1303720), _1303716), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303714), _1303718), _1303716) = _1303720)], (27568 ^ _782652) ^ [_1303944, _1303946, _1303948, _1303950] : [class_Rings_Odivision__ring(_1303944), -(_1303946 = c_Groups_Ozero__class_Ozero(_1303944)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303944), _1303948), _1303946) = _1303950, -(_1303948 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303944), _1303950), _1303946))], (27582 ^ _782652) ^ [_1304174, _1304176] : [class_Rings_Odivision__ring__inverse__zero(_1304174), 27585 ^ _782652 : [(27586 ^ _782652) ^ [] : [_1304176 = c_Groups_Ozero__class_Ozero(_1304174), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304174), _1304176), _1304176) = c_Groups_Ozero__class_Ozero(_1304174))], (27592 ^ _782652) ^ [] : [-(_1304176 = c_Groups_Ozero__class_Ozero(_1304174)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304174), _1304176), _1304176) = c_Groups_Oone__class_Oone(_1304174))]]], (27598 ^ _782652) ^ [_1304396, _1304398] : [class_Rings_Odivision__ring(_1304396), -(_1304398 = c_Groups_Ozero__class_Ozero(_1304396)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304396), _1304398), _1304398) = c_Groups_Oone__class_Oone(_1304396))], (27608 ^ _782652) ^ [_1304510, _1304512, _1304514] : [class_Rings_Odivision__ring(_1304510), -(_1304512 = c_Groups_Ozero__class_Ozero(_1304510)), 27615 ^ _782652 : [(27616 ^ _782652) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304510), _1304514), _1304512) = c_Groups_Oone__class_Oone(_1304510), -(_1304514 = _1304512)], (27622 ^ _782652) ^ [] : [_1304514 = _1304512, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304510), _1304514), _1304512) = c_Groups_Oone__class_Oone(_1304510))]]], (27628 ^ _782652) ^ [_1304812, _1304814, _1304816] : [class_Rings_Odivision__ring(_1304812), -(_1304814 = c_Groups_Ozero__class_Ozero(_1304812)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1304812), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304812), _1304816), _1304814)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304812), _1304816), hAPP(c_Groups_Ouminus__class_Ouminus(_1304812), _1304814)))], (27638 ^ _782652) ^ [_1304960, _1304962, _1304964] : [class_Rings_Odivision__ring(_1304960), -(_1304962 = c_Groups_Ozero__class_Ozero(_1304960)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304960), hAPP(c_Groups_Ouminus__class_Ouminus(_1304960), _1304964)), hAPP(c_Groups_Ouminus__class_Ouminus(_1304960), _1304962)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304960), _1304964), _1304962))], (27648 ^ _782652) ^ [_1305108, _1305110, _1305112] : [class_Rings_Ocomm__semiring__1(_1305108), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1305108), _1305110), hAPP(c_Nat_OSuc, _1305112)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305108), _1305110), hAPP(hAPP(c_Power_Opower__class_Opower(_1305108), _1305110), _1305112)))], (27654 ^ _782652) ^ [_1305239, _1305241, _1305243] : [class_Rings_Ocomm__semiring__1(_1305239), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305239), _1305241), hAPP(hAPP(c_Power_Opower__class_Opower(_1305239), _1305241), _1305243)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1305239), _1305241), hAPP(c_Nat_OSuc, _1305243)))], (27660 ^ _782652) ^ [_1305370, _1305372, _1305374] : [class_Rings_Ocomm__semiring__1(_1305370), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305370), hAPP(hAPP(c_Power_Opower__class_Opower(_1305370), _1305372), _1305374)), _1305372) = hAPP(hAPP(c_Power_Opower__class_Opower(_1305370), _1305372), hAPP(c_Nat_OSuc, _1305374)))], (27666 ^ _782652) ^ [_1305501, _1305503] : [class_Rings_Ocomm__semiring__1(_1305501), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1305501), _1305503), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1305501))], (27672 ^ _782652) ^ [_1305596, _1305598, _1305600, _1305602] : [class_Rings_Ocomm__semiring__1(_1305596), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305596), hAPP(hAPP(c_Power_Opower__class_Opower(_1305596), _1305598), _1305600)), hAPP(hAPP(c_Power_Opower__class_Opower(_1305596), _1305598), _1305602)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1305596), _1305598), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1305600), _1305602)))], (27678 ^ _782652) ^ [_1305751, _1305753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305751)), -(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), _1305751), _1305753))))], (27684 ^ _782652) ^ [_1305848, _1305850, _1305852] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1305848), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1305850), _1305852)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1305848), _1305850)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1305848), _1305852)))], (27686 ^ _782652) ^ [_1305905, _1305907, _1305909] : [class_Rings_Oring__1(_1305905), hBOOL(hAPP(hAPP(c_member(_1305905), _1305907), c_Int_Oring__1__class_OInts(_1305905))), -(hBOOL(hAPP(hAPP(c_member(_1305905), hAPP(hAPP(c_Power_Opower__class_Opower(_1305905), _1305907), _1305909)), c_Int_Oring__1__class_OInts(_1305905))))], (27696 ^ _782652) ^ [_1306088, _1306090, _1306092, _1306094, _1306096] : [class_Fields_Ofield__inverse__zero(_1306088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306090), _1306092)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1306090, _1306088), hAPP(hAPP(c_COMBS(_1306090, _1306088, _1306088), hAPP(hAPP(c_COMBB(_1306088, tc_fun(_1306088, _1306088), _1306090), c_Rings_Oinverse__class_Odivide(_1306088)), _1306094)), _1306096)), _1306092) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306088), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1306090, _1306088), _1306094), _1306092)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1306090, _1306088), _1306096), _1306092)))], (27706 ^ _782652) ^ [_1306355, _1306357, _1306359] : [class_Fields_Ofield(_1306355), -(_1306357 = c_Groups_Oone__class_Oone(_1306355)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1306355), hAPP(c_Power_Opower__class_Opower(_1306355), _1306357)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1306359)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306355), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1306355), hAPP(hAPP(c_Power_Opower__class_Opower(_1306355), _1306357), _1306359)), c_Groups_Oone__class_Oone(_1306355))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1306355), _1306357), c_Groups_Oone__class_Oone(_1306355))))], (27716 ^ _782652) ^ [_1306557, _1306559] : [-(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), _1306557)), _1306559))))], (27718 ^ _782652) ^ [_1306593, _1306595, _1306597, _1306599] : [class_Groups_Ocomm__monoid__mult(_1306593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306595), _1306597)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1306595, _1306593), hAPP(c_COMBK(_1306593, _1306595), _1306599)), _1306597) = hAPP(hAPP(c_Power_Opower__class_Opower(_1306593), _1306599), hAPP(c_Finite__Set_Ocard(_1306595), _1306597)))], (27728 ^ _782652) ^ [_1306801, _1306803] : [_1306801 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1306803), _1306801) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27734 ^ _782652) ^ [_1306884, _1306886] : [-(_1306884 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1306886), _1306884) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1306886), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1306886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1306884), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (27750 ^ _782652) ^ [_1307110, _1307112] : [27751 ^ _782652 : [(27752 ^ _782652) ^ [] : [-(_1307110 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27754 ^ _782652) ^ [] : [_1307112 = 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), _1307110)), _1307112))))], (27740 ^ _782652) ^ [_1306961, _1306963] : [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), _1306961)), _1306963))), _1306961 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1306963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27758 ^ _782652) ^ [_1307246, _1307248, _1307250, _1307252] : [class_Rings_Olinordered__semidom(_1307246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307246), _1307248), _1307250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307246), c_Groups_Ozero__class_Ozero(_1307246)), _1307248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1307252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307246), hAPP(hAPP(c_Power_Opower__class_Opower(_1307246), _1307248), _1307252)), hAPP(hAPP(c_Power_Opower__class_Opower(_1307246), _1307250), _1307252))))], (27776 ^ _782652) ^ [_1307575, _1307577, _1307579, _1307581] : [class_Fields_Ofield(_1307575), -(_1307577 = c_Groups_Ozero__class_Ozero(_1307575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1307579), _1307581)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1307575), _1307577), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1307581), _1307579)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307575), hAPP(hAPP(c_Power_Opower__class_Opower(_1307575), _1307577), _1307581)), hAPP(hAPP(c_Power_Opower__class_Opower(_1307575), _1307577), _1307579)))], (27790 ^ _782652) ^ [_1307859, _1307861, _1307863] : [class_Rings_Olinordered__semidom(_1307859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307859), c_Groups_Oone__class_Oone(_1307859)), _1307861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1307863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307859), c_Groups_Oone__class_Oone(_1307859)), hAPP(hAPP(c_Power_Opower__class_Opower(_1307859), _1307861), _1307863))))], (27804 ^ _782652) ^ [_1308100, _1308102, _1308104, _1308106] : [class_Rings_Olinordered__semidom(_1308100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308100), c_Groups_Oone__class_Oone(_1308100)), _1308102)), 27811 ^ _782652 : [(27812 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308100), hAPP(hAPP(c_Power_Opower__class_Opower(_1308100), _1308102), _1308104)), hAPP(hAPP(c_Power_Opower__class_Opower(_1308100), _1308102), _1308106))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308104), _1308106)))], (27818 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308104), _1308106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308100), hAPP(hAPP(c_Power_Opower__class_Opower(_1308100), _1308102), _1308104)), hAPP(hAPP(c_Power_Opower__class_Opower(_1308100), _1308102), _1308106))))]]], (27824 ^ _782652) ^ [_1308475, _1308477, _1308479] : [class_Rings_Oring__1__no__zero__divisors(_1308475), -(_1308477 = c_Groups_Ozero__class_Ozero(_1308475)), hAPP(hAPP(c_Power_Opower__class_Opower(_1308475), _1308477), _1308479) = c_Groups_Ozero__class_Ozero(_1308475)], (27834 ^ _782652) ^ [_1308634] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1308634) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27846 ^ _782652) ^ [_1308773, _1308775] : [27847 ^ _782652 : [(27848 ^ _782652) ^ [] : [_1308775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27850 ^ _782652) ^ [] : [_1308773 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1308773), _1308775) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27836 ^ _782652) ^ [_1308675, _1308677] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1308675), _1308677) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1308677 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1308675 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27864 ^ _782652) ^ [_1309023, _1309025] : [27865 ^ _782652 : [(27866 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1309023))], (27868 ^ _782652) ^ [] : [_1309025 = 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), _1309023), _1309025))))], (27854 ^ _782652) ^ [_1308917, _1308919] : [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), _1308917), _1308919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1308917))), -(_1308919 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27872 ^ _782652) ^ [_1309160, _1309162, _1309164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1309160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1309160), _1309162)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1309160), _1309164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1309162), _1309164)))], (27882 ^ _782652) ^ [_1309341, _1309343, _1309345] : [class_Groups_Omonoid__mult(_1309341), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309341), hAPP(hAPP(c_Power_Opower__class_Opower(_1309341), _1309343), _1309345)), _1309343) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309341), _1309343), hAPP(hAPP(c_Power_Opower__class_Opower(_1309341), _1309343), _1309345)))], (27888 ^ _782652) ^ [_1309482, _1309484, _1309486, _1309488] : [class_Groups_Ocomm__monoid__mult(_1309482), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1309482), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309482), _1309484), _1309486)), _1309488) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309482), hAPP(hAPP(c_Power_Opower__class_Opower(_1309482), _1309484), _1309488)), hAPP(hAPP(c_Power_Opower__class_Opower(_1309482), _1309486), _1309488)))], (27894 ^ _782652) ^ [_1309641, _1309643] : [class_Groups_Omonoid__mult(_1309641), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1309641), c_Groups_Oone__class_Oone(_1309641)), _1309643) = c_Groups_Oone__class_Oone(_1309641))], (27900 ^ _782652) ^ [_1309740, _1309742, _1309744] : [class_Rings_Osemiring__1(_1309740), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1309740), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1309742), _1309744)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1309740), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1309740), _1309742)), _1309744))], (27906 ^ _782652) ^ [_1309865, _1309867, _1309869, _1309871] : [class_Groups_Omonoid__mult(_1309865), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1309865), _1309867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1309869), _1309871)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1309865), hAPP(hAPP(c_Power_Opower__class_Opower(_1309865), _1309867), _1309869)), _1309871))], (27912 ^ _782652) ^ [_1310004, _1310006, _1310008, _1310010] : [class_Fields_Ofield__inverse__zero(_1310004), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1310004), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310004), _1310006), _1310008)), _1310010) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1310004), hAPP(hAPP(c_Power_Opower__class_Opower(_1310004), _1310006), _1310010)), hAPP(hAPP(c_Power_Opower__class_Opower(_1310004), _1310008), _1310010)))], (27918 ^ _782652) ^ [_1310163, _1310165, _1310167] : [class_Rings_Olinordered__idom(_1310163), -(hAPP(c_Groups_Oabs__class_Oabs(_1310163), hAPP(hAPP(c_Power_Opower__class_Opower(_1310163), _1310165), _1310167)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1310163), hAPP(c_Groups_Oabs__class_Oabs(_1310163), _1310165)), _1310167))], (27924 ^ _782652) ^ [_1310292, _1310294] : [class_Groups_Omonoid__mult(_1310292), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1310292), _1310294), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1310294)], (27930 ^ _782652) ^ [_1310383, _1310385, _1310387, _1310389] : [class_Rings_Olinordered__semidom(_1310383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310383), _1310385), _1310387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310383), c_Groups_Ozero__class_Ozero(_1310383)), _1310385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310383), hAPP(hAPP(c_Power_Opower__class_Opower(_1310383), _1310385), _1310389)), hAPP(hAPP(c_Power_Opower__class_Opower(_1310383), _1310387), _1310389))))], (27944 ^ _782652) ^ [_1310652, _1310654, _1310656] : [class_Rings_Olinordered__semidom(_1310652), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310652), c_Groups_Ozero__class_Ozero(_1310652)), _1310654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310652), c_Groups_Ozero__class_Ozero(_1310652)), hAPP(hAPP(c_Power_Opower__class_Opower(_1310652), _1310654), _1310656))))], (27954 ^ _782652) ^ [_1310835, _1310837, _1310839] : [class_Rings_Olinordered__semidom(_1310835), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310835), c_Groups_Ozero__class_Ozero(_1310835)), _1310837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1310835), c_Groups_Ozero__class_Ozero(_1310835)), hAPP(hAPP(c_Power_Opower__class_Opower(_1310835), _1310837), _1310839))))], (27964 ^ _782652) ^ [_1311018, _1311020, _1311022] : [class_Power_Opower(_1311018), class_Rings_Omult__zero(_1311018), class_Rings_Ono__zero__divisors(_1311018), class_Rings_Ozero__neq__one(_1311018), 27979 ^ _782652 : [(27980 ^ _782652) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1311018), _1311020), _1311022) = c_Groups_Ozero__class_Ozero(_1311018), 27983 ^ _782652 : [(27984 ^ _782652) ^ [] : [-(_1311020 = c_Groups_Ozero__class_Ozero(_1311018))], (27986 ^ _782652) ^ [] : [_1311022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (27988 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1311018), _1311020), _1311022) = c_Groups_Ozero__class_Ozero(_1311018)), _1311020 = c_Groups_Ozero__class_Ozero(_1311018), -(_1311022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (27998 ^ _782652) ^ [_1311510, _1311512, _1311514] : [class_Rings_Olinordered__semidom(_1311510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311510), c_Groups_Oone__class_Oone(_1311510)), _1311512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1311510), c_Groups_Oone__class_Oone(_1311510)), hAPP(hAPP(c_Power_Opower__class_Opower(_1311510), _1311512), _1311514))))], (28008 ^ _782652) ^ [_1311693, _1311695] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1311693), c_Groups_Ozero__class_Ozero(_1311693)), hAPP(c_Nat_OSuc, _1311695)) = c_Groups_Ozero__class_Ozero(_1311693)), class_Power_Opower(_1311693), class_Rings_Osemiring__0(_1311693)], (28018 ^ _782652) ^ [_1311848, _1311850, _1311852, _1311854] : [class_Rings_Olinordered__semidom(_1311848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311848), c_Groups_Oone__class_Oone(_1311848)), _1311850)), 28025 ^ _782652 : [(28026 ^ _782652) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1311848), _1311850), _1311852) = hAPP(hAPP(c_Power_Opower__class_Opower(_1311848), _1311850), _1311854), -(_1311852 = _1311854)], (28032 ^ _782652) ^ [] : [_1311852 = _1311854, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1311848), _1311850), _1311852) = hAPP(hAPP(c_Power_Opower__class_Opower(_1311848), _1311850), _1311854))]]], (28038 ^ _782652) ^ [_1312187, _1312189, _1312191] : [class_Groups_Omonoid__mult(_1312187), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1312187), _1312189), hAPP(c_Nat_OSuc, _1312191)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312187), hAPP(hAPP(c_Power_Opower__class_Opower(_1312187), _1312189), _1312191)), _1312189))], (28044 ^ _782652) ^ [_1312318, _1312320, _1312322] : [class_Power_Opower(_1312318), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1312318), _1312320), hAPP(c_Nat_OSuc, _1312322)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312318), _1312320), hAPP(hAPP(c_Power_Opower__class_Opower(_1312318), _1312320), _1312322)))], (28050 ^ _782652) ^ [_1312449, _1312451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1312449)), -(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), _1312449), _1312451))))], (28056 ^ _782652) ^ [_1312546, _1312548] : [class_Power_Opower(_1312546), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1312546), _1312548), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1312546))], (28062 ^ _782652) ^ [_1312641, _1312643, _1312645, _1312647] : [class_Groups_Omonoid__mult(_1312641), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1312641), _1312643), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1312645), _1312647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312641), hAPP(hAPP(c_Power_Opower__class_Opower(_1312641), _1312643), _1312645)), hAPP(hAPP(c_Power_Opower__class_Opower(_1312641), _1312643), _1312647)))], (28068 ^ _782652) ^ [_1312796, _1312798, _1312800, _1312802] : [class_Fields_Ofield(_1312796), -(_1312798 = c_Groups_Ozero__class_Ozero(_1312796)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1312796), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312796), _1312800), _1312798)), _1312802) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312796), hAPP(hAPP(c_Power_Opower__class_Opower(_1312796), _1312800), _1312802)), hAPP(hAPP(c_Power_Opower__class_Opower(_1312796), _1312798), _1312802)))], (28078 ^ _782652) ^ [_1312974, _1312976, _1312978] : [class_Fields_Ofield__inverse__zero(_1312974), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312974), c_Groups_Oone__class_Oone(_1312974)), hAPP(hAPP(c_Power_Opower__class_Opower(_1312974), _1312976), _1312978)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1312974), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1312974), c_Groups_Oone__class_Oone(_1312974)), _1312976)), _1312978))], (28084 ^ _782652) ^ [_1313123, _1313125, _1313127] : [class_Rings_Olinordered__idom(_1313123), -(hAPP(c_Groups_Oabs__class_Oabs(_1313123), hAPP(hAPP(c_Power_Opower__class_Opower(_1313123), hAPP(c_Groups_Ouminus__class_Ouminus(_1313123), _1313125)), _1313127)) = hAPP(c_Groups_Oabs__class_Oabs(_1313123), hAPP(hAPP(c_Power_Opower__class_Opower(_1313123), _1313125), _1313127)))], (28090 ^ _782652) ^ [_1313262, _1313264, _1313266, _1313268] : [class_Rings_Olinordered__semidom(_1313262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313262), hAPP(hAPP(c_Power_Opower__class_Opower(_1313262), _1313264), _1313266)), hAPP(hAPP(c_Power_Opower__class_Opower(_1313262), _1313268), _1313266))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313262), c_Groups_Ozero__class_Ozero(_1313262)), _1313268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313262), _1313264), _1313268)))], (28104 ^ _782652) ^ [_1313531, _1313533, _1313535, _1313537] : [class_Rings_Olinordered__semidom(_1313531), hAPP(hAPP(c_Power_Opower__class_Opower(_1313531), _1313533), hAPP(c_Nat_OSuc, _1313535)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1313531), _1313537), hAPP(c_Nat_OSuc, _1313535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313531), c_Groups_Ozero__class_Ozero(_1313531)), _1313533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313531), c_Groups_Ozero__class_Ozero(_1313531)), _1313537)), -(_1313533 = _1313537)], (28122 ^ _782652) ^ [_1313858, _1313860, _1313862, _1313864] : [class_Rings_Olinordered__semidom(_1313858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313858), hAPP(hAPP(c_Power_Opower__class_Opower(_1313858), _1313860), hAPP(c_Nat_OSuc, _1313862))), hAPP(hAPP(c_Power_Opower__class_Opower(_1313858), _1313864), hAPP(c_Nat_OSuc, _1313862)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313858), c_Groups_Ozero__class_Ozero(_1313858)), _1313864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313858), _1313860), _1313864)))], (28136 ^ _782652) ^ [_1314139, _1314141, _1314143] : [class_Rings_Olinordered__semidom(_1314139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314139), c_Groups_Oone__class_Oone(_1314139)), _1314141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314139), c_Groups_Oone__class_Oone(_1314139)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1314139), _1314141), hAPP(hAPP(c_Power_Opower__class_Opower(_1314139), _1314141), _1314143)))))], (28146 ^ _782652) ^ [_1314338, _1314340, _1314342] : [class_Rings_Olinordered__semidom(_1314338), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314338), c_Groups_Oone__class_Oone(_1314338)), _1314340)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314338), hAPP(hAPP(c_Power_Opower__class_Opower(_1314338), _1314340), _1314342)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1314338), _1314340), hAPP(hAPP(c_Power_Opower__class_Opower(_1314338), _1314340), _1314342)))))], (28156 ^ _782652) ^ [_1314549, _1314551] : [class_Power_Opower(_1314549), class_Rings_Osemiring__0(_1314549), 28163 ^ _782652 : [(28164 ^ _782652) ^ [] : [_1314551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1314549), c_Groups_Ozero__class_Ozero(_1314549)), _1314551) = c_Groups_Oone__class_Oone(_1314549))], (28170 ^ _782652) ^ [] : [-(_1314551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1314549), c_Groups_Ozero__class_Ozero(_1314549)), _1314551) = c_Groups_Ozero__class_Ozero(_1314549))]]], (28176 ^ _782652) ^ [_1314823, _1314825, _1314827] : [class_Rings_Olinordered__semidom(_1314823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314823), c_Groups_Oone__class_Oone(_1314823)), _1314825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1314823), c_Groups_Oone__class_Oone(_1314823)), hAPP(hAPP(c_Power_Opower__class_Opower(_1314823), _1314825), hAPP(c_Nat_OSuc, _1314827)))))], (28186 ^ _782652) ^ [_1315012, _1315014, _1315016, _1315018] : [class_Rings_Olinordered__semidom(_1315012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1315014), _1315016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315012), c_Groups_Oone__class_Oone(_1315012)), _1315018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315012), hAPP(hAPP(c_Power_Opower__class_Opower(_1315012), _1315018), _1315014)), hAPP(hAPP(c_Power_Opower__class_Opower(_1315012), _1315018), _1315016))))], (28200 ^ _782652) ^ [_1315277, _1315279, _1315281, _1315283] : [class_Rings_Olinordered__semidom(_1315277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315277), c_Groups_Oone__class_Oone(_1315277)), _1315279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315277), hAPP(hAPP(c_Power_Opower__class_Opower(_1315277), _1315279), _1315281)), hAPP(hAPP(c_Power_Opower__class_Opower(_1315277), _1315279), _1315283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1315281), _1315283)))], (28214 ^ _782652) ^ [_1315542, _1315544, _1315546, _1315548] : [class_Rings_Olinordered__semidom(_1315542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315542), c_Groups_Oone__class_Oone(_1315542)), _1315544)), 28221 ^ _782652 : [(28222 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315542), hAPP(hAPP(c_Power_Opower__class_Opower(_1315542), _1315544), _1315546)), hAPP(hAPP(c_Power_Opower__class_Opower(_1315542), _1315544), _1315548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1315546), _1315548)))], (28228 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1315546), _1315548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315542), hAPP(hAPP(c_Power_Opower__class_Opower(_1315542), _1315544), _1315546)), hAPP(hAPP(c_Power_Opower__class_Opower(_1315542), _1315544), _1315548))))]]], (28234 ^ _782652) ^ [_1315917, _1315919, _1315921] : [class_Rings_Olinordered__idom(_1315917), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315917), c_Groups_Ozero__class_Ozero(_1315917)), hAPP(hAPP(c_Power_Opower__class_Opower(_1315917), hAPP(c_Groups_Oabs__class_Oabs(_1315917), _1315919)), _1315921))))], (28240 ^ _782652) ^ [_1316038, _1316040, _1316042, _1316044] : [class_Rings_Olinordered__semidom(_1316038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1316040), _1316042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316038), c_Groups_Oone__class_Oone(_1316038)), _1316044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316038), hAPP(hAPP(c_Power_Opower__class_Opower(_1316038), _1316044), _1316040)), hAPP(hAPP(c_Power_Opower__class_Opower(_1316038), _1316044), _1316042))))], (28254 ^ _782652) ^ [_1316303, _1316305, _1316307] : [class_Rings_Oring__1(_1316303), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1316303), hAPP(c_Groups_Ouminus__class_Ouminus(_1316303), _1316305)), _1316307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1316303), hAPP(hAPP(c_Power_Opower__class_Opower(_1316303), hAPP(c_Groups_Ouminus__class_Ouminus(_1316303), c_Groups_Oone__class_Oone(_1316303))), _1316307)), hAPP(hAPP(c_Power_Opower__class_Opower(_1316303), _1316305), _1316307)))], (28260 ^ _782652) ^ [_1316468, _1316470, _1316472] : [class_Rings_Olinordered__semidom(_1316468), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316468), c_Groups_Ozero__class_Ozero(_1316468)), _1316470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316468), _1316470), c_Groups_Oone__class_Oone(_1316468))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1316468), _1316470), hAPP(hAPP(c_Power_Opower__class_Opower(_1316468), _1316470), _1316472))), hAPP(hAPP(c_Power_Opower__class_Opower(_1316468), _1316470), _1316472))))], (28274 ^ _782652) ^ [_1316751, _1316753, _1316755, _1316757] : [class_Rings_Olinordered__semidom(_1316751), hAPP(hAPP(c_Power_Opower__class_Opower(_1316751), _1316753), _1316755) = hAPP(hAPP(c_Power_Opower__class_Opower(_1316751), _1316757), _1316755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316751), c_Groups_Ozero__class_Ozero(_1316751)), _1316753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316751), c_Groups_Ozero__class_Ozero(_1316751)), _1316757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1316755)), -(_1316753 = _1316757)], (28296 ^ _782652) ^ [_1317126, _1317128, _1317130] : [class_Rings_Olinordered__semidom(_1317126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317126), c_Groups_Ozero__class_Ozero(_1317126)), _1317128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317126), _1317128), c_Groups_Oone__class_Oone(_1317126))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317126), hAPP(hAPP(c_Power_Opower__class_Opower(_1317126), _1317128), hAPP(c_Nat_OSuc, _1317130))), c_Groups_Oone__class_Oone(_1317126))))], (28310 ^ _782652) ^ [_1317387, _1317389, _1317391, _1317393] : [class_Rings_Olinordered__semidom(_1317387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1317389), _1317391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317387), c_Groups_Ozero__class_Ozero(_1317387)), _1317393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317387), _1317393), c_Groups_Oone__class_Oone(_1317387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317387), hAPP(hAPP(c_Power_Opower__class_Opower(_1317387), _1317393), _1317391)), hAPP(hAPP(c_Power_Opower__class_Opower(_1317387), _1317393), _1317389))))], (28328 ^ _782652) ^ [_1317726, _1317728, _1317730, _1317732] : [class_Rings_Olinordered__semidom(_1317726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1317728), _1317730)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317726), c_Groups_Ozero__class_Ozero(_1317726)), _1317732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317726), _1317732), c_Groups_Oone__class_Oone(_1317726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317726), hAPP(hAPP(c_Power_Opower__class_Opower(_1317726), _1317732), _1317730)), hAPP(hAPP(c_Power_Opower__class_Opower(_1317726), _1317732), _1317728))))], (28346 ^ _782652) ^ [_1318065, _1318067, _1318069, _1318071] : [class_Rings_Olinordered__semidom(_1318065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318065), c_Groups_Oone__class_Oone(_1318065)), _1318067)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318065), hAPP(hAPP(c_Power_Opower__class_Opower(_1318065), _1318067), _1318069)), hAPP(hAPP(c_Power_Opower__class_Opower(_1318065), _1318067), _1318071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1318069), _1318071)))], (28360 ^ _782652) ^ [_1318330, _1318332, _1318334, _1318336] : [class_Fields_Olinordered__field__inverse__zero(_1318330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318330), _1318332), _1318334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318330), _1318336), c_Groups_Ozero__class_Ozero(_1318330))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318330), c_Groups_Ozero__class_Ozero(_1318330)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318330), _1318332), _1318334))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318330), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318330), _1318336), _1318332)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318330), _1318336), _1318334))))], (28378 ^ _782652) ^ [_1318689, _1318691, _1318693, _1318695] : [class_Fields_Olinordered__field(_1318689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318689), _1318691), _1318693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318689), c_Groups_Ozero__class_Ozero(_1318689)), _1318695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318689), c_Groups_Ozero__class_Ozero(_1318689)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1318689), _1318693), _1318691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318689), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318689), _1318695), _1318693)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1318689), _1318695), _1318691))))], (28396 ^ _782652) ^ [_1319048, _1319050, _1319052, _1319054] : [class_Fields_Olinordered__field(_1319048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319048), _1319050), c_Groups_Ozero__class_Ozero(_1319048))), 28403 ^ _782652 : [(28404 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319048), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319048), _1319052), _1319050)), _1319054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319048), _1319054), _1319050)), _1319052)))], (28410 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319048), _1319054), _1319050)), _1319052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319048), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319048), _1319052), _1319050)), _1319054)))]]], (28416 ^ _782652) ^ [_1319429, _1319431, _1319433, _1319435] : [class_Fields_Olinordered__field(_1319429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319429), _1319431), c_Groups_Ozero__class_Ozero(_1319429))), 28423 ^ _782652 : [(28424 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319429), _1319433), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319429), _1319435), _1319431))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319429), _1319435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319429), _1319433), _1319431))))], (28430 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319429), _1319435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319429), _1319433), _1319431))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319429), _1319433), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319429), _1319435), _1319431))))]]], (28436 ^ _782652) ^ [_1319810, _1319812, _1319814, _1319816, _1319818] : [class_Fields_Ofield__inverse__zero(_1319810), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319810), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319810), _1319812), _1319814)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319810), _1319816), _1319818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319810), _1319812), _1319816)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319810), _1319814), _1319818)))], (28442 ^ _782652) ^ [_1319987, _1319989, _1319991] : [class_Fields_Ofield__inverse__zero(_1319987), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319987), hAPP(c_Groups_Ouminus__class_Ouminus(_1319987), _1319989)), hAPP(c_Groups_Ouminus__class_Ouminus(_1319987), _1319991)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1319987), _1319989), _1319991))], (28448 ^ _782652) ^ [_1320116, _1320118, _1320120] : [class_Fields_Ofield__inverse__zero(_1320116), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1320116), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320116), _1320118), _1320120)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320116), _1320118), hAPP(c_Groups_Ouminus__class_Ouminus(_1320116), _1320120)))], (28454 ^ _782652) ^ [_1320245, _1320247, _1320249] : [class_Fields_Olinordered__field__inverse__zero(_1320245), -(hAPP(c_Groups_Oabs__class_Oabs(_1320245), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320245), _1320247), _1320249)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320245), hAPP(c_Groups_Oabs__class_Oabs(_1320245), _1320247)), hAPP(c_Groups_Oabs__class_Oabs(_1320245), _1320249)))], (28460 ^ _782652) ^ [_1320384, _1320386, _1320388] : [class_Fields_Olinordered__field__inverse__zero(_1320384), 28463 ^ _782652 : [(28464 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), c_Groups_Ozero__class_Ozero(_1320384)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320384), _1320386), _1320388))), 28469 ^ _782652 : [(28470 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), c_Groups_Ozero__class_Ozero(_1320384)), _1320386)))], (28472 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), c_Groups_Ozero__class_Ozero(_1320384)), _1320388)))]], 28473 ^ _782652 : [(28474 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), _1320386), c_Groups_Ozero__class_Ozero(_1320384))))], (28476 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), _1320388), c_Groups_Ozero__class_Ozero(_1320384))))]]], (28478 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), c_Groups_Ozero__class_Ozero(_1320384)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320384), _1320386), _1320388)))), 28479 ^ _782652 : [(28480 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), c_Groups_Ozero__class_Ozero(_1320384)), _1320386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), c_Groups_Ozero__class_Ozero(_1320384)), _1320388))], (28486 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), _1320386), c_Groups_Ozero__class_Ozero(_1320384))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320384), _1320388), c_Groups_Ozero__class_Ozero(_1320384)))]]]]], (28494 ^ _782652) ^ [_1320974, _1320976, _1320978] : [class_Fields_Olinordered__field__inverse__zero(_1320974), 28497 ^ _782652 : [(28498 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320974), _1320976), _1320978)), c_Groups_Ozero__class_Ozero(_1320974))), 28503 ^ _782652 : [(28504 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), c_Groups_Ozero__class_Ozero(_1320974)), _1320976)))], (28506 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), _1320978), c_Groups_Ozero__class_Ozero(_1320974))))]], 28507 ^ _782652 : [(28508 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), _1320976), c_Groups_Ozero__class_Ozero(_1320974))))], (28510 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), c_Groups_Ozero__class_Ozero(_1320974)), _1320978)))]]], (28512 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1320974), _1320976), _1320978)), c_Groups_Ozero__class_Ozero(_1320974)))), 28513 ^ _782652 : [(28514 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), c_Groups_Ozero__class_Ozero(_1320974)), _1320976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), _1320978), c_Groups_Ozero__class_Ozero(_1320974)))], (28520 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), _1320976), c_Groups_Ozero__class_Ozero(_1320974))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320974), c_Groups_Ozero__class_Ozero(_1320974)), _1320978))]]]]], (28528 ^ _782652) ^ [_1321564, _1321566, _1321568, _1321570] : [class_Fields_Olinordered__field__inverse__zero(_1321564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321564), _1321566), _1321568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321564), c_Groups_Ozero__class_Ozero(_1321564)), _1321570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321564), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321564), _1321566), _1321570)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321564), _1321568), _1321570))))], (28542 ^ _782652) ^ [_1321833, _1321835, _1321837, _1321839] : [class_Fields_Olinordered__field__inverse__zero(_1321833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321833), _1321835), _1321837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321833), _1321839), c_Groups_Ozero__class_Ozero(_1321833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321833), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321833), _1321837), _1321839)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1321833), _1321835), _1321839))))], (28556 ^ _782652) ^ [_1322102, _1322104, _1322106] : [class_Fields_Olinordered__field__inverse__zero(_1322102), 28559 ^ _782652 : [(28560 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), c_Groups_Ozero__class_Ozero(_1322102)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322102), _1322104), _1322106))), 28565 ^ _782652 : [(28566 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), c_Groups_Ozero__class_Ozero(_1322102)), _1322104)))], (28568 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), c_Groups_Ozero__class_Ozero(_1322102)), _1322106)))]], 28569 ^ _782652 : [(28570 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), _1322104), c_Groups_Ozero__class_Ozero(_1322102))))], (28572 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), _1322106), c_Groups_Ozero__class_Ozero(_1322102))))]]], (28574 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), c_Groups_Ozero__class_Ozero(_1322102)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322102), _1322104), _1322106)))), 28575 ^ _782652 : [(28576 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), c_Groups_Ozero__class_Ozero(_1322102)), _1322104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), c_Groups_Ozero__class_Ozero(_1322102)), _1322106))], (28582 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), _1322104), c_Groups_Ozero__class_Ozero(_1322102))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322102), _1322106), c_Groups_Ozero__class_Ozero(_1322102)))]]]]], (28590 ^ _782652) ^ [_1322692, _1322694, _1322696] : [class_Fields_Olinordered__field__inverse__zero(_1322692), 28593 ^ _782652 : [(28594 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322692), _1322694), _1322696)), c_Groups_Ozero__class_Ozero(_1322692))), 28599 ^ _782652 : [(28600 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), c_Groups_Ozero__class_Ozero(_1322692)), _1322694)))], (28602 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), _1322696), c_Groups_Ozero__class_Ozero(_1322692))))]], 28603 ^ _782652 : [(28604 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), _1322694), c_Groups_Ozero__class_Ozero(_1322692))))], (28606 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), c_Groups_Ozero__class_Ozero(_1322692)), _1322696)))]]], (28608 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1322692), _1322694), _1322696)), c_Groups_Ozero__class_Ozero(_1322692)))), 28609 ^ _782652 : [(28610 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), c_Groups_Ozero__class_Ozero(_1322692)), _1322694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), _1322696), c_Groups_Ozero__class_Ozero(_1322692)))], (28616 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), _1322694), c_Groups_Ozero__class_Ozero(_1322692))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1322692), c_Groups_Ozero__class_Ozero(_1322692)), _1322696))]]]]], (28624 ^ _782652) ^ [_1323282, _1323284, _1323286] : [class_Fields_Olinordered__field(_1323282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323282), c_Groups_Ozero__class_Ozero(_1323282)), _1323284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323282), c_Groups_Ozero__class_Ozero(_1323282)), _1323286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323282), c_Groups_Ozero__class_Ozero(_1323282)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323282), _1323284), _1323286))))], (28638 ^ _782652) ^ [_1323537, _1323539, _1323541] : [class_Fields_Olinordered__field(_1323537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323537), c_Groups_Ozero__class_Ozero(_1323537)), _1323539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323537), _1323541), c_Groups_Ozero__class_Ozero(_1323537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323537), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323537), _1323539), _1323541)), c_Groups_Ozero__class_Ozero(_1323537))))], (28652 ^ _782652) ^ [_1323792, _1323794, _1323796] : [class_Fields_Olinordered__field(_1323792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323792), _1323794), c_Groups_Ozero__class_Ozero(_1323792))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323792), c_Groups_Ozero__class_Ozero(_1323792)), _1323796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1323792), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1323792), _1323794), _1323796)), c_Groups_Ozero__class_Ozero(_1323792))))], (28666 ^ _782652) ^ [_1324047, _1324049, _1324051] : [class_Fields_Olinordered__field(_1324047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324047), _1324049), c_Groups_Ozero__class_Ozero(_1324047))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324047), _1324051), c_Groups_Ozero__class_Ozero(_1324047))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324047), c_Groups_Ozero__class_Ozero(_1324047)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324047), _1324049), _1324051))))], (28680 ^ _782652) ^ [_1324302, _1324304, _1324306, _1324308] : [class_Fields_Olinordered__field(_1324302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324302), _1324304), _1324306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324302), c_Groups_Ozero__class_Ozero(_1324302)), _1324308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324302), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324302), _1324304), _1324308)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324302), _1324306), _1324308))))], (28694 ^ _782652) ^ [_1324571, _1324573, _1324575, _1324577] : [class_Fields_Olinordered__field(_1324571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324571), _1324573), _1324575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324571), _1324577), c_Groups_Ozero__class_Ozero(_1324571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324571), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324571), _1324575), _1324577)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324571), _1324573), _1324577))))], (28708 ^ _782652) ^ [_1324840, _1324842, _1324844, _1324846, _1324848] : [class_Fields_Ofield(_1324840), -(_1324842 = c_Groups_Ozero__class_Ozero(_1324840)), -(_1324844 = c_Groups_Ozero__class_Ozero(_1324840)), 28719 ^ _782652 : [(28720 ^ _782652) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324840), _1324846), _1324842) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324840), _1324848), _1324844), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324840), _1324846), _1324844) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324840), _1324848), _1324842))], (28726 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324840), _1324846), _1324844) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1324840), _1324848), _1324842), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324840), _1324846), _1324842) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324840), _1324848), _1324844))]]], (28732 ^ _782652) ^ [_1325289, _1325291, _1325293, _1325295] : [class_Fields_Ofield__inverse__zero(_1325289), -(_1325291 = c_Groups_Ozero__class_Ozero(_1325289)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325289), _1325291), _1325293)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325289), _1325291), _1325295)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325289), _1325293), _1325295))], (28742 ^ _782652) ^ [_1325451, _1325453, _1325455, _1325457] : [class_Fields_Ofield__inverse__zero(_1325451), -(_1325453 = c_Groups_Ozero__class_Ozero(_1325451)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325451), _1325455), _1325453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325451), _1325457), _1325453)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325451), _1325455), _1325457))], (28752 ^ _782652) ^ [_1325613, _1325615, _1325617, _1325619] : [class_Fields_Ofield__inverse__zero(_1325613), 28755 ^ _782652 : [(28772 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325613), _1325615), _1325617) = _1325619), 28775 ^ _782652 : [(28776 ^ _782652) ^ [] : [_1325617 = c_Groups_Ozero__class_Ozero(_1325613)], (28778 ^ _782652) ^ [] : [_1325615 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325613), _1325619), _1325617)]], 28779 ^ _782652 : [(28780 ^ _782652) ^ [] : [-(_1325617 = c_Groups_Ozero__class_Ozero(_1325613))], (28782 ^ _782652) ^ [] : [_1325619 = c_Groups_Ozero__class_Ozero(_1325613)]]], (28756 ^ _782652) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325613), _1325615), _1325617) = _1325619, 28759 ^ _782652 : [(28760 ^ _782652) ^ [] : [-(_1325617 = c_Groups_Ozero__class_Ozero(_1325613)), -(_1325615 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325613), _1325619), _1325617))], (28766 ^ _782652) ^ [] : [_1325617 = c_Groups_Ozero__class_Ozero(_1325613), -(_1325619 = c_Groups_Ozero__class_Ozero(_1325613))]]]]], (28786 ^ _782652) ^ [_1326107, _1326109, _1326111, _1326113] : [class_Fields_Ofield__inverse__zero(_1326107), 28789 ^ _782652 : [(28806 ^ _782652) ^ [] : [-(_1326109 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326107), _1326111), _1326113)), 28809 ^ _782652 : [(28810 ^ _782652) ^ [] : [_1326113 = c_Groups_Ozero__class_Ozero(_1326107)], (28812 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326107), _1326109), _1326113) = _1326111]], 28813 ^ _782652 : [(28814 ^ _782652) ^ [] : [-(_1326113 = c_Groups_Ozero__class_Ozero(_1326107))], (28816 ^ _782652) ^ [] : [_1326109 = c_Groups_Ozero__class_Ozero(_1326107)]]], (28790 ^ _782652) ^ [] : [_1326109 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326107), _1326111), _1326113), 28793 ^ _782652 : [(28794 ^ _782652) ^ [] : [-(_1326113 = c_Groups_Ozero__class_Ozero(_1326107)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326107), _1326109), _1326113) = _1326111)], (28800 ^ _782652) ^ [] : [_1326113 = c_Groups_Ozero__class_Ozero(_1326107), -(_1326109 = c_Groups_Ozero__class_Ozero(_1326107))]]]]], (28820 ^ _782652) ^ [_1326601, _1326603, _1326605] : [class_Fields_Olinordered__field(_1326601), -(_1326603 = c_Groups_Ozero__class_Ozero(_1326601)), -(hAPP(c_Groups_Oabs__class_Oabs(_1326601), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326601), _1326605), _1326603)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326601), hAPP(c_Groups_Oabs__class_Oabs(_1326601), _1326605)), hAPP(c_Groups_Oabs__class_Oabs(_1326601), _1326603)))], (28830 ^ _782652) ^ [_1326759, _1326761, _1326763] : [class_Fields_Olinordered__field(_1326759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326759), _1326761), c_Groups_Ozero__class_Ozero(_1326759))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326759), _1326763), c_Groups_Ozero__class_Ozero(_1326759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326759), c_Groups_Ozero__class_Ozero(_1326759)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1326759), _1326761), _1326763))))], (28844 ^ _782652) ^ [_1327014, _1327016, _1327018] : [class_Fields_Olinordered__field(_1327014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327014), _1327016), c_Groups_Ozero__class_Ozero(_1327014))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327014), c_Groups_Ozero__class_Ozero(_1327014)), _1327018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327014), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327014), _1327016), _1327018)), c_Groups_Ozero__class_Ozero(_1327014))))], (28858 ^ _782652) ^ [_1327269, _1327271, _1327273, _1327275, _1327277] : [class_Fields_Olinordered__field(_1327269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327269), c_Groups_Ozero__class_Ozero(_1327269)), _1327271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327269), _1327271), _1327273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327269), c_Groups_Ozero__class_Ozero(_1327269)), _1327275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327269), _1327275), _1327277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327269), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327269), _1327271), _1327277)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327269), _1327273), _1327275))))], (28880 ^ _782652) ^ [_1327692, _1327694, _1327696, _1327698, _1327700] : [class_Fields_Olinordered__field(_1327692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327692), c_Groups_Ozero__class_Ozero(_1327692)), _1327694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327692), _1327694), _1327696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327692), c_Groups_Ozero__class_Ozero(_1327692)), _1327698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327692), _1327698), _1327700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327692), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327692), _1327694), _1327700)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327692), _1327696), _1327698))))], (28902 ^ _782652) ^ [_1328115, _1328117, _1328119, _1328121, _1328123] : [class_Fields_Olinordered__field(_1328115), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328115), c_Groups_Ozero__class_Ozero(_1328115)), _1328117)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328115), _1328117), _1328119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328115), c_Groups_Ozero__class_Ozero(_1328115)), _1328121)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328115), _1328121), _1328123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328115), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328115), _1328117), _1328123)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328115), _1328119), _1328121))))], (28924 ^ _782652) ^ [_1328538, _1328540, _1328542] : [class_Fields_Olinordered__field(_1328538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328538), c_Groups_Ozero__class_Ozero(_1328538)), _1328540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328538), _1328542), c_Groups_Ozero__class_Ozero(_1328538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328538), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328538), _1328540), _1328542)), c_Groups_Ozero__class_Ozero(_1328538))))], (28938 ^ _782652) ^ [_1328793, _1328795, _1328797] : [class_Fields_Olinordered__field(_1328793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328793), c_Groups_Ozero__class_Ozero(_1328793)), _1328795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328793), c_Groups_Ozero__class_Ozero(_1328793)), _1328797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328793), c_Groups_Ozero__class_Ozero(_1328793)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328793), _1328795), _1328797))))], (28952 ^ _782652) ^ [_1329048, _1329050, _1329052, _1329054] : [class_Fields_Olinordered__field__inverse__zero(_1329048), 28955 ^ _782652 : [(28982 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329050), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329048), _1329052), _1329054)))), 28985 ^ _782652 : [(28986 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), c_Groups_Ozero__class_Ozero(_1329048)), _1329054)))], (28988 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329048), _1329050), _1329054)), _1329052))]], 28989 ^ _782652 : [(28990 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), c_Groups_Ozero__class_Ozero(_1329048)), _1329054))], (28992 ^ _782652) ^ [] : [28993 ^ _782652 : [(28994 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329054), c_Groups_Ozero__class_Ozero(_1329048))))], (28996 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329048), _1329050), _1329054)))]], 28997 ^ _782652 : [(28998 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329054), c_Groups_Ozero__class_Ozero(_1329048)))], (29000 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329050), c_Groups_Ozero__class_Ozero(_1329048)))]]]]], (28956 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329050), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329048), _1329052), _1329054))), 28959 ^ _782652 : [(28960 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), c_Groups_Ozero__class_Ozero(_1329048)), _1329054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329048), _1329050), _1329054)), _1329052)))], (28966 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), c_Groups_Ozero__class_Ozero(_1329048)), _1329054))), 28969 ^ _782652 : [(28970 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329054), c_Groups_Ozero__class_Ozero(_1329048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329048), _1329050), _1329054))))], (28976 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329054), c_Groups_Ozero__class_Ozero(_1329048)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329048), _1329050), c_Groups_Ozero__class_Ozero(_1329048))))]]]]]]], (29004 ^ _782652) ^ [_1330001, _1330003, _1330005, _1330007] : [class_Fields_Olinordered__field__inverse__zero(_1330001), 29007 ^ _782652 : [(29034 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330001), _1330003), _1330005)), _1330007))), 29037 ^ _782652 : [(29038 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), c_Groups_Ozero__class_Ozero(_1330001)), _1330005)))], (29040 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), _1330003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330001), _1330007), _1330005)))]], 29041 ^ _782652 : [(29042 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), c_Groups_Ozero__class_Ozero(_1330001)), _1330005))], (29044 ^ _782652) ^ [] : [29045 ^ _782652 : [(29046 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), _1330005), c_Groups_Ozero__class_Ozero(_1330001))))], (29048 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330001), _1330007), _1330005)), _1330003))]], 29049 ^ _782652 : [(29050 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), _1330005), c_Groups_Ozero__class_Ozero(_1330001)))], (29052 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), c_Groups_Ozero__class_Ozero(_1330001)), _1330007))]]]]], (29008 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330001), _1330003), _1330005)), _1330007)), 29011 ^ _782652 : [(29012 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), c_Groups_Ozero__class_Ozero(_1330001)), _1330005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), _1330003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330001), _1330007), _1330005))))], (29018 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), c_Groups_Ozero__class_Ozero(_1330001)), _1330005))), 29021 ^ _782652 : [(29022 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), _1330005), c_Groups_Ozero__class_Ozero(_1330001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330001), _1330007), _1330005)), _1330003)))], (29028 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), _1330005), c_Groups_Ozero__class_Ozero(_1330001)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330001), c_Groups_Ozero__class_Ozero(_1330001)), _1330007)))]]]]]]], (29056 ^ _782652) ^ [_1330954, _1330956, _1330958, _1330960] : [class_Fields_Olinordered__field(_1330954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330954), c_Groups_Ozero__class_Ozero(_1330954)), _1330956)), 29063 ^ _782652 : [(29064 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330954), _1330958), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330954), _1330960), _1330956))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330954), _1330958), _1330956)), _1330960)))], (29070 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330954), _1330958), _1330956)), _1330960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330954), _1330958), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330954), _1330960), _1330956))))]]], (29076 ^ _782652) ^ [_1331335, _1331337, _1331339, _1331341] : [class_Fields_Olinordered__field(_1331335), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331335), c_Groups_Ozero__class_Ozero(_1331335)), _1331337)), 29083 ^ _782652 : [(29084 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331335), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331335), _1331339), _1331337)), _1331341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331335), _1331339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1331335), _1331341), _1331337))))], (29090 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331335), _1331339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1331335), _1331341), _1331337))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331335), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331335), _1331339), _1331337)), _1331341)))]]], (29096 ^ _782652) ^ [_1331716, _1331718, _1331720, _1331722] : [class_Fields_Olinordered__field(_1331716), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331716), c_Groups_Ozero__class_Ozero(_1331716)), _1331718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331716), _1331720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1331716), _1331722), _1331718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331716), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331716), _1331720), _1331718)), _1331722)))], (29110 ^ _782652) ^ [_1331985, _1331987, _1331989, _1331991] : [class_Fields_Olinordered__field(_1331985), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331985), c_Groups_Ozero__class_Ozero(_1331985)), _1331987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1331985), _1331989), _1331987)), _1331991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1331985), _1331989), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331985), _1331991), _1331987))))], (29124 ^ _782652) ^ [_1332254, _1332256, _1332258, _1332260] : [class_Fields_Olinordered__field(_1332254), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332254), _1332256), c_Groups_Ozero__class_Ozero(_1332254))), 29131 ^ _782652 : [(29132 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332254), _1332258), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1332254), _1332260), _1332256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332254), _1332260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332254), _1332258), _1332256))))], (29138 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332254), _1332260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332254), _1332258), _1332256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332254), _1332258), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1332254), _1332260), _1332256))))]]], (29144 ^ _782652) ^ [_1332635, _1332637, _1332639, _1332641] : [class_Fields_Olinordered__field(_1332635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332635), _1332637), c_Groups_Ozero__class_Ozero(_1332635))), 29151 ^ _782652 : [(29152 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332635), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1332635), _1332639), _1332637)), _1332641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332635), _1332641), _1332637)), _1332639)))], (29158 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332635), _1332641), _1332637)), _1332639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1332635), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1332635), _1332639), _1332637)), _1332641)))]]], (29164 ^ _782652) ^ [_1333016, _1333018, _1333020, _1333022] : [class_Fields_Olinordered__field(_1333016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1333016), _1333018), _1333020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1333016), c_Groups_Ozero__class_Ozero(_1333016)), _1333022)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1333016), c_Groups_Ozero__class_Ozero(_1333016)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333016), _1333020), _1333018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1333016), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333016), _1333022), _1333020)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333016), _1333022), _1333018))))], (29182 ^ _782652) ^ [_1333375, _1333377, _1333379, _1333381] : [class_Fields_Olinordered__field(_1333375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1333375), _1333377), _1333379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1333375), _1333381), c_Groups_Ozero__class_Ozero(_1333375))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1333375), c_Groups_Ozero__class_Ozero(_1333375)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333375), _1333377), _1333379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1333375), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333375), _1333381), _1333377)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333375), _1333381), _1333379))))], (29200 ^ _782652) ^ [_1333734, _1333736, _1333738, _1333740, _1333742] : [class_Fields_Ofield(_1333734), -(_1333736 = c_Groups_Ozero__class_Ozero(_1333734)), -(_1333738 = c_Groups_Ozero__class_Ozero(_1333734)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1333734), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333734), _1333740), _1333736)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333734), _1333742), _1333738)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333734), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1333734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333734), _1333740), _1333738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333734), _1333742), _1333736))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333734), _1333736), _1333738)))], (29214 ^ _782652) ^ [_1333981, _1333983, _1333985, _1333987] : [class_Fields_Ofield(_1333981), -(_1333983 = c_Groups_Ozero__class_Ozero(_1333981)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1333981), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333981), _1333985), _1333983)), _1333987) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1333981), _1333985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333981), _1333983), _1333987))), _1333983))], (29224 ^ _782652) ^ [_1334159, _1334161, _1334163, _1334165] : [class_Fields_Ofield__inverse__zero(_1334159), -(_1334161 = c_Groups_Ozero__class_Ozero(_1334159)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334159), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334159), _1334163), _1334161)), _1334165) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334159), _1334163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334159), _1334165), _1334161))), _1334161))], (29234 ^ _782652) ^ [_1334337, _1334339, _1334341, _1334343] : [class_Fields_Ofield(_1334337), -(_1334339 = c_Groups_Ozero__class_Ozero(_1334337)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334337), _1334341), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334337), _1334343), _1334339)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334337), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334337), _1334339), _1334341)), _1334343)), _1334339))], (29244 ^ _782652) ^ [_1334515, _1334517, _1334519, _1334521] : [class_Fields_Ofield__inverse__zero(_1334515), -(_1334517 = c_Groups_Ozero__class_Ozero(_1334515)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334515), _1334519), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334515), _1334521), _1334517)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334515), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334515), _1334521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334515), _1334519), _1334517))), _1334517))], (29254 ^ _782652) ^ [_1334693, _1334695, _1334697, _1334699] : [class_Fields_Ofield(_1334693), -(_1334695 = c_Groups_Ozero__class_Ozero(_1334693)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1334693), _1334697), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334693), _1334699), _1334695)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334693), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1334693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334693), _1334695), _1334697)), _1334699)), _1334695))], (29264 ^ _782652) ^ [_1334871, _1334873, _1334875, _1334877] : [class_Fields_Ofield(_1334871), -(_1334873 = c_Groups_Ozero__class_Ozero(_1334871)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1334871), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334871), _1334875), _1334873)), _1334877) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334871), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1334871), _1334875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334871), _1334873), _1334877))), _1334873))], (29274 ^ _782652) ^ [_1335049, _1335051, _1335053, _1335055, _1335057] : [class_Fields_Ofield(_1335049), -(_1335051 = c_Groups_Ozero__class_Ozero(_1335049)), -(_1335053 = c_Groups_Ozero__class_Ozero(_1335049)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1335049), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335049), _1335055), _1335051)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335049), _1335057), _1335053)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335049), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1335049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335049), _1335055), _1335053)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335049), _1335057), _1335051))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335049), _1335051), _1335053)))], (29288 ^ _782652) ^ [_1335296, _1335298, _1335300] : [class_Fields_Olinordered__field(_1335296), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335296), _1335298), _1335300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335296), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1335296), _1335298), _1335300)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1335296), c_Groups_Oone__class_Oone(_1335296)), c_Groups_Oone__class_Oone(_1335296)))), _1335300)))], (29298 ^ _782652) ^ [_1335511, _1335513, _1335515] : [class_Fields_Olinordered__field(_1335511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335511), _1335513), _1335515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335511), _1335513), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335511), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1335511), _1335513), _1335515)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1335511), c_Groups_Oone__class_Oone(_1335511)), c_Groups_Oone__class_Oone(_1335511))))))], (29308 ^ _782652) ^ [_1335726, _1335728, _1335730] : [class_Fields_Olinordered__field__inverse__zero(_1335726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335726), c_Groups_Ozero__class_Ozero(_1335726)), _1335728)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335726), hAPP(c_Groups_Oabs__class_Oabs(_1335726), _1335730)), _1335728) = hAPP(c_Groups_Oabs__class_Oabs(_1335726), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335726), _1335730), _1335728)))], (29318 ^ _782652) ^ [_1335927, _1335929, _1335931, _1335933] : [class_Fields_Olinordered__field__inverse__zero(_1335927), 29321 ^ _782652 : [(29348 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335927), _1335929), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335927), _1335931), _1335933)))), 29351 ^ _782652 : [(29352 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335927), c_Groups_Ozero__class_Ozero(_1335927)), _1335933)))], (29354 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335927), _1335929), _1335933)), _1335931))]], 29355 ^ _782652 : [(29356 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335927), c_Groups_Ozero__class_Ozero(_1335927)), _1335933))], (29358 ^ _782652) ^ [] : [29359 ^ _782652 : [(29360 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335927), _1335933), c_Groups_Ozero__class_Ozero(_1335927))))], (29362 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335927), _1335931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335927), _1335929), _1335933)))]], 29363 ^ _782652 : [(29364 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335927), _1335933), c_Groups_Ozero__class_Ozero(_1335927)))], (29366 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335927), _1335929), c_Groups_Ozero__class_Ozero(_1335927)))]]]]], (29322 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335927), _1335929), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1335927), _1335931), _1335933))), 29325 ^ _782652 : [(29326 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335927), c_Groups_Ozero__class_Ozero(_1335927)), _1335933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335927), _1335929), _1335933)), _1335931)))], (29332 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335927), c_Groups_Ozero__class_Ozero(_1335927)), _1335933))), 29335 ^ _782652 : [(29336 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335927), _1335933), c_Groups_Ozero__class_Ozero(_1335927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335927), _1335931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335927), _1335929), _1335933))))], (29342 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335927), _1335933), c_Groups_Ozero__class_Ozero(_1335927)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335927), _1335929), c_Groups_Ozero__class_Ozero(_1335927))))]]]]]]], (29370 ^ _782652) ^ [_1336880, _1336882, _1336884, _1336886] : [class_Fields_Olinordered__field__inverse__zero(_1336880), 29373 ^ _782652 : [(29400 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336880), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1336880), _1336882), _1336884)), _1336886))), 29403 ^ _782652 : [(29404 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336880), c_Groups_Ozero__class_Ozero(_1336880)), _1336884)))], (29406 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336880), _1336882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336880), _1336886), _1336884)))]], 29407 ^ _782652 : [(29408 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336880), c_Groups_Ozero__class_Ozero(_1336880)), _1336884))], (29410 ^ _782652) ^ [] : [29411 ^ _782652 : [(29412 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336880), _1336884), c_Groups_Ozero__class_Ozero(_1336880))))], (29414 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336880), _1336886), _1336884)), _1336882))]], 29415 ^ _782652 : [(29416 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336880), _1336884), c_Groups_Ozero__class_Ozero(_1336880)))], (29418 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336880), c_Groups_Ozero__class_Ozero(_1336880)), _1336886))]]]]], (29374 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336880), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1336880), _1336882), _1336884)), _1336886)), 29377 ^ _782652 : [(29378 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336880), c_Groups_Ozero__class_Ozero(_1336880)), _1336884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336880), _1336882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336880), _1336886), _1336884))))], (29384 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336880), c_Groups_Ozero__class_Ozero(_1336880)), _1336884))), 29387 ^ _782652 : [(29388 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336880), _1336884), c_Groups_Ozero__class_Ozero(_1336880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336880), _1336886), _1336884)), _1336882)))], (29394 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1336880), _1336884), c_Groups_Ozero__class_Ozero(_1336880)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336880), c_Groups_Ozero__class_Ozero(_1336880)), _1336886)))]]]]]]], (29422 ^ _782652) ^ [_1337833, _1337835, _1337837, _1337839] : [class_Fields_Olinordered__field(_1337833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337833), c_Groups_Ozero__class_Ozero(_1337833)), _1337835)), 29429 ^ _782652 : [(29430 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337833), _1337837), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1337833), _1337839), _1337835))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337833), _1337837), _1337835)), _1337839)))], (29436 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337833), _1337837), _1337835)), _1337839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337833), _1337837), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1337833), _1337839), _1337835))))]]], (29442 ^ _782652) ^ [_1338214, _1338216, _1338218, _1338220] : [class_Fields_Olinordered__field(_1338214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338214), c_Groups_Ozero__class_Ozero(_1338214)), _1338216)), 29449 ^ _782652 : [(29450 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338214), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1338214), _1338218), _1338216)), _1338220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338214), _1338218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338214), _1338220), _1338216))))], (29456 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338214), _1338218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338214), _1338220), _1338216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338214), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1338214), _1338218), _1338216)), _1338220)))]]], (29462 ^ _782652) ^ [_1338595, _1338597, _1338599, _1338601] : [class_Fields_Olinordered__field(_1338595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338595), c_Groups_Ozero__class_Ozero(_1338595)), _1338597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338595), _1338599), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338595), _1338601), _1338597))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338595), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1338595), _1338599), _1338597)), _1338601)))], (29476 ^ _782652) ^ [_1338864, _1338866, _1338868, _1338870] : [class_Fields_Olinordered__field(_1338864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338864), c_Groups_Ozero__class_Ozero(_1338864)), _1338866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338864), _1338868), _1338866)), _1338870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338864), _1338868), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1338864), _1338870), _1338866))))], (29490 ^ _782652) ^ [_1339133, _1339135, _1339137] : [29492 ^ _782652 : [(29493 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339133), 29491 ^ [_1339133, _1339135, _1339137]), _1339135)))], (29495 ^ _782652) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1339137, 29491 ^ [_1339133, _1339135, _1339137]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339133, tc_Int_Oint), _1339137), _1339135) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339133, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1339133), c_Int_Onat), _1339137)), _1339135)))], (29499 ^ _782652) ^ [_1339363, _1339365, _1339367, _1339369, _1339371] : [class_Fields_Ofield(_1339363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339365), _1339367)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339365), _1339369)), 29513 ^ _782652 : [(29514 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339365), 29512 ^ [_1339363, _1339365, _1339367, _1339369, _1339371]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339365, tc_HOL_Obool)), _1339367), _1339369))))], (29516 ^ _782652) ^ [] : [-(hAPP(_1339371, 29512 ^ [_1339363, _1339365, _1339367, _1339369, _1339371]) = c_Groups_Ozero__class_Ozero(_1339363))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339365, _1339363), _1339371), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339365, tc_HOL_Obool)), _1339367), _1339369)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1339363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339363), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339365, _1339363), _1339371), _1339367)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339365, _1339363), _1339371), _1339369))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339365, _1339363), _1339371), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339365, tc_HOL_Obool)), _1339367), _1339369))))], (29520 ^ _782652) ^ [_1339859] : [class_Power_Opower(_1339859), -(c_Power_Opower__class_Opower(_1339859) = c_Power_Opower_Opower(_1339859, c_Groups_Oone__class_Oone(_1339859), c_Groups_Otimes__class_Otimes(_1339859)))], (29526 ^ _782652) ^ [_1339952, _1339954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1339952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339954)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1339954), _1339952)), _1339954) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1339954), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1339952), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (29536 ^ _782652) ^ [_1340137, _1340139] : [class_Divides_Osemiring__div(_1340137), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1340137), _1340139), c_Groups_Oone__class_Oone(_1340137)) = _1340139)], (29542 ^ _782652) ^ [_1340232, _1340234] : [c_Nat__Transfer_Ois__nat(_1340232), c_Nat__Transfer_Ois__nat(_1340234), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1340232), _1340234)))], (29552 ^ _782652) ^ [_1340367, _1340369] : [class_Divides_Osemiring__div(_1340367), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1340367), _1340369), c_Groups_Ozero__class_Ozero(_1340367)) = c_Groups_Ozero__class_Ozero(_1340367))], (29558 ^ _782652) ^ [_1340466, _1340468] : [class_Divides_Osemiring__div(_1340466), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1340466), c_Groups_Ozero__class_Ozero(_1340466)), _1340468) = c_Groups_Ozero__class_Ozero(_1340466))], (29564 ^ _782652) ^ [_1340565] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340565) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29566 ^ _782652) ^ [_1340591, _1340593] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1340591)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1340593)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1340591), _1340593))], (29568 ^ _782652) ^ [_1340634, _1340636] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1340634), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1340636)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1340634)), _1340636))], (29570 ^ _782652) ^ [_1340677, _1340679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340679)), -(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), _1340677), _1340679))))], (29580 ^ _782652) ^ [_1340830, _1340832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340830)), 29583 ^ _782652 : [(29584 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1340832), _1340830)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1340832), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29590 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1340832), 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), _1340832), _1340830)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29596 ^ _782652) ^ [_1341089, _1341091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1341089), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29599 ^ _782652 : [(29600 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1341091), _1341089)), 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)), _1341091)))], (29606 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1341091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1341091), _1341089)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29612 ^ _782652) ^ [_1341345, _1341347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1341345), 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)), _1341347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1341345), _1341347)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29622 ^ _782652) ^ [_1341506] : [-(_1341506 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1341506), _1341506) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (29628 ^ _782652) ^ [_1341546, _1341548, _1341550, _1341552] : [class_Divides_Osemiring__div(_1341546), -(_1341548 = c_Groups_Ozero__class_Ozero(_1341546)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1341546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341546), _1341548), _1341550)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341546), _1341548), _1341552)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1341546), _1341550), _1341552))], (29638 ^ _782652) ^ [_1341708, _1341710, _1341712, _1341714] : [class_Divides_Osemiring__div(_1341708), -(_1341710 = c_Groups_Ozero__class_Ozero(_1341708)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1341708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341708), _1341712), _1341710)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341708), _1341714), _1341710)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1341708), _1341712), _1341714))], (29648 ^ _782652) ^ [_1341870, _1341872, _1341874] : [class_Divides_Osemiring__div(_1341870), -(_1341872 = c_Groups_Ozero__class_Ozero(_1341870)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1341870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341870), _1341872), _1341874)), _1341872) = _1341874)], (29658 ^ _782652) ^ [_1341998, _1342000, _1342002] : [class_Divides_Osemiring__div(_1341998), -(_1342000 = c_Groups_Ozero__class_Ozero(_1341998)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1341998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341998), _1342002), _1342000)), _1342000) = _1342002)], (29668 ^ _782652) ^ [_1342126, _1342128, _1342130, _1342132] : [class_Divides_Osemiring__div(_1342126), 29671 ^ _782652 : [(29672 ^ _782652) ^ [] : [_1342128 = c_Groups_Ozero__class_Ozero(_1342126), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1342126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342126), _1342128), _1342130)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342126), _1342128), _1342132)) = c_Groups_Ozero__class_Ozero(_1342126))], (29678 ^ _782652) ^ [] : [-(_1342128 = c_Groups_Ozero__class_Ozero(_1342126)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1342126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342126), _1342128), _1342130)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342126), _1342128), _1342132)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1342126), _1342130), _1342132))]]], (29684 ^ _782652) ^ [_1342432, _1342434] : [class_Divides_Osemiring__div(_1342432), -(_1342434 = c_Groups_Ozero__class_Ozero(_1342432)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1342432), _1342434), _1342434) = c_Groups_Oone__class_Oone(_1342432))], (29694 ^ _782652) ^ [_1342546, _1342548, _1342550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342546), _1342548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342550), 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), _1342548), _1342550)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1342546), _1342550))))], (29704 ^ _782652) ^ [_1342733, _1342735, _1342737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342733), _1342735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1342737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1342733), _1342737)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1342735), _1342737))))], (29714 ^ _782652) ^ [_1342914, _1342916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342914), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342916), _1342914)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1342914), _1342916) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29724 ^ _782652) ^ [_1343075, _1343077, _1343079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1343075), 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)), _1343077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1343077), _1343079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1343075), _1343077)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1343075), _1343079))))], (29738 ^ _782652) ^ [_1343320, _1343322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1343320), 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)), _1343322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1343320), _1343322)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29748 ^ _782652) ^ [_1343485, _1343487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1343485), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29751 ^ _782652 : [(29752 ^ _782652) ^ [] : [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), _1343487), _1343485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1343487), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29758 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1343487), 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), _1343487), _1343485))))]]], (29764 ^ _782652) ^ [_1343741, _1343743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1343741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1343741), _1343743)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1343741), _1343743) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29774 ^ _782652) ^ [_1343896, _1343898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1343896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1343898), 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), _1343896), _1343898)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29784 ^ _782652) ^ [_1344061, _1344063, _1344065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344063)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1344063), _1344065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1344061), _1344065)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1344061), _1344063))))], (29798 ^ _782652) ^ [_1344300, _1344302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344300)), 29801 ^ _782652 : [(29802 ^ _782652) ^ [] : [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), _1344300), _1344302))), 29805 ^ _782652 : [(29806 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1344302), _1344300)))], (29808 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344302)))]]], (29810 ^ _782652) ^ [] : [-(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), _1344300), _1344302)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1344302), _1344300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344302))]]], (29820 ^ _782652) ^ [_1344628, _1344630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344628)), 29823 ^ _782652 : [(29824 ^ _782652) ^ [] : [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), _1344630), _1344628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1344628), _1344630)))], (29830 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1344628), _1344630)), -(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), _1344630), _1344628))))]]], (29836 ^ _782652) ^ [_1344878, _1344880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344878)), 29839 ^ _782652 : [(29840 ^ _782652) ^ [] : [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), _1344880), _1344878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344880)))], (29846 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1344880)), -(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), _1344880), _1344878))))]]], (29852 ^ _782652) ^ [_1345134, _1345136] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1345134), _1345136) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1345136 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29861 ^ _782652 : [(29862 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1345134)))], (29864 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1345134), _1345136)))]], 29865 ^ _782652 : [(29866 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1345134), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29868 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1345136), _1345134)))]]], (29870 ^ _782652) ^ [_1345365, _1345367] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1345365), _1345367) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29871 ^ _782652 : [(29872 ^ _782652) ^ [] : [_1345367 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (29874 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1345365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1345365), _1345367))], (29880 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1345365), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1345367), _1345365))]]], (29888 ^ _782652) ^ [_1345660, _1345662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1345660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1345662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1345660), _1345662)), _1345660)))], (29898 ^ _782652) ^ [_1345819, _1345821, _1345823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1345819)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1345821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1345823), _1345819)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1345821), _1345823)), _1345819))], (29904 ^ _782652) ^ [_1345950, _1345952, _1345954, _1345956] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1345950, _1345952, _1345954), _1345956), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1345952)], (29906 ^ _782652) ^ [_1345989, _1345991, _1345993, _1345995, _1345997] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1345989, _1345991, _1345993), _1345995), hAPP(c_Nat_OSuc, _1345997)) = hAPP(hAPP(_1345993, _1345995), hAPP(hAPP(c_Power_Opower_Opower(_1345989, _1345991, _1345993), _1345995), _1345997)))], (29908 ^ _782652) ^ [_1346049, _1346051, _1346053, _1346055] : [class_Divides_Osemiring__div(_1346049), -(_1346051 = c_Groups_Ozero__class_Ozero(_1346049)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1346049), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346049), _1346053), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346049), _1346055), _1346051))), _1346051) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346049), _1346055), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1346049), _1346053), _1346051)))], (29918 ^ _782652) ^ [_1346227, _1346229, _1346231, _1346233] : [class_Divides_Osemiring__div(_1346227), -(_1346229 = c_Groups_Ozero__class_Ozero(_1346227)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1346227), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346227), _1346231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346227), _1346229), _1346233))), _1346229) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346227), _1346233), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1346227), _1346231), _1346229)))], (29928 ^ _782652) ^ [_1346405, _1346407, _1346409] : [class_Divides_Osemiring__div(_1346405), -(_1346407 = c_Groups_Ozero__class_Ozero(_1346405)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1346405), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346405), _1346407), _1346409)), _1346407) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346405), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1346405), _1346409), _1346407)), c_Groups_Oone__class_Oone(_1346405)))], (29938 ^ _782652) ^ [_1346569, _1346571, _1346573] : [class_Divides_Osemiring__div(_1346569), -(_1346571 = c_Groups_Ozero__class_Ozero(_1346569)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1346569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346569), _1346573), _1346571)), _1346571) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346569), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1346569), _1346573), _1346571)), c_Groups_Oone__class_Oone(_1346569)))], (29994 ^ _782652) ^ [_1347711, _1347713, _1347715] : [-(hBOOL(hAPP(_1347711, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1347713), _1347715)))), 29997 ^ _782652 : [(29998 ^ _782652) ^ [] : [-(_1347715 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30000 ^ _782652) ^ [] : [hBOOL(hAPP(_1347711, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 30003 ^ _782652 : [(30004 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347715)))], (30008 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30006 ^ [_1347711, _1347713, _1347715])))], (30010 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 30006 ^ [_1347711, _1347713, _1347715]), _1347715)))], (30012 ^ _782652) ^ [] : [-(_1347713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1347715), 30005 ^ [_1347711, _1347713, _1347715])), 30006 ^ [_1347711, _1347713, _1347715]))], (30014 ^ _782652) ^ [] : [hBOOL(hAPP(_1347711, 30005 ^ [_1347711, _1347713, _1347715]))]], 30015 ^ _782652 : [(30016 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1347715), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30020 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1347715), 30018 ^ [_1347711, _1347713, _1347715])))], (30022 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 30018 ^ [_1347711, _1347713, _1347715]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30024 ^ _782652) ^ [] : [-(_1347713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1347715), 30017 ^ [_1347711, _1347713, _1347715])), 30018 ^ [_1347711, _1347713, _1347715]))], (30026 ^ _782652) ^ [] : [hBOOL(hAPP(_1347711, 30017 ^ [_1347711, _1347713, _1347715]))]]], (29948 ^ _782652) ^ [_1346751, _1346753, _1346755] : [hBOOL(hAPP(_1346751, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1346753), _1346755))), 29951 ^ _782652 : [(29952 ^ _782652) ^ [] : [_1346755 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1346751, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29958 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346755)), 29961 ^ _782652 : [(29962 ^ _782652) ^ [_1347085] : [-(hBOOL(hAPP(_1346751, _1347085))), 29963 ^ _782652 : [(29964 ^ _782652) ^ [_1347156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1347156), _1346755)), _1346753 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1346755), _1347085)), _1347156)]]]]], (29976 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346755), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29979 ^ _782652 : [(29980 ^ _782652) ^ [_1347415] : [-(hBOOL(hAPP(_1346751, _1347415))), 29981 ^ _782652 : [(29982 ^ _782652) ^ [_1347489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346755), _1347489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1347489), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1346753 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1346755), _1347415)), _1347489)]]]]]]], (30030 ^ _782652) ^ [_1348425, _1348427, _1348429, _1348431] : [_1348425 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1348427), _1348429)), _1348431), -(_1348427 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1348425), _1348427) = _1348429), 30037 ^ _782652 : [(30038 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1348427)))], (30040 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1348431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1348431), _1348427))]], 30045 ^ _782652 : [(30046 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1348427))], (30048 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1348427), _1348431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1348431), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (30060 ^ _782652) ^ [_1348903, _1348905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1348903)), -(c_SMT_Oz3div(_1348905, _1348903) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1348905), _1348903))], (30066 ^ _782652) ^ [_1348996, _1348998] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1348996))), -(c_SMT_Oz3div(_1348998, _1348996) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1348998), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1348996))))], (30072 ^ _782652) ^ [_1349051, _1349053, _1349055, _1349057, _1349059] : [class_Groups_Ocomm__monoid__mult(_1349051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349053), _1349055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1349053, tc_HOL_Obool)), _1349057), _1349055)), 30086 ^ _782652 : [(30087 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1349053), 30085 ^ [_1349051, _1349053, _1349055, _1349057, _1349059]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1349053, tc_HOL_Obool)), _1349055), _1349057))))], (30089 ^ _782652) ^ [] : [hAPP(_1349059, 30085 ^ [_1349051, _1349053, _1349055, _1349057, _1349059]) = c_Groups_Oone__class_Oone(_1349051)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1349053, _1349051), _1349059), _1349057) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1349053, _1349051), _1349059), _1349055))], (30093 ^ _782652) ^ [_1349502, _1349504] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1349502), _1349504)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1349502, tc_HOL_Obool)), hAPP(c_Set_OPow(_1349502), _1349504)) = 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(_1349502), _1349504)))], (30099 ^ _782652) ^ [_1349629, _1349631, _1349633] : [class_Fields_Olinordered__field__inverse__zero(_1349629), 30105 ^ _782652 : [(30106 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1349629), c_Groups_Ozero__class_Ozero(_1349629)), 30104 ^ [_1349629, _1349631, _1349633])))], (30108 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1349629), 30104 ^ [_1349629, _1349631, _1349633]), c_Groups_Oone__class_Oone(_1349629))))], (30110 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349629), 30104 ^ [_1349629, _1349631, _1349633]), _1349631)), _1349633))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349629), _1349631), _1349633)))], (30114 ^ _782652) ^ [_1349978, _1349980, _1349982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1349978, tc_HOL_Obool)), _1349980), _1349982)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1349978, tc_HOL_Obool)), _1349980), hAPP(c_Set_OPow(_1349978), _1349982))))], (30120 ^ _782652) ^ [_1350107, _1350109] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1350107), _1350109)), _1350107)))], (30122 ^ _782652) ^ [_1350143, _1350145, _1350147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1350143), _1350145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1350143), _1350147)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1350145), _1350147))))], (30128 ^ _782652) ^ [_1350266, _1350268, _1350270] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1350266), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1350268), _1350270)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1350266), _1350268)), _1350270))], (30130 ^ _782652) ^ [_1350317, _1350319, _1350321] : [-(hAPP(c_Set_OPow(_1350317), hAPP(hAPP(c_Set_Oinsert(_1350317), _1350319), _1350321)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1350317, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1350317), _1350321)), hAPP(c_Set_Oimage(tc_fun(_1350317, tc_HOL_Obool), tc_fun(_1350317, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1350317), _1350319)), hAPP(c_Set_OPow(_1350317), _1350321))))], (30132 ^ _782652) ^ [_1350399, _1350401, _1350403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350399, tc_HOL_Obool)), _1350401), _1350403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1350399, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1350399), _1350401)), hAPP(c_Set_OPow(_1350399), _1350403))))], (30138 ^ _782652) ^ [_1350544, _1350546, _1350548] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1350544, tc_HOL_Obool)), _1350546), hAPP(c_Set_OPow(_1350544), _1350548))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350544, tc_HOL_Obool)), _1350546), _1350548)))], (30144 ^ _782652) ^ [_1350691, _1350693, _1350695] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1350691, tc_HOL_Obool)), _1350693), hAPP(c_Set_OPow(_1350691), _1350695))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350691, tc_HOL_Obool)), _1350693), _1350695)))], (30150 ^ _782652) ^ [_1350816, _1350818, _1350820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350816, tc_HOL_Obool)), _1350818), _1350820)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1350816, tc_HOL_Obool)), _1350818), hAPP(c_Set_OPow(_1350816), _1350820))))], (30156 ^ _782652) ^ [_1350947, _1350949, _1350951, _1350953, _1350955] : [hAPP(c_Set_Oimage(_1350947, _1350949, _1350951), _1350953) = _1350955, -(hAPP(c_Set_Oimage(tc_fun(_1350947, tc_HOL_Obool), tc_fun(_1350949, tc_HOL_Obool), c_Set_Oimage(_1350947, _1350949, _1350951)), hAPP(c_Set_OPow(_1350947), _1350953)) = hAPP(c_Set_OPow(_1350949), _1350955))], (30162 ^ _782652) ^ [_1351098] : [-(hAPP(c_Set_OPow(_1351098), c_Orderings_Otop__class_Otop(tc_fun(_1351098, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1351098, tc_HOL_Obool), tc_HOL_Obool)))], (30164 ^ _782652) ^ [_1351139, _1351141, _1351143] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1351139, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1351139, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1351139), _1351141)), hAPP(c_Set_OPow(_1351139), _1351143))), hAPP(c_Set_OPow(_1351139), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351139, tc_HOL_Obool)), _1351141), _1351143)))))], (30166 ^ _782652) ^ [_1351219, _1351221, _1351223] : [-(hAPP(c_Set_OPow(_1351219), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1351219, tc_HOL_Obool)), _1351221), _1351223)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1351219, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1351219), _1351221)), hAPP(c_Set_OPow(_1351219), _1351223)))], (30168 ^ _782652) ^ [_1351302, _1351304, _1351306] : [hAPP(c_Set_Oimage(_1351304, tc_fun(_1351304, tc_HOL_Obool), _1351302), _1351306) = hAPP(c_Set_OPow(_1351304), _1351306)], (30170 ^ _782652) ^ [_1351344, _1351346] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1351344, tc_HOL_Obool)), _1351346), hAPP(c_Set_OPow(_1351344), _1351346))))], (30172 ^ _782652) ^ [_1351396, _1351398] : [hAPP(c_Set_OPow(_1351396), _1351398) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1351396, tc_HOL_Obool), tc_HOL_Obool))], (30174 ^ _782652) ^ [_1351434, _1351436] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1351434, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1351434, tc_HOL_Obool))), hAPP(c_Set_OPow(_1351434), _1351436))))], (30176 ^ _782652) ^ [_1351479] : [-(hAPP(c_Set_OPow(_1351479), c_Orderings_Obot__class_Obot(tc_fun(_1351479, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1351479, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1351479, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1351479, tc_HOL_Obool), tc_HOL_Obool))))], (30178 ^ _782652) ^ [_1351536, _1351538, _1351540, _1351542] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1351536, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1351538, tc_fun(tc_fun(_1351536, tc_HOL_Obool), tc_HOL_Obool)), _1351540), hAPP(hAPP(c_COMBB(tc_fun(_1351536, tc_HOL_Obool), tc_fun(tc_fun(_1351536, tc_HOL_Obool), tc_HOL_Obool), _1351538), c_Set_OPow(_1351536)), _1351542))), hAPP(c_Set_OPow(_1351536), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1351538, tc_fun(_1351536, tc_HOL_Obool)), _1351540), _1351542)))))], (30180 ^ _782652) ^ [_1351631] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1351631), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1351631)], (30182 ^ _782652) ^ [_1351660, _1351662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1351660), _1351662)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1351660), _1351662) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30188 ^ _782652) ^ [_1351771, _1351773, _1351775] : [_1351771 = 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), _1351771), _1351773)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1351771), _1351775)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30194 ^ _782652) ^ [_1351880, _1351882, _1351884] : [-(_1351880 = 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), _1351880), _1351882)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1351880), _1351884)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1351882), _1351884))], (30200 ^ _782652) ^ [_1351944, _1351946] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1351944)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1351946)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1351944), _1351946)))], (30202 ^ _782652) ^ [_1351990, _1351992] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1351990), _1351992)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1351990)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1351992)))], (30204 ^ _782652) ^ [_1352036, _1352038, _1352040, _1352042, _1352044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1352036, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1352038, _1352036, _1352040), _1352042)), _1352044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1352036, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1352038, tc_HOL_Obool), tc_fun(_1352036, tc_HOL_Obool), c_Set_Oimage(_1352038, _1352036, _1352040)), hAPP(c_Set_OPow(_1352038), _1352042))), hAPP(c_Set_OPow(_1352036), _1352044))))], (30210 ^ _782652) ^ [_1352233, _1352235, _1352237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1352233), _1352235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1352237), _1352235)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1352237), _1352233))))], (30220 ^ _782652) ^ [_1352414, _1352416, _1352418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352414)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1352414), _1352416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1352414), _1352418)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1352416), _1352418))], (30226 ^ _782652) ^ [_1352545, _1352547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352545)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1352545), _1352547)), _1352545) = _1352547)], (30232 ^ _782652) ^ [_1352650, _1352652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352650)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1352652), _1352650)), _1352650) = _1352652)], (30238 ^ _782652) ^ [_1352755, _1352757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1352755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1352757), _1352755)), _1352757)))], (30248 ^ _782652) ^ [_1352914, _1352916] : [-(hAPP(c_Set_OPow(_1352914), _1352916) = hAPP(c_Set_OCollect(tc_fun(_1352914, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1352914, tc_HOL_Obool), tc_fun(_1352914, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1352914, tc_HOL_Obool))), _1352916)))], (30250 ^ _782652) ^ [_1352988, _1352990] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1352988, tc_HOL_Obool)), hAPP(c_Set_OPow(_1352988), _1352990))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1352988), _1352990)))], (30256 ^ _782652) ^ [_1353093, _1353095] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1353093), _1353095)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1353093, tc_HOL_Obool)), hAPP(c_Set_OPow(_1353093), _1353095))))], (30262 ^ _782652) ^ [_1353204, _1353206] : [-(hAPP(c_Set_OPow(_1353204), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1353204, tc_HOL_Obool)), _1353206)) = hAPP(c_Set_OCollect(tc_fun(_1353204, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1353204, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1353204, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1353204, tc_HOL_Obool), tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1353204, tc_HOL_Obool)), c_COMBS(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1353204, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1353204, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1353204, tc_HOL_Obool), tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_fun(_1353204, tc_HOL_Obool)), tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_fun(_1353204, tc_HOL_Obool)), tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1353204, tc_HOL_Obool)), c_COMBB(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1353204, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1353204, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1353204, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1353204, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1353204, tc_HOL_Obool)), _1353206)), c_Set_OPow(_1353204))))))], (30264 ^ _782652) ^ [_1353484, _1353486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1353484)), 30267 ^ _782652 : [(30268 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1353486), _1353484)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1353486), _1353484) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30274 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1353486), _1353484))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1353486), _1353484) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1353486), _1353484)), _1353484)))]]], (30280 ^ _782652) ^ [_1353738, _1353740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1353738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1353740), _1353738))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1353740), _1353738) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1353740), _1353738)), _1353738)))], (30314 ^ _782652) ^ [_1354341, _1354343, _1354345] : [-(hBOOL(hAPP(_1354341, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1354343), _1354345)))), 30317 ^ _782652 : [(30318 ^ _782652) ^ [] : [-(_1354345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30320 ^ _782652) ^ [] : [hBOOL(hAPP(_1354341, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 30321 ^ _782652 : [(30322 ^ _782652) ^ [] : [_1354345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30326 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30324 ^ [_1354341, _1354343, _1354345]), _1354345)))], (30328 ^ _782652) ^ [] : [-(_1354343 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1354345), 30323 ^ [_1354341, _1354343, _1354345])), 30324 ^ [_1354341, _1354343, _1354345]))], (30330 ^ _782652) ^ [] : [hBOOL(hAPP(_1354341, 30323 ^ [_1354341, _1354343, _1354345]))]]], (30290 ^ _782652) ^ [_1353904, _1353906, _1353908] : [hBOOL(hAPP(_1353904, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1353906), _1353908))), 30293 ^ _782652 : [(30294 ^ _782652) ^ [] : [_1353908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1353904, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (30300 ^ _782652) ^ [] : [-(_1353908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30303 ^ _782652 : [(30304 ^ _782652) ^ [_1354156, _1354158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1354156), _1353908)), _1353906 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1353908), _1354158)), _1354156), -(hBOOL(hAPP(_1353904, _1354158)))]]]]], (30334 ^ _782652) ^ [_1354763, _1354765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354763)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1354763), _1354765)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1354763)), hAPP(c_Int_Onat, _1354765)))], (30340 ^ _782652) ^ [_1354886, _1354888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354888)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1354886)), hAPP(c_Int_Onat, _1354888)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1354886), _1354888)))], (30350 ^ _782652) ^ [_1355065, _1355067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1355065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1355065), _1355067)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1355067), _1355065) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1355067), _1355065)), _1355065)))], (30360 ^ _782652) ^ [_1355268, _1355270, _1355272] : [hBOOL(hAPP(_1355268, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1355270), _1355272))), 30365 ^ _782652 : [(30366 ^ _782652) ^ [] : [-(_1355272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30368 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1355268, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 30370 ^ _782652 : [(30371 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355272), 30369 ^ [_1355268, _1355270, _1355272])), _1355270)))], (30373 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1355270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355272), hAPP(c_Nat_OSuc, 30369 ^ [_1355268, _1355270, _1355272])))))], (30375 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1355268, 30369 ^ [_1355268, _1355270, _1355272])))]]], (30377 ^ _782652) ^ [_1355572, _1355574, _1355576] : [-(hBOOL(hAPP(_1355572, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1355574), _1355576)))), 30378 ^ _782652 : [(30379 ^ _782652) ^ [] : [_1355576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1355572, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30385 ^ _782652) ^ [_1355740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355576), _1355740)), _1355574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1355574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355576), hAPP(c_Nat_OSuc, _1355740)))), hBOOL(hAPP(_1355572, _1355740))]]], (30397 ^ _782652) ^ [_1355970, _1355972, _1355974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1355970)), 30400 ^ _782652 : [(30411 ^ _782652) ^ [] : [_1355972 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1355974), _1355970), 30414 ^ _782652 : [(30415 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355970), _1355972)), _1355974)))], (30417 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1355974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355970), hAPP(c_Nat_OSuc, _1355972)))))]]], (30401 ^ _782652) ^ [] : [-(_1355972 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1355974), _1355970)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355970), _1355972)), _1355974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1355974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355970), hAPP(c_Nat_OSuc, _1355972))))]]], (30419 ^ _782652) ^ [_1356354, _1356356] : [-(c_Nitpick_Onat__lcm(_1356354, _1356356) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1356354), _1356356)), c_Nitpick_Onat__gcd(_1356354, _1356356)))], (30421 ^ _782652) ^ [_1356415, _1356417, _1356419] : [hBOOL(hAPP(c_Predicate_OPowp(_1356415, hAPP(hAPP(c_COMBC(_1356415, tc_fun(_1356415, tc_HOL_Obool), tc_HOL_Obool), c_member(_1356415)), _1356417)), _1356419)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356415, tc_HOL_Obool)), _1356419), hAPP(c_Set_OPow(_1356415), _1356417))))], (30427 ^ _782652) ^ [_1356560, _1356562, _1356564] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1356560, tc_HOL_Obool)), _1356564), hAPP(c_Set_OPow(_1356560), _1356562))), -(hBOOL(hAPP(c_Predicate_OPowp(_1356560, hAPP(hAPP(c_COMBC(_1356560, tc_fun(_1356560, tc_HOL_Obool), tc_HOL_Obool), c_member(_1356560)), _1356562)), _1356564)))], (30433 ^ _782652) ^ [_1356711, _1356713, _1356715, _1356717, _1356719] : [class_Groups_Ocomm__monoid__add(_1356711), class_Groups_Ocomm__monoid__mult(_1356711), _1356713 = _1356715, c_Nat__Transfer_Onat__set(_1356715), 30451 ^ _782652 : [(30452 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30450 ^ [_1356711, _1356713, _1356715, _1356717, _1356719])))], (30454 ^ _782652) ^ [] : [hAPP(_1356717, 30450 ^ [_1356711, _1356713, _1356715, _1356717, _1356719]) = hAPP(_1356719, 30450 ^ [_1356711, _1356713, _1356715, _1356717, _1356719])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1356711), _1356717), _1356713) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1356711), _1356719), _1356715))], (30458 ^ _782652) ^ [_1357174, _1357176, _1357178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357174), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30461 ^ _782652 : [(30480 ^ _782652) ^ [] : [30483 ^ _782652 : [(30484 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357174), 30482 ^ [_1357174, _1357176, _1357178])))], (30486 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 30482 ^ [_1357174, _1357176, _1357178]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30488 ^ _782652) ^ [] : [-(_1357178 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1357174), 30481 ^ [_1357174, _1357176, _1357178])), 30482 ^ [_1357174, _1357176, _1357178]))], (30490 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1357176, 30481 ^ [_1357174, _1357176, _1357178]), 30482 ^ [_1357174, _1357176, _1357178]))]], -(hBOOL(hAPP(hAPP(_1357176, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1357178), _1357174)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357178, _1357174))))], (30462 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1357176, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1357178), _1357174)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357178, _1357174))), 30465 ^ _782652 : [(30466 ^ _782652) ^ [_1357384, _1357386] : [-(hBOOL(hAPP(hAPP(_1357176, _1357386), _1357384))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357174), _1357384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1357384), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1357178 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1357174), _1357386)), _1357384)]]]]], (30494 ^ _782652) ^ [_1357907, _1357909] : [c_Nat__Transfer_Ois__nat(_1357907), c_Nat__Transfer_Ois__nat(_1357909), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1357907, _1357909)))], (30504 ^ _782652) ^ [_1358038, _1358040, _1358042] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1358038), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358040, _1358042)), _1358042) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1358038), _1358040), _1358042))], (30506 ^ _782652) ^ [_1358089, _1358091, _1358093] : [-(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, _1358089, _1358091)), _1358093), _1358091) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1358089), _1358093), _1358091))], (30508 ^ _782652) ^ [_1358140, _1358142] : [-(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, _1358140, _1358142)), _1358142) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1358140), _1358142))], (30510 ^ _782652) ^ [_1358183, _1358185] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1358183), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1358185)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358183, _1358185)))], (30512 ^ _782652) ^ [_1358225, _1358227] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358225, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1358227)) = 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), _1358225), _1358227)))], (30514 ^ _782652) ^ [_1358267, _1358269, _1358271, _1358273] : [class_Divides_Oring__div(_1358267), -(c_Divides_Odiv__class_Omod(_1358267, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358267), _1358269), _1358271), _1358273) = c_Divides_Odiv__class_Omod(_1358267, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358267), _1358269), c_Divides_Odiv__class_Omod(_1358267, _1358271, _1358273)), _1358273))], (30520 ^ _782652) ^ [_1358402, _1358404, _1358406, _1358408] : [class_Divides_Oring__div(_1358402), -(c_Divides_Odiv__class_Omod(_1358402, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358402), _1358404), _1358406), _1358408) = c_Divides_Odiv__class_Omod(_1358402, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358402), c_Divides_Odiv__class_Omod(_1358402, _1358404, _1358408)), _1358406), _1358408))], (30526 ^ _782652) ^ [_1358537, _1358539, _1358541, _1358543] : [class_Divides_Oring__div(_1358537), -(c_Divides_Odiv__class_Omod(_1358537, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358537), _1358539), _1358541), _1358543) = c_Divides_Odiv__class_Omod(_1358537, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358537), c_Divides_Odiv__class_Omod(_1358537, _1358539, _1358543)), c_Divides_Odiv__class_Omod(_1358537, _1358541, _1358543)), _1358543))], (30532 ^ _782652) ^ [_1358680, _1358682, _1358684, _1358686, _1358688, _1358690] : [class_Divides_Oring__div(_1358680), c_Divides_Odiv__class_Omod(_1358680, _1358682, _1358684) = c_Divides_Odiv__class_Omod(_1358680, _1358686, _1358684), c_Divides_Odiv__class_Omod(_1358680, _1358688, _1358684) = c_Divides_Odiv__class_Omod(_1358680, _1358690, _1358684), -(c_Divides_Odiv__class_Omod(_1358680, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358680), _1358682), _1358688), _1358684) = c_Divides_Odiv__class_Omod(_1358680, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1358680), _1358686), _1358690), _1358684))], (30546 ^ _782652) ^ [_1358963] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1358963, _1358963) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30548 ^ _782652) ^ [_1358990] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1358990) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30550 ^ _782652) ^ [_1359017, _1359019, _1359021, _1359023] : [class_Divides_Oring__div(_1359017), c_Divides_Odiv__class_Omod(_1359017, _1359019, _1359021) = c_Divides_Odiv__class_Omod(_1359017, _1359023, _1359021), -(c_Divides_Odiv__class_Omod(_1359017, hAPP(c_Groups_Ouminus__class_Ouminus(_1359017), _1359019), _1359021) = c_Divides_Odiv__class_Omod(_1359017, hAPP(c_Groups_Ouminus__class_Ouminus(_1359017), _1359023), _1359021))], (30560 ^ _782652) ^ [_1359204, _1359206, _1359208] : [class_Divides_Oring__div(_1359204), -(c_Divides_Odiv__class_Omod(_1359204, hAPP(c_Groups_Ouminus__class_Ouminus(_1359204), _1359206), _1359208) = c_Divides_Odiv__class_Omod(_1359204, hAPP(c_Groups_Ouminus__class_Ouminus(_1359204), c_Divides_Odiv__class_Omod(_1359204, _1359206, _1359208)), _1359208))], (30566 ^ _782652) ^ [_1359325, _1359327, _1359329] : [class_Divides_Osemiring__div(_1359325), -(c_Divides_Odiv__class_Omod(_1359325, c_Divides_Odiv__class_Omod(_1359325, _1359327, _1359329), _1359329) = c_Divides_Odiv__class_Omod(_1359325, _1359327, _1359329))], (30572 ^ _782652) ^ [_1359426, _1359428] : [class_Divides_Osemiring__div(_1359426), -(c_Divides_Odiv__class_Omod(_1359426, _1359428, _1359428) = c_Groups_Ozero__class_Ozero(_1359426))], (30578 ^ _782652) ^ [_1359513, _1359515] : [class_Divides_Osemiring__div(_1359513), -(c_Divides_Odiv__class_Omod(_1359513, _1359515, c_Groups_Ozero__class_Ozero(_1359513)) = _1359515)], (30584 ^ _782652) ^ [_1359600, _1359602] : [class_Divides_Osemiring__div(_1359600), -(c_Divides_Odiv__class_Omod(_1359600, c_Groups_Ozero__class_Ozero(_1359600), _1359602) = c_Groups_Ozero__class_Ozero(_1359600))], (30590 ^ _782652) ^ [_1359691, _1359693, _1359695, _1359697, _1359699, _1359701] : [class_Divides_Osemiring__div(_1359691), c_Divides_Odiv__class_Omod(_1359691, _1359693, _1359695) = c_Divides_Odiv__class_Omod(_1359691, _1359697, _1359695), c_Divides_Odiv__class_Omod(_1359691, _1359699, _1359695) = c_Divides_Odiv__class_Omod(_1359691, _1359701, _1359695), -(c_Divides_Odiv__class_Omod(_1359691, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359691), _1359693), _1359699), _1359695) = c_Divides_Odiv__class_Omod(_1359691, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359691), _1359697), _1359701), _1359695))], (30604 ^ _782652) ^ [_1359974, _1359976, _1359978, _1359980] : [class_Divides_Osemiring__div(_1359974), -(c_Divides_Odiv__class_Omod(_1359974, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359974), c_Divides_Odiv__class_Omod(_1359974, _1359976, _1359978)), _1359980), _1359978) = c_Divides_Odiv__class_Omod(_1359974, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359974), _1359976), _1359980), _1359978))], (30610 ^ _782652) ^ [_1360109, _1360111, _1360113, _1360115] : [class_Divides_Osemiring__div(_1360109), -(c_Divides_Odiv__class_Omod(_1360109, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360109), _1360111), _1360113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360109), _1360115), _1360113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360109), c_Divides_Odiv__class_Omod(_1360109, _1360111, _1360115)), _1360113))], (30616 ^ _782652) ^ [_1360252, _1360254, _1360256, _1360258] : [class_Divides_Osemiring__div(_1360252), -(c_Divides_Odiv__class_Omod(_1360252, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360252), _1360254), _1360256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360252), _1360254), _1360258)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360252), _1360254), c_Divides_Odiv__class_Omod(_1360252, _1360256, _1360258)))], (30622 ^ _782652) ^ [_1360395, _1360397, _1360399, _1360401] : [class_Divides_Osemiring__div(_1360395), -(c_Divides_Odiv__class_Omod(_1360395, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360395), _1360397), _1360399), _1360401) = c_Divides_Odiv__class_Omod(_1360395, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360395), c_Divides_Odiv__class_Omod(_1360395, _1360397, _1360401)), c_Divides_Odiv__class_Omod(_1360395, _1360399, _1360401)), _1360401))], (30628 ^ _782652) ^ [_1360538, _1360540, _1360542, _1360544] : [class_Divides_Osemiring__div(_1360538), -(c_Divides_Odiv__class_Omod(_1360538, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360538), _1360540), _1360542), _1360544) = c_Divides_Odiv__class_Omod(_1360538, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360538), c_Divides_Odiv__class_Omod(_1360538, _1360540, _1360544)), _1360542), _1360544))], (30634 ^ _782652) ^ [_1360673, _1360675, _1360677, _1360679] : [class_Divides_Osemiring__div(_1360673), -(c_Divides_Odiv__class_Omod(_1360673, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360673), _1360675), _1360677), _1360679) = c_Divides_Odiv__class_Omod(_1360673, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360673), _1360675), c_Divides_Odiv__class_Omod(_1360673, _1360677, _1360679)), _1360679))], (30640 ^ _782652) ^ [_1360808, _1360810, _1360812, _1360814, _1360816, _1360818] : [class_Divides_Osemiring__div(_1360808), c_Divides_Odiv__class_Omod(_1360808, _1360810, _1360812) = c_Divides_Odiv__class_Omod(_1360808, _1360814, _1360812), c_Divides_Odiv__class_Omod(_1360808, _1360816, _1360812) = c_Divides_Odiv__class_Omod(_1360808, _1360818, _1360812), -(c_Divides_Odiv__class_Omod(_1360808, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1360808), _1360810), _1360816), _1360812) = c_Divides_Odiv__class_Omod(_1360808, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1360808), _1360814), _1360818), _1360812))], (30654 ^ _782652) ^ [_1361091, _1361093, _1361095, _1361097] : [class_Divides_Osemiring__div(_1361091), -(c_Divides_Odiv__class_Omod(_1361091, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361091), c_Divides_Odiv__class_Omod(_1361091, _1361093, _1361095)), _1361097), _1361095) = c_Divides_Odiv__class_Omod(_1361091, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361091), _1361093), _1361097), _1361095))], (30660 ^ _782652) ^ [_1361226, _1361228, _1361230, _1361232] : [class_Divides_Osemiring__div(_1361226), -(c_Divides_Odiv__class_Omod(_1361226, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361226), _1361228), c_Divides_Odiv__class_Omod(_1361226, _1361230, _1361232)), _1361232) = c_Divides_Odiv__class_Omod(_1361226, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361226), _1361228), _1361230), _1361232))], (30666 ^ _782652) ^ [_1361361, _1361363, _1361365, _1361367] : [class_Divides_Osemiring__div(_1361361), -(c_Divides_Odiv__class_Omod(_1361361, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361361), _1361363), _1361365), _1361367) = c_Divides_Odiv__class_Omod(_1361361, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361361), c_Divides_Odiv__class_Omod(_1361361, _1361363, _1361367)), c_Divides_Odiv__class_Omod(_1361361, _1361365, _1361367)), _1361367))], (30672 ^ _782652) ^ [_1361504, _1361506, _1361508, _1361510] : [class_Divides_Osemiring__div(_1361504), -(c_Divides_Odiv__class_Omod(_1361504, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361504), _1361506), _1361508), _1361510) = c_Divides_Odiv__class_Omod(_1361504, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361504), c_Divides_Odiv__class_Omod(_1361504, _1361506, _1361510)), _1361508), _1361510))], (30678 ^ _782652) ^ [_1361639, _1361641, _1361643, _1361645] : [class_Divides_Osemiring__div(_1361639), -(c_Divides_Odiv__class_Omod(_1361639, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361639), _1361641), _1361643), _1361645) = c_Divides_Odiv__class_Omod(_1361639, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361639), _1361641), c_Divides_Odiv__class_Omod(_1361639, _1361643, _1361645)), _1361645))], (30684 ^ _782652) ^ [_1361774, _1361776, _1361778] : [class_Divides_Osemiring__div(_1361774), -(c_Divides_Odiv__class_Omod(_1361774, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361774), _1361776), _1361778), _1361776) = c_Divides_Odiv__class_Omod(_1361774, _1361778, _1361776))], (30690 ^ _782652) ^ [_1361883, _1361885, _1361887] : [class_Divides_Osemiring__div(_1361883), -(c_Divides_Odiv__class_Omod(_1361883, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1361883), _1361885), _1361887), _1361887) = c_Divides_Odiv__class_Omod(_1361883, _1361885, _1361887))], (30696 ^ _782652) ^ [_1361992, _1361994, _1361996] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1361992), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1361994, _1361996)), _1361996) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1361992), _1361994), _1361996))], (30698 ^ _782652) ^ [_1362043, _1362045, _1362047] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1362043), _1362045), _1362047) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1362043), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1362045, _1362047)), _1362047))], (30700 ^ _782652) ^ [_1362094, _1362096, _1362098] : [-(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, _1362094, _1362096)), _1362098), _1362096) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1362094), _1362098), _1362096))], (30702 ^ _782652) ^ [_1362145, _1362147, _1362149] : [class_Divides_Osemiring__div(_1362145), -(c_Divides_Odiv__class_Omod(_1362145, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362145), _1362147), _1362149), _1362147) = c_Groups_Ozero__class_Ozero(_1362145))], (30708 ^ _782652) ^ [_1362250, _1362252, _1362254] : [class_Divides_Osemiring__div(_1362250), -(c_Divides_Odiv__class_Omod(_1362250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362250), _1362252), _1362254), _1362254) = c_Groups_Ozero__class_Ozero(_1362250))], (30714 ^ _782652) ^ [_1362355, _1362357, _1362359, _1362361] : [class_Divides_Osemiring__div(_1362355), -(c_Divides_Odiv__class_Omod(_1362355, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362355), _1362357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362355), _1362359), _1362361)), _1362359) = c_Divides_Odiv__class_Omod(_1362355, _1362357, _1362359))], (30720 ^ _782652) ^ [_1362482, _1362484, _1362486, _1362488] : [class_Divides_Osemiring__div(_1362482), -(c_Divides_Odiv__class_Omod(_1362482, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362482), _1362484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362482), _1362486), _1362488)), _1362488) = c_Divides_Odiv__class_Omod(_1362482, _1362484, _1362488))], (30726 ^ _782652) ^ [_1362609, _1362611] : [class_Divides_Osemiring__div(_1362609), -(c_Divides_Odiv__class_Omod(_1362609, _1362611, c_Groups_Oone__class_Oone(_1362609)) = c_Groups_Ozero__class_Ozero(_1362609))], (30732 ^ _782652) ^ [_1362700, _1362702, _1362704] : [class_Divides_Osemiring__div(_1362700), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1362700), c_Divides_Odiv__class_Omod(_1362700, _1362702, _1362704)), _1362704) = c_Groups_Ozero__class_Ozero(_1362700))], (30738 ^ _782652) ^ [_1362805, _1362807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1362805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1362805, _1362807)), _1362805)))], (30744 ^ _782652) ^ [_1362904, _1362906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1362904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1362906)), -(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, _1362904, _1362906))))], (30754 ^ _782652) ^ [_1363053, _1363055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1363053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363055, _1363053)), _1363053)))], (30760 ^ _782652) ^ [_1363152, _1363154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1363152), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1363152), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363154, _1363152))))], (30766 ^ _782652) ^ [_1363272, _1363274] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363272, _1363274) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1363272 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1363274), 30769 ^ [_1363272, _1363274]))], (30773 ^ _782652) ^ [_1363377, _1363379] : [30774 ^ _782652 : [(30775 ^ _782652) ^ [_1363426] : [_1363377 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1363379), _1363426)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363377, _1363379) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30779 ^ _782652) ^ [_1363488, _1363490] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1363488), _1363490) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363488, _1363490) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (30785 ^ _782652) ^ [_1363578, _1363580] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363578, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1363580)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363578, _1363580) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (30791 ^ _782652) ^ [_1363669, _1363671] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363669, _1363671)), _1363671) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30793 ^ _782652) ^ [_1363702] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1363702), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30795 ^ _782652) ^ [_1363728] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363728, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1363728)], (30797 ^ _782652) ^ [_1363757, _1363759, _1363761] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1363757), _1363759)), _1363761) = 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), _1363757), _1363761)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1363759), _1363761))), 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, _1363757, _1363761)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1363759, _1363761))), _1363761)))], (30799 ^ _782652) ^ [_1363840, _1363842, _1363844] : [class_Divides_Osemiring__div(_1363840), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363840), c_Divides_Odiv__class_Omod(_1363840, _1363842, _1363844)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363840), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1363840), _1363842), _1363844)), _1363844)) = _1363842)], (30805 ^ _782652) ^ [_1363973, _1363975, _1363977] : [class_Divides_Osemiring__div(_1363973), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363973), _1363975), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1363973), _1363977), _1363975))), c_Divides_Odiv__class_Omod(_1363973, _1363977, _1363975)) = _1363977)], (30811 ^ _782652) ^ [_1364106, _1364108, _1364110] : [class_Divides_Osemiring__div(_1364106), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364106), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1364106), _1364108), _1364110)), _1364110)), c_Divides_Odiv__class_Omod(_1364106, _1364108, _1364110)) = _1364108)], (30817 ^ _782652) ^ [_1364239, _1364241, _1364243, _1364245] : [class_Divides_Osemiring__div(_1364239), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364239), _1364241), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1364239), _1364243), _1364241))), c_Divides_Odiv__class_Omod(_1364239, _1364243, _1364241))), _1364245) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364239), _1364243), _1364245))], (30823 ^ _782652) ^ [_1364406, _1364408, _1364410, _1364412] : [class_Divides_Osemiring__div(_1364406), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364406), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364406), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1364406), _1364408), _1364410)), _1364410)), c_Divides_Odiv__class_Omod(_1364406, _1364408, _1364410))), _1364412) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364406), _1364408), _1364412))], (30829 ^ _782652) ^ [_1364573, _1364575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1364573), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364575), _1364573)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1364573, _1364575) = _1364573)], (30839 ^ _782652) ^ [_1364730, _1364732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364730), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30842 ^ _782652 : [(30843 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1364732, _1364730)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30845 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364730), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1364732, _1364730))))]]], (30847 ^ _782652) ^ [_1364879, _1364881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364879), 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, _1364881, _1364879)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30853 ^ _782652) ^ [_1364984, _1364986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1364984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364984), _1364986)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1364984, _1364986) = _1364984)], (30863 ^ _782652) ^ [_1365135, _1365137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1365135)), 30866 ^ _782652 : [(30867 ^ _782652) ^ [] : [-(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, _1365137, _1365135))))], (30869 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365137, _1365135)), _1365135)))]]], (30871 ^ _782652) ^ [_1365272, _1365274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1365272)), -(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, _1365274, _1365272))))], (30877 ^ _782652) ^ [_1365374, _1365376] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365374, _1365376) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365374, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1365376)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30883 ^ _782652) ^ [_1365467, _1365469] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365467, _1365469) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365467, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1365469)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365467, _1365469)), _1365469))], (30889 ^ _782652) ^ [_1365535, _1365537] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365535, _1365537) = 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), _1365535), _1365537) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30895 ^ _782652) ^ [_1365628, _1365630] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365628, _1365630) = 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), _1365628), _1365630) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1365630), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365628, _1365630)))], (30901 ^ _782652) ^ [_1365687, _1365689] : [-(_1365687 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1365689), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1365687), _1365689))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365687, _1365689)))], (30903 ^ _782652) ^ [_1365734, _1365736, _1365738] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1365734), _1365736)), _1365738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1365734), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1365736), _1365738))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1365734), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365736, _1365738))), _1365738)))], (30905 ^ _782652) ^ [_1365807, _1365809, _1365811] : [-(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), _1365807), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1365809), _1365807))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365809, _1365807))), _1365811) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1365809), _1365811))], (30907 ^ _782652) ^ [_1365868, _1365870, _1365872] : [-(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), _1365868), _1365870)), _1365870)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365868, _1365870))), _1365872) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1365868), _1365872))], (30909 ^ _782652) ^ [_1365929, _1365931] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1365929), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1365931), _1365929)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1365931), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365931, _1365929)))], (30911 ^ _782652) ^ [_1365976, _1365978] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1365976, _1365978) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1365976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1365976), _1365978)), _1365978)))], (30913 ^ _782652) ^ [_1366023, _1366025, _1366027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1366023, tc_HOL_Obool)), _1366025), _1366027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1366023, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1366023, _1366025)), c_Predicate_OPowp(_1366023, _1366027))))], (30919 ^ _782652) ^ [_1366160, _1366162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1366160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1366160), _1366162)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1366160, _1366162) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1366160), _1366162))], (30975 ^ _782652) ^ [_1367230, _1367232, _1367234] : [-(hBOOL(hAPP(_1367230, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1367232, _1367234)))), 30978 ^ _782652 : [(30979 ^ _782652) ^ [] : [-(_1367234 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30981 ^ _782652) ^ [] : [hBOOL(hAPP(_1367230, _1367232))]], 30984 ^ _782652 : [(30985 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367234)))], (30989 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30987 ^ [_1367230, _1367232, _1367234])))], (30991 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 30987 ^ [_1367230, _1367232, _1367234]), _1367234)))], (30993 ^ _782652) ^ [] : [-(_1367232 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1367234), 30986 ^ [_1367230, _1367232, _1367234])), 30987 ^ [_1367230, _1367232, _1367234]))], (30995 ^ _782652) ^ [] : [hBOOL(hAPP(_1367230, 30987 ^ [_1367230, _1367232, _1367234]))]], 30996 ^ _782652 : [(30997 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1367234), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31001 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1367234), 30999 ^ [_1367230, _1367232, _1367234])))], (31003 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 30999 ^ [_1367230, _1367232, _1367234]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31005 ^ _782652) ^ [] : [-(_1367232 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1367234), 30998 ^ [_1367230, _1367232, _1367234])), 30999 ^ [_1367230, _1367232, _1367234]))], (31007 ^ _782652) ^ [] : [hBOOL(hAPP(_1367230, 30999 ^ [_1367230, _1367232, _1367234]))]]], (30929 ^ _782652) ^ [_1366353, _1366355, _1366357] : [hBOOL(hAPP(_1366353, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1366355, _1366357))), 30932 ^ _782652 : [(30933 ^ _782652) ^ [] : [_1366357 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1366353, _1366355)))], (30939 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1366357)), 30942 ^ _782652 : [(30943 ^ _782652) ^ [_1366683, _1366685] : [-(hBOOL(hAPP(_1366353, _1366683))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1366683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1366683), _1366357)), _1366355 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1366357), _1366685)), _1366683)]]], (30957 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1366357), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30960 ^ _782652 : [(30961 ^ _782652) ^ [_1366975, _1366977] : [-(hBOOL(hAPP(_1366353, _1366975))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1366357), _1366975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1366975), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1366355 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1366357), _1366977)), _1366975)]]]]], (31011 ^ _782652) ^ [_1367942, _1367944, _1367946, _1367948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1367944), _1367946)), -(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), _1367946), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1367948, _1367942))), _1367944))))], (31025 ^ _782652) ^ [_1368189, _1368191, _1368193, _1368195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368191), _1368193)), -(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), _1368193), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1368195, _1368189))), _1368191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1368193), _1368189))))], (31039 ^ _782652) ^ [_1368454, _1368456, _1368458, _1368460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368456), _1368458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1368458), 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), _1368456), _1368454)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1368456), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1368460, _1368454))), _1368458))))], (31053 ^ _782652) ^ [_1368725, _1368727, _1368729, _1368731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368727), _1368729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1368729), 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), _1368727), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1368731, _1368725))), _1368729)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31067 ^ _782652) ^ [_1368984, _1368986, _1368988, _1368990] : [_1368984 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1368986), _1368988)), _1368990), -(_1368986 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1368984, _1368986) = _1368990), 31074 ^ _782652 : [(31075 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368986)))], (31077 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368990), _1368986))]], 31082 ^ _782652 : [(31083 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368986))], (31085 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368986), _1368990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1368990), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (31097 ^ _782652) ^ [_1369449, _1369451, _1369453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1369449)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1369451, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1369453), _1369449)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1369453), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1369451), _1369453), _1369449))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1369451, _1369453)))], (31103 ^ _782652) ^ [_1369603, _1369605] : [-(_1369603 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31106 ^ _782652 : [(31107 ^ _782652) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1369605, _1369603) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1369605), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1369603)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1369605), _1369603)))], (31113 ^ _782652) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1369605, _1369603) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1369605), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1369603)) = 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), _1369605), _1369603))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (31119 ^ _782652) ^ [_1369876, _1369878] : [-(_1369876 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31122 ^ _782652 : [(31123 ^ _782652) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1369878, _1369876) = 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), _1369878)), _1369876) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1369878), _1369876)))], (31129 ^ _782652) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1369878, _1369876) = 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), _1369878)), _1369876) = 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), _1369878), _1369876))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (31135 ^ _782652) ^ [_1370150, _1370152, _1370154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370150)), 31138 ^ _782652 : [(31157 ^ _782652) ^ [] : [31160 ^ _782652 : [(31161 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31159 ^ [_1370150, _1370152, _1370154])))], (31163 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 31159 ^ [_1370150, _1370152, _1370154]), _1370150)))], (31165 ^ _782652) ^ [] : [-(_1370154 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1370150), 31158 ^ [_1370150, _1370152, _1370154])), 31159 ^ [_1370150, _1370152, _1370154]))], (31167 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1370152, 31158 ^ [_1370150, _1370152, _1370154]), 31159 ^ [_1370150, _1370152, _1370154]))]], -(hBOOL(hAPP(hAPP(_1370152, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1370154), _1370150)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1370154, _1370150))))], (31139 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1370152, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1370154), _1370150)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1370154, _1370150))), 31142 ^ _782652 : [(31143 ^ _782652) ^ [_1370351, _1370353] : [-(hBOOL(hAPP(hAPP(_1370152, _1370353), _1370351))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370351), _1370150)), _1370154 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1370150), _1370353)), _1370351)]]]]], (31171 ^ _782652) ^ [_1370874, _1370876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370874)), -(c_SMT_Oz3mod(_1370876, _1370874) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1370876, _1370874))], (31177 ^ _782652) ^ [_1370963, _1370965] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370963))), -(c_SMT_Oz3mod(_1370965, _1370963) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1370965, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1370963)))], (31183 ^ _782652) ^ [_1371013, _1371015] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1371013), _1371015) = 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), _1371013)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1371015)))))], (31185 ^ _782652) ^ [_1371062, _1371064, _1371066] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1371062), _1371064)), 31191 ^ _782652 : [(31192 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1371062), 31190 ^ [_1371062, _1371064, _1371066]), _1371064)))], (31194 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1371066, 31190 ^ [_1371062, _1371064, _1371066])))]], -(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(_1371062, tc_Nat_Onat), _1371066), _1371064))))], (31198 ^ _782652) ^ [_1371323, _1371325, _1371327] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1371323), _1371325)), c_Fun_Oinj__on(_1371323, tc_fun(tc_fun(_1371323, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1371323, tc_fun(tc_prod(_1371323, _1371323), tc_HOL_Obool), tc_fun(tc_fun(_1371323, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1371323, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1371323, _1371323), tc_HOL_Obool), tc_fun(tc_fun(_1371323, tc_HOL_Obool), tc_HOL_Obool)), _1371323), c_Equiv__Relations_Oquotient(_1371323)), hAPP(hAPP(c_COMBC(_1371323, tc_fun(_1371323, tc_HOL_Obool), tc_fun(_1371323, tc_HOL_Obool)), c_Set_Oinsert(_1371323)), c_Orderings_Obot__class_Obot(tc_fun(_1371323, tc_HOL_Obool))))), _1371327), _1371325), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1371323, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371323), _1371325), _1371327)) = hAPP(c_Finite__Set_Ocard(_1371323), _1371325))], (31208 ^ _782652) ^ [_1371672, _1371674] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1371672), _1371674) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1371672, _1371674)), _1371674))], (31210 ^ _782652) ^ [_1371715, _1371717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1371715), _1371717)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1371715, _1371717) = _1371715)], (31216 ^ _782652) ^ [_1371810, _1371812, _1371814] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1371810, _1371812)), _1371814) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1371810), _1371814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1371812), _1371814)))], (31218 ^ _782652) ^ [_1371863, _1371865, _1371867] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1371863), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1371865, _1371867)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1371863), _1371865), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1371863), _1371867)))], (31220 ^ _782652) ^ [_1371916, _1371918] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1371916, _1371918)), _1371916)))], (31222 ^ _782652) ^ [_1371968, _1371970, _1371972] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1371968), _1371970), _1371972) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1371968, tc_HOL_Obool), tc_HOL_Obool)), -(_1371970 = c_Orderings_Obot__class_Obot(tc_fun(_1371968, tc_HOL_Obool)))], (31228 ^ _782652) ^ [_1372085, _1372087, _1372089] : [_1372087 = c_Orderings_Obot__class_Obot(tc_fun(_1372085, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1372085), _1372087), _1372089) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1372085, tc_HOL_Obool), tc_HOL_Obool)))], (31234 ^ _782652) ^ [_1372226, _1372228, _1372230] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1372226, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1372226), _1372228), _1372230), -(_1372228 = c_Orderings_Obot__class_Obot(tc_fun(_1372226, tc_HOL_Obool)))], (31240 ^ _782652) ^ [_1372343, _1372345, _1372347] : [_1372345 = c_Orderings_Obot__class_Obot(tc_fun(_1372343, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1372343, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1372343), _1372345), _1372347))], (31246 ^ _782652) ^ [_1372466, _1372468] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1372466), c_Orderings_Obot__class_Obot(tc_fun(_1372466, tc_HOL_Obool))), _1372468) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1372466, tc_HOL_Obool), tc_HOL_Obool)))], (31248 ^ _782652) ^ [_1372521, _1372523] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372521, _1372523)) = _1372523, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1372521), _1372523) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31254 ^ _782652) ^ [_1372620, _1372622] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372620, _1372622)) = _1372622), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1372620), _1372622) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372620, _1372622)))], (31260 ^ _782652) ^ [_1372679] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372679, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31262 ^ _782652) ^ [_1372706, _1372708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1372706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372708, _1372706)), _1372706)))], (31268 ^ _782652) ^ [_1372820, _1372822] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372820, _1372822) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1372820 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1372822), 31271 ^ [_1372820, _1372822]))], (31275 ^ _782652) ^ [_1372925, _1372927] : [31276 ^ _782652 : [(31277 ^ _782652) ^ [_1372974] : [_1372925 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1372927), _1372974)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1372925, _1372927) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31281 ^ _782652) ^ [_1373033, _1373035] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1373033), _1373035))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373033, _1373035) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1373033), _1373035), _1373035))], (31287 ^ _782652) ^ [_1373097, _1373099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1373097), _1373099)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373097, _1373099) = _1373097)], (31293 ^ _782652) ^ [_1373186, _1373188] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1373186), _1373188))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373186, _1373188) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1373186), _1373188), _1373188))], (31299 ^ _782652) ^ [_1373243, _1373245, _1373247] : [-(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), _1373243), _1373245)), _1373247), _1373245) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373247, _1373245))], (31301 ^ _782652) ^ [_1373290, _1373292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1373290), _1373292)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373292, _1373290) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1373292), _1373290), _1373290))], (31307 ^ _782652) ^ [_1373405, _1373407] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373405), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373407)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373405, _1373407)))], (31309 ^ _782652) ^ [_1373447, _1373449] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373447, _1373449)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373447), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373449)))], (31311 ^ _782652) ^ [_1373489, _1373491, _1373493] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1373489), _1373491)), _1373493) = 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), _1373489), _1373493)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1373491), _1373493))), 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, _1373489, _1373493)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373491, _1373493))), _1373493)))], (31313 ^ _782652) ^ [_1373581, _1373583] : [_1373581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1373583, _1373581) = _1373583)], (31319 ^ _782652) ^ [_1373658, _1373660] : [-(_1373658 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1373660, _1373658) = c_Nitpick_Onat__gcd(_1373658, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373660, _1373658)))], (31325 ^ _782652) ^ [_1373706, _1373708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1373706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373708, _1373706)), _1373706)))], (31331 ^ _782652) ^ [_1373805, _1373807, _1373809] : [-(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), _1373805), _1373807)), _1373809)), _1373807) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1373809), _1373807))], (31333 ^ _782652) ^ [_1373858, _1373860, _1373862] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373858, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1373860), _1373862)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1373860), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1373858), _1373860), _1373862))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373858, _1373860)))], (31335 ^ _782652) ^ [_1373921, _1373923, _1373925] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1373921), _1373923)), _1373925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1373921), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1373923), _1373925))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1373921), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373923, _1373925))), _1373925)))], (31337 ^ _782652) ^ [_1373994, _1373996] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1373994), _1373996)), _1373996) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1373994), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373994, _1373996)))], (31339 ^ _782652) ^ [_1374041, _1374043] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1374041), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1374043), _1374041)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1374043), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1374043, _1374041)))], (31341 ^ _782652) ^ [_1374088, _1374090] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1374088, _1374090) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1374088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1374088), _1374090)), _1374090)))], (31343 ^ _782652) ^ [_1374135, _1374137, _1374139, _1374141] : [c_Fun_Oinj__on(_1374135, tc_fun(tc_fun(_1374135, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1374135, tc_fun(tc_prod(_1374135, _1374135), tc_HOL_Obool), tc_fun(tc_fun(_1374135, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374135, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1374135, _1374135), tc_HOL_Obool), tc_fun(tc_fun(_1374135, tc_HOL_Obool), tc_HOL_Obool)), _1374135), c_Equiv__Relations_Oquotient(_1374135)), hAPP(hAPP(c_COMBC(_1374135, tc_fun(_1374135, tc_HOL_Obool), tc_fun(_1374135, tc_HOL_Obool)), c_Set_Oinsert(_1374135)), c_Orderings_Obot__class_Obot(tc_fun(_1374135, tc_HOL_Obool))))), _1374137), _1374139), hBOOL(hAPP(hAPP(c_member(_1374135), _1374141), _1374139)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374135), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1374135, tc_HOL_Obool)), _1374139), hAPP(hAPP(c_Set_Oinsert(_1374135), _1374141), c_Orderings_Obot__class_Obot(tc_fun(_1374135, tc_HOL_Obool))))), _1374137) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1374135, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374135), _1374139), _1374137)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1374135), hAPP(hAPP(c_Set_Oinsert(_1374135), _1374141), c_Orderings_Obot__class_Obot(tc_fun(_1374135, tc_HOL_Obool)))), _1374137)))], (31377 ^ _782652) ^ [_1375053, _1375055, _1375057] : [-(hBOOL(hAPP(_1375053, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1375055, _1375057)))), 31380 ^ _782652 : [(31381 ^ _782652) ^ [] : [-(_1375057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31383 ^ _782652) ^ [] : [hBOOL(hAPP(_1375053, _1375055))]], 31384 ^ _782652 : [(31385 ^ _782652) ^ [] : [_1375057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31389 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31387 ^ [_1375053, _1375055, _1375057]), _1375057)))], (31391 ^ _782652) ^ [] : [-(_1375055 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1375057), 31386 ^ [_1375053, _1375055, _1375057])), 31387 ^ [_1375053, _1375055, _1375057]))], (31393 ^ _782652) ^ [] : [hBOOL(hAPP(_1375053, 31387 ^ [_1375053, _1375055, _1375057]))]]], (31353 ^ _782652) ^ [_1374620, _1374622, _1374624] : [hBOOL(hAPP(_1374620, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1374622, _1374624))), 31356 ^ _782652 : [(31357 ^ _782652) ^ [] : [_1374624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1374620, _1374622)))], (31363 ^ _782652) ^ [] : [-(_1374624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31366 ^ _782652 : [(31367 ^ _782652) ^ [_1374868, _1374870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1374868), _1374624)), _1374622 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1374624), _1374870)), _1374868), -(hBOOL(hAPP(_1374620, _1374868)))]]]]], (31397 ^ _782652) ^ [_1375462, _1375464, _1375466, _1375468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1375462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1375464), _1375466)), -(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), _1375466), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1375468, _1375462))), _1375464)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1375466), _1375462))))], (31407 ^ _782652) ^ [_1375667, _1375669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1375667)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1375667), _1375669)), _1375667) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31413 ^ _782652) ^ [_1375774, _1375776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375776)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1375774), hAPP(c_Int_Onat, _1375776)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1375774, _1375776)))], (31423 ^ _782652) ^ [_1375945, _1375947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375947)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1375945, _1375947)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1375945), hAPP(c_Int_Onat, _1375947)))], (31433 ^ _782652) ^ [_1376116, _1376118, _1376120] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1376116), _1376118), _1376120) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376116, tc_fun(tc_fun(_1376116, tc_HOL_Obool), tc_HOL_Obool)), _1376118), hAPP(hAPP(c_COMBC(_1376116, tc_fun(tc_fun(_1376116, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1376116, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376116, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1376116, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1376116, tc_HOL_Obool), tc_HOL_Obool)), _1376116), c_Set_Oinsert(tc_fun(_1376116, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1376116, tc_HOL_Obool), tc_fun(_1376116, tc_HOL_Obool), _1376116), c_Relation_OImage(_1376116, _1376116, _1376120)), hAPP(hAPP(c_COMBC(_1376116, tc_fun(_1376116, tc_HOL_Obool), tc_fun(_1376116, tc_HOL_Obool)), c_Set_Oinsert(_1376116)), c_Orderings_Obot__class_Obot(tc_fun(_1376116, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1376116, tc_HOL_Obool), tc_HOL_Obool)))))], (31435 ^ _782652) ^ [_1376272, _1376274, _1376276] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1376272), hAPP(hAPP(c_Set_Oinsert(_1376272), _1376274), c_Orderings_Obot__class_Obot(tc_fun(_1376272, tc_HOL_Obool)))), _1376276) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1376272, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1376272, _1376272, _1376276), hAPP(hAPP(c_Set_Oinsert(_1376272), _1376274), c_Orderings_Obot__class_Obot(tc_fun(_1376272, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1376272, tc_HOL_Obool), tc_HOL_Obool))))], (31437 ^ _782652) ^ [_1376359, _1376361, _1376363, _1376365] : [hBOOL(hAPP(hAPP(c_member(_1376359), _1376361), _1376363)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1376359, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1376359, _1376359, _1376365), hAPP(hAPP(c_Set_Oinsert(_1376359), _1376361), c_Orderings_Obot__class_Obot(tc_fun(_1376359, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1376359), _1376363), _1376365))))], (31443 ^ _782652) ^ [_1376530, _1376532, _1376534, _1376536] : [class_Groups_Ocomm__monoid__mult(_1376530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376532), _1376534)), 31453 ^ _782652 : [(31454 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376532), 31452 ^ [_1376530, _1376532, _1376534, _1376536]), _1376534)))], (31456 ^ _782652) ^ [] : [hAPP(_1376536, 31452 ^ [_1376530, _1376532, _1376534, _1376536]) = c_Groups_Oone__class_Oone(_1376530)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1376530, _1376532, c_Groups_Otimes__class_Otimes(_1376530)), _1376536), c_Groups_Oone__class_Oone(_1376530)), _1376534) = c_Groups_Oone__class_Oone(_1376530))], (31460 ^ _782652) ^ [_1376871, _1376873, _1376875, _1376877] : [-(hAPP(c_Relation_OImage(_1376871, _1376873, _1376875), _1376877) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1376871, tc_fun(_1376873, tc_HOL_Obool)), _1376877), hAPP(hAPP(c_COMBB(tc_fun(_1376871, tc_HOL_Obool), tc_fun(_1376873, tc_HOL_Obool), _1376871), c_Relation_OImage(_1376871, _1376873, _1376875)), hAPP(hAPP(c_COMBC(_1376871, tc_fun(_1376871, tc_HOL_Obool), tc_fun(_1376871, tc_HOL_Obool)), c_Set_Oinsert(_1376871)), c_Orderings_Obot__class_Obot(tc_fun(_1376871, tc_HOL_Obool))))))], (31462 ^ _782652) ^ [_1376962, _1376964, _1376966, _1376968, _1376970] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376962, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1376964, _1376962, _1376966), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376964, tc_HOL_Obool)), _1376968), _1376970))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376962, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1376964, _1376962, _1376966), _1376968)), hAPP(c_Relation_OImage(_1376964, _1376962, _1376966), _1376970)))))], (31464 ^ _782652) ^ [_1377046, _1377048, _1377050, _1377052, _1377054, _1377056] : [-(hAPP(c_Relation_OImage(_1377046, _1377048, _1377050), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377052, tc_fun(_1377046, tc_HOL_Obool)), _1377054), _1377056)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1377052, tc_fun(_1377048, tc_HOL_Obool)), _1377054), hAPP(hAPP(c_COMBB(tc_fun(_1377046, tc_HOL_Obool), tc_fun(_1377048, tc_HOL_Obool), _1377052), c_Relation_OImage(_1377046, _1377048, _1377050)), _1377056)))], (31466 ^ _782652) ^ [_1377130, _1377132, _1377134, _1377136] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1377130, tc_HOL_Obool)), _1377132), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377130), _1377134), _1377136))), 31470 ^ _782652 : [(31471 ^ _782652) ^ [] : [-(_1377132 = hAPP(c_Relation_OImage(_1377130, _1377130, _1377136), hAPP(hAPP(c_Set_Oinsert(_1377130), 31469 ^ [_1377130, _1377132, _1377134, _1377136]), c_Orderings_Obot__class_Obot(tc_fun(_1377130, tc_HOL_Obool)))))], (31473 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377130), 31469 ^ [_1377130, _1377132, _1377134, _1377136]), _1377134)))]]], (31475 ^ _782652) ^ [_1377358, _1377360, _1377362] : [-(hAPP(c_Relation_OImage(_1377358, _1377360, _1377362), c_Orderings_Obot__class_Obot(tc_fun(_1377358, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1377360, tc_HOL_Obool)))], (31477 ^ _782652) ^ [_1377402, _1377404, _1377406, _1377408, _1377410, _1377412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1377402, _1377404), tc_HOL_Obool)), _1377406), _1377408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377402, tc_HOL_Obool)), _1377410), _1377412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377404, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1377402, _1377404, _1377406), _1377410)), hAPP(c_Relation_OImage(_1377402, _1377404, _1377408), _1377412))))], (31487 ^ _782652) ^ [_1377641, _1377643, _1377645, _1377647, _1377649] : [-(hAPP(c_Relation_OImage(_1377641, _1377643, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1377641, _1377643), tc_HOL_Obool)), _1377645), _1377647)), _1377649) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377643, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1377641, _1377643, _1377645), _1377649)), hAPP(c_Relation_OImage(_1377641, _1377643, _1377647), _1377649)))], (31489 ^ _782652) ^ [_1377718, _1377720, _1377722, _1377724, _1377726] : [-(hAPP(c_Relation_OImage(_1377718, _1377720, _1377722), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377718, tc_HOL_Obool)), _1377724), _1377726)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377720, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1377718, _1377720, _1377722), _1377724)), hAPP(c_Relation_OImage(_1377718, _1377720, _1377722), _1377726)))], (31491 ^ _782652) ^ [_1377792, _1377794, _1377796] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1377792, _1377794) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1377796, _1377794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1377796), _1377792)), -(_1377792 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1377796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1377794), 31498 ^ [_1377792, _1377794, _1377796])))], (31502 ^ _782652) ^ [_1377989, _1377991] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1377989), _1377991)), 31508 ^ _782652 : [(31509 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377989), 31507 ^ [_1377989, _1377991]), _1377991)))], (31511 ^ _782652) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1377989), _1377991) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31515 ^ _782652) ^ [_1378189, _1378191, _1378193] : [31517 ^ _782652 : [(31518 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31516 ^ [_1378189, _1378191, _1378193]), _1378189)))], (31520 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1378191, 31516 ^ [_1378189, _1378191, _1378193])))], (31522 ^ _782652) ^ [] : [hBOOL(hAPP(_1378191, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 31516 ^ [_1378189, _1378191, _1378193]), _1378189)))]], hBOOL(hAPP(_1378191, _1378193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1378193), _1378189)), -(hBOOL(hAPP(_1378191, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31534 ^ _782652) ^ [_1378551, _1378553, _1378555, _1378557, _1378559, _1378561] : [class_Groups_Oab__semigroup__mult(_1378551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378553), _1378555)), 31544 ^ _782652 : [(31545 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378553), 31543 ^ [_1378551, _1378553, _1378555, _1378557, _1378559, _1378561]), _1378555)))], (31547 ^ _782652) ^ [] : [hAPP(_1378557, 31543 ^ [_1378551, _1378553, _1378555, _1378557, _1378559, _1378561]) = hAPP(_1378559, 31543 ^ [_1378551, _1378553, _1378555, _1378557, _1378559, _1378561])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1378551, _1378553, c_Groups_Otimes__class_Otimes(_1378551)), _1378557), _1378561), _1378555) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1378551, _1378553, c_Groups_Otimes__class_Otimes(_1378551)), _1378559), _1378561), _1378555))], (31551 ^ _782652) ^ [_1378956, _1378958, _1378960] : [_1378956 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1378958, _1378958), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1378958, _1378958), tc_HOL_Obool)), _1378956), _1378960)))], (31557 ^ _782652) ^ [_1379077, _1379079, _1379081] : [class_Orderings_Olinorder(_1379077), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379077), _1379079)), 31567 ^ _782652 : [(31568 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1379077), 31566 ^ [_1379077, _1379079, _1379081]), _1379079)))], (31570 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379077), _1379081), 31566 ^ [_1379077, _1379079, _1379081]))]], hBOOL(hAPP(hAPP(c_member(_1379077), _1379081), _1379079)), -(c_Big__Operators_Olinorder__class_OMin(_1379077, _1379079) = _1379081)], (31578 ^ _782652) ^ [_1379449, _1379451, _1379453] : [class_Orderings_Olinorder(_1379449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379449), _1379451)), 31588 ^ _782652 : [(31589 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1379449), 31587 ^ [_1379449, _1379451, _1379453]), _1379451)))], (31591 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379449), 31587 ^ [_1379449, _1379451, _1379453]), _1379453))]], hBOOL(hAPP(hAPP(c_member(_1379449), _1379453), _1379451)), -(c_Big__Operators_Olinorder__class_OMax(_1379449, _1379451) = _1379453)], (31599 ^ _782652) ^ [_1379821] : [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), _1379821))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379821) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379821)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (31605 ^ _782652) ^ [_1379936, _1379938, _1379940, _1379942, _1379944] : [c_Equiv__Relations_Oequiv(_1379936, _1379938, _1379940), hBOOL(hAPP(hAPP(c_member(tc_fun(_1379936, tc_HOL_Obool)), _1379942), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1379936), _1379938), _1379940))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1379936, tc_HOL_Obool)), _1379944), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1379936), _1379938), _1379940))), -(_1379942 = _1379944), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1379936, tc_HOL_Obool)), _1379942), _1379944) = c_Orderings_Obot__class_Obot(tc_fun(_1379936, tc_HOL_Obool)))], (31623 ^ _782652) ^ [_1380254, _1380256] : [class_Int_Onumber__ring(_1380254), 31626 ^ _782652 : [(31627 ^ _782652) ^ [] : [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), _1380256))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1380254), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380256)) = hAPP(c_Int_Onumber__class_Onumber__of(_1380254), _1380256))], (31633 ^ _782652) ^ [] : [-(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), _1380256)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1380254), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380256)) = c_Groups_Ozero__class_Ozero(_1380254))]]], (31639 ^ _782652) ^ [_1380494, _1380496] : [class_Int_Onumber__ring(_1380494), 31642 ^ _782652 : [(31643 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1380496))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1380494), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380496)) = c_Groups_Ozero__class_Ozero(_1380494))], (31649 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1380496)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1380494), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380496)) = hAPP(c_Int_Onumber__class_Onumber__of(_1380494), _1380496))]]], (31655 ^ _782652) ^ [_1380734, _1380736] : [class_Int_Onumber__ring(_1380734), -(hAPP(c_Int_Onumber__class_Onumber__of(_1380734), _1380736) = hAPP(c_Int_Oring__1__class_Oof__int(_1380734), _1380736))], (31661 ^ _782652) ^ [_1380829, _1380831] : [class_Int_Onumber__ring(_1380829), -(hAPP(c_Int_Oring__1__class_Oof__int(_1380829), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1380831)) = hAPP(c_Int_Onumber__class_Onumber__of(_1380829), _1380831))], (31667 ^ _782652) ^ [_1380930, _1380932, _1380934] : [class_Int_Onumber__ring(_1380930), class_Int_Oring__char__0(_1380930), 31674 ^ _782652 : [(31675 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1380930), _1380932) = hAPP(c_Int_Onumber__class_Onumber__of(_1380930), _1380934), -(_1380932 = _1380934)], (31681 ^ _782652) ^ [] : [_1380932 = _1380934, -(hAPP(c_Int_Onumber__class_Onumber__of(_1380930), _1380932) = hAPP(c_Int_Onumber__class_Onumber__of(_1380930), _1380934))]]], (31687 ^ _782652) ^ [_1381225, _1381227, _1381229] : [class_Int_Onumber(_1381225), 31690 ^ _782652 : [(31691 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1381225), _1381227) = _1381229, -(_1381229 = hAPP(c_Int_Onumber__class_Onumber__of(_1381225), _1381227))], (31697 ^ _782652) ^ [] : [_1381229 = hAPP(c_Int_Onumber__class_Onumber__of(_1381225), _1381227), -(hAPP(c_Int_Onumber__class_Onumber__of(_1381225), _1381227) = _1381229)]]], (31703 ^ _782652) ^ [_1381466, _1381468, _1381470] : [class_Int_Onumber(_1381466), class_Orderings_Olinorder(_1381466), 31710 ^ _782652 : [(31711 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1381466), hAPP(c_Int_Onumber__class_Onumber__of(_1381466), _1381468)), hAPP(c_Int_Onumber__class_Onumber__of(_1381466), _1381470))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381466), hAPP(c_Int_Onumber__class_Onumber__of(_1381466), _1381470)), hAPP(c_Int_Onumber__class_Onumber__of(_1381466), _1381468)))], (31717 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381466), hAPP(c_Int_Onumber__class_Onumber__of(_1381466), _1381470)), hAPP(c_Int_Onumber__class_Onumber__of(_1381466), _1381468)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1381466), hAPP(c_Int_Onumber__class_Onumber__of(_1381466), _1381468)), hAPP(c_Int_Onumber__class_Onumber__of(_1381466), _1381470))))]]], (31723 ^ _782652) ^ [_1381793, _1381795, _1381797, _1381799] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381793), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1381793), _1381795), _1381797)), hAPP(c_Int_Onumber__class_Onumber__of(_1381793), _1381799)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1381793), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381793), _1381795), hAPP(c_Int_Onumber__class_Onumber__of(_1381793), _1381799))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381793), _1381797), hAPP(c_Int_Onumber__class_Onumber__of(_1381793), _1381799)))), class_Int_Onumber(_1381793), class_Rings_Osemiring(_1381793)], (31733 ^ _782652) ^ [_1382036, _1382038, _1382040, _1382042] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382036), hAPP(c_Int_Onumber__class_Onumber__of(_1382036), _1382038)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382036), _1382040), _1382042)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382036), hAPP(c_Int_Onumber__class_Onumber__of(_1382036), _1382038)), _1382040)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382036), hAPP(c_Int_Onumber__class_Onumber__of(_1382036), _1382038)), _1382042))), class_Int_Onumber(_1382036), class_Rings_Osemiring(_1382036)], (31743 ^ _782652) ^ [_1382279, _1382281, _1382283, _1382285] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382279), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382279), _1382281), _1382283)), hAPP(c_Int_Onumber__class_Onumber__of(_1382279), _1382285)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382279), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382279), _1382281), hAPP(c_Int_Onumber__class_Onumber__of(_1382279), _1382285))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382279), _1382283), hAPP(c_Int_Onumber__class_Onumber__of(_1382279), _1382285)))), class_Int_Onumber(_1382279), class_Rings_Oring(_1382279)], (31753 ^ _782652) ^ [_1382522, _1382524, _1382526, _1382528] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382522), hAPP(c_Int_Onumber__class_Onumber__of(_1382522), _1382524)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382522), _1382526), _1382528)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382522), hAPP(c_Int_Onumber__class_Onumber__of(_1382522), _1382524)), _1382526)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382522), hAPP(c_Int_Onumber__class_Onumber__of(_1382522), _1382524)), _1382528))), class_Int_Onumber(_1382522), class_Rings_Oring(_1382522)], (31763 ^ _782652) ^ [_1382765, _1382767, _1382769] : [class_Int_Onumber__ring(_1382765), class_Rings_Olinordered__idom(_1382765), 31770 ^ _782652 : [(31771 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382765), hAPP(c_Int_Onumber__class_Onumber__of(_1382765), _1382767)), hAPP(c_Int_Onumber__class_Onumber__of(_1382765), _1382769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1382767), _1382769)))], (31777 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1382767), _1382769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382765), hAPP(c_Int_Onumber__class_Onumber__of(_1382765), _1382767)), hAPP(c_Int_Onumber__class_Onumber__of(_1382765), _1382769))))]]], (31783 ^ _782652) ^ [_1383096, _1383098, _1383100] : [class_Int_Onumber__ring(_1383096), class_Rings_Olinordered__idom(_1383096), 31790 ^ _782652 : [(31791 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383096), hAPP(c_Int_Onumber__class_Onumber__of(_1383096), _1383098)), hAPP(c_Int_Onumber__class_Onumber__of(_1383096), _1383100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1383098), _1383100)))], (31797 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1383098), _1383100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383096), hAPP(c_Int_Onumber__class_Onumber__of(_1383096), _1383098)), hAPP(c_Int_Onumber__class_Onumber__of(_1383096), _1383100))))]]], (31803 ^ _782652) ^ [_1383427, _1383429, _1383431] : [class_Int_Onumber(_1383427), class_Orderings_Oord(_1383427), 31810 ^ _782652 : [(31811 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383427), hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383429)), hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383431))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383427), hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383429)), hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383431)) = hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383429))], (31817 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383427), hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383429)), hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383431)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383427), hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383429)), hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383431)) = hAPP(c_Int_Onumber__class_Onumber__of(_1383427), _1383431))]]], (31823 ^ _782652) ^ [_1383819, _1383821, _1383823] : [class_Int_Onumber(_1383819), class_Orderings_Oord(_1383819), 31830 ^ _782652 : [(31831 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383819), hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383821)), hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383823))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1383819), hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383821)), hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383823)) = hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383823))], (31837 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383819), hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383821)), hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383823)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1383819), hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383821)), hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383823)) = hAPP(c_Int_Onumber__class_Onumber__of(_1383819), _1383821))]]], (31843 ^ _782652) ^ [_1384211, _1384213, _1384215] : [class_Int_Onumber__ring(_1384211), -(hAPP(c_Int_Onumber__class_Onumber__of(_1384211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384213), _1384215)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384211), hAPP(c_Int_Onumber__class_Onumber__of(_1384211), _1384213)), hAPP(c_Int_Onumber__class_Onumber__of(_1384211), _1384215)))], (31849 ^ _782652) ^ [_1384346, _1384348, _1384350] : [class_Int_Onumber__ring(_1384346), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384346), hAPP(c_Int_Onumber__class_Onumber__of(_1384346), _1384348)), hAPP(c_Int_Onumber__class_Onumber__of(_1384346), _1384350)) = hAPP(c_Int_Onumber__class_Onumber__of(_1384346), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384348), _1384350)))], (31855 ^ _782652) ^ [_1384481, _1384483, _1384485, _1384487] : [class_Int_Onumber__ring(_1384481), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384481), hAPP(c_Int_Onumber__class_Onumber__of(_1384481), _1384483)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384481), hAPP(c_Int_Onumber__class_Onumber__of(_1384481), _1384485)), _1384487)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384481), hAPP(c_Int_Onumber__class_Onumber__of(_1384481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384483), _1384485))), _1384487))], (31861 ^ _782652) ^ [_1384650, _1384652, _1384654] : [class_Int_Onumber__ring(_1384650), -(hAPP(c_Int_Onumber__class_Onumber__of(_1384650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384652), _1384654)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384650), hAPP(c_Int_Onumber__class_Onumber__of(_1384650), _1384652)), hAPP(c_Int_Onumber__class_Onumber__of(_1384650), _1384654)))], (31867 ^ _782652) ^ [_1384785, _1384787, _1384789] : [class_Int_Onumber__ring(_1384785), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384785), hAPP(c_Int_Onumber__class_Onumber__of(_1384785), _1384787)), hAPP(c_Int_Onumber__class_Onumber__of(_1384785), _1384789)) = hAPP(c_Int_Onumber__class_Onumber__of(_1384785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384787), _1384789)))], (31873 ^ _782652) ^ [_1384920, _1384922, _1384924, _1384926] : [class_Int_Onumber__ring(_1384920), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384920), hAPP(c_Int_Onumber__class_Onumber__of(_1384920), _1384922)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384920), hAPP(c_Int_Onumber__class_Onumber__of(_1384920), _1384924)), _1384926)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384920), hAPP(c_Int_Onumber__class_Onumber__of(_1384920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384922), _1384924))), _1384926))], (31879 ^ _782652) ^ [_1385089, _1385091, _1385093] : [class_Int_Onumber__ring(_1385089), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385091), _1385093)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1385089), hAPP(c_Int_Onumber__class_Onumber__of(_1385089), _1385091)), hAPP(c_Int_Onumber__class_Onumber__of(_1385089), _1385093)))], (31885 ^ _782652) ^ [_1385224, _1385226] : [class_Int_Onumber__ring(_1385224), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1385224), hAPP(c_Int_Onumber__class_Onumber__of(_1385224), _1385226)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385224), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385226)))], (31891 ^ _782652) ^ [_1385335, _1385337] : [class_Int_Onumber__ring(_1385335), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385335), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385337)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1385335), hAPP(c_Int_Onumber__class_Onumber__of(_1385335), _1385337)))], (31897 ^ _782652) ^ [_1385446, _1385448] : [class_Int_Onumber__ring(_1385446), -(hBOOL(hAPP(hAPP(c_member(_1385446), hAPP(c_Int_Onumber__class_Onumber__of(_1385446), _1385448)), c_Int_Oring__1__class_OInts(_1385446))))], (31903 ^ _782652) ^ [_1385549, _1385551, _1385553, _1385555] : [class_Fields_Ofield__inverse__zero(_1385549), class_Int_Onumber(_1385549), 31910 ^ _782652 : [(31927 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385549), _1385551), hAPP(c_Int_Onumber__class_Onumber__of(_1385549), _1385553)) = _1385555), 31930 ^ _782652 : [(31931 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1385549), _1385553) = c_Groups_Ozero__class_Ozero(_1385549)], (31933 ^ _782652) ^ [] : [_1385551 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385549), _1385555), hAPP(c_Int_Onumber__class_Onumber__of(_1385549), _1385553))]], 31934 ^ _782652 : [(31935 ^ _782652) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1385549), _1385553) = c_Groups_Ozero__class_Ozero(_1385549))], (31937 ^ _782652) ^ [] : [_1385555 = c_Groups_Ozero__class_Ozero(_1385549)]]], (31911 ^ _782652) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385549), _1385551), hAPP(c_Int_Onumber__class_Onumber__of(_1385549), _1385553)) = _1385555, 31914 ^ _782652 : [(31915 ^ _782652) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1385549), _1385553) = c_Groups_Ozero__class_Ozero(_1385549)), -(_1385551 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385549), _1385555), hAPP(c_Int_Onumber__class_Onumber__of(_1385549), _1385553)))], (31921 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1385549), _1385553) = c_Groups_Ozero__class_Ozero(_1385549), -(_1385555 = c_Groups_Ozero__class_Ozero(_1385549))]]]]], (31941 ^ _782652) ^ [_1386159, _1386161, _1386163, _1386165] : [class_Fields_Ofield__inverse__zero(_1386159), class_Int_Onumber(_1386159), 31948 ^ _782652 : [(31965 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386159), _1386161), _1386163) = hAPP(c_Int_Onumber__class_Onumber__of(_1386159), _1386165)), 31968 ^ _782652 : [(31969 ^ _782652) ^ [] : [_1386163 = c_Groups_Ozero__class_Ozero(_1386159)], (31971 ^ _782652) ^ [] : [_1386161 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386159), hAPP(c_Int_Onumber__class_Onumber__of(_1386159), _1386165)), _1386163)]], 31972 ^ _782652 : [(31973 ^ _782652) ^ [] : [-(_1386163 = c_Groups_Ozero__class_Ozero(_1386159))], (31975 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1386159), _1386165) = c_Groups_Ozero__class_Ozero(_1386159)]]], (31949 ^ _782652) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386159), _1386161), _1386163) = hAPP(c_Int_Onumber__class_Onumber__of(_1386159), _1386165), 31952 ^ _782652 : [(31953 ^ _782652) ^ [] : [-(_1386163 = c_Groups_Ozero__class_Ozero(_1386159)), -(_1386161 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386159), hAPP(c_Int_Onumber__class_Onumber__of(_1386159), _1386165)), _1386163))], (31959 ^ _782652) ^ [] : [_1386163 = c_Groups_Ozero__class_Ozero(_1386159), -(hAPP(c_Int_Onumber__class_Onumber__of(_1386159), _1386165) = c_Groups_Ozero__class_Ozero(_1386159))]]]]], (31979 ^ _782652) ^ [_1386754, _1386756, _1386758, _1386760] : [class_Fields_Ofield__inverse__zero(_1386754), class_Int_Onumber(_1386754), 31986 ^ _782652 : [(32003 ^ _782652) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1386754), _1386756) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386754), _1386758), _1386760)), 32006 ^ _782652 : [(32007 ^ _782652) ^ [] : [_1386760 = c_Groups_Ozero__class_Ozero(_1386754)], (32009 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386754), hAPP(c_Int_Onumber__class_Onumber__of(_1386754), _1386756)), _1386760) = _1386758]], 32010 ^ _782652 : [(32011 ^ _782652) ^ [] : [-(_1386760 = c_Groups_Ozero__class_Ozero(_1386754))], (32013 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1386754), _1386756) = c_Groups_Ozero__class_Ozero(_1386754)]]], (31987 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1386754), _1386756) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386754), _1386758), _1386760), 31990 ^ _782652 : [(31991 ^ _782652) ^ [] : [-(_1386760 = c_Groups_Ozero__class_Ozero(_1386754)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386754), hAPP(c_Int_Onumber__class_Onumber__of(_1386754), _1386756)), _1386760) = _1386758)], (31997 ^ _782652) ^ [] : [_1386760 = c_Groups_Ozero__class_Ozero(_1386754), -(hAPP(c_Int_Onumber__class_Onumber__of(_1386754), _1386756) = c_Groups_Ozero__class_Ozero(_1386754))]]]]], (32017 ^ _782652) ^ [_1387349, _1387351, _1387353, _1387355] : [class_Fields_Ofield__inverse__zero(_1387349), class_Int_Onumber(_1387349), 32024 ^ _782652 : [(32041 ^ _782652) ^ [] : [-(_1387351 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387349), _1387353), hAPP(c_Int_Onumber__class_Onumber__of(_1387349), _1387355))), 32044 ^ _782652 : [(32045 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1387349), _1387355) = c_Groups_Ozero__class_Ozero(_1387349)], (32047 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387349), _1387351), hAPP(c_Int_Onumber__class_Onumber__of(_1387349), _1387355)) = _1387353]], 32048 ^ _782652 : [(32049 ^ _782652) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1387349), _1387355) = c_Groups_Ozero__class_Ozero(_1387349))], (32051 ^ _782652) ^ [] : [_1387351 = c_Groups_Ozero__class_Ozero(_1387349)]]], (32025 ^ _782652) ^ [] : [_1387351 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387349), _1387353), hAPP(c_Int_Onumber__class_Onumber__of(_1387349), _1387355)), 32028 ^ _782652 : [(32029 ^ _782652) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1387349), _1387355) = c_Groups_Ozero__class_Ozero(_1387349)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387349), _1387351), hAPP(c_Int_Onumber__class_Onumber__of(_1387349), _1387355)) = _1387353)], (32035 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1387349), _1387355) = c_Groups_Ozero__class_Ozero(_1387349), -(_1387351 = c_Groups_Ozero__class_Ozero(_1387349))]]]]], (32055 ^ _782652) ^ [_1387959, _1387961, _1387963, _1387965] : [class_Int_Onumber__ring(_1387959), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387959), hAPP(c_Int_Onumber__class_Onumber__of(_1387959), _1387961)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387959), hAPP(c_Int_Onumber__class_Onumber__of(_1387959), _1387963)), _1387965)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387959), hAPP(c_Int_Onumber__class_Onumber__of(_1387959), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1387961), _1387963))), _1387965))], (32061 ^ _782652) ^ [_1388128, _1388130, _1388132] : [class_Int_Onumber__ring(_1388128), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388128), hAPP(c_Groups_Ouminus__class_Ouminus(_1388128), hAPP(c_Int_Onumber__class_Onumber__of(_1388128), _1388130))), _1388132) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388128), hAPP(c_Int_Onumber__class_Onumber__of(_1388128), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1388130))), _1388132))], (32067 ^ _782652) ^ [_1388273, _1388275, _1388277] : [class_Int_Onumber__ring(_1388273), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388273), hAPP(c_Int_Onumber__class_Onumber__of(_1388273), _1388275)), hAPP(c_Int_Onumber__class_Onumber__of(_1388273), _1388277)) = hAPP(c_Int_Onumber__class_Onumber__of(_1388273), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1388275), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1388277))))], (32073 ^ _782652) ^ [_1388414, _1388416, _1388418, _1388420] : [class_Fields_Olinordered__field__inverse__zero(_1388414), class_Int_Onumber(_1388414), 32080 ^ _782652 : [(32107 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388414), _1388416), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418))), _1388420))), 32110 ^ _782652 : [(32111 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), c_Groups_Ozero__class_Ozero(_1388414)), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418))))], (32113 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), _1388416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388414), _1388420), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418))))]], 32114 ^ _782652 : [(32115 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), c_Groups_Ozero__class_Ozero(_1388414)), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418)))], (32117 ^ _782652) ^ [] : [32118 ^ _782652 : [(32119 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418)), c_Groups_Ozero__class_Ozero(_1388414))))], (32121 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388414), _1388420), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418))), _1388416))]], 32122 ^ _782652 : [(32123 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418)), c_Groups_Ozero__class_Ozero(_1388414)))], (32125 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), c_Groups_Ozero__class_Ozero(_1388414)), _1388420))]]]]], (32081 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388414), _1388416), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418))), _1388420)), 32084 ^ _782652 : [(32085 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), c_Groups_Ozero__class_Ozero(_1388414)), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), _1388416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388414), _1388420), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418)))))], (32091 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), c_Groups_Ozero__class_Ozero(_1388414)), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418)))), 32094 ^ _782652 : [(32095 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418)), c_Groups_Ozero__class_Ozero(_1388414))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388414), _1388420), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418))), _1388416)))], (32101 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), hAPP(c_Int_Onumber__class_Onumber__of(_1388414), _1388418)), c_Groups_Ozero__class_Ozero(_1388414)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388414), c_Groups_Ozero__class_Ozero(_1388414)), _1388420)))]]]]]]], (32129 ^ _782652) ^ [_1389528, _1389530, _1389532, _1389534] : [class_Fields_Olinordered__field__inverse__zero(_1389528), class_Int_Onumber(_1389528), 32136 ^ _782652 : [(32163 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1389528), _1389530), _1389532)), hAPP(c_Int_Onumber__class_Onumber__of(_1389528), _1389534)))), 32166 ^ _782652 : [(32167 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), c_Groups_Ozero__class_Ozero(_1389528)), _1389532)))], (32169 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), _1389530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389528), hAPP(c_Int_Onumber__class_Onumber__of(_1389528), _1389534)), _1389532)))]], 32170 ^ _782652 : [(32171 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), c_Groups_Ozero__class_Ozero(_1389528)), _1389532))], (32173 ^ _782652) ^ [] : [32174 ^ _782652 : [(32175 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), _1389532), c_Groups_Ozero__class_Ozero(_1389528))))], (32177 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389528), hAPP(c_Int_Onumber__class_Onumber__of(_1389528), _1389534)), _1389532)), _1389530))]], 32178 ^ _782652 : [(32179 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), _1389532), c_Groups_Ozero__class_Ozero(_1389528)))], (32181 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), c_Groups_Ozero__class_Ozero(_1389528)), hAPP(c_Int_Onumber__class_Onumber__of(_1389528), _1389534)))]]]]], (32137 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1389528), _1389530), _1389532)), hAPP(c_Int_Onumber__class_Onumber__of(_1389528), _1389534))), 32140 ^ _782652 : [(32141 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), c_Groups_Ozero__class_Ozero(_1389528)), _1389532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), _1389530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389528), hAPP(c_Int_Onumber__class_Onumber__of(_1389528), _1389534)), _1389532))))], (32147 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), c_Groups_Ozero__class_Ozero(_1389528)), _1389532))), 32150 ^ _782652 : [(32151 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), _1389532), c_Groups_Ozero__class_Ozero(_1389528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389528), hAPP(c_Int_Onumber__class_Onumber__of(_1389528), _1389534)), _1389532)), _1389530)))], (32157 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), _1389532), c_Groups_Ozero__class_Ozero(_1389528)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389528), c_Groups_Ozero__class_Ozero(_1389528)), hAPP(c_Int_Onumber__class_Onumber__of(_1389528), _1389534))))]]]]]]], (32185 ^ _782652) ^ [_1390597, _1390599, _1390601, _1390603] : [class_Fields_Olinordered__field__inverse__zero(_1390597), class_Int_Onumber(_1390597), 32192 ^ _782652 : [(32219 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), hAPP(c_Int_Onumber__class_Onumber__of(_1390597), _1390599)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390597), _1390601), _1390603)))), 32222 ^ _782652 : [(32223 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), c_Groups_Ozero__class_Ozero(_1390597)), _1390603)))], (32225 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390597), hAPP(c_Int_Onumber__class_Onumber__of(_1390597), _1390599)), _1390603)), _1390601))]], 32226 ^ _782652 : [(32227 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), c_Groups_Ozero__class_Ozero(_1390597)), _1390603))], (32229 ^ _782652) ^ [] : [32230 ^ _782652 : [(32231 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), _1390603), c_Groups_Ozero__class_Ozero(_1390597))))], (32233 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), _1390601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390597), hAPP(c_Int_Onumber__class_Onumber__of(_1390597), _1390599)), _1390603)))]], 32234 ^ _782652 : [(32235 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), _1390603), c_Groups_Ozero__class_Ozero(_1390597)))], (32237 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), hAPP(c_Int_Onumber__class_Onumber__of(_1390597), _1390599)), c_Groups_Ozero__class_Ozero(_1390597)))]]]]], (32193 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), hAPP(c_Int_Onumber__class_Onumber__of(_1390597), _1390599)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390597), _1390601), _1390603))), 32196 ^ _782652 : [(32197 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), c_Groups_Ozero__class_Ozero(_1390597)), _1390603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390597), hAPP(c_Int_Onumber__class_Onumber__of(_1390597), _1390599)), _1390603)), _1390601)))], (32203 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), c_Groups_Ozero__class_Ozero(_1390597)), _1390603))), 32206 ^ _782652 : [(32207 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), _1390603), c_Groups_Ozero__class_Ozero(_1390597))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), _1390601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390597), hAPP(c_Int_Onumber__class_Onumber__of(_1390597), _1390599)), _1390603))))], (32213 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), _1390603), c_Groups_Ozero__class_Ozero(_1390597)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390597), hAPP(c_Int_Onumber__class_Onumber__of(_1390597), _1390599)), c_Groups_Ozero__class_Ozero(_1390597))))]]]]]]], (32241 ^ _782652) ^ [_1391666, _1391668, _1391670, _1391672] : [class_Fields_Olinordered__field__inverse__zero(_1391666), class_Int_Onumber(_1391666), 32248 ^ _782652 : [(32275 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), _1391668), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391666), _1391670), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672))))), 32278 ^ _782652 : [(32279 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), c_Groups_Ozero__class_Ozero(_1391666)), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672))))], (32281 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391666), _1391668), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672))), _1391670))]], 32282 ^ _782652 : [(32283 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), c_Groups_Ozero__class_Ozero(_1391666)), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672)))], (32285 ^ _782652) ^ [] : [32286 ^ _782652 : [(32287 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672)), c_Groups_Ozero__class_Ozero(_1391666))))], (32289 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), _1391670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391666), _1391668), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672))))]], 32290 ^ _782652 : [(32291 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672)), c_Groups_Ozero__class_Ozero(_1391666)))], (32293 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), _1391668), c_Groups_Ozero__class_Ozero(_1391666)))]]]]], (32249 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), _1391668), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391666), _1391670), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672)))), 32252 ^ _782652 : [(32253 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), c_Groups_Ozero__class_Ozero(_1391666)), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391666), _1391668), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672))), _1391670)))], (32259 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), c_Groups_Ozero__class_Ozero(_1391666)), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672)))), 32262 ^ _782652 : [(32263 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672)), c_Groups_Ozero__class_Ozero(_1391666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), _1391670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391666), _1391668), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672)))))], (32269 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), hAPP(c_Int_Onumber__class_Onumber__of(_1391666), _1391672)), c_Groups_Ozero__class_Ozero(_1391666)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391666), _1391668), c_Groups_Ozero__class_Ozero(_1391666))))]]]]]]], (32297 ^ _782652) ^ [_1392780, _1392782] : [class_Int_Onumber__ring(_1392780), class_Rings_Olinordered__idom(_1392780), 32304 ^ _782652 : [(32305 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392780), hAPP(c_Int_Onumber__class_Onumber__of(_1392780), _1392782)), c_Groups_Ozero__class_Ozero(_1392780))), -(hAPP(c_Groups_Oabs__class_Oabs(_1392780), hAPP(c_Int_Onumber__class_Onumber__of(_1392780), _1392782)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1392780), hAPP(c_Int_Onumber__class_Onumber__of(_1392780), _1392782)))], (32311 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392780), hAPP(c_Int_Onumber__class_Onumber__of(_1392780), _1392782)), c_Groups_Ozero__class_Ozero(_1392780)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1392780), hAPP(c_Int_Onumber__class_Onumber__of(_1392780), _1392782)) = hAPP(c_Int_Onumber__class_Onumber__of(_1392780), _1392782))]]], (32317 ^ _782652) ^ [_1393132, _1393134, _1393136, _1393138] : [class_Int_Onumber__ring(_1393132), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1393132), hAPP(c_Int_Onumber__class_Onumber__of(_1393132), _1393134)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1393132), _1393136), hAPP(c_Int_Onumber__class_Onumber__of(_1393132), _1393138))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1393132), hAPP(c_Int_Onumber__class_Onumber__of(_1393132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393134), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1393138)))), _1393136))], (32323 ^ _782652) ^ [_1393307, _1393309, _1393311, _1393313] : [class_Fields_Olinordered__field__inverse__zero(_1393307), class_Int_Onumber(_1393307), 32330 ^ _782652 : [(32357 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393307), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393307), _1393309), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311))), _1393313))), 32360 ^ _782652 : [(32361 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393307), c_Groups_Ozero__class_Ozero(_1393307)), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311))))], (32363 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393307), _1393309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393307), _1393313), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311))))]], 32364 ^ _782652 : [(32365 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393307), c_Groups_Ozero__class_Ozero(_1393307)), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311)))], (32367 ^ _782652) ^ [] : [32368 ^ _782652 : [(32369 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393307), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311)), c_Groups_Ozero__class_Ozero(_1393307))))], (32371 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393307), _1393313), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311))), _1393309))]], 32372 ^ _782652 : [(32373 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393307), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311)), c_Groups_Ozero__class_Ozero(_1393307)))], (32375 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393307), c_Groups_Ozero__class_Ozero(_1393307)), _1393313))]]]]], (32331 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393307), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393307), _1393309), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311))), _1393313)), 32334 ^ _782652 : [(32335 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393307), c_Groups_Ozero__class_Ozero(_1393307)), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393307), _1393309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393307), _1393313), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311)))))], (32341 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393307), c_Groups_Ozero__class_Ozero(_1393307)), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311)))), 32344 ^ _782652 : [(32345 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393307), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311)), c_Groups_Ozero__class_Ozero(_1393307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393307), _1393313), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311))), _1393309)))], (32351 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393307), hAPP(c_Int_Onumber__class_Onumber__of(_1393307), _1393311)), c_Groups_Ozero__class_Ozero(_1393307)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393307), c_Groups_Ozero__class_Ozero(_1393307)), _1393313)))]]]]]]], (32379 ^ _782652) ^ [_1394421, _1394423, _1394425, _1394427] : [class_Fields_Olinordered__field__inverse__zero(_1394421), class_Int_Onumber(_1394421), 32386 ^ _782652 : [(32413 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394421), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1394421), _1394423), _1394425)), hAPP(c_Int_Onumber__class_Onumber__of(_1394421), _1394427)))), 32416 ^ _782652 : [(32417 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394421), c_Groups_Ozero__class_Ozero(_1394421)), _1394425)))], (32419 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394421), _1394423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394421), hAPP(c_Int_Onumber__class_Onumber__of(_1394421), _1394427)), _1394425)))]], 32420 ^ _782652 : [(32421 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394421), c_Groups_Ozero__class_Ozero(_1394421)), _1394425))], (32423 ^ _782652) ^ [] : [32424 ^ _782652 : [(32425 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394421), _1394425), c_Groups_Ozero__class_Ozero(_1394421))))], (32427 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394421), hAPP(c_Int_Onumber__class_Onumber__of(_1394421), _1394427)), _1394425)), _1394423))]], 32428 ^ _782652 : [(32429 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394421), _1394425), c_Groups_Ozero__class_Ozero(_1394421)))], (32431 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394421), c_Groups_Ozero__class_Ozero(_1394421)), hAPP(c_Int_Onumber__class_Onumber__of(_1394421), _1394427)))]]]]], (32387 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394421), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1394421), _1394423), _1394425)), hAPP(c_Int_Onumber__class_Onumber__of(_1394421), _1394427))), 32390 ^ _782652 : [(32391 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394421), c_Groups_Ozero__class_Ozero(_1394421)), _1394425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394421), _1394423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394421), hAPP(c_Int_Onumber__class_Onumber__of(_1394421), _1394427)), _1394425))))], (32397 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394421), c_Groups_Ozero__class_Ozero(_1394421)), _1394425))), 32400 ^ _782652 : [(32401 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394421), _1394425), c_Groups_Ozero__class_Ozero(_1394421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394421), hAPP(c_Int_Onumber__class_Onumber__of(_1394421), _1394427)), _1394425)), _1394423)))], (32407 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394421), _1394425), c_Groups_Ozero__class_Ozero(_1394421)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394421), c_Groups_Ozero__class_Ozero(_1394421)), hAPP(c_Int_Onumber__class_Onumber__of(_1394421), _1394427))))]]]]]]], (32435 ^ _782652) ^ [_1395490, _1395492, _1395494, _1395496] : [class_Fields_Olinordered__field__inverse__zero(_1395490), class_Int_Onumber(_1395490), 32442 ^ _782652 : [(32469 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395490), hAPP(c_Int_Onumber__class_Onumber__of(_1395490), _1395492)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395490), _1395494), _1395496)))), 32472 ^ _782652 : [(32473 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395490), c_Groups_Ozero__class_Ozero(_1395490)), _1395496)))], (32475 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395490), hAPP(c_Int_Onumber__class_Onumber__of(_1395490), _1395492)), _1395496)), _1395494))]], 32476 ^ _782652 : [(32477 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395490), c_Groups_Ozero__class_Ozero(_1395490)), _1395496))], (32479 ^ _782652) ^ [] : [32480 ^ _782652 : [(32481 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395490), _1395496), c_Groups_Ozero__class_Ozero(_1395490))))], (32483 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395490), _1395494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395490), hAPP(c_Int_Onumber__class_Onumber__of(_1395490), _1395492)), _1395496)))]], 32484 ^ _782652 : [(32485 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395490), _1395496), c_Groups_Ozero__class_Ozero(_1395490)))], (32487 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395490), hAPP(c_Int_Onumber__class_Onumber__of(_1395490), _1395492)), c_Groups_Ozero__class_Ozero(_1395490)))]]]]], (32443 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395490), hAPP(c_Int_Onumber__class_Onumber__of(_1395490), _1395492)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395490), _1395494), _1395496))), 32446 ^ _782652 : [(32447 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395490), c_Groups_Ozero__class_Ozero(_1395490)), _1395496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395490), hAPP(c_Int_Onumber__class_Onumber__of(_1395490), _1395492)), _1395496)), _1395494)))], (32453 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395490), c_Groups_Ozero__class_Ozero(_1395490)), _1395496))), 32456 ^ _782652 : [(32457 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395490), _1395496), c_Groups_Ozero__class_Ozero(_1395490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395490), _1395494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395490), hAPP(c_Int_Onumber__class_Onumber__of(_1395490), _1395492)), _1395496))))], (32463 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395490), _1395496), c_Groups_Ozero__class_Ozero(_1395490)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395490), hAPP(c_Int_Onumber__class_Onumber__of(_1395490), _1395492)), c_Groups_Ozero__class_Ozero(_1395490))))]]]]]]], (32491 ^ _782652) ^ [_1396559, _1396561, _1396563, _1396565] : [class_Fields_Olinordered__field__inverse__zero(_1396559), class_Int_Onumber(_1396559), 32498 ^ _782652 : [(32525 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396559), _1396561), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1396559), _1396563), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565))))), 32528 ^ _782652 : [(32529 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396559), c_Groups_Ozero__class_Ozero(_1396559)), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565))))], (32531 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396559), _1396561), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565))), _1396563))]], 32532 ^ _782652 : [(32533 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396559), c_Groups_Ozero__class_Ozero(_1396559)), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565)))], (32535 ^ _782652) ^ [] : [32536 ^ _782652 : [(32537 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396559), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565)), c_Groups_Ozero__class_Ozero(_1396559))))], (32539 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396559), _1396563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396559), _1396561), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565))))]], 32540 ^ _782652 : [(32541 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396559), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565)), c_Groups_Ozero__class_Ozero(_1396559)))], (32543 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396559), _1396561), c_Groups_Ozero__class_Ozero(_1396559)))]]]]], (32499 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396559), _1396561), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1396559), _1396563), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565)))), 32502 ^ _782652 : [(32503 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396559), c_Groups_Ozero__class_Ozero(_1396559)), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396559), _1396561), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565))), _1396563)))], (32509 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396559), c_Groups_Ozero__class_Ozero(_1396559)), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565)))), 32512 ^ _782652 : [(32513 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396559), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565)), c_Groups_Ozero__class_Ozero(_1396559))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396559), _1396563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396559), _1396561), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565)))))], (32519 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396559), hAPP(c_Int_Onumber__class_Onumber__of(_1396559), _1396565)), c_Groups_Ozero__class_Ozero(_1396559)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396559), _1396561), c_Groups_Ozero__class_Ozero(_1396559))))]]]]]]], (32547 ^ _782652) ^ [_1397673, _1397675, _1397677, _1397679] : [c_Equiv__Relations_Oequiv(_1397673, _1397675, _1397677), hBOOL(hAPP(hAPP(c_member(_1397673), _1397679), _1397675)), -(hBOOL(hAPP(hAPP(c_member(_1397673), _1397679), hAPP(c_Relation_OImage(_1397673, _1397673, _1397677), hAPP(hAPP(c_Set_Oinsert(_1397673), _1397679), c_Orderings_Obot__class_Obot(tc_fun(_1397673, tc_HOL_Obool)))))))], (32557 ^ _782652) ^ [_1397880, _1397882, _1397884, _1397886, _1397888, _1397890, _1397892, _1397894, _1397896, _1397898] : [c_Equiv__Relations_Oequiv(_1397880, _1397882, _1397884), c_Equiv__Relations_Oequiv(_1397886, _1397888, _1397890), c_Equiv__Relations_Ocongruent2(_1397880, _1397886, tc_fun(_1397892, tc_HOL_Obool), _1397884, _1397890, _1397894), hBOOL(hAPP(hAPP(c_member(_1397880), _1397896), _1397882)), hBOOL(hAPP(hAPP(c_member(_1397886), _1397898), _1397888)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397880, tc_fun(_1397892, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1397880, _1397880, _1397884), hAPP(hAPP(c_Set_Oinsert(_1397880), _1397896), c_Orderings_Obot__class_Obot(tc_fun(_1397880, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1397886, tc_fun(_1397892, tc_HOL_Obool)), tc_fun(_1397892, tc_HOL_Obool), _1397880), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1397886, tc_fun(_1397892, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1397886, _1397886, _1397890), hAPP(hAPP(c_Set_Oinsert(_1397886), _1397898), c_Orderings_Obot__class_Obot(tc_fun(_1397886, tc_HOL_Obool)))))), _1397894)) = hAPP(hAPP(_1397894, _1397896), _1397898))], (32579 ^ _782652) ^ [_1398463, _1398465, _1398467, _1398469, _1398471, _1398473] : [c_Equiv__Relations_Oequiv(_1398463, _1398465, _1398467), c_Equiv__Relations_Ocongruent(_1398463, tc_fun(_1398469, tc_HOL_Obool), _1398467, _1398471), hBOOL(hAPP(hAPP(c_member(_1398463), _1398473), _1398465)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1398463, tc_fun(_1398469, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1398463, _1398463, _1398467), hAPP(hAPP(c_Set_Oinsert(_1398463), _1398473), c_Orderings_Obot__class_Obot(tc_fun(_1398463, tc_HOL_Obool))))), _1398471) = hAPP(_1398471, _1398473))], (32593 ^ _782652) ^ [_1398770] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398770))), -(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), _1398770)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (32599 ^ _782652) ^ [_1398863] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398863)))), -(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), _1398863)) = 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), _1398863))))], (32605 ^ _782652) ^ [_1398921] : [-(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), _1398921)) = 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), _1398921))))], (32607 ^ _782652) ^ [_1398974, _1398976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398974)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398976))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1398974), _1398976)))], (32613 ^ _782652) ^ [_1399079, _1399081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1399079), _1399081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399079)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399081))))], (32619 ^ _782652) ^ [_1399190, _1399192] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399190)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399192)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1399190), _1399192)))], (32621 ^ _782652) ^ [_1399236] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399236) = _1399236)], (32623 ^ _782652) ^ [_1399277, _1399279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399277)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399277), _1399279)))], (32629 ^ _782652) ^ [_1399382, _1399384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399382), _1399384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399382)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399384))))], (32635 ^ _782652) ^ [_1399493, _1399495] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399493)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399495)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1399493), _1399495)))], (32637 ^ _782652) ^ [_1399539] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399539)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1399539)))], (32639 ^ _782652) ^ [_1399574] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399574) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1399574))], (32641 ^ _782652) ^ [_1399603] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399603)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1399603))], (32643 ^ _782652) ^ [_1399635] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1399635) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399635)))], (32645 ^ _782652) ^ [_1399667, _1399669, _1399671, _1399673, _1399675, _1399677, _1399679, _1399681] : [c_Equiv__Relations_Oequiv(_1399667, _1399669, _1399671), c_Equiv__Relations_Ocongruent2(_1399667, _1399673, _1399675, _1399671, _1399677, _1399679), hBOOL(hAPP(hAPP(c_member(_1399667), _1399681), _1399669)), -(c_Equiv__Relations_Ocongruent(_1399673, _1399675, _1399677, hAPP(_1399679, _1399681)))], (32659 ^ _782652) ^ [_1399918, _1399920] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399918)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399920)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1399918), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1399920))))], (32661 ^ _782652) ^ [_1399967] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399967))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1399967) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32667 ^ _782652) ^ [_1400073, _1400075] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400073) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400075), 32670 ^ _782652 : [(32671 ^ _782652) ^ [] : [-(_1400073 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400075)))], (32673 ^ _782652) ^ [] : [-(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), _1400075))))]]], (32675 ^ _782652) ^ [_1400206, _1400208] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400206) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400208)), _1400206 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400208)), 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), _1400208)))], (32711 ^ _782652) ^ [_1400771, _1400773] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400771) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400773)), 32714 ^ _782652 : [(32715 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400771))))], (32717 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400773)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 32718 ^ _782652 : [(32719 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400771)))], (32721 ^ _782652) ^ [] : [32722 ^ _782652 : [(32723 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400773))))], (32725 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400771) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 32726 ^ _782652 : [(32727 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400773)))], (32729 ^ _782652) ^ [] : [_1400771 = _1400773]]]]], (32685 ^ _782652) ^ [_1400386, _1400388] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400386) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400388), 32688 ^ _782652 : [(32689 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400388)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32695 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400386)))), 32698 ^ _782652 : [(32699 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400388))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400386) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32705 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400388)))), -(_1400386 = _1400388)]]]]], (32733 ^ _782652) ^ [_1401184, _1401186, _1401188] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401184))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401184)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401186)), _1401188)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401186)), _1401188))], (32739 ^ _782652) ^ [_1401322, _1401324, _1401326] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401322)))), 32742 ^ _782652 : [(32743 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401324))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401322)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401324)), _1401326)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401322)), _1401326))], (32749 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401324)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401322)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401324)), _1401326)) = 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), _1401322), _1401324))), _1401326))]]], (32755 ^ _782652) ^ [_1401653] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401653))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401653)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32761 ^ _782652) ^ [_1401744] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401744)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401744)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401744))], (32767 ^ _782652) ^ [_1401803, _1401805] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401803))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401803), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401805)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32773 ^ _782652) ^ [_1401905, _1401907] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401905)))), 32776 ^ _782652 : [(32777 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401907))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401905), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401907)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401905))], (32783 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401907)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401905), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401907)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401905), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401907))))]]], (32789 ^ _782652) ^ [_1402178, _1402180, _1402182, _1402184, _1402186, _1402188, _1402190, _1402192, _1402194] : [c_Equiv__Relations_Oequiv(_1402178, _1402180, _1402182), c_Equiv__Relations_Oequiv(_1402184, _1402186, _1402188), c_Equiv__Relations_Ocongruent2(_1402178, _1402184, tc_fun(_1402190, tc_HOL_Obool), _1402182, _1402188, _1402192), hBOOL(hAPP(hAPP(c_member(_1402184), _1402194), _1402186)), -(c_Equiv__Relations_Ocongruent(_1402178, tc_fun(_1402190, tc_HOL_Obool), _1402182, hAPP(hAPP(c_COMBB(tc_fun(_1402184, tc_fun(_1402190, tc_HOL_Obool)), tc_fun(_1402190, tc_HOL_Obool), _1402178), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402184, tc_fun(_1402190, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1402184, _1402184, _1402188), hAPP(hAPP(c_Set_Oinsert(_1402184), _1402194), c_Orderings_Obot__class_Obot(tc_fun(_1402184, tc_HOL_Obool)))))), _1402192)))], (32807 ^ _782652) ^ [_1402614, _1402616] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402614))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402614)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402616)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32813 ^ _782652) ^ [_1402719, _1402721] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402719)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402719)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402721)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402719)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402721))))], (32819 ^ _782652) ^ [_1402798, _1402800] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402798))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402798)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402800)) = 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), _1402800)))], (32825 ^ _782652) ^ [_1402915, _1402917] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402915)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402915)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402917)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402915)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402917))))], (32831 ^ _782652) ^ [_1402994, _1402996] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402994))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402994)), _1402996) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1402996))], (32837 ^ _782652) ^ [_1403099, _1403101] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403099)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403099)), _1403101) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403099)), _1403101)))], (32843 ^ _782652) ^ [_1403172, _1403174] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403172))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403172)), _1403174)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1403174))], (32849 ^ _782652) ^ [_1403283, _1403285] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403283)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403283)), _1403285)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1403283))), _1403285))], (32855 ^ _782652) ^ [_1403358, _1403360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1403358), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403360)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403358)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403360))], (32861 ^ _782652) ^ [_1403469, _1403471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1403469), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403471)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403469)) = 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), _1403471), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1403469)))), 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)))], (32867 ^ _782652) ^ [_1403542, _1403544] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403542)), hAPP(c_Nat_OSuc, _1403544)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1403542))), 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)), _1403544)))))], (32869 ^ _782652) ^ [_1403599, _1403601] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1403599)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403601)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1403601))), 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), _1403599)), c_Int_Onat)))))], (32871 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (32873 ^ _782652) ^ [_1403680] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1403680), c_Int_OPls) = _1403680)], (32875 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (32877 ^ _782652) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32879 ^ _782652) ^ [_1403751] : [-(c_Int_Osucc(c_Int_Opred(_1403751)) = _1403751)], (32881 ^ _782652) ^ [_1403778] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1403778) = c_Int_OPls)], (32883 ^ _782652) ^ [_1403804] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1403804) = _1403804)], (32885 ^ _782652) ^ [_1403830] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1403830), c_Int_OPls) = _1403830)], (32887 ^ _782652) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (32889 ^ _782652) ^ [_1403877] : [class_Int_Onumber__ring(_1403877), -(c_Groups_Ozero__class_Ozero(_1403877) = hAPP(c_Int_Onumber__class_Onumber__of(_1403877), c_Int_OPls))], (32895 ^ _782652) ^ [_1403964] : [class_Int_Onumber__ring(_1403964), -(hAPP(c_Int_Onumber__class_Onumber__of(_1403964), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1403964))], (32901 ^ _782652) ^ [_1404051, _1404053] : [class_Int_Onumber__ring(_1404051), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1404051), _1404053), hAPP(c_Int_Onumber__class_Onumber__of(_1404051), c_Int_OPls)) = _1404053)], (32907 ^ _782652) ^ [_1404152, _1404154] : [class_Int_Onumber__ring(_1404152), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1404152), hAPP(c_Int_Onumber__class_Onumber__of(_1404152), c_Int_OPls)), _1404154) = _1404154)], (32913 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (32915 ^ _782652) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (32917 ^ _782652) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32919 ^ _782652) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (32921 ^ _782652) ^ [_1404331, _1404333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1404331)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1404333)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404331)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1404333), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1404331))))], (32927 ^ _782652) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (32929 ^ _782652) ^ [_1404488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404488), 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), _1404488)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (32935 ^ _782652) ^ [_1404579] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404579), 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), _1404579)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1404579)))], (32941 ^ _782652) ^ [_1404637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404637), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404637)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (32947 ^ _782652) ^ [_1404734] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404734), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404734)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1404734)))], (32953 ^ _782652) ^ [_1404804, _1404806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404804), _1404806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1404804)), _1404806)))], (32959 ^ _782652) ^ [_1404901, _1404903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1404901)), _1404903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404901), _1404903)))], (32965 ^ _782652) ^ [_1405004] : [-(c_Int_Opred(_1405004) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1405004), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32967 ^ _782652) ^ [_1405041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405041), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405041)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32973 ^ _782652) ^ [_1405138] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405138), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405138)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1405138)))], (32979 ^ _782652) ^ [_1405193, _1405195] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1405193), _1405195), hAPP(c_Int_Onumber__class_Onumber__of(_1405193), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1405193)), class_Fields_Ofield__inverse__zero(_1405193), class_Int_Onumber__ring(_1405193)], (32989 ^ _782652) ^ [_1405360] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405360), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405360), c_Int_OPls)))], (32995 ^ _782652) ^ [_1405447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405447), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405447))], (33001 ^ _782652) ^ [_1405552] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405552) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405552), c_Int_OPls)))], (33007 ^ _782652) ^ [_1405639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405639), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405639) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33013 ^ _782652) ^ [] : [-(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))))], (33015 ^ _782652) ^ [_1405765, _1405767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405765)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405767))), 33018 ^ _782652 : [(33025 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405765), _1405767)))], (33019 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405765), _1405767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1405767)))]]], (33027 ^ _782652) ^ [_1405968, _1405970] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405968)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405970)))), 33030 ^ _782652 : [(33031 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405968), _1405970)))], (33033 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1405970))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405968), _1405970))], (33049 ^ _782652) ^ [_1406323, _1406325] : [33050 ^ _782652 : [(33051 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406323), _1406325))], (33053 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406323), 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), _1406323)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406325))))], (33039 ^ _782652) ^ [_1406193, _1406195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406193)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406193), _1406195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406193), c_Int_OPls)))], (33057 ^ _782652) ^ [_1406484] : [-(c_Int_Osucc(_1406484) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1406484), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33059 ^ _782652) ^ [_1406515, _1406517] : [class_Int_Onumber__ring(_1406515), class_Rings_Olinordered__idom(_1406515), 33066 ^ _782652 : [(33067 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406515), c_Groups_Ozero__class_Ozero(_1406515)), hAPP(c_Int_Onumber__class_Onumber__of(_1406515), _1406517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1406517)))], (33073 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1406517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406515), c_Groups_Ozero__class_Ozero(_1406515)), hAPP(c_Int_Onumber__class_Onumber__of(_1406515), _1406517))))]]], (33079 ^ _782652) ^ [_1406820, _1406822] : [class_Int_Onumber__ring(_1406820), class_Rings_Olinordered__idom(_1406820), 33086 ^ _782652 : [(33087 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406820), hAPP(c_Int_Onumber__class_Onumber__of(_1406820), _1406822)), c_Groups_Ozero__class_Ozero(_1406820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406822), c_Int_OPls)))], (33093 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406822), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406820), hAPP(c_Int_Onumber__class_Onumber__of(_1406820), _1406822)), c_Groups_Ozero__class_Ozero(_1406820))))]]], (33099 ^ _782652) ^ [_1407134, _1407136] : [class_Int_Onumber__ring(_1407134), class_Rings_Olinordered__idom(_1407134), 33106 ^ _782652 : [(33107 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407134), c_Groups_Ozero__class_Ozero(_1407134)), hAPP(c_Int_Onumber__class_Onumber__of(_1407134), _1407136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1407136)))], (33113 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1407136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407134), c_Groups_Ozero__class_Ozero(_1407134)), hAPP(c_Int_Onumber__class_Onumber__of(_1407134), _1407136))))]]], (33119 ^ _782652) ^ [_1407439, _1407441] : [class_Int_Onumber__ring(_1407439), class_Rings_Olinordered__idom(_1407439), 33126 ^ _782652 : [(33127 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407439), hAPP(c_Int_Onumber__class_Onumber__of(_1407439), _1407441)), c_Groups_Ozero__class_Ozero(_1407439))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407441), c_Int_OPls)))], (33133 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407441), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407439), hAPP(c_Int_Onumber__class_Onumber__of(_1407439), _1407441)), c_Groups_Ozero__class_Ozero(_1407439))))]]], (33139 ^ _782652) ^ [_1407765] : [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), _1407765))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1407765)))], (33145 ^ _782652) ^ [_1407850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1407850)), -(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), _1407850))))], (33151 ^ _782652) ^ [_1407950, _1407952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407950), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407950)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407952)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407952))], (33157 ^ _782652) ^ [_1408062, _1408064] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408062), c_Int_OPls))), 33160 ^ _782652 : [(33161 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408064), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408062)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408064)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408062))], (33167 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408064), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408062)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408064)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1408062), _1408064)))]]], (33173 ^ _782652) ^ [_1408335, _1408337] : [class_Int_Onumber__ring(_1408335), -(hAPP(c_Int_Onumber__class_Onumber__of(_1408335), c_Int_Osucc(_1408337)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408335), c_Groups_Oone__class_Oone(_1408335)), hAPP(c_Int_Onumber__class_Onumber__of(_1408335), _1408337)))], (33179 ^ _782652) ^ [_1408454, _1408456] : [class_Int_Onumber__ring(_1408454), -(hAPP(c_Int_Onumber__class_Onumber__of(_1408454), c_Int_Opred(_1408456)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408454), hAPP(c_Groups_Ouminus__class_Ouminus(_1408454), c_Groups_Oone__class_Oone(_1408454))), hAPP(c_Int_Onumber__class_Onumber__of(_1408454), _1408456)))], (33185 ^ _782652) ^ [_1408595, _1408597, _1408599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408595), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408595)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408597)), _1408599)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33191 ^ _782652) ^ [_1408714, _1408716, _1408718] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408714), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408714)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408716)), _1408718)) = 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), _1408714), _1408716))), _1408718))], (33197 ^ _782652) ^ [_1408801, _1408803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408801), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408801)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408803)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33203 ^ _782652) ^ [_1408906, _1408908] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408906), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408906)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408908)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1408906), _1408908)))], (33209 ^ _782652) ^ [_1408982] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1408982)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408982) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33215 ^ _782652) ^ [_1409073] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409073) = 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(_1409073)))))], (33221 ^ _782652) ^ [_1409185, _1409187] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409185) = hAPP(c_Nat_OSuc, _1409187), -(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(_1409185))), 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)), _1409187))))))], (33227 ^ _782652) ^ [_1409308, _1409310] : [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(_1409308))), 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)), _1409310))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409308) = hAPP(c_Nat_OSuc, _1409310))], (33233 ^ _782652) ^ [_1409452, _1409454] : [hAPP(c_Nat_OSuc, _1409452) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409454), -(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(_1409454))), 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)), _1409452))))))], (33239 ^ _782652) ^ [_1409575, _1409577] : [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(_1409577))), 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)), _1409575))))), -(hAPP(c_Nat_OSuc, _1409575) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409577))], (33245 ^ _782652) ^ [_1409704, _1409706, _1409708, _1409710] : [-(c_Nat_Onat_Onat__case(_1409704, _1409706, _1409708, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409710)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1409704), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1409710))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1409704, _1409704), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1409704, tc_fun(_1409704, _1409704)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1409704, tc_fun(_1409704, _1409704)), tc_Int_Oint), c_If(_1409704)), c_Nat__Numeral_Oneg)), _1409706)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1409704, tc_Int_Oint), _1409708), c_Int_Onat))))], (33247 ^ _782652) ^ [_1409821, _1409823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1409821)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409823))), -(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(_1409823))), 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), _1409821)), c_Int_Onat))))))], (33253 ^ _782652) ^ [_1409966, _1409968] : [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(_1409968))), 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), _1409966)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1409966)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409968))))], (33259 ^ _782652) ^ [_1410132, _1410134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410132)), hAPP(c_Nat_OSuc, _1410134))), -(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(_1410132))), 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)), _1410134)))))], (33265 ^ _782652) ^ [_1410259, _1410261] : [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(_1410259))), 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)), _1410261)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410259)), hAPP(c_Nat_OSuc, _1410261))))], (33271 ^ _782652) ^ [_1410407, _1410409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410407)), hAPP(c_Nat_OSuc, _1410409))), -(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(_1410407))), 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)), _1410409)))))], (33277 ^ _782652) ^ [_1410534, _1410536] : [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(_1410534))), 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)), _1410536)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410534)), hAPP(c_Nat_OSuc, _1410536))))], (33283 ^ _782652) ^ [_1410682, _1410684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410682)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410684))), -(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(_1410684))), 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), _1410682)), c_Int_Onat))))))], (33289 ^ _782652) ^ [_1410827, _1410829] : [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(_1410829))), 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), _1410827)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410827)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410829))))], (33295 ^ _782652) ^ [_1410984] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1410984))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410984)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33301 ^ _782652) ^ [_1411075] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1411075)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411075)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1411075)))], (33307 ^ _782652) ^ [_1411127, _1411129] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411127)), hAPP(c_Nat_OSuc, _1411129)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1411127))), 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, _1411129))), 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)), _1411129)))))], (33309 ^ _782652) ^ [_1411193, _1411195] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1411193)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411195)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1411195))), 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, _1411193))), 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), _1411193)), c_Int_Onat)))))], (33311 ^ _782652) ^ [_1411265, _1411267, _1411269, _1411271, _1411273] : [-(c_Nat_Onat_Onat__case(_1411265, _1411267, _1411269, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411271)), _1411273)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1411265), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1411271))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1411265, _1411265), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1411265, tc_fun(_1411265, _1411265)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1411265, tc_fun(_1411265, _1411265)), tc_Int_Oint), c_If(_1411265)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1411265, _1411267, _1411269, _1411273))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1411265, tc_Int_Oint), _1411269), 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)), _1411273)))))], (33313 ^ _782652) ^ [_1411383, _1411385, _1411387, _1411389, _1411391] : [-(hAPP(c_Nat_Onat_Onat__rec(_1411383, _1411385, _1411387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411389)), _1411391)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1411383), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1411389))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1411383, _1411383), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1411383, tc_fun(_1411383, _1411383)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1411383, tc_fun(_1411383, _1411383)), tc_Int_Oint), c_If(_1411383)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1411383, _1411385, _1411387), _1411391))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1411383, _1411383), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1411383, _1411383), tc_Int_Oint), _1411387), 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)), _1411391))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1411383, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1411383, _1411385, _1411387)), 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)), _1411391))))))], (33315 ^ _782652) ^ [_1411535, _1411537, _1411539, _1411541] : [-(hAPP(c_Nat_Onat_Onat__rec(_1411535, _1411537, _1411539), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411541)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1411535), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1411541))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1411535, _1411535), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1411535, tc_fun(_1411535, _1411535)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1411535, tc_fun(_1411535, _1411535)), tc_Int_Oint), c_If(_1411535)), c_Nat__Numeral_Oneg)), _1411537)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1411535, _1411535), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1411535, _1411535), tc_Int_Oint), _1411539), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1411535, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1411535, _1411537, _1411539)), c_Int_Onat)))))], (33317 ^ _782652) ^ [_1411666, _1411668, _1411670, _1411672, _1411674, _1411676, _1411678, _1411680, _1411682, _1411684, _1411686] : [c_Equiv__Relations_Oequiv(_1411666, _1411668, _1411670), c_Equiv__Relations_Oequiv(_1411672, _1411674, _1411676), c_Equiv__Relations_Ocongruent2(_1411666, _1411672, tc_fun(_1411678, tc_HOL_Obool), _1411670, _1411676, _1411680), hBOOL(hAPP(hAPP(c_member(tc_fun(_1411666, tc_HOL_Obool)), _1411682), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1411666), _1411668), _1411670))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1411672, tc_HOL_Obool)), _1411684), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1411672), _1411674), _1411676))), 33339 ^ _782652 : [(33340 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411666), 33338 ^ [_1411666, _1411668, _1411670, _1411672, _1411674, _1411676, _1411678, _1411680, _1411682, _1411684, _1411686]), _1411668)))], (33343 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411672), 33341 ^ [_1411666, _1411668, _1411670, _1411672, _1411674, _1411676, _1411678, _1411680, _1411682, _1411684, _1411686]), _1411674)))], (33345 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1411678, tc_HOL_Obool)), hAPP(hAPP(_1411680, 33338 ^ [_1411666, _1411668, _1411670, _1411672, _1411674, _1411676, _1411678, _1411680, _1411682, _1411684, _1411686]), 33341 ^ [_1411666, _1411668, _1411670, _1411672, _1411674, _1411676, _1411678, _1411680, _1411682, _1411684, _1411686])), _1411686))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1411678, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411666, tc_fun(_1411678, tc_HOL_Obool)), _1411682), hAPP(hAPP(c_COMBB(tc_fun(_1411672, tc_fun(_1411678, tc_HOL_Obool)), tc_fun(_1411678, tc_HOL_Obool), _1411666), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411672, tc_fun(_1411678, tc_HOL_Obool)), _1411684)), _1411680))), _1411686)))], (33349 ^ _782652) ^ [_1412668, _1412670, _1412672, _1412674, _1412676, _1412678, _1412680] : [c_Equiv__Relations_Oequiv(_1412668, _1412670, _1412672), c_Equiv__Relations_Ocongruent(_1412668, tc_fun(_1412674, tc_HOL_Obool), _1412672, _1412676), hBOOL(hAPP(hAPP(c_member(tc_fun(_1412668, tc_HOL_Obool)), _1412678), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1412668), _1412670), _1412672))), 33363 ^ _782652 : [(33364 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412668), 33362 ^ [_1412668, _1412670, _1412672, _1412674, _1412676, _1412678, _1412680]), _1412670)))], (33366 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1412674, tc_HOL_Obool)), hAPP(_1412676, 33362 ^ [_1412668, _1412670, _1412672, _1412674, _1412676, _1412678, _1412680])), _1412680))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1412674, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412668, tc_fun(_1412674, tc_HOL_Obool)), _1412678), _1412676)), _1412680)))], (33370 ^ _782652) ^ [_1413179, _1413181, _1413183] : [-(hAPP(c_Nat_Onat_Onat__rec(_1413179, _1413181, _1413183), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1413181)], (33372 ^ _782652) ^ [_1413213, _1413215, _1413217, _1413219] : [-(hAPP(c_Nat_Onat_Onat__rec(_1413213, _1413215, _1413217), hAPP(c_Nat_OSuc, _1413219)) = hAPP(hAPP(_1413217, _1413219), hAPP(c_Nat_Onat_Onat__rec(_1413213, _1413215, _1413217), _1413219)))], (33374 ^ _782652) ^ [_1413265, _1413267] : [class_Int_Onumber__ring(_1413265), 33377 ^ _782652 : [(33378 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413265), _1413267) = c_Groups_Ozero__class_Ozero(_1413265), -(c_Int_Oiszero(_1413265, hAPP(c_Int_Onumber__class_Onumber__of(_1413265), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413267), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (33384 ^ _782652) ^ [] : [c_Int_Oiszero(_1413265, hAPP(c_Int_Onumber__class_Onumber__of(_1413265), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413267), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413265), _1413267) = c_Groups_Ozero__class_Ozero(_1413265))]]], (33390 ^ _782652) ^ [_1413524, _1413526] : [class_Int_Onumber__ring(_1413524), 33393 ^ _782652 : [(33394 ^ _782652) ^ [] : [c_Groups_Ozero__class_Ozero(_1413524) = hAPP(c_Int_Onumber__class_Onumber__of(_1413524), _1413526), -(c_Int_Oiszero(_1413524, hAPP(c_Int_Onumber__class_Onumber__of(_1413524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1413526)))))], (33400 ^ _782652) ^ [] : [c_Int_Oiszero(_1413524, hAPP(c_Int_Onumber__class_Onumber__of(_1413524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1413526)))), -(c_Groups_Ozero__class_Ozero(_1413524) = hAPP(c_Int_Onumber__class_Onumber__of(_1413524), _1413526))]]], (33406 ^ _782652) ^ [_1413783, _1413785, _1413787] : [class_Int_Onumber__ring(_1413783), 33409 ^ _782652 : [(33410 ^ _782652) ^ [] : [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), _1413785))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1413783), hAPP(c_Int_Onumber__class_Onumber__of(_1413783), _1413787)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1413785))) = hAPP(hAPP(c_HOL_OLet(_1413783, _1413783), hAPP(hAPP(c_Power_Opower__class_Opower(_1413783), hAPP(c_Int_Onumber__class_Onumber__of(_1413783), _1413787)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413785))), hAPP(hAPP(c_COMBS(_1413783, _1413783, _1413783), hAPP(hAPP(c_COMBB(_1413783, tc_fun(_1413783, _1413783), _1413783), c_Groups_Otimes__class_Otimes(_1413783)), hAPP(c_Groups_Otimes__class_Otimes(_1413783), hAPP(c_Int_Onumber__class_Onumber__of(_1413783), _1413787)))), c_COMBI(_1413783))))], (33416 ^ _782652) ^ [] : [-(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), _1413785)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1413783), hAPP(c_Int_Onumber__class_Onumber__of(_1413783), _1413787)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1413785))) = c_Groups_Oone__class_Oone(_1413783))]]], (33422 ^ _782652) ^ [_1414190, _1414192] : [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), _1414190))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414192), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1414190))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414192), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414190))), 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), _1414192))), c_COMBI(tc_Int_Oint))))], (33428 ^ _782652) ^ [_1414347, _1414349] : [-(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), _1414347)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1414349), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1414347))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (33434 ^ _782652) ^ [_1414401, _1414403] : [c_Int_Oiszero(_1414401, hAPP(c_Int_Onumber__class_Onumber__of(_1414401), c_Int_OBit1(_1414403))), class_Int_Onumber__ring(_1414401), class_Int_Oring__char__0(_1414401)], (33444 ^ _782652) ^ [_1414556, _1414558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1414556)), c_Int_OBit1(_1414558))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1414556), _1414558)))], (33450 ^ _782652) ^ [_1414657, _1414659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1414657), _1414659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1414657)), c_Int_OBit1(_1414659))))], (33456 ^ _782652) ^ [_1414779, _1414781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1414779)), c_Int_OBit1(_1414781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1414779), _1414781)))], (33462 ^ _782652) ^ [_1414880, _1414882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1414880), _1414882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1414880)), c_Int_OBit1(_1414882))))], (33468 ^ _782652) ^ [_1415002, _1415004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1415002)), c_Int_OBit1(_1415004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1415002), _1415004)))], (33474 ^ _782652) ^ [_1415103, _1415105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1415103), _1415105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1415103)), c_Int_OBit1(_1415105))))], (33480 ^ _782652) ^ [_1415225, _1415227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1415225)), c_Int_OBit1(_1415227))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1415225), _1415227)))], (33486 ^ _782652) ^ [_1415326, _1415328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1415326), _1415328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1415326)), c_Int_OBit1(_1415328))))], (33492 ^ _782652) ^ [_1415448, _1415450] : [c_Int_OBit1(_1415448) = c_Int_OBit1(_1415450), -(_1415448 = _1415450)], (33498 ^ _782652) ^ [_1415529, _1415531] : [_1415529 = _1415531, -(c_Int_OBit1(_1415529) = c_Int_OBit1(_1415531))], (33504 ^ _782652) ^ [_1415625] : [c_Int_OPls = c_Int_OBit1(_1415625)], (33506 ^ _782652) ^ [_1415659] : [c_Int_OBit1(_1415659) = c_Int_OPls], (33508 ^ _782652) ^ [_1415684] : [class_Int_Onumber__ring(_1415684), c_Int_Oiszero(_1415684, hAPP(c_Int_Onumber__class_Onumber__of(_1415684), c_Int_OBit1(c_Int_OPls)))], (33514 ^ _782652) ^ [_1415768] : [class_Rings_Osemiring__1(_1415768), -(c_Int_Oiszero(_1415768, c_Groups_Ozero__class_Ozero(_1415768)))], (33520 ^ _782652) ^ [_1415845, _1415847] : [class_Rings_Osemiring__1(_1415845), 33523 ^ _782652 : [(33524 ^ _782652) ^ [] : [c_Int_Oiszero(_1415845, _1415847), -(_1415847 = c_Groups_Ozero__class_Ozero(_1415845))], (33530 ^ _782652) ^ [] : [_1415847 = c_Groups_Ozero__class_Ozero(_1415845), -(c_Int_Oiszero(_1415845, _1415847))]]], (33536 ^ _782652) ^ [_1416056] : [class_Rings_Osemiring__1(_1416056), c_Int_Oiszero(_1416056, c_Groups_Oone__class_Oone(_1416056))], (33542 ^ _782652) ^ [_1416146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1416146)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416146), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33548 ^ _782652) ^ [_1416241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416241), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1416241)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33554 ^ _782652) ^ [_1416354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1416354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1416354)))], (33560 ^ _782652) ^ [_1416437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1416437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1416437))))], (33566 ^ _782652) ^ [_1416538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1416538)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416538), c_Int_OPls)))], (33572 ^ _782652) ^ [_1416633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1416633), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1416633)), c_Int_OPls)))], (33578 ^ _782652) ^ [_1416734] : [-(c_Int_OBit1(_1416734) = 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)), _1416734)), _1416734))], (33580 ^ _782652) ^ [_1416780] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1416780)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416780))))], (33586 ^ _782652) ^ [_1416875] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416875))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1416875)))))], (33592 ^ _782652) ^ [_1416976] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1416976)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1416976))))], (33594 ^ _782652) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (33596 ^ _782652) ^ [_1417029, _1417031] : [class_Int_Onumber__ring(_1417029), -(hAPP(c_Int_Onumber__class_Onumber__of(_1417029), c_Int_OBit1(_1417031)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1417029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1417029), c_Groups_Oone__class_Oone(_1417029)), hAPP(c_Int_Onumber__class_Onumber__of(_1417029), _1417031))), hAPP(c_Int_Onumber__class_Onumber__of(_1417029), _1417031)))], (33602 ^ _782652) ^ [_1417174, _1417176] : [class_Int_Onumber__ring(_1417174), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417174), _1417176), hAPP(c_Int_Onumber__class_Onumber__of(_1417174), c_Int_OBit1(c_Int_OPls))) = _1417176)], (33608 ^ _782652) ^ [_1417275, _1417277] : [class_Int_Onumber__ring(_1417275), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417275), hAPP(c_Int_Onumber__class_Onumber__of(_1417275), c_Int_OBit1(c_Int_OPls))), _1417277) = _1417277)], (33614 ^ _782652) ^ [_1417376] : [class_Int_Onumber__ring(_1417376), -(hAPP(c_Int_Onumber__class_Onumber__of(_1417376), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1417376))], (33620 ^ _782652) ^ [_1417463] : [class_Int_Onumber__ring(_1417463), -(c_Groups_Oone__class_Oone(_1417463) = hAPP(c_Int_Onumber__class_Onumber__of(_1417463), c_Int_OBit1(c_Int_OPls)))], (33626 ^ _782652) ^ [_1417562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1417562)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417562), c_Int_OPls)))], (33632 ^ _782652) ^ [_1417657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1417657), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1417657)), c_Int_OPls)))], (33638 ^ _782652) ^ [_1417770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1417770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1417770)))], (33644 ^ _782652) ^ [_1417853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1417853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1417853))))], (33650 ^ _782652) ^ [_1417942, _1417944] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1417942), _1417944), hAPP(c_Int_Onumber__class_Onumber__of(_1417942), c_Int_OBit1(c_Int_OPls))) = _1417944), class_Fields_Ofield(_1417942), class_Int_Onumber__ring(_1417942)], (33660 ^ _782652) ^ [_1418093, _1418095] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418093), _1418095), hAPP(c_Int_Onumber__class_Onumber__of(_1418093), c_Int_OBit1(c_Int_OPls))) = _1418095), class_Fields_Ofield(_1418093), class_Int_Onumber__ring(_1418093)], (33670 ^ _782652) ^ [_1418244, _1418246] : [class_Int_Onumber__ring(_1418244), 33673 ^ _782652 : [(33674 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1418244), _1418246) = c_Groups_Oone__class_Oone(_1418244), -(c_Int_Oiszero(_1418244, hAPP(c_Int_Onumber__class_Onumber__of(_1418244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418246), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (33680 ^ _782652) ^ [] : [c_Int_Oiszero(_1418244, hAPP(c_Int_Onumber__class_Onumber__of(_1418244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418246), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1418244), _1418246) = c_Groups_Oone__class_Oone(_1418244))]]], (33686 ^ _782652) ^ [_1418503, _1418505] : [class_Int_Onumber__ring(_1418503), 33689 ^ _782652 : [(33690 ^ _782652) ^ [] : [c_Groups_Oone__class_Oone(_1418503) = hAPP(c_Int_Onumber__class_Onumber__of(_1418503), _1418505), -(c_Int_Oiszero(_1418503, hAPP(c_Int_Onumber__class_Onumber__of(_1418503), 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), _1418505)))))], (33696 ^ _782652) ^ [] : [c_Int_Oiszero(_1418503, hAPP(c_Int_Onumber__class_Onumber__of(_1418503), 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), _1418505)))), -(c_Groups_Oone__class_Oone(_1418503) = hAPP(c_Int_Onumber__class_Onumber__of(_1418503), _1418505))]]], (33702 ^ _782652) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (33704 ^ _782652) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33706 ^ _782652) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (33708 ^ _782652) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (33710 ^ _782652) ^ [_1418834] : [class_Int_Onumber__ring(_1418834), -(c_Int_Oiszero(_1418834, hAPP(c_Int_Onumber__class_Onumber__of(_1418834), c_Int_OPls)))], (33716 ^ _782652) ^ [] : [-(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)))))], (33718 ^ _782652) ^ [] : [-(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)))], (33720 ^ _782652) ^ [_1418953, _1418955] : [class_Groups_Omonoid__mult(_1418953), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1418953), _1418955), 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(_1418953), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418953), _1418955), _1418955)), _1418955))], (33726 ^ _782652) ^ [] : [-(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))))))], (33728 ^ _782652) ^ [_1419094] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1419094))) = 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)))), _1419094))], (33730 ^ _782652) ^ [] : [-(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)))))], (33732 ^ _782652) ^ [] : [-(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)))))], (33734 ^ _782652) ^ [_1419165, _1419167] : [class_Int_Onumber__ring(_1419165), class_Rings_Olinordered__idom(_1419165), 33741 ^ _782652 : [(33742 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419165), c_Groups_Oone__class_Oone(_1419165)), hAPP(c_Int_Onumber__class_Onumber__of(_1419165), _1419167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1419167)))], (33748 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1419167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419165), c_Groups_Oone__class_Oone(_1419165)), hAPP(c_Int_Onumber__class_Onumber__of(_1419165), _1419167))))]]], (33754 ^ _782652) ^ [_1419470, _1419472] : [class_Int_Onumber__ring(_1419470), class_Rings_Olinordered__idom(_1419470), 33761 ^ _782652 : [(33762 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419470), hAPP(c_Int_Onumber__class_Onumber__of(_1419470), _1419472)), c_Groups_Oone__class_Oone(_1419470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419472), c_Int_OBit1(c_Int_OPls))))], (33768 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419472), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419470), hAPP(c_Int_Onumber__class_Onumber__of(_1419470), _1419472)), c_Groups_Oone__class_Oone(_1419470))))]]], (33774 ^ _782652) ^ [_1419784, _1419786] : [class_Int_Onumber__ring(_1419784), class_Rings_Olinordered__idom(_1419784), 33781 ^ _782652 : [(33782 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419784), c_Groups_Oone__class_Oone(_1419784)), hAPP(c_Int_Onumber__class_Onumber__of(_1419784), _1419786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1419786)))], (33788 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1419786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419784), c_Groups_Oone__class_Oone(_1419784)), hAPP(c_Int_Onumber__class_Onumber__of(_1419784), _1419786))))]]], (33794 ^ _782652) ^ [_1420089, _1420091] : [class_Int_Onumber__ring(_1420089), class_Rings_Olinordered__idom(_1420089), 33801 ^ _782652 : [(33802 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420089), hAPP(c_Int_Onumber__class_Onumber__of(_1420089), _1420091)), c_Groups_Oone__class_Oone(_1420089))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420091), c_Int_OBit1(c_Int_OPls))))], (33808 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420091), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420089), hAPP(c_Int_Onumber__class_Onumber__of(_1420089), _1420091)), c_Groups_Oone__class_Oone(_1420089))))]]], (33814 ^ _782652) ^ [_1420403, _1420405] : [class_Int_Onumber__ring(_1420403), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420403), hAPP(c_Int_Onumber__class_Onumber__of(_1420403), _1420405)), c_Groups_Oone__class_Oone(_1420403)) = hAPP(c_Int_Onumber__class_Onumber__of(_1420403), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1420405), c_Int_OBit1(c_Int_OPls))))], (33820 ^ _782652) ^ [_1420530, _1420532] : [class_Int_Onumber__ring(_1420530), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420530), c_Groups_Oone__class_Oone(_1420530)), hAPP(c_Int_Onumber__class_Onumber__of(_1420530), _1420532)) = hAPP(c_Int_Onumber__class_Onumber__of(_1420530), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1420532)))], (33826 ^ _782652) ^ [_1420651, _1420653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1420651)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1420653)), _1420651) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1420653), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1420651), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (33832 ^ _782652) ^ [_1420774, _1420776] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1420774, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1420776)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1420774, 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)))), _1420776)))], (33834 ^ _782652) ^ [_1420819, _1420821] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1420819))), _1420821) = 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)))), _1420819), _1420821))], (33836 ^ _782652) ^ [_1420864, _1420866] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1420864))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420866)) = 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)))), _1420864), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420866)))], (33838 ^ _782652) ^ [_1420915, _1420917] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1420915), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1420917)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1420915), 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)))), _1420917)))], (33840 ^ _782652) ^ [_1420964, _1420966] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1420964)))), _1420966) = 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)))), _1420964)), _1420966))], (33842 ^ _782652) ^ [_1421013, _1421015] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1421013)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421015)) = 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)))), _1421013)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421015)))], (33844 ^ _782652) ^ [_1421068, _1421070, _1421072] : [class_Int_Onumber__ring(_1421068), 33847 ^ _782652 : [(33848 ^ _782652) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1421068), _1421070) = hAPP(c_Int_Onumber__class_Onumber__of(_1421068), _1421072), -(c_Int_Oiszero(_1421068, hAPP(c_Int_Onumber__class_Onumber__of(_1421068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1421070), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1421072)))))], (33854 ^ _782652) ^ [] : [c_Int_Oiszero(_1421068, hAPP(c_Int_Onumber__class_Onumber__of(_1421068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1421070), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1421072)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1421068), _1421070) = hAPP(c_Int_Onumber__class_Onumber__of(_1421068), _1421072))]]], (33860 ^ _782652) ^ [_1421351, _1421353] : [class_Int_Onumber__ring(_1421351), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1421351), hAPP(c_Int_Onumber__class_Onumber__of(_1421351), _1421353)), c_Groups_Oone__class_Oone(_1421351)) = hAPP(c_Int_Onumber__class_Onumber__of(_1421351), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1421353), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (33866 ^ _782652) ^ [_1421478, _1421480] : [class_Int_Onumber__ring(_1421478), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1421478), c_Groups_Oone__class_Oone(_1421478)), hAPP(c_Int_Onumber__class_Onumber__of(_1421478), _1421480)) = hAPP(c_Int_Onumber__class_Onumber__of(_1421478), 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), _1421480))))], (33872 ^ _782652) ^ [_1421611] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421611))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1421611)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33878 ^ _782652) ^ [_1421700] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1421700)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1421700)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421700)), 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)))))], (33884 ^ _782652) ^ [_1421755, _1421757, _1421759] : [class_Int_Onumber__ring(_1421755), 33887 ^ _782652 : [(33888 ^ _782652) ^ [] : [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), _1421757))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421755), _1421759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1421757))) = hAPP(hAPP(c_HOL_OLet(_1421755, _1421755), hAPP(hAPP(c_Power_Opower__class_Opower(_1421755), _1421759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421757))), hAPP(hAPP(c_COMBS(_1421755, _1421755, _1421755), hAPP(hAPP(c_COMBB(_1421755, tc_fun(_1421755, _1421755), _1421755), c_Groups_Otimes__class_Otimes(_1421755)), hAPP(c_Groups_Otimes__class_Otimes(_1421755), _1421759))), c_COMBI(_1421755))))], (33894 ^ _782652) ^ [] : [-(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), _1421757)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421755), _1421759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1421757))) = c_Groups_Oone__class_Oone(_1421755))]]], (33900 ^ _782652) ^ [_1422122, _1422124] : [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), _1422122))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1422124)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1422122))) = 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), _1422124), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422122)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33906 ^ _782652) ^ [_1422269, _1422271] : [-(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), _1422269)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1422271)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1422269))) = 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), _1422271)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422269)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33912 ^ _782652) ^ [_1422351, _1422353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1422351), 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)))), _1422353)), 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)))), _1422351)) = 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), _1422353), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1422351))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33918 ^ _782652) ^ [_1422502, _1422504, _1422506] : [-(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), _1422502)), 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))), _1422504))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1422506))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1422506)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1422502), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1422502), 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), _1422506), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1422504)))))], (33920 ^ _782652) ^ [_1422589, _1422591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1422589)), -(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)))), _1422591))), 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)))), _1422589)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1422591), _1422589))], (33926 ^ _782652) ^ [_1422724, _1422726] : [c_Int_OBit1(_1422724) = c_Int_OBit0(_1422726)], (33928 ^ _782652) ^ [_1422765, _1422767] : [c_Int_OBit0(_1422765) = c_Int_OBit1(_1422767)], (33930 ^ _782652) ^ [_1422806] : [c_Int_OBit0(_1422806) = c_Int_OPls, -(_1422806 = c_Int_OPls)], (33936 ^ _782652) ^ [_1422881] : [_1422881 = c_Int_OPls, -(c_Int_OBit0(_1422881) = c_Int_OPls)], (33942 ^ _782652) ^ [_1422974] : [c_Int_OPls = c_Int_OBit0(_1422974), -(c_Int_OPls = _1422974)], (33948 ^ _782652) ^ [_1423049] : [c_Int_OPls = _1423049, -(c_Int_OPls = c_Int_OBit0(_1423049))], (33954 ^ _782652) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (33956 ^ _782652) ^ [_1423148] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1423148)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1423148)))], (33958 ^ _782652) ^ [_1423196, _1423198] : [c_Int_OBit0(_1423196) = c_Int_OBit0(_1423198), -(_1423196 = _1423198)], (33964 ^ _782652) ^ [_1423277, _1423279] : [_1423277 = _1423279, -(c_Int_OBit0(_1423277) = c_Int_OBit0(_1423279))], (33970 ^ _782652) ^ [_1423364, _1423366] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1423364)), _1423366) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1423364), _1423366)))], (33972 ^ _782652) ^ [_1423405, _1423407] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1423405)), c_Int_OBit0(_1423407)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1423405), _1423407)))], (33974 ^ _782652) ^ [_1423448] : [-(c_Int_OBit0(_1423448) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1423448), _1423448))], (33976 ^ _782652) ^ [_1423494, _1423496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1423494)), c_Int_OBit0(_1423496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423494), _1423496)))], (33982 ^ _782652) ^ [_1423595, _1423597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423595), _1423597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1423595)), c_Int_OBit0(_1423597))))], (33988 ^ _782652) ^ [_1423717, _1423719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1423717)), c_Int_OBit0(_1423719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423717), _1423719)))], (33994 ^ _782652) ^ [_1423818, _1423820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423818), _1423820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1423818)), c_Int_OBit0(_1423820))))], (34000 ^ _782652) ^ [_1423925, _1423927] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1423925)), c_Int_OBit0(_1423927)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1423925), _1423927)))], (34002 ^ _782652) ^ [_1423983, _1423985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1423983)), c_Int_OBit0(_1423985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1423983), _1423985)))], (34008 ^ _782652) ^ [_1424084, _1424086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424084), _1424086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1424084)), c_Int_OBit0(_1424086))))], (34014 ^ _782652) ^ [_1424206, _1424208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1424206)), c_Int_OBit0(_1424208))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424206), _1424208)))], (34020 ^ _782652) ^ [_1424307, _1424309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424307), _1424309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1424307)), c_Int_OBit0(_1424309))))], (34026 ^ _782652) ^ [_1424426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1424426)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424426), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34032 ^ _782652) ^ [_1424521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424521), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1424521)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34038 ^ _782652) ^ [_1424634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1424634)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424634), c_Int_OPls)))], (34044 ^ _782652) ^ [_1424729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424729), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1424729)), c_Int_OPls)))], (34050 ^ _782652) ^ [_1424842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1424842))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1424842)))], (34056 ^ _782652) ^ [_1424925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1424925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1424925))))], (34062 ^ _782652) ^ [_1425029, _1425031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1425029)), c_Int_OBit1(_1425031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425029), _1425031)))], (34068 ^ _782652) ^ [_1425130, _1425132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425130), _1425132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1425130)), c_Int_OBit1(_1425132))))], (34074 ^ _782652) ^ [_1425252, _1425254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1425252)), c_Int_OBit1(_1425254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425252), _1425254)))], (34080 ^ _782652) ^ [_1425353, _1425355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425353), _1425355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1425353)), c_Int_OBit1(_1425355))))], (34086 ^ _782652) ^ [_1425472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1425472)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425472), c_Int_OPls)))], (34092 ^ _782652) ^ [_1425567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425567), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1425567)), c_Int_OPls)))], (34098 ^ _782652) ^ [_1425680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1425680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1425680)))], (34104 ^ _782652) ^ [_1425763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1425763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1425763))))], (34110 ^ _782652) ^ [_1425867, _1425869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1425867)), c_Int_OBit0(_1425869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425867), _1425869)))], (34116 ^ _782652) ^ [_1425968, _1425970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425968), _1425970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1425968)), c_Int_OBit0(_1425970))))], (34122 ^ _782652) ^ [_1426090, _1426092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426090)), c_Int_OBit0(_1426092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426090), _1426092)))], (34128 ^ _782652) ^ [_1426191, _1426193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426191), _1426193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426191)), c_Int_OBit0(_1426193))))], (34134 ^ _782652) ^ [_1426298, _1426300] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1426298)), c_Int_OBit0(_1426300)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426298), _1426300)))], (34136 ^ _782652) ^ [_1426341, _1426343] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1426341)), c_Int_OBit1(_1426343)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426341), _1426343)))], (34138 ^ _782652) ^ [_1426384] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1426384)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1426384)))], (34140 ^ _782652) ^ [_1426417, _1426419] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1426417)), c_Int_OBit0(_1426419)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1426417), _1426419)))], (34142 ^ _782652) ^ [_1426460, _1426462] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1426460)), c_Int_OBit1(_1426462)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1426460), _1426462)))], (34144 ^ _782652) ^ [_1426503, _1426505] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1426503))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1426505))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426503)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426505)))], (34146 ^ _782652) ^ [_1426568] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1426568)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426568))))], (34152 ^ _782652) ^ [_1426663] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426663))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1426663)))))], (34158 ^ _782652) ^ [_1426764] : [-(c_Int_Opred(c_Int_OBit0(_1426764)) = c_Int_OBit1(c_Int_Opred(_1426764)))], (34160 ^ _782652) ^ [_1426795] : [-(c_Int_Opred(c_Int_OBit1(_1426795)) = c_Int_OBit0(_1426795))], (34162 ^ _782652) ^ [_1426824, _1426826] : [class_Int_Onumber__ring(_1426824), class_Int_Oring__char__0(_1426824), 34169 ^ _782652 : [(34170 ^ _782652) ^ [] : [c_Int_Oiszero(_1426824, hAPP(c_Int_Onumber__class_Onumber__of(_1426824), c_Int_OBit0(_1426826))), -(c_Int_Oiszero(_1426824, hAPP(c_Int_Onumber__class_Onumber__of(_1426824), _1426826)))], (34176 ^ _782652) ^ [] : [c_Int_Oiszero(_1426824, hAPP(c_Int_Onumber__class_Onumber__of(_1426824), _1426826)), -(c_Int_Oiszero(_1426824, hAPP(c_Int_Onumber__class_Onumber__of(_1426824), c_Int_OBit0(_1426826))))]]], (34182 ^ _782652) ^ [_1427117] : [-(c_Int_Osucc(c_Int_OBit1(_1427117)) = c_Int_OBit0(c_Int_Osucc(_1427117)))], (34184 ^ _782652) ^ [_1427148] : [-(c_Int_Osucc(c_Int_OBit0(_1427148)) = c_Int_OBit1(_1427148))], (34186 ^ _782652) ^ [_1427177] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1427177)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427177)), 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))))], (34188 ^ _782652) ^ [_1427214, _1427216] : [class_Int_Onumber__ring(_1427214), -(hAPP(c_Int_Onumber__class_Onumber__of(_1427214), c_Int_OBit0(_1427216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427214), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427214), c_Groups_Ozero__class_Ozero(_1427214)), hAPP(c_Int_Onumber__class_Onumber__of(_1427214), _1427216))), hAPP(c_Int_Onumber__class_Onumber__of(_1427214), _1427216)))], (34194 ^ _782652) ^ [_1427374, _1427376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1427374)), c_Int_OBit1(_1427376))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427374), _1427376)))], (34200 ^ _782652) ^ [_1427475, _1427477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427475), _1427477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1427475)), c_Int_OBit1(_1427477))))], (34206 ^ _782652) ^ [_1427597, _1427599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1427597)), c_Int_OBit1(_1427599))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427597), _1427599)))], (34212 ^ _782652) ^ [_1427698, _1427700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427698), _1427700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1427698)), c_Int_OBit1(_1427700))))], (34218 ^ _782652) ^ [_1427820, _1427822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427820)), c_Int_OBit0(_1427822))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427820), _1427822)))], (34224 ^ _782652) ^ [_1427921, _1427923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427921), _1427923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427921)), c_Int_OBit0(_1427923))))], (34230 ^ _782652) ^ [_1428043, _1428045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1428043)), c_Int_OBit0(_1428045))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1428043), _1428045)))], (34236 ^ _782652) ^ [_1428144, _1428146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1428144), _1428146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1428144)), c_Int_OBit0(_1428146))))], (34242 ^ _782652) ^ [] : [-(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))))], (34244 ^ _782652) ^ [_1428269, _1428271] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1428269)), _1428271) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1428269), _1428271))), _1428271))], (34246 ^ _782652) ^ [_1428316, _1428318] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1428316)), c_Int_OBit1(_1428318)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1428316)), _1428318)))], (34248 ^ _782652) ^ [_1428361, _1428363] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1428361)), c_Int_OBit1(_1428363)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428361), c_Int_Osucc(_1428363))))], (34250 ^ _782652) ^ [_1428406, _1428408, _1428410] : [class_Int_Onumber__ring(_1428406), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428406), _1428408), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1428410))) = hAPP(hAPP(c_HOL_OLet(_1428406, _1428406), hAPP(hAPP(c_Power_Opower__class_Opower(_1428406), _1428408), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428410))), hAPP(hAPP(c_COMBS(_1428406, _1428406, _1428406), c_Groups_Otimes__class_Otimes(_1428406)), c_COMBI(_1428406))))], (34256 ^ _782652) ^ [_1428577, _1428579] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428577), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1428579))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428577), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428579))), 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))))], (34258 ^ _782652) ^ [_1428628, _1428630] : [class_Int_Onumber__ring(_1428628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1428628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1428628), c_Groups_Oone__class_Oone(_1428628)), c_Groups_Oone__class_Oone(_1428628))), hAPP(c_Int_Onumber__class_Onumber__of(_1428628), _1428630)) = hAPP(c_Int_Onumber__class_Onumber__of(_1428628), c_Int_OBit0(_1428630)))], (34264 ^ _782652) ^ [_1428767] : [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), _1428767))), 34267 ^ _782652 : [(34268 ^ _782652) ^ [] : [-(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(_1428767)))))], (34270 ^ _782652) ^ [] : [-(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(_1428767)))))]]], (34272 ^ _782652) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34274 ^ _782652) ^ [_1428924, _1428926, _1428928] : [class_Int_Onumber__ring(_1428924), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428924), hAPP(c_Int_Onumber__class_Onumber__of(_1428924), _1428926)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1428928))) = hAPP(hAPP(c_HOL_OLet(_1428924, _1428924), hAPP(hAPP(c_Power_Opower__class_Opower(_1428924), hAPP(c_Int_Onumber__class_Onumber__of(_1428924), _1428926)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428928))), hAPP(hAPP(c_COMBS(_1428924, _1428924, _1428924), c_Groups_Otimes__class_Otimes(_1428924)), c_COMBI(_1428924))))], (34280 ^ _782652) ^ [_1429115, _1429117] : [class_Int_Onumber__ring(_1429115), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429115), _1429117), hAPP(c_Int_Onumber__class_Onumber__of(_1429115), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429115), _1429117), _1429117))], (34286 ^ _782652) ^ [_1429232, _1429234] : [class_Int_Onumber__ring(_1429232), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429232), hAPP(c_Int_Onumber__class_Onumber__of(_1429232), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1429234) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429232), _1429234), _1429234))], (34292 ^ _782652) ^ [_1429349] : [class_Int_Onumber__ring(_1429349), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429349), c_Groups_Oone__class_Oone(_1429349)), c_Groups_Oone__class_Oone(_1429349)) = hAPP(c_Int_Onumber__class_Onumber__of(_1429349), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (34298 ^ _782652) ^ [_1429456, _1429458] : [class_Rings_Oring__1__no__zero__divisors(_1429456), 34301 ^ _782652 : [(34302 ^ _782652) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1429456), _1429458), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1429456), -(_1429458 = c_Groups_Ozero__class_Ozero(_1429456))], (34308 ^ _782652) ^ [] : [_1429458 = c_Groups_Ozero__class_Ozero(_1429456), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1429456), _1429458), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1429456))]]], (34314 ^ _782652) ^ [_1429697] : [class_Rings_Osemiring__1(_1429697), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1429697), c_Groups_Ozero__class_Ozero(_1429697)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1429697))], (34320 ^ _782652) ^ [] : [-(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))))], (34322 ^ _782652) ^ [] : [-(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))))], (34324 ^ _782652) ^ [_1429830, _1429832] : [class_Rings_Ocomm__semiring__1(_1429830), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429830), _1429832), _1429832) = hAPP(hAPP(c_Power_Opower__class_Opower(_1429830), _1429832), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34330 ^ _782652) ^ [_1429937, _1429939] : [class_Groups_Omonoid__mult(_1429937), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1429937), _1429939), 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(_1429937), _1429939), _1429939))], (34336 ^ _782652) ^ [] : [-(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))))))], (34338 ^ _782652) ^ [_1430062] : [-(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)))), _1430062) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1430062)))], (34340 ^ _782652) ^ [_1430094] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430094), 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, _1430094)))], (34342 ^ _782652) ^ [_1430129] : [class_Rings_Osemiring__1(_1430129), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430129), c_Groups_Oone__class_Oone(_1430129)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1430129))], (34348 ^ _782652) ^ [_1430226, _1430228] : [class_Rings_Oring__1(_1430226), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430226), hAPP(c_Groups_Ouminus__class_Ouminus(_1430226), _1430228)), 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(_1430226), _1430228), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34354 ^ _782652) ^ [_1430343] : [-(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)))), _1430343) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430343), _1430343))], (34356 ^ _782652) ^ [_1430375] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1430375), 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), _1430375), _1430375))], (34358 ^ _782652) ^ [_1430410, _1430412, _1430414] : [class_Groups_Omonoid__mult(_1430410), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430410), _1430412), 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)))), _1430414)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1430410), hAPP(hAPP(c_Power_Opower__class_Opower(_1430410), _1430412), _1430414)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34364 ^ _782652) ^ [] : [-(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)))))], (34366 ^ _782652) ^ [] : [-(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)))))], (34368 ^ _782652) ^ [_1430577, _1430579] : [class_Rings_Olinordered__idom(_1430577), -(hAPP(c_Groups_Oabs__class_Oabs(_1430577), hAPP(hAPP(c_Power_Opower__class_Opower(_1430577), _1430579), 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(_1430577), _1430579), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34374 ^ _782652) ^ [_1430694, _1430696] : [class_Rings_Olinordered__idom(_1430694), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430694), hAPP(c_Groups_Oabs__class_Oabs(_1430694), _1430696)), 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(_1430694), _1430696), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34380 ^ _782652) ^ [] : [-(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))))], (34382 ^ _782652) ^ [_1430829] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1430829)), 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, _1430829, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34384 ^ _782652) ^ [_1430866] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1430866))), 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), _1430866), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34386 ^ _782652) ^ [_1430910, _1430912] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1430910)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1430912))) = 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), _1430910), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430912))))], (34388 ^ _782652) ^ [_1430962] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1430962), _1430962)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1430962)], (34390 ^ _782652) ^ [_1430997, _1430999] : [class_Fields_Olinordered__field__inverse__zero(_1430997), class_Int_Onumber__ring(_1430997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), c_Groups_Ozero__class_Ozero(_1430997)), _1430999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), c_Groups_Ozero__class_Ozero(_1430997)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1430997), _1430999), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34404 ^ _782652) ^ [_1431238, _1431240] : [class_Fields_Olinordered__field__inverse__zero(_1431238), class_Int_Onumber__ring(_1431238), 34411 ^ _782652 : [(34412 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431238), c_Groups_Ozero__class_Ozero(_1431238)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1431238), _1431240), hAPP(c_Int_Onumber__class_Onumber__of(_1431238), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431238), c_Groups_Ozero__class_Ozero(_1431238)), _1431240)))], (34418 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431238), c_Groups_Ozero__class_Ozero(_1431238)), _1431240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431238), c_Groups_Ozero__class_Ozero(_1431238)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1431238), _1431240), hAPP(c_Int_Onumber__class_Onumber__of(_1431238), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (34424 ^ _782652) ^ [_1431588, _1431590, _1431592] : [class_Rings_Olinordered__semidom(_1431588), hAPP(hAPP(c_Power_Opower__class_Opower(_1431588), _1431590), 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(_1431588), _1431592), 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(_1431588), c_Groups_Ozero__class_Ozero(_1431588)), _1431590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431588), c_Groups_Ozero__class_Ozero(_1431588)), _1431592)), -(_1431590 = _1431592)], (34442 ^ _782652) ^ [_1431895, _1431897, _1431899] : [class_Rings_Olinordered__semidom(_1431895), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431895), hAPP(hAPP(c_Power_Opower__class_Opower(_1431895), _1431897), 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(_1431895), _1431899), 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(_1431895), c_Groups_Ozero__class_Ozero(_1431895)), _1431899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431895), _1431897), _1431899)))], (34456 ^ _782652) ^ [_1432158, _1432160] : [class_Rings_Olinordered__idom(_1432158), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432158), c_Groups_Ozero__class_Ozero(_1432158)), hAPP(hAPP(c_Power_Opower__class_Opower(_1432158), _1432160), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34462 ^ _782652) ^ [_1432267, _1432269] : [class_Rings_Olinordered__idom(_1432267), 34465 ^ _782652 : [(34466 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432267), c_Groups_Ozero__class_Ozero(_1432267)), hAPP(hAPP(c_Power_Opower__class_Opower(_1432267), _1432269), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1432269 = c_Groups_Ozero__class_Ozero(_1432267)], (34472 ^ _782652) ^ [] : [-(_1432269 = c_Groups_Ozero__class_Ozero(_1432267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432267), c_Groups_Ozero__class_Ozero(_1432267)), hAPP(hAPP(c_Power_Opower__class_Opower(_1432267), _1432269), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (34478 ^ _782652) ^ [_1432491, _1432493] : [class_Rings_Olinordered__idom(_1432491), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432491), hAPP(hAPP(c_Power_Opower__class_Opower(_1432491), _1432493), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1432491)))], (34484 ^ _782652) ^ [_1432601, _1432603, _1432605] : [class_Rings_Olinordered__idom(_1432601), 34487 ^ _782652 : [(34488 ^ _782652) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432601), hAPP(hAPP(c_Power_Opower__class_Opower(_1432601), _1432603), 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(_1432601), _1432605), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1432601), 34491 ^ _782652 : [(34492 ^ _782652) ^ [] : [-(_1432603 = c_Groups_Ozero__class_Ozero(_1432601))], (34494 ^ _782652) ^ [] : [-(_1432605 = c_Groups_Ozero__class_Ozero(_1432601))]]], (34496 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432601), hAPP(hAPP(c_Power_Opower__class_Opower(_1432601), _1432603), 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(_1432601), _1432605), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1432601)), _1432603 = c_Groups_Ozero__class_Ozero(_1432601), _1432605 = c_Groups_Ozero__class_Ozero(_1432601)]]], (34506 ^ _782652) ^ [_1432976, _1432978] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1432976), hAPP(c_Int_Onumber__class_Onumber__of(_1432976), _1432978)), 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(_1432976), hAPP(c_Int_Onumber__class_Onumber__of(_1432976), _1432978)), hAPP(c_Int_Onumber__class_Onumber__of(_1432976), _1432978))), class_Groups_Omonoid__mult(_1432976), class_Int_Onumber(_1432976)], (34516 ^ _782652) ^ [_1433163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1433163), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1433163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1433163 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34526 ^ _782652) ^ [] : [-(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))))], (34528 ^ _782652) ^ [_1433279, _1433281] : [class_Rings_Oring__1__no__zero__divisors(_1433279), 34531 ^ _782652 : [(34542 ^ _782652) ^ [] : [34543 ^ _782652 : [(34544 ^ _782652) ^ [] : [_1433281 = c_Groups_Oone__class_Oone(_1433279)], (34546 ^ _782652) ^ [] : [_1433281 = hAPP(c_Groups_Ouminus__class_Ouminus(_1433279), c_Groups_Oone__class_Oone(_1433279))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1433279), _1433281), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1433279))], (34532 ^ _782652) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1433279), _1433281), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1433279), -(_1433281 = c_Groups_Oone__class_Oone(_1433279)), -(_1433281 = hAPP(c_Groups_Ouminus__class_Ouminus(_1433279), c_Groups_Oone__class_Oone(_1433279)))]]], (34550 ^ _782652) ^ [_1433586, _1433588, _1433590] : [class_Rings_Ocomm__semiring__1(_1433586), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1433586), _1433588), 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)))), _1433590)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433586), hAPP(hAPP(c_Power_Opower__class_Opower(_1433586), _1433588), _1433590)), hAPP(hAPP(c_Power_Opower__class_Opower(_1433586), _1433588), _1433590)))], (34556 ^ _782652) ^ [_1433733, _1433735, _1433737] : [class_Rings_Oring__1(_1433733), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1433733), hAPP(c_Groups_Ouminus__class_Ouminus(_1433733), _1433735)), 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)))), _1433737)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1433733), _1433735), 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)))), _1433737)))], (34562 ^ _782652) ^ [_1433864, _1433866, _1433868] : [class_Rings_Olinordered__semidom(_1433864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433864), hAPP(hAPP(c_Power_Opower__class_Opower(_1433864), _1433866), 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(_1433864), _1433868), 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(_1433864), c_Groups_Ozero__class_Ozero(_1433864)), _1433868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433864), _1433866), _1433868)))], (34576 ^ _782652) ^ [_1434127, _1434129, _1434131] : [class_Rings_Olinordered__idom(_1434127), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434127), c_Groups_Ozero__class_Ozero(_1434127)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434127), hAPP(hAPP(c_Power_Opower__class_Opower(_1434127), _1434129), 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(_1434127), _1434131), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (34582 ^ _782652) ^ [_1434270, _1434272, _1434274] : [class_Rings_Olinordered__idom(_1434270), 34585 ^ _782652 : [(34586 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434270), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434270), hAPP(hAPP(c_Power_Opower__class_Opower(_1434270), _1434272), 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(_1434270), _1434274), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1434270))), 34589 ^ _782652 : [(34590 ^ _782652) ^ [] : [-(_1434272 = c_Groups_Ozero__class_Ozero(_1434270))], (34592 ^ _782652) ^ [] : [-(_1434274 = c_Groups_Ozero__class_Ozero(_1434270))]]], (34594 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434270), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434270), hAPP(hAPP(c_Power_Opower__class_Opower(_1434270), _1434272), 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(_1434270), _1434274), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1434270)))), _1434272 = c_Groups_Ozero__class_Ozero(_1434270), _1434274 = c_Groups_Ozero__class_Ozero(_1434270)]]], (34604 ^ _782652) ^ [_1434666, _1434668, _1434670] : [class_Rings_Olinordered__idom(_1434666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434666), hAPP(hAPP(c_Power_Opower__class_Opower(_1434666), _1434668), 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(_1434666), _1434670), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1434666)))], (34610 ^ _782652) ^ [_1434810, _1434812, _1434814] : [class_Rings_Olinordered__idom(_1434810), 34613 ^ _782652 : [(34624 ^ _782652) ^ [] : [34625 ^ _782652 : [(34626 ^ _782652) ^ [] : [-(_1434812 = c_Groups_Ozero__class_Ozero(_1434810))], (34628 ^ _782652) ^ [] : [-(_1434814 = c_Groups_Ozero__class_Ozero(_1434810))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434810), c_Groups_Ozero__class_Ozero(_1434810)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434810), hAPP(hAPP(c_Power_Opower__class_Opower(_1434810), _1434812), 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(_1434810), _1434814), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (34614 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434810), c_Groups_Ozero__class_Ozero(_1434810)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434810), hAPP(hAPP(c_Power_Opower__class_Opower(_1434810), _1434812), 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(_1434810), _1434814), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1434812 = c_Groups_Ozero__class_Ozero(_1434810), _1434814 = c_Groups_Ozero__class_Ozero(_1434810)]]], (34632 ^ _782652) ^ [_1435185, _1435187, _1435189] : [class_Int_Onumber__ring(_1435185), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435185), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1435185), _1435187), _1435189)), 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(_1435185), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1435185), hAPP(hAPP(c_Power_Opower__class_Opower(_1435185), _1435187), 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(_1435185), _1435189), 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(_1435185), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435185), hAPP(c_Int_Onumber__class_Onumber__of(_1435185), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1435187)), _1435189)))], (34638 ^ _782652) ^ [_1435400, _1435402, _1435404] : [class_Rings_Olinordered__idom(_1435400), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435400), c_Groups_Ozero__class_Ozero(_1435400)), hAPP(hAPP(c_Power_Opower__class_Opower(_1435400), _1435402), 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)))), _1435404)))))], (34644 ^ _782652) ^ [_1435517, _1435519, _1435521] : [class_Rings_Ocomm__semiring__1(_1435517), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435517), _1435519), 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)))), _1435521))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435517), _1435519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435517), hAPP(hAPP(c_Power_Opower__class_Opower(_1435517), _1435519), _1435521)), hAPP(hAPP(c_Power_Opower__class_Opower(_1435517), _1435519), _1435521))))], (34650 ^ _782652) ^ [_1435686, _1435688, _1435690] : [class_Groups_Omonoid__mult(_1435686), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435686), _1435688), 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)))), _1435690))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435686), _1435688), hAPP(hAPP(c_Power_Opower__class_Opower(_1435686), hAPP(hAPP(c_Power_Opower__class_Opower(_1435686), _1435688), _1435690)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34656 ^ _782652) ^ [_1435839, _1435841] : [class_Rings_Oring__1(_1435839), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435839), hAPP(c_Groups_Ouminus__class_Ouminus(_1435839), c_Groups_Oone__class_Oone(_1435839))), 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)))), _1435841)) = c_Groups_Oone__class_Oone(_1435839))], (34662 ^ _782652) ^ [_1435963, _1435965] : [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), _1435963))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1435965))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1435963))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435965)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1435963)))], (34668 ^ _782652) ^ [_1436100, _1436102] : [-(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), _1436100)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1436102))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1436100))) = 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), _1436102)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436100)))], (34674 ^ _782652) ^ [_1436189] : [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, _1436189, 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, _1436189, 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))], (34680 ^ _782652) ^ [_1436280] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1436280, 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, _1436280, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34686 ^ _782652) ^ [_1436377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1436377)), -(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), _1436377), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34692 ^ _782652) ^ [_1436472, _1436474, _1436476] : [class_Int_Onumber__ring(_1436472), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1436472), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1436472), _1436474), _1436476)), 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(_1436472), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1436472), hAPP(hAPP(c_Power_Opower__class_Opower(_1436472), _1436474), 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(_1436472), _1436476), 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(_1436472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1436472), hAPP(c_Int_Onumber__class_Onumber__of(_1436472), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1436474)), _1436476)))], (34698 ^ _782652) ^ [_1436687, _1436689, _1436691] : [class_Rings_Olinordered__idom(_1436687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436687), c_Groups_Ozero__class_Ozero(_1436687)), hAPP(hAPP(c_Power_Opower__class_Opower(_1436687), _1436689), 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)))), _1436691))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436687), c_Groups_Ozero__class_Ozero(_1436687)), _1436689)))], (34708 ^ _782652) ^ [_1436882, _1436884, _1436886] : [class_Rings_Olinordered__idom(_1436882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436882), _1436884), c_Groups_Ozero__class_Ozero(_1436882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436882), hAPP(hAPP(c_Power_Opower__class_Opower(_1436882), _1436884), 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)))), _1436886)))), c_Groups_Ozero__class_Ozero(_1436882))))], (34718 ^ _782652) ^ [_1437077, _1437079] : [class_Rings_Oring__1(_1437077), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1437077), hAPP(c_Groups_Ouminus__class_Ouminus(_1437077), c_Groups_Oone__class_Oone(_1437077))), 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)))), _1437079))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1437077), c_Groups_Oone__class_Oone(_1437077)))], (34724 ^ _782652) ^ [_1437208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1437208)), -(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), _1437208), 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)))))))], (34730 ^ _782652) ^ [_1437315, _1437317] : [class_Rings_Osemiring__1(_1437315), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437317)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1437315), 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)))), _1437317))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1437315), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1437315), hAPP(c_Int_Onat, _1437317))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1437315), hAPP(c_Int_Onat, _1437317))))], (34740 ^ _782652) ^ [_1437516, _1437518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437516)), -(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)))), _1437518)), 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)))), _1437516)) = 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, _1437518, _1437516))))], (34746 ^ _782652) ^ [_1437643, _1437645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437643), 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)))), _1437645))), 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)))), _1437643)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1437645), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1437643))], (34752 ^ _782652) ^ [_1437790] : [_1437790 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1437790) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34758 ^ _782652) ^ [_1437866] : [-(_1437866 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 34761 ^ _782652 : [(34762 ^ _782652) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1437866, 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, _1437866) = 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), _1437866), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34768 ^ _782652) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1437866, 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, _1437866) = 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), _1437866), 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)))]]], (34774 ^ _782652) ^ [_1438126, _1438128] : [class_Rings_Oring__1(_1438126), 34777 ^ _782652 : [(34778 ^ _782652) ^ [] : [_1438128 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1438126), _1438128) = c_Groups_Ozero__class_Ozero(_1438126))], (34784 ^ _782652) ^ [] : [-(_1438128 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34787 ^ _782652 : [(34788 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1438128), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1438126), _1438128) = hAPP(c_Groups_Ouminus__class_Ouminus(_1438126), hAPP(c_Int_Oring__1__class_Oof__int(_1438126), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1438128))))], (34794 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1438128), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1438126), _1438128) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1438126), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1438126, _1438126)), tc_fun(tc_Int_Oint, _1438126)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1438126, _1438126), _1438126), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1438126, _1438126)), tc_fun(tc_Int_Oint, _1438126)), tc_Int_Oint), c_COMBB(tc_fun(_1438126, _1438126), _1438126, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1438126, tc_fun(tc_fun(_1438126, _1438126), _1438126), tc_Int_Oint), c_HOL_OLet(_1438126, _1438126)), c_Int_Oring__1__class_Oof__int(_1438126)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1438126, _1438126), tc_fun(_1438126, _1438126)), hAPP(hAPP(c_COMBB(tc_fun(_1438126, tc_fun(_1438126, _1438126)), tc_fun(tc_fun(_1438126, _1438126), tc_fun(_1438126, _1438126)), tc_Int_Oint), c_COMBS(_1438126, _1438126, _1438126)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1438126, _1438126), tc_fun(_1438126, tc_fun(_1438126, _1438126))), hAPP(hAPP(c_COMBB(tc_fun(_1438126, tc_fun(_1438126, _1438126)), tc_fun(tc_fun(_1438126, _1438126), tc_fun(_1438126, tc_fun(_1438126, _1438126))), tc_Int_Oint), c_COMBB(_1438126, tc_fun(_1438126, _1438126), _1438126)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1438126, tc_fun(_1438126, _1438126)), tc_Int_Oint), c_If(_1438126)), 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(_1438126, _1438126, _1438126), c_Groups_Oplus__class_Oplus(_1438126)), c_COMBI(_1438126))))), hAPP(hAPP(c_COMBC(_1438126, _1438126, _1438126), hAPP(hAPP(c_COMBB(_1438126, tc_fun(_1438126, _1438126), _1438126), c_Groups_Oplus__class_Oplus(_1438126)), hAPP(hAPP(c_COMBS(_1438126, _1438126, _1438126), c_Groups_Oplus__class_Oplus(_1438126)), c_COMBI(_1438126)))), c_Groups_Oone__class_Oone(_1438126))))), c_Divides_Odivmod__int(_1438128, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (34800 ^ _782652) ^ [_1439039, _1439041] : [class_Int_Onumber__ring(_1439039), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1439039), hAPP(c_Int_Onumber__class_Onumber__of(_1439039), 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)))), _1439041))) = hAPP(c_Int_Onumber__class_Onumber__of(_1439039), c_Int_OMin))], (34806 ^ _782652) ^ [_1439171] : [c_Int_OMin = c_Int_OBit0(_1439171)], (34808 ^ _782652) ^ [_1439205] : [c_Int_OBit0(_1439205) = c_Int_OMin], (34810 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (34812 ^ _782652) ^ [] : [-(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))], (34814 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (34816 ^ _782652) ^ [] : [c_Int_OMin = c_Int_OPls], (34818 ^ _782652) ^ [] : [c_Int_OPls = c_Int_OMin], (34820 ^ _782652) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (34822 ^ _782652) ^ [_1439368] : [c_Int_OMin = c_Int_OBit1(_1439368), -(c_Int_OMin = _1439368)], (34828 ^ _782652) ^ [_1439443] : [c_Int_OMin = _1439443, -(c_Int_OMin = c_Int_OBit1(_1439443))], (34834 ^ _782652) ^ [_1439536] : [c_Int_OBit1(_1439536) = c_Int_OMin, -(_1439536 = c_Int_OMin)], (34840 ^ _782652) ^ [_1439611] : [_1439611 = c_Int_OMin, -(c_Int_OBit1(_1439611) = c_Int_OMin)], (34846 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34848 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (34850 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (34852 ^ _782652) ^ [_1439764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1439764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1439764)))], (34858 ^ _782652) ^ [_1439847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1439847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1439847))))], (34864 ^ _782652) ^ [_1439948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1439948)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439948), c_Int_OMin)))], (34870 ^ _782652) ^ [_1440043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1440043), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1440043)), c_Int_OMin)))], (34876 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (34878 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (34880 ^ _782652) ^ [_1440198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1440198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1440198)))], (34886 ^ _782652) ^ [_1440281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1440281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1440281))))], (34892 ^ _782652) ^ [_1440382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1440382)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440382), c_Int_OMin)))], (34898 ^ _782652) ^ [_1440477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440477), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1440477)), c_Int_OMin)))], (34904 ^ _782652) ^ [_1440590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1440590)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1440590), c_Int_OMin)))], (34910 ^ _782652) ^ [_1440685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1440685), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1440685)), c_Int_OMin)))], (34916 ^ _782652) ^ [_1440798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1440798))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1440798)))], (34922 ^ _782652) ^ [_1440881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1440881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1440881))))], (34928 ^ _782652) ^ [] : [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)], (34930 ^ _782652) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34932 ^ _782652) ^ [_1441012] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1441012) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1441012))], (34934 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (34936 ^ _782652) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (34938 ^ _782652) ^ [_1441077] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1441077) = c_Int_Opred(_1441077))], (34940 ^ _782652) ^ [_1441105] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1441105), c_Int_OMin) = c_Int_Opred(_1441105))], (34942 ^ _782652) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (34944 ^ _782652) ^ [_1441154] : [class_Int_Onumber__ring(_1441154), c_Int_Oiszero(_1441154, hAPP(c_Int_Onumber__class_Onumber__of(_1441154), c_Int_OMin))], (34950 ^ _782652) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (34952 ^ _782652) ^ [_1441256] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1441256), c_Int_OMin) = c_Int_Osucc(_1441256))], (34954 ^ _782652) ^ [_1441287, _1441289] : [class_Int_Onumber__ring(_1441287), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441287), hAPP(c_Int_Onumber__class_Onumber__of(_1441287), c_Int_OMin)), _1441289) = hAPP(c_Groups_Ouminus__class_Ouminus(_1441287), _1441289))], (34960 ^ _782652) ^ [_1441398, _1441400] : [class_Int_Onumber__ring(_1441398), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441398), _1441400), hAPP(c_Int_Onumber__class_Onumber__of(_1441398), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1441398), _1441400))], (34966 ^ _782652) ^ [_1441509] : [class_Int_Onumber__ring(_1441509), -(hAPP(c_Int_Onumber__class_Onumber__of(_1441509), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1441509), c_Groups_Oone__class_Oone(_1441509)))], (34972 ^ _782652) ^ [_1441606] : [class_Int_Onumber__ring(_1441606), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1441606), c_Groups_Oone__class_Oone(_1441606)) = hAPP(c_Int_Onumber__class_Onumber__of(_1441606), c_Int_OMin))], (34978 ^ _782652) ^ [_1441703] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1441703), hAPP(c_Int_Onumber__class_Onumber__of(_1441703), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1441703)), class_Int_Onumber__ring(_1441703), class_Rings_Olinordered__idom(_1441703)], (34988 ^ _782652) ^ [_1441848, _1441850] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1441848), _1441850), hAPP(c_Int_Onumber__class_Onumber__of(_1441848), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1441848), _1441850)), class_Fields_Ofield__inverse__zero(_1441848), class_Int_Onumber__ring(_1441848)], (34998 ^ _782652) ^ [_1442021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1442021)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1442021), c_Int_OMin)))], (35004 ^ _782652) ^ [_1442116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1442116), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1442116)), c_Int_OMin)))], (35010 ^ _782652) ^ [_1442229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1442229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1442229)))], (35016 ^ _782652) ^ [_1442312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1442312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1442312))))], (35022 ^ _782652) ^ [_1442401] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1442401, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35024 ^ _782652) ^ [_1442428] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1442428)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1442428)))], (35026 ^ _782652) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (35028 ^ _782652) ^ [_1442479, _1442481] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1442479), _1442481) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1442479 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1442479 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35038 ^ _782652) ^ [_1442596, _1442598] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1442596), _1442598) = c_Groups_Oone__class_Oone(tc_Int_Oint), 35043 ^ _782652 : [(35044 ^ _782652) ^ [] : [-(_1442596 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35046 ^ _782652) ^ [] : [-(_1442598 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 35047 ^ _782652 : [(35048 ^ _782652) ^ [] : [-(_1442596 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35050 ^ _782652) ^ [] : [-(_1442598 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (35052 ^ _782652) ^ [_1442780, _1442782] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1442780), _1442782) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 35053 ^ _782652 : [(35054 ^ _782652) ^ [] : [_1442780 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1442782 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (35060 ^ _782652) ^ [] : [_1442780 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1442782 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (35068 ^ _782652) ^ [_1443006] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1443006)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1443006)))], (35070 ^ _782652) ^ [_1443039] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1443039)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1443039)))], (35072 ^ _782652) ^ [_1443072] : [class_Int_Onumber__ring(_1443072), -(hAPP(c_Int_Oring__1__class_Oof__int(_1443072), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1443072), c_Int_OMin))], (35078 ^ _782652) ^ [_1443165] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1443165), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1443165))], (35080 ^ _782652) ^ [] : [-(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))], (35082 ^ _782652) ^ [_1443215, _1443217] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1443215), hAPP(c_Int_Onumber__class_Onumber__of(_1443215), c_Int_OMin)), _1443217) = hAPP(c_Groups_Ouminus__class_Ouminus(_1443215), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1443215), c_Groups_Oone__class_Oone(_1443215)), _1443217))), class_Fields_Ofield__inverse__zero(_1443215), class_Int_Onumber__ring(_1443215)], (35092 ^ _782652) ^ [_1443396, _1443398] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1443396), hAPP(hAPP(c_Power_Opower__class_Opower(_1443396), hAPP(c_Int_Onumber__class_Onumber__of(_1443396), c_Int_OMin)), _1443398)) = c_Groups_Oone__class_Oone(_1443396)), class_Int_Onumber__ring(_1443396), class_Rings_Olinordered__idom(_1443396)], (35102 ^ _782652) ^ [_1443561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1443561)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1443561) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35108 ^ _782652) ^ [_1443646, _1443648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1443646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443646), _1443648)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1443646), _1443648) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35118 ^ _782652) ^ [_1443813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1443813)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1443813) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1443813), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35124 ^ _782652) ^ [] : [-(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)))], (35126 ^ _782652) ^ [_1443930, _1443932] : [class_Int_Onumber__ring(_1443930), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1443930), hAPP(c_Int_Onumber__class_Onumber__of(_1443930), 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)))), _1443932)) = c_Groups_Oone__class_Oone(_1443930))], (35132 ^ _782652) ^ [] : [-(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)))))], (35134 ^ _782652) ^ [_1444059] : [-(c_Int_Oint__ge__less__than(_1444059) = 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), _1444059)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (35136 ^ _782652) ^ [_1444105] : [-(c_Int_Oint__ge__less__than2(_1444105) = 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), _1444105)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (35138 ^ _782652) ^ [_1444151, _1444153] : [-(c_Fun_Oinj__on(tc_fun(_1444151, _1444153), tc_fun(tc_prod(_1444151, _1444153), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1444151, _1444153), tc_HOL_Obool), tc_fun(tc_prod(_1444151, _1444153), tc_HOL_Obool), tc_fun(_1444151, _1444153)), c_Set_OCollect(tc_prod(_1444151, _1444153))), hAPP(hAPP(c_COMBB(tc_fun(_1444151, tc_fun(_1444153, tc_HOL_Obool)), tc_fun(tc_prod(_1444151, _1444153), tc_HOL_Obool), tc_fun(_1444151, _1444153)), c_Product__Type_Oprod_Oprod__case(_1444151, _1444153, tc_HOL_Obool)), hAPP(c_COMBB(_1444153, tc_fun(_1444153, tc_HOL_Obool), _1444151), hAPP(c_COMBC(_1444153, _1444153, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1444151, _1444153), tc_HOL_Obool))))], (35140 ^ _782652) ^ [_1444271, _1444273, _1444275, _1444277] : [-(c_Nitpick_Oprod(_1444271, _1444273, _1444275, _1444277) = hAPP(c_Set_OCollect(tc_prod(_1444271, _1444273)), hAPP(c_Product__Type_Oprod_Oprod__case(_1444271, _1444273, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1444271, tc_fun(_1444273, tc_HOL_Obool), tc_fun(_1444273, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1444273, tc_HOL_Obool), tc_fun(_1444273, tc_HOL_Obool)), _1444271), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1444273)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1444271), c_fconj), hAPP(hAPP(c_COMBC(_1444271, tc_fun(_1444271, tc_HOL_Obool), tc_HOL_Obool), c_member(_1444271)), _1444275)))), hAPP(hAPP(c_COMBC(_1444273, tc_fun(_1444273, tc_HOL_Obool), tc_HOL_Obool), c_member(_1444273)), _1444277)))))], (35142 ^ _782652) ^ [_1444408, _1444410] : [_1444408 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1444408, _1444410) = _1444410)], (35148 ^ _782652) ^ [_1444485, _1444487] : [-(_1444485 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1444485, _1444487) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1444485), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1444487)))], (35154 ^ _782652) ^ [_1444538, _1444540] : [-(c_Divides_Odivmod__int__rel(_1444538, _1444540) = 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, _1444538))), 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), _1444540)))))), 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)), _1444540))), 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)), _1444540))))), 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)), _1444540)))), 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), _1444540))), 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))))))))], (35156 ^ _782652) ^ [_1444649, _1444651] : [-(_1444649 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1444651, _1444649), c_Divides_Odivmod__int(_1444651, _1444649))))], (35162 ^ _782652) ^ [_1444693] : [-(c_Wellfounded_Ofinite__psubset(_1444693) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1444693, tc_HOL_Obool), tc_fun(_1444693, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1444693, tc_HOL_Obool), tc_fun(_1444693, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1444693, tc_HOL_Obool), tc_fun(tc_fun(_1444693, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1444693, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1444693, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1444693, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1444693, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1444693, tc_HOL_Obool)), c_COMBS(tc_fun(_1444693, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1444693, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1444693, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1444693, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1444693, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1444693, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1444693)))))], (35164 ^ _782652) ^ [_1444853, _1444855, _1444857, _1444859, _1444861] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1444853, _1444855), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1444857), _1444859))), -(_1444855 = 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)), _1444861)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1444853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1444855), _1444861)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1444857), _1444861)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1444855), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1444857, _1444861))), _1444859)))))], (35178 ^ _782652) ^ [] : [-(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))], (35180 ^ _782652) ^ [_1445204, _1445206, _1445208, _1445210, _1445212, _1445214] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445204, tc_fun(_1445206, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1445204, tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_fun(_1445206, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445206, tc_fun(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_fun(_1445206, tc_HOL_Obool)), _1445204), c_COMBC(_1445206, tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445206, tc_prod(_1445204, _1445206)), tc_fun(_1445206, tc_fun(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_HOL_Obool)), _1445204), hAPP(c_COMBB(tc_prod(_1445204, _1445206), tc_fun(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_HOL_Obool), _1445206), c_member(tc_prod(_1445204, _1445206)))), c_Product__Type_OPair(_1445204, _1445206)))), _1445208)), hAPP(hAPP(c_COMBC(_1445204, tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_fun(_1445206, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445206, tc_fun(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_fun(_1445206, tc_HOL_Obool)), _1445204), c_COMBC(_1445206, tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445206, tc_prod(_1445204, _1445206)), tc_fun(_1445206, tc_fun(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_HOL_Obool)), _1445204), hAPP(c_COMBB(tc_prod(_1445204, _1445206), tc_fun(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool), tc_HOL_Obool), _1445206), c_member(tc_prod(_1445204, _1445206)))), c_Product__Type_OPair(_1445204, _1445206)))), _1445210)), _1445212), _1445214)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1445204, _1445206)), hAPP(hAPP(c_Product__Type_OPair(_1445204, _1445206), _1445212), _1445214)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1445204, _1445206), tc_HOL_Obool)), _1445208), _1445210))))], (35186 ^ _782652) ^ [_1445861, _1445863, _1445865, _1445867, _1445869, _1445871] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1445861, _1445863)), hAPP(hAPP(c_Product__Type_OPair(_1445861, _1445863), _1445869), _1445871)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool)), _1445865), _1445867))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445861, tc_fun(_1445863, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1445861, tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_fun(_1445863, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445863, tc_fun(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_fun(_1445863, tc_HOL_Obool)), _1445861), c_COMBC(_1445863, tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445863, tc_prod(_1445861, _1445863)), tc_fun(_1445863, tc_fun(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_HOL_Obool)), _1445861), hAPP(c_COMBB(tc_prod(_1445861, _1445863), tc_fun(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_HOL_Obool), _1445863), c_member(tc_prod(_1445861, _1445863)))), c_Product__Type_OPair(_1445861, _1445863)))), _1445865)), hAPP(hAPP(c_COMBC(_1445861, tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_fun(_1445863, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445863, tc_fun(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_fun(_1445863, tc_HOL_Obool)), _1445861), c_COMBC(_1445863, tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445863, tc_prod(_1445861, _1445863)), tc_fun(_1445863, tc_fun(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_HOL_Obool)), _1445861), hAPP(c_COMBB(tc_prod(_1445861, _1445863), tc_fun(tc_fun(tc_prod(_1445861, _1445863), tc_HOL_Obool), tc_HOL_Obool), _1445863), c_member(tc_prod(_1445861, _1445863)))), c_Product__Type_OPair(_1445861, _1445863)))), _1445867)), _1445869), _1445871)))], (35192 ^ _782652) ^ [_1446545, _1446547, _1446549, _1446551] : [hAPP(hAPP(c_COMBC(_1446545, tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_fun(_1446547, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446547, tc_fun(tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_fun(_1446547, tc_HOL_Obool)), _1446545), c_COMBC(_1446547, tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446547, tc_prod(_1446545, _1446547)), tc_fun(_1446547, tc_fun(tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_HOL_Obool)), _1446545), hAPP(c_COMBB(tc_prod(_1446545, _1446547), tc_fun(tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_HOL_Obool), _1446547), c_member(tc_prod(_1446545, _1446547)))), c_Product__Type_OPair(_1446545, _1446547)))), _1446549) = hAPP(hAPP(c_COMBC(_1446545, tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_fun(_1446547, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446547, tc_fun(tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_fun(_1446547, tc_HOL_Obool)), _1446545), c_COMBC(_1446547, tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446547, tc_prod(_1446545, _1446547)), tc_fun(_1446547, tc_fun(tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_HOL_Obool)), _1446545), hAPP(c_COMBB(tc_prod(_1446545, _1446547), tc_fun(tc_fun(tc_prod(_1446545, _1446547), tc_HOL_Obool), tc_HOL_Obool), _1446547), c_member(tc_prod(_1446545, _1446547)))), c_Product__Type_OPair(_1446545, _1446547)))), _1446551), -(_1446549 = _1446551)], (35198 ^ _782652) ^ [_1447094, _1447096, _1447098, _1447100] : [_1447098 = _1447100, -(hAPP(hAPP(c_COMBC(_1447094, tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_fun(_1447096, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447096, tc_fun(tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_fun(_1447096, tc_HOL_Obool)), _1447094), c_COMBC(_1447096, tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447096, tc_prod(_1447094, _1447096)), tc_fun(_1447096, tc_fun(tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_HOL_Obool)), _1447094), hAPP(c_COMBB(tc_prod(_1447094, _1447096), tc_fun(tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_HOL_Obool), _1447096), c_member(tc_prod(_1447094, _1447096)))), c_Product__Type_OPair(_1447094, _1447096)))), _1447098) = hAPP(hAPP(c_COMBC(_1447094, tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_fun(_1447096, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447096, tc_fun(tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_fun(_1447096, tc_HOL_Obool)), _1447094), c_COMBC(_1447096, tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447096, tc_prod(_1447094, _1447096)), tc_fun(_1447096, tc_fun(tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_HOL_Obool)), _1447094), hAPP(c_COMBB(tc_prod(_1447094, _1447096), tc_fun(tc_fun(tc_prod(_1447094, _1447096), tc_HOL_Obool), tc_HOL_Obool), _1447096), c_member(tc_prod(_1447094, _1447096)))), c_Product__Type_OPair(_1447094, _1447096)))), _1447100))], (35204 ^ _782652) ^ [_1447670, _1447672, _1447674, _1447676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447670, tc_fun(_1447672, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1447670, tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_fun(_1447672, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447672, tc_fun(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_fun(_1447672, tc_HOL_Obool)), _1447670), c_COMBC(_1447672, tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447672, tc_prod(_1447670, _1447672)), tc_fun(_1447672, tc_fun(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_HOL_Obool)), _1447670), hAPP(c_COMBB(tc_prod(_1447670, _1447672), tc_fun(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_HOL_Obool), _1447672), c_member(tc_prod(_1447670, _1447672)))), c_Product__Type_OPair(_1447670, _1447672)))), _1447674)), hAPP(hAPP(c_COMBC(_1447670, tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_fun(_1447672, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447672, tc_fun(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_fun(_1447672, tc_HOL_Obool)), _1447670), c_COMBC(_1447672, tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447672, tc_prod(_1447670, _1447672)), tc_fun(_1447672, tc_fun(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_HOL_Obool)), _1447670), hAPP(c_COMBB(tc_prod(_1447670, _1447672), tc_fun(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool), tc_HOL_Obool), _1447672), c_member(tc_prod(_1447670, _1447672)))), c_Product__Type_OPair(_1447670, _1447672)))), _1447676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1447670, _1447672), tc_HOL_Obool)), _1447674), _1447676)))], (35210 ^ _782652) ^ [_1448271, _1448273, _1448275, _1448277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool)), _1448275), _1448277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1448271, tc_fun(_1448273, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1448271, tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_fun(_1448273, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1448273, tc_fun(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_fun(_1448273, tc_HOL_Obool)), _1448271), c_COMBC(_1448273, tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1448273, tc_prod(_1448271, _1448273)), tc_fun(_1448273, tc_fun(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_HOL_Obool)), _1448271), hAPP(c_COMBB(tc_prod(_1448271, _1448273), tc_fun(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_HOL_Obool), _1448273), c_member(tc_prod(_1448271, _1448273)))), c_Product__Type_OPair(_1448271, _1448273)))), _1448275)), hAPP(hAPP(c_COMBC(_1448271, tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_fun(_1448273, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1448273, tc_fun(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_fun(_1448273, tc_HOL_Obool)), _1448271), c_COMBC(_1448273, tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1448273, tc_prod(_1448271, _1448273)), tc_fun(_1448273, tc_fun(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_HOL_Obool)), _1448271), hAPP(c_COMBB(tc_prod(_1448271, _1448273), tc_fun(tc_fun(tc_prod(_1448271, _1448273), tc_HOL_Obool), tc_HOL_Obool), _1448273), c_member(tc_prod(_1448271, _1448273)))), c_Product__Type_OPair(_1448271, _1448273)))), _1448277))))], (35216 ^ _782652) ^ [_1448878, _1448880, _1448882, _1448884, _1448886, _1448888] : [c_Equiv__Relations_Ocongruent(_1448878, _1448880, _1448882, _1448884), hBOOL(hAPP(hAPP(c_member(tc_prod(_1448878, _1448878)), hAPP(hAPP(c_Product__Type_OPair(_1448878, _1448878), _1448886), _1448888)), _1448882)), -(hAPP(_1448884, _1448886) = hAPP(_1448884, _1448888))], (35226 ^ _782652) ^ [_1449077, _1449079, _1449081, _1449083, _1449085, _1449087, _1449089, _1449091, _1449093, _1449095] : [c_Equiv__Relations_Ocongruent2(_1449077, _1449079, _1449081, _1449083, _1449085, _1449087), hBOOL(hAPP(hAPP(c_member(tc_prod(_1449077, _1449077)), hAPP(hAPP(c_Product__Type_OPair(_1449077, _1449077), _1449089), _1449091)), _1449083)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1449079, _1449079)), hAPP(hAPP(c_Product__Type_OPair(_1449079, _1449079), _1449093), _1449095)), _1449085)), -(hAPP(hAPP(_1449087, _1449089), _1449093) = hAPP(hAPP(_1449087, _1449091), _1449095))], (35240 ^ _782652) ^ [_1449441, _1449443, _1449445, _1449447, _1449449, _1449451] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1449441, tc_fun(_1449443, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1449441, tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_fun(_1449443, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449443, tc_fun(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_fun(_1449443, tc_HOL_Obool)), _1449441), c_COMBC(_1449443, tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449443, tc_prod(_1449441, _1449443)), tc_fun(_1449443, tc_fun(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_HOL_Obool)), _1449441), hAPP(c_COMBB(tc_prod(_1449441, _1449443), tc_fun(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_HOL_Obool), _1449443), c_member(tc_prod(_1449441, _1449443)))), c_Product__Type_OPair(_1449441, _1449443)))), _1449445)), hAPP(hAPP(c_COMBC(_1449441, tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_fun(_1449443, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449443, tc_fun(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_fun(_1449443, tc_HOL_Obool)), _1449441), c_COMBC(_1449443, tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449443, tc_prod(_1449441, _1449443)), tc_fun(_1449443, tc_fun(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_HOL_Obool)), _1449441), hAPP(c_COMBB(tc_prod(_1449441, _1449443), tc_fun(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool), tc_HOL_Obool), _1449443), c_member(tc_prod(_1449441, _1449443)))), c_Product__Type_OPair(_1449441, _1449443)))), _1449447)), _1449449), _1449451)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1449441, _1449443)), hAPP(hAPP(c_Product__Type_OPair(_1449441, _1449443), _1449449), _1449451)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1449441, _1449443), tc_HOL_Obool)), _1449445), _1449447))))], (35246 ^ _782652) ^ [_1450098, _1450100, _1450102, _1450104, _1450106, _1450108] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450098, _1450100)), hAPP(hAPP(c_Product__Type_OPair(_1450098, _1450100), _1450106), _1450108)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool)), _1450102), _1450104))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1450098, tc_fun(_1450100, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1450098, tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_fun(_1450100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450100, tc_fun(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_fun(_1450100, tc_HOL_Obool)), _1450098), c_COMBC(_1450100, tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450100, tc_prod(_1450098, _1450100)), tc_fun(_1450100, tc_fun(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_HOL_Obool)), _1450098), hAPP(c_COMBB(tc_prod(_1450098, _1450100), tc_fun(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_HOL_Obool), _1450100), c_member(tc_prod(_1450098, _1450100)))), c_Product__Type_OPair(_1450098, _1450100)))), _1450102)), hAPP(hAPP(c_COMBC(_1450098, tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_fun(_1450100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450100, tc_fun(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_fun(_1450100, tc_HOL_Obool)), _1450098), c_COMBC(_1450100, tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450100, tc_prod(_1450098, _1450100)), tc_fun(_1450100, tc_fun(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_HOL_Obool)), _1450098), hAPP(c_COMBB(tc_prod(_1450098, _1450100), tc_fun(tc_fun(tc_prod(_1450098, _1450100), tc_HOL_Obool), tc_HOL_Obool), _1450100), c_member(tc_prod(_1450098, _1450100)))), c_Product__Type_OPair(_1450098, _1450100)))), _1450104)), _1450106), _1450108)))], (35252 ^ _782652) ^ [_1450782, _1450784, _1450786, _1450788] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1450782, tc_fun(_1450784, tc_HOL_Obool))), _1450786), _1450788)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450782, _1450784)), hAPP(hAPP(c_Product__Type_OPair(_1450782, _1450784), _1450786), _1450788)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1450782, _1450784), tc_HOL_Obool)))))], (35258 ^ _782652) ^ [_1450939, _1450941, _1450943, _1450945] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450939, _1450941)), hAPP(hAPP(c_Product__Type_OPair(_1450939, _1450941), _1450943), _1450945)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1450939, _1450941), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1450939, tc_fun(_1450941, tc_HOL_Obool))), _1450943), _1450945)))], (35264 ^ _782652) ^ [_1451102, _1451104, _1451106, _1451108, _1451110, _1451112] : [hBOOL(hAPP(hAPP(c_member(_1451102), _1451104), _1451106)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1451102, _1451108)), hAPP(hAPP(c_Product__Type_OPair(_1451102, _1451108), _1451104), _1451110)), _1451112)), -(hBOOL(hAPP(hAPP(c_member(_1451108), _1451110), hAPP(c_Relation_OImage(_1451102, _1451108, _1451112), _1451106))))], (35274 ^ _782652) ^ [_1451351, _1451353, _1451355, _1451357, _1451359] : [hBOOL(hAPP(hAPP(c_member(_1451351), _1451353), hAPP(c_Relation_OImage(_1451355, _1451351, _1451357), _1451359))), 35278 ^ _782652 : [(35279 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451355), 35277 ^ [_1451351, _1451353, _1451355, _1451357, _1451359]), _1451359)))], (35281 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451355, _1451351)), hAPP(hAPP(c_Product__Type_OPair(_1451355, _1451351), 35277 ^ [_1451351, _1451353, _1451355, _1451357, _1451359]), _1451353)), _1451357)))]]], (35283 ^ _782652) ^ [_1451567, _1451569, _1451571, _1451573, _1451575] : [-(hBOOL(hAPP(hAPP(c_member(_1451567), _1451569), hAPP(c_Relation_OImage(_1451571, _1451567, _1451573), _1451575)))), 35284 ^ _782652 : [(35285 ^ _782652) ^ [_1451653] : [hBOOL(hAPP(hAPP(c_member(_1451571), _1451653), _1451575)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1451571, _1451567)), hAPP(hAPP(c_Product__Type_OPair(_1451571, _1451567), _1451653), _1451569)), _1451573))]]], (35293 ^ _782652) ^ [_1451829] : [-(_1451829 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1451829), 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)))))], (35299 ^ _782652) ^ [_1451868, _1451870, _1451872] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451868, _1451868), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451870), _1451872))), -(_1451868 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1451872 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35309 ^ _782652) ^ [_1451984, _1451986, _1451988, _1451990, _1451992, _1451994] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451984, _1451986), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451988), _1451990))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451984, _1451986), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451992), _1451994))), -(_1451986 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1451988 = _1451992)], (35323 ^ _782652) ^ [_1452188, _1452190, _1452192, _1452194, _1452196, _1452198] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452188, _1452190), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452192), _1452194))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452188, _1452190), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452196), _1452198))), -(_1452190 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1452194 = _1452198)], (35337 ^ _782652) ^ [_1452419, _1452421, _1452423, _1452425, _1452427, _1452429] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1452419, tc_fun(_1452421, tc_fun(_1452423, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1452419, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1452421, _1452423), tc_HOL_Obool), tc_fun(_1452421, tc_fun(_1452423, tc_HOL_Obool)), _1452419), hAPP(c_COMBC(_1452421, tc_fun(tc_prod(_1452421, _1452423), tc_HOL_Obool), tc_fun(_1452423, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452423, tc_fun(tc_fun(tc_prod(_1452421, _1452423), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452421, _1452423), tc_HOL_Obool), tc_fun(_1452423, tc_HOL_Obool)), _1452421), c_COMBC(_1452423, tc_fun(tc_prod(_1452421, _1452423), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452423, tc_prod(_1452421, _1452423)), tc_fun(_1452423, tc_fun(tc_fun(tc_prod(_1452421, _1452423), tc_HOL_Obool), tc_HOL_Obool)), _1452421), hAPP(c_COMBB(tc_prod(_1452421, _1452423), tc_fun(tc_fun(tc_prod(_1452421, _1452423), tc_HOL_Obool), tc_HOL_Obool), _1452423), c_member(tc_prod(_1452421, _1452423)))), c_Product__Type_OPair(_1452421, _1452423))))), _1452425)), _1452427), _1452429)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452421, _1452423)), hAPP(hAPP(c_Product__Type_OPair(_1452421, _1452423), _1452427), _1452429)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1452419, tc_fun(tc_prod(_1452421, _1452423), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1452419, tc_HOL_Obool))), _1452425))))], (35343 ^ _782652) ^ [_1452902, _1452904, _1452906, _1452908, _1452910, _1452912] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1452904, _1452906)), hAPP(hAPP(c_Product__Type_OPair(_1452904, _1452906), _1452910), _1452912)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1452902, tc_fun(tc_prod(_1452904, _1452906), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1452902, tc_HOL_Obool))), _1452908))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1452902, tc_fun(_1452904, tc_fun(_1452906, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1452902, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1452904, _1452906), tc_HOL_Obool), tc_fun(_1452904, tc_fun(_1452906, tc_HOL_Obool)), _1452902), hAPP(c_COMBC(_1452904, tc_fun(tc_prod(_1452904, _1452906), tc_HOL_Obool), tc_fun(_1452906, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452906, tc_fun(tc_fun(tc_prod(_1452904, _1452906), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452904, _1452906), tc_HOL_Obool), tc_fun(_1452906, tc_HOL_Obool)), _1452904), c_COMBC(_1452906, tc_fun(tc_prod(_1452904, _1452906), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452906, tc_prod(_1452904, _1452906)), tc_fun(_1452906, tc_fun(tc_fun(tc_prod(_1452904, _1452906), tc_HOL_Obool), tc_HOL_Obool)), _1452904), hAPP(c_COMBB(tc_prod(_1452904, _1452906), tc_fun(tc_fun(tc_prod(_1452904, _1452906), tc_HOL_Obool), tc_HOL_Obool), _1452906), c_member(tc_prod(_1452904, _1452906)))), c_Product__Type_OPair(_1452904, _1452906))))), _1452908)), _1452910), _1452912)))], (35349 ^ _782652) ^ [_1453391, _1453393, _1453395] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1453391, _1453391), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1453393), _1453395))), -(_1453391 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1453393 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35359 ^ _782652) ^ [_1453507, _1453509, _1453511, _1453513] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1453507, _1453509), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1453511), _1453513))), -(_1453509 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1453507, _1453509) = _1453513)], (35369 ^ _782652) ^ [_1453633, _1453635, _1453637, _1453639] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1453633, _1453635), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1453637), _1453639))), -(_1453635 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1453633), _1453635) = _1453637)], (35379 ^ _782652) ^ [_1453763, _1453765] : [-(c_Divides_Odivmod__int(_1453763, _1453765) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1453763), _1453765)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1453763, _1453765)))], (35381 ^ _782652) ^ [_1453831, _1453833, _1453835, _1453837, _1453839] : [hBOOL(hAPP(hAPP(c_member(_1453831), _1453833), hAPP(c_Relation_OImage(_1453835, _1453831, _1453837), hAPP(hAPP(c_Set_Oinsert(_1453835), _1453839), c_Orderings_Obot__class_Obot(tc_fun(_1453835, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1453835, _1453831)), hAPP(hAPP(c_Product__Type_OPair(_1453835, _1453831), _1453839), _1453833)), _1453837)))], (35387 ^ _782652) ^ [_1454002, _1454004, _1454006, _1454008, _1454010] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1454006, _1454002)), hAPP(hAPP(c_Product__Type_OPair(_1454006, _1454002), _1454010), _1454004)), _1454008)), -(hBOOL(hAPP(hAPP(c_member(_1454002), _1454004), hAPP(c_Relation_OImage(_1454006, _1454002, _1454008), hAPP(hAPP(c_Set_Oinsert(_1454006), _1454010), c_Orderings_Obot__class_Obot(tc_fun(_1454006, tc_HOL_Obool)))))))], (35393 ^ _782652) ^ [_1454179, _1454181, _1454183, _1454185, _1454187] : [c_Equiv__Relations_Oequiv(_1454179, _1454181, _1454183), hBOOL(hAPP(hAPP(c_member(tc_prod(_1454179, _1454179)), hAPP(hAPP(c_Product__Type_OPair(_1454179, _1454179), _1454185), _1454187)), _1454183)), -(hAPP(c_Relation_OImage(_1454179, _1454179, _1454183), hAPP(hAPP(c_Set_Oinsert(_1454179), _1454185), c_Orderings_Obot__class_Obot(tc_fun(_1454179, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1454179, _1454179, _1454183), hAPP(hAPP(c_Set_Oinsert(_1454179), _1454187), c_Orderings_Obot__class_Obot(tc_fun(_1454179, tc_HOL_Obool)))))], (35403 ^ _782652) ^ [_1454440, _1454442, _1454444, _1454446, _1454448, _1454450, _1454452] : [c_Equiv__Relations_Oequiv(_1454440, _1454442, _1454444), hBOOL(hAPP(hAPP(c_member(tc_fun(_1454440, tc_HOL_Obool)), _1454446), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1454440), _1454442), _1454444))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1454440, tc_HOL_Obool)), _1454448), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1454440), _1454442), _1454444))), hBOOL(hAPP(hAPP(c_member(_1454440), _1454450), _1454446)), hBOOL(hAPP(hAPP(c_member(_1454440), _1454452), _1454448)), 35422 ^ _782652 : [(35423 ^ _782652) ^ [] : [_1454446 = _1454448, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1454440, _1454440)), hAPP(hAPP(c_Product__Type_OPair(_1454440, _1454440), _1454450), _1454452)), _1454444)))], (35429 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1454440, _1454440)), hAPP(hAPP(c_Product__Type_OPair(_1454440, _1454440), _1454450), _1454452)), _1454444)), -(_1454446 = _1454448)]]], (35435 ^ _782652) ^ [_1455084, _1455086, _1455088, _1455090, _1455092, _1455094, _1455096] : [c_Equiv__Relations_Oequiv(_1455084, _1455086, _1455088), hBOOL(hAPP(hAPP(c_member(tc_fun(_1455084, tc_HOL_Obool)), _1455090), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1455084), _1455086), _1455088))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1455084, tc_HOL_Obool)), _1455092), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1455084), _1455086), _1455088))), hBOOL(hAPP(hAPP(c_member(_1455084), _1455094), _1455090)), hBOOL(hAPP(hAPP(c_member(_1455084), _1455096), _1455092)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1455084, _1455084)), hAPP(hAPP(c_Product__Type_OPair(_1455084, _1455084), _1455094), _1455096)), _1455088)), -(_1455090 = _1455092)], (35461 ^ _782652) ^ [_1455617, _1455619] : [-(_1455617 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1455619, _1455617), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1455619), _1455617)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1455619, _1455617)))))], (35467 ^ _782652) ^ [_1455674, _1455676, _1455678, _1455680] : [-(hAPP(c_Relation_OImage(_1455674, _1455676, _1455678), hAPP(hAPP(c_Set_Oinsert(_1455674), _1455680), c_Orderings_Obot__class_Obot(tc_fun(_1455674, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1455676), hAPP(hAPP(c_COMBC(_1455676, tc_fun(tc_prod(_1455674, _1455676), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1455674, _1455676), tc_fun(tc_fun(tc_prod(_1455674, _1455676), tc_HOL_Obool), tc_HOL_Obool), _1455676), c_member(tc_prod(_1455674, _1455676))), hAPP(c_Product__Type_OPair(_1455674, _1455676), _1455680))), _1455678)))], (35469 ^ _782652) ^ [_1455777, _1455779, _1455781, _1455783, _1455785] : [hAPP(c_Relation_OImage(_1455777, _1455777, _1455779), hAPP(hAPP(c_Set_Oinsert(_1455777), _1455781), c_Orderings_Obot__class_Obot(tc_fun(_1455777, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1455777, _1455777, _1455779), hAPP(hAPP(c_Set_Oinsert(_1455777), _1455783), c_Orderings_Obot__class_Obot(tc_fun(_1455777, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1455777, _1455785, _1455779), hBOOL(hAPP(hAPP(c_member(_1455777), _1455783), _1455785)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1455777, _1455777)), hAPP(hAPP(c_Product__Type_OPair(_1455777, _1455777), _1455781), _1455783)), _1455779)))], (35483 ^ _782652) ^ [_1456110, _1456112, _1456114, _1456116, _1456118] : [c_Equiv__Relations_Oequiv(_1456110, _1456112, _1456114), hBOOL(hAPP(hAPP(c_member(_1456110), _1456116), _1456112)), hBOOL(hAPP(hAPP(c_member(_1456110), _1456118), _1456112)), 35494 ^ _782652 : [(35495 ^ _782652) ^ [] : [hAPP(c_Relation_OImage(_1456110, _1456110, _1456114), hAPP(hAPP(c_Set_Oinsert(_1456110), _1456116), c_Orderings_Obot__class_Obot(tc_fun(_1456110, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1456110, _1456110, _1456114), hAPP(hAPP(c_Set_Oinsert(_1456110), _1456118), c_Orderings_Obot__class_Obot(tc_fun(_1456110, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1456110, _1456110)), hAPP(hAPP(c_Product__Type_OPair(_1456110, _1456110), _1456116), _1456118)), _1456114)))], (35501 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1456110, _1456110)), hAPP(hAPP(c_Product__Type_OPair(_1456110, _1456110), _1456116), _1456118)), _1456114)), -(hAPP(c_Relation_OImage(_1456110, _1456110, _1456114), hAPP(hAPP(c_Set_Oinsert(_1456110), _1456116), c_Orderings_Obot__class_Obot(tc_fun(_1456110, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1456110, _1456110, _1456114), hAPP(hAPP(c_Set_Oinsert(_1456110), _1456118), c_Orderings_Obot__class_Obot(tc_fun(_1456110, tc_HOL_Obool)))))]]], (35507 ^ _782652) ^ [_1456658, _1456660, _1456662, _1456664, _1456666] : [c_Equiv__Relations_Oequiv(_1456658, _1456660, _1456662), 35510 ^ _782652 : [(35511 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1456658, _1456658)), hAPP(hAPP(c_Product__Type_OPair(_1456658, _1456658), _1456664), _1456666)), _1456662)), 35514 ^ _782652 : [(35515 ^ _782652) ^ [] : [-(hAPP(c_Relation_OImage(_1456658, _1456658, _1456662), hAPP(hAPP(c_Set_Oinsert(_1456658), _1456664), c_Orderings_Obot__class_Obot(tc_fun(_1456658, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1456658, _1456658, _1456662), hAPP(hAPP(c_Set_Oinsert(_1456658), _1456666), c_Orderings_Obot__class_Obot(tc_fun(_1456658, tc_HOL_Obool)))))], (35517 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456658), _1456664), _1456660)))], (35519 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456658), _1456666), _1456660)))]]], (35521 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1456658, _1456658)), hAPP(hAPP(c_Product__Type_OPair(_1456658, _1456658), _1456664), _1456666)), _1456662))), hAPP(c_Relation_OImage(_1456658, _1456658, _1456662), hAPP(hAPP(c_Set_Oinsert(_1456658), _1456664), c_Orderings_Obot__class_Obot(tc_fun(_1456658, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1456658, _1456658, _1456662), hAPP(hAPP(c_Set_Oinsert(_1456658), _1456666), c_Orderings_Obot__class_Obot(tc_fun(_1456658, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1456658), _1456664), _1456660)), hBOOL(hAPP(hAPP(c_member(_1456658), _1456666), _1456660))]]], (35535 ^ _782652) ^ [_1457258, _1457260, _1457262, _1457264, _1457266] : [c_Equiv__Relations_Oequiv(_1457258, _1457260, _1457262), hBOOL(hAPP(hAPP(c_member(tc_prod(_1457258, _1457258)), hAPP(hAPP(c_Product__Type_OPair(_1457258, _1457258), _1457264), _1457266)), _1457262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1457258, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1457258, _1457258, _1457262), hAPP(hAPP(c_Set_Oinsert(_1457258), _1457264), c_Orderings_Obot__class_Obot(tc_fun(_1457258, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1457258, _1457258, _1457262), hAPP(hAPP(c_Set_Oinsert(_1457258), _1457266), c_Orderings_Obot__class_Obot(tc_fun(_1457258, tc_HOL_Obool)))))))], (35545 ^ _782652) ^ [_1457539, _1457541, _1457543, _1457545, _1457547] : [c_Equiv__Relations_Oequiv(_1457539, _1457541, _1457543), hBOOL(hAPP(hAPP(c_member(_1457539), _1457545), _1457541)), hBOOL(hAPP(hAPP(c_member(_1457539), _1457547), _1457541)), 35556 ^ _782652 : [(35557 ^ _782652) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457539), hAPP(hAPP(c_Set_Oinsert(_1457539), _1457545), c_Orderings_Obot__class_Obot(tc_fun(_1457539, tc_HOL_Obool)))), _1457543) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457539), hAPP(hAPP(c_Set_Oinsert(_1457539), _1457547), c_Orderings_Obot__class_Obot(tc_fun(_1457539, tc_HOL_Obool)))), _1457543), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457539, _1457539)), hAPP(hAPP(c_Product__Type_OPair(_1457539, _1457539), _1457545), _1457547)), _1457543)))], (35563 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1457539, _1457539)), hAPP(hAPP(c_Product__Type_OPair(_1457539, _1457539), _1457545), _1457547)), _1457543)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457539), hAPP(hAPP(c_Set_Oinsert(_1457539), _1457545), c_Orderings_Obot__class_Obot(tc_fun(_1457539, tc_HOL_Obool)))), _1457543) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457539), hAPP(hAPP(c_Set_Oinsert(_1457539), _1457547), c_Orderings_Obot__class_Obot(tc_fun(_1457539, tc_HOL_Obool)))), _1457543))]]], (35569 ^ _782652) ^ [_1458093, _1458095, _1458097, _1458099, _1458101, _1458103, _1458105] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1458093, _1458095), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1458097), _1458099))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1458101, _1458095), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1458103), _1458105))), -(_1458095 = 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), _1458093), _1458101), _1458095), 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), _1458097), _1458103)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1458099), _1458105)), _1458095))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1458099), _1458105), _1458095)))))], (35583 ^ _782652) ^ [_1458403, _1458405, _1458407, _1458409] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1458403, _1458405), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1458407), _1458409))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1458403), _1458405), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1458409), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1458407)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1458407)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1458409), 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), _1458405), _1458409))))))], (35589 ^ _782652) ^ [_1458630, _1458632, _1458634, _1458636, _1458638] : [c_Equiv__Relations_Oequiv(_1458630, _1458632, _1458634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458630, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1458630, _1458630, _1458634), hAPP(hAPP(c_Set_Oinsert(_1458630), _1458636), c_Orderings_Obot__class_Obot(tc_fun(_1458630, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1458630, _1458630, _1458634), hAPP(hAPP(c_Set_Oinsert(_1458630), _1458638), c_Orderings_Obot__class_Obot(tc_fun(_1458630, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1458630), _1458636), _1458632)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1458630, _1458630)), hAPP(hAPP(c_Product__Type_OPair(_1458630, _1458630), _1458638), _1458636)), _1458634)))], (35603 ^ _782652) ^ [_1458983, _1458985, _1458987, _1458989, _1458991, _1458993] : [c_Equiv__Relations_Oequiv(_1458983, _1458985, _1458987), hBOOL(hAPP(hAPP(c_member(_1458983), _1458989), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458983, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1458983, _1458983, _1458987), hAPP(hAPP(c_Set_Oinsert(_1458983), _1458991), c_Orderings_Obot__class_Obot(tc_fun(_1458983, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1458983, _1458983, _1458987), hAPP(hAPP(c_Set_Oinsert(_1458983), _1458993), c_Orderings_Obot__class_Obot(tc_fun(_1458983, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1458983, _1458983)), hAPP(hAPP(c_Product__Type_OPair(_1458983, _1458983), _1458991), _1458993)), _1458987)))], (35613 ^ _782652) ^ [_1459284, _1459286, _1459288, _1459290] : [_1459284 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1459286), _1459288)), _1459290), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1459284, _1459286), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1459288), _1459290)))), 35620 ^ _782652 : [(35621 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1459286)))], (35623 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1459290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1459290), _1459286))]], 35628 ^ _782652 : [(35629 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1459286))], (35631 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1459286), _1459290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1459290), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (35639 ^ _782652) ^ [_1459746, _1459748, _1459750, _1459752, _1459754] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1459746, _1459748), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1459750), _1459752))), -(_1459748 = 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), _1459754), _1459746), _1459748), 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), _1459754), _1459750)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1459754), _1459752)), _1459748))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1459754), _1459752), _1459748)))))], (35649 ^ _782652) ^ [_1459968, _1459970, _1459972, _1459974, _1459976, _1459978, _1459980] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1459968, _1459970)), hAPP(hAPP(c_Product__Type_OPair(_1459968, _1459970), _1459972), _1459974)), _1459976)), -(hBOOL(hAPP(hAPP(c_member(_1459978), hAPP(hAPP(_1459980, _1459972), _1459974)), hAPP(c_Set_Oimage(tc_prod(_1459968, _1459970), _1459978, hAPP(c_Product__Type_Oprod_Oprod__case(_1459968, _1459970, _1459978), _1459980)), _1459976))))], (35655 ^ _782652) ^ [_1460162, _1460164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1460162), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1460164, _1460162) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1460164), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1460162)))], (35661 ^ _782652) ^ [_1460268, _1460270] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1460268), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 35664 ^ _782652 : [(35665 ^ _782652) ^ [] : [35666 ^ _782652 : [(35667 ^ _782652) ^ [] : [_1460270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (35669 ^ _782652) ^ [] : [_1460268 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1460270, _1460268) = 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)))], (35673 ^ _782652) ^ [] : [-(c_Nitpick_Onorm__frac(_1460270, _1460268) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1460270), _1460268)), 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), _1460270))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1460268)))), -(_1460270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1460268 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (35683 ^ _782652) ^ [_1460566, _1460568, _1460570] : [-(hAPP(c_Divides_Oadjust(_1460566), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1460568), _1460570)) = 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), _1460570), _1460566)), 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)))), _1460568)), 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)))), _1460568)), _1460570))))], (35685 ^ _782652) ^ [_1460646, _1460648, _1460650, _1460652, _1460654, _1460656] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460646, tc_fun(_1460648, tc_HOL_Obool))), _1460650), _1460652), _1460654), _1460656)), -(hBOOL(hAPP(hAPP(_1460650, _1460654), _1460656))), -(hBOOL(hAPP(hAPP(_1460652, _1460654), _1460656)))], (35695 ^ _782652) ^ [_1460804, _1460806, _1460808, _1460810, _1460812, _1460814] : [35696 ^ _782652 : [(35697 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1460804, _1460806), _1460808))], (35699 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1460810, _1460806), _1460808))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460812, tc_fun(_1460814, tc_HOL_Obool))), _1460810), _1460804), _1460806), _1460808)))], (35703 ^ _782652) ^ [_1460987, _1460989, _1460991, _1460993, _1460995, _1460997] : [hBOOL(hAPP(hAPP(_1460987, _1460989), _1460991)), hBOOL(hAPP(hAPP(_1460993, _1460989), _1460991)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460995, tc_fun(_1460997, tc_HOL_Obool))), _1460987), _1460993), _1460989), _1460991)))], (35713 ^ _782652) ^ [_1461190, _1461192, _1461194, _1461196, _1461198, _1461200] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461190, tc_fun(_1461192, tc_HOL_Obool))), _1461194), _1461196), _1461198), _1461200)), 35716 ^ _782652 : [(35717 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1461194, _1461198), _1461200)))], (35719 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1461196, _1461198), _1461200)))]]], (35721 ^ _782652) ^ [_1461363, _1461365, _1461367, _1461369, _1461371, _1461373, _1461375] : [hBOOL(hAPP(hAPP(c_member(_1461363), _1461365), hAPP(hAPP(_1461367, _1461369), _1461371))), -(hBOOL(hAPP(hAPP(c_member(_1461363), _1461365), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1461373, _1461375, tc_fun(_1461363, tc_HOL_Obool)), _1461367), hAPP(hAPP(c_Product__Type_OPair(_1461373, _1461375), _1461369), _1461371)))))], (35727 ^ _782652) ^ [_1461534, _1461536, _1461538, _1461540, _1461542] : [hBOOL(hAPP(hAPP(_1461534, _1461536), _1461538)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1461540, _1461542, tc_HOL_Obool), _1461534), hAPP(hAPP(c_Product__Type_OPair(_1461540, _1461542), _1461536), _1461538))))], (35733 ^ _782652) ^ [_1461663, _1461665, _1461667, _1461669, _1461671] : [hBOOL(hAPP(hAPP(_1461663, _1461665), _1461667)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1461669, _1461671, tc_HOL_Obool), _1461663), hAPP(hAPP(c_Product__Type_OPair(_1461669, _1461671), _1461665), _1461667))))], (35739 ^ _782652) ^ [_1461810, _1461812, _1461814, _1461816] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1461810, tc_fun(_1461812, tc_HOL_Obool))), _1461814), _1461816))], (35741 ^ _782652) ^ [_1461852, _1461854, _1461856, _1461858, _1461860, _1461862, _1461864] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1461852, _1461854, tc_fun(_1461856, tc_HOL_Obool)), _1461858), hAPP(hAPP(c_Product__Type_OPair(_1461852, _1461854), _1461860), _1461862)), _1461864)), -(hBOOL(hAPP(hAPP(hAPP(_1461858, _1461860), _1461862), _1461864)))], (35747 ^ _782652) ^ [_1462003, _1462005, _1462007] : [-(c_Fun_Oinj__on(tc_prod(_1462003, _1462005), tc_prod(_1462005, _1462003), hAPP(c_Product__Type_Oprod_Oprod__case(_1462003, _1462005, tc_prod(_1462005, _1462003)), hAPP(c_COMBC(_1462005, _1462003, tc_prod(_1462005, _1462003)), c_Product__Type_OPair(_1462005, _1462003))), _1462007))], (35749 ^ _782652) ^ [_1462061, _1462063, _1462065, _1462067, _1462069, _1462071] : [hBOOL(hAPP(hAPP(_1462061, _1462063), _1462065)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462067, tc_fun(_1462069, tc_HOL_Obool))), _1462061), _1462071), _1462063), _1462065)))], (35755 ^ _782652) ^ [_1462194, _1462196, _1462198, _1462200, _1462202, _1462204] : [hBOOL(hAPP(hAPP(_1462194, _1462196), _1462198)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462200, tc_fun(_1462202, tc_HOL_Obool))), _1462204), _1462194), _1462196), _1462198)))], (35761 ^ _782652) ^ [_1462327, _1462329, _1462331, _1462333, _1462335, _1462337] : [hBOOL(hAPP(hAPP(_1462327, _1462329), _1462331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462333, tc_fun(_1462335, tc_HOL_Obool))), _1462327), _1462337)), -(hBOOL(hAPP(hAPP(_1462337, _1462329), _1462331)))], (35771 ^ _782652) ^ [_1462518, _1462520, _1462522, _1462524, _1462526, _1462528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462518, tc_fun(_1462520, tc_HOL_Obool))), _1462522), _1462524)), hBOOL(hAPP(hAPP(_1462522, _1462526), _1462528)), -(hBOOL(hAPP(hAPP(_1462524, _1462526), _1462528)))], (35781 ^ _782652) ^ [_1462709, _1462711, _1462713, _1462715, _1462717, _1462719] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462709, tc_fun(_1462711, tc_HOL_Obool))), _1462713), _1462715), _1462717), _1462719)), -(hBOOL(hAPP(hAPP(_1462713, _1462717), _1462719)))], (35787 ^ _782652) ^ [_1462842, _1462844, _1462846, _1462848, _1462850, _1462852] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462842, tc_fun(_1462844, tc_HOL_Obool))), _1462846), _1462848), _1462850), _1462852)), -(hBOOL(hAPP(hAPP(_1462848, _1462850), _1462852)))], (35793 ^ _782652) ^ [_1462993, _1462995, _1462997] : [hBOOL(hAPP(_1462993, 35794 ^ [_1462993, _1462995, _1462997])), 35797 ^ _782652 : [(35798 ^ _782652) ^ [_1463104, _1463106] : [-(hBOOL(hAPP(_1462993, hAPP(hAPP(c_Product__Type_OPair(_1462995, _1462997), _1463106), _1463104))))]]], (35800 ^ _782652) ^ [_1463140, _1463142, _1463144] : [hBOOL(hAPP(_1463140, hAPP(hAPP(c_Product__Type_OPair(_1463142, _1463144), 35801 ^ [_1463140, _1463142, _1463144]), 35802 ^ [_1463140, _1463142, _1463144]))), 35805 ^ _782652 : [(35806 ^ _782652) ^ [_1463287] : [-(hBOOL(hAPP(_1463140, _1463287)))]]], (35808 ^ _782652) ^ [_1463345, _1463347, _1463349, _1463351, _1463353, _1463355] : [hAPP(hAPP(c_Product__Type_OPair(_1463345, _1463347), _1463349), _1463351) = hAPP(hAPP(c_Product__Type_OPair(_1463345, _1463347), _1463353), _1463355), 35811 ^ _782652 : [(35812 ^ _782652) ^ [] : [-(_1463349 = _1463353)], (35814 ^ _782652) ^ [] : [-(_1463351 = _1463355)]]], (35816 ^ _782652) ^ [_1463488, _1463490, _1463492, _1463494, _1463496, _1463498] : [-(hAPP(hAPP(c_Product__Type_OPair(_1463488, _1463490), _1463492), _1463494) = hAPP(hAPP(c_Product__Type_OPair(_1463488, _1463490), _1463496), _1463498)), _1463492 = _1463496, _1463494 = _1463498], (35826 ^ _782652) ^ [_1463671, _1463673, _1463675, _1463677, _1463679, _1463681] : [hAPP(hAPP(c_Product__Type_OPair(_1463671, _1463673), _1463675), _1463677) = hAPP(hAPP(c_Product__Type_OPair(_1463671, _1463673), _1463679), _1463681), 35829 ^ _782652 : [(35830 ^ _782652) ^ [] : [-(_1463675 = _1463679)], (35832 ^ _782652) ^ [] : [-(_1463677 = _1463681)]]], (35834 ^ _782652) ^ [_1463822, _1463824, _1463826, _1463828, _1463830, _1463832] : [_1463822 = _1463824, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1463826, _1463828, _1463830), _1463832), _1463822) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1463826, _1463828, _1463830), _1463832), _1463824))], (35840 ^ _782652) ^ [_1463965, _1463967, _1463969] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1463965, tc_HOL_Obool), tc_fun(_1463965, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1463965, tc_HOL_Obool), tc_fun(_1463965, tc_HOL_Obool)), _1463967), _1463969)), c_Wellfounded_Ofinite__psubset(_1463965))), 35843 ^ _782652 : [(35844 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1463965, tc_HOL_Obool)), _1463967), _1463969)))], (35846 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1463965), _1463969)))]]], (35848 ^ _782652) ^ [_1464160, _1464162, _1464164] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1464160, tc_HOL_Obool), tc_fun(_1464160, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1464160, tc_HOL_Obool), tc_fun(_1464160, tc_HOL_Obool)), _1464162), _1464164)), c_Wellfounded_Ofinite__psubset(_1464160)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1464160, tc_HOL_Obool)), _1464162), _1464164)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464160), _1464164))], (35858 ^ _782652) ^ [_1464389, _1464391, _1464393, _1464395, _1464397, _1464399, _1464401, _1464403] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464389, _1464391, _1464393), _1464395), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464397, _1464399, tc_prod(_1464389, _1464391)), _1464401), _1464403)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464397, _1464399, _1464393), hAPP(hAPP(c_COMBB(tc_fun(_1464399, tc_prod(_1464389, _1464391)), tc_fun(_1464399, _1464393), _1464397), hAPP(c_COMBB(tc_prod(_1464389, _1464391), _1464393, _1464399), hAPP(c_Product__Type_Oprod_Oprod__case(_1464389, _1464391, _1464393), _1464395))), _1464401)), _1464403))], (35860 ^ _782652) ^ [_1464495, _1464497, _1464499, _1464501, _1464503, _1464505] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464495, _1464497, _1464499), _1464501), hAPP(hAPP(c_Product__Type_OPair(_1464495, _1464497), _1464503), _1464505)) = hAPP(hAPP(_1464501, _1464503), _1464505))], (35862 ^ _782652) ^ [_1464553, _1464555, _1464557, _1464559, _1464561, _1464563] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464553, _1464555, _1464557), _1464559), hAPP(hAPP(c_Product__Type_OPair(_1464553, _1464555), _1464561), _1464563)) = hAPP(hAPP(_1464559, _1464561), _1464563))], (35864 ^ _782652) ^ [_1464611, _1464613, _1464615, _1464617, _1464619] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1464611, _1464613, tc_HOL_Obool), _1464615), hAPP(hAPP(c_Product__Type_OPair(_1464611, _1464613), _1464617), _1464619))), -(hBOOL(hAPP(hAPP(_1464615, _1464617), _1464619)))], (35870 ^ _782652) ^ [_1464740, _1464742, _1464744, _1464746] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1464740, _1464742, _1464744), hAPP(hAPP(c_COMBB(tc_fun(_1464742, tc_prod(_1464740, _1464742)), tc_fun(_1464742, _1464744), _1464740), hAPP(c_COMBB(tc_prod(_1464740, _1464742), _1464744, _1464742), _1464746)), c_Product__Type_OPair(_1464740, _1464742))) = _1464746)], (35872 ^ _782652) ^ [_1464808, _1464810, _1464812, _1464814] : [-(c_HOL_OThe(tc_prod(_1464808, _1464810), hAPP(c_Product__Type_Oprod_Oprod__case(_1464808, _1464810, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1464808, tc_fun(_1464810, tc_HOL_Obool), tc_fun(_1464810, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1464810, tc_HOL_Obool), tc_fun(_1464810, tc_HOL_Obool)), _1464808), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1464810)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1464808), c_fconj), hAPP(c_fequal, _1464812)))), hAPP(c_fequal, _1464814)))) = hAPP(hAPP(c_Product__Type_OPair(_1464808, _1464810), _1464812), _1464814))], (35874 ^ _782652) ^ [_1464914, _1464916, _1464918] : [-(c_HOL_OThe(tc_prod(_1464914, _1464916), _1464918) = c_HOL_OThe(tc_prod(_1464914, _1464916), hAPP(c_Product__Type_Oprod_Oprod__case(_1464914, _1464916, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1464916, tc_prod(_1464914, _1464916)), tc_fun(_1464916, tc_HOL_Obool), _1464914), hAPP(c_COMBB(tc_prod(_1464914, _1464916), tc_HOL_Obool, _1464916), _1464918)), c_Product__Type_OPair(_1464914, _1464916)))))], (35876 ^ _782652) ^ [_1464992] : [-(c_Divides_Oadjust(_1464992) = 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)), _1464992))))), 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)), _1464992))))), 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))))))))], (35878 ^ _782652) ^ [_1465077, _1465079, _1465081, _1465083, _1465085] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1465077, _1465079, _1465081), _1465083), _1465085)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1465077, _1465079)), hAPP(hAPP(c_Product__Type_OPair(_1465077, _1465079), _1465083), _1465085)), _1465081)))], (35884 ^ _782652) ^ [_1465212, _1465214, _1465216, _1465218, _1465220] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1465212, _1465214)), hAPP(hAPP(c_Product__Type_OPair(_1465212, _1465214), _1465218), _1465220)), _1465216)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1465212, _1465214, _1465216), _1465218), _1465220)))], (35890 ^ _782652) ^ [_1465353, _1465355] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1465353, _1465355) = 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), _1465353), _1465355)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1465353, _1465355)))], (35892 ^ _782652) ^ [_1465397] : [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), _1465397))), 35895 ^ _782652 : [(35896 ^ _782652) ^ [] : [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), _1465397)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1465397)) = 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), _1465397))))], (35902 ^ _782652) ^ [] : [-(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), _1465397))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1465397)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1465397)), 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), _1465397)))))]]], (35908 ^ _782652) ^ [_1465687, _1465689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1465687), 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)), _1465689)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1465687, _1465689), c_Divides_OnegDivAlg(_1465687, _1465689))))], (35918 ^ _782652) ^ [_1465846, _1465848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1465846), 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)), _1465848)), -(c_Divides_OnegDivAlg(_1465846, _1465848) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1465846), _1465848)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1465846, _1465848)))], (35928 ^ _782652) ^ [_1466027] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1466027) = 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), _1466027), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35930 ^ _782652) ^ [_1466071, _1466073] : [35931 ^ _782652 : [(35932 ^ _782652) ^ [] : [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), _1466071), _1466073)))], (35934 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1466073), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1466071, _1466073) = 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), _1466071), _1466073)))], (35938 ^ _782652) ^ [_1466230, _1466232] : [-(c_Divides_OnegDivAlg(_1466230, _1466232) = hAPP(c_Divides_Oadjust(_1466232), c_Divides_OnegDivAlg(_1466230, 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)))), _1466232)))), -(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), _1466230), _1466232)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1466232), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35948 ^ _782652) ^ [_1466302, _1466304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1466302)), 35951 ^ _782652 : [(35952 ^ _782652) ^ [] : [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), _1466304), _1466302))), -(c_Divides_OnegDivAlg(_1466304, _1466302) = 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), _1466304), _1466302)))], (35958 ^ _782652) ^ [] : [-(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), _1466304), _1466302)))), -(c_Divides_OnegDivAlg(_1466304, _1466302) = hAPP(c_Divides_Oadjust(_1466302), c_Divides_OnegDivAlg(_1466304, 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)))), _1466302))))]]], (35964 ^ _782652) ^ [_1466566, _1466568] : [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), _1466566))), 35967 ^ _782652 : [(35968 ^ _782652) ^ [] : [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), _1466568)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466566)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466568), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466566)) = 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), _1466568)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466566))))], (35974 ^ _782652) ^ [] : [-(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), _1466568)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466566))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466568), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466566)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466566)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1466568), 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), _1466566)))))]]], (35980 ^ _782652) ^ [_1466929, _1466931] : [c_Nitpick_Orefl_H(_1466929, _1466931), 35983 ^ _782652 : [(35984 ^ _782652) ^ [_1467007] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1466929, _1466929)), hAPP(hAPP(c_Product__Type_OPair(_1466929, _1466929), _1467007), _1467007)), _1466931)))]]], (35986 ^ _782652) ^ [_1467049, _1467051] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1467049, _1467049)), hAPP(hAPP(c_Product__Type_OPair(_1467049, _1467049), 35987 ^ [_1467049, _1467051]), 35987 ^ [_1467049, _1467051])), _1467051)), -(c_Nitpick_Orefl_H(_1467049, _1467051))], (35993 ^ _782652) ^ [_1467216] : [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), _1467216))), 35996 ^ _782652 : [(35997 ^ _782652) ^ [] : [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), _1467216))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1467216)) = 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)))], (36003 ^ _782652) ^ [] : [-(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), _1467216)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1467216)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1467216)), 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), _1467216)))))]]], (36009 ^ _782652) ^ [_1467485, _1467487] : [36010 ^ _782652 : [(36011 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467485), _1467487))], (36013 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1467487), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1467485, _1467487) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467485))], (36017 ^ _782652) ^ [_1467626, _1467628] : [-(c_Divides_OposDivAlg(_1467626, _1467628) = hAPP(c_Divides_Oadjust(_1467628), c_Divides_OposDivAlg(_1467626, 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)))), _1467628)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467626), _1467628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1467628), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36027 ^ _782652) ^ [_1467695] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1467695) = 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)))], (36029 ^ _782652) ^ [_1467721, _1467723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467721)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467723)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1467721, _1467723), c_Divides_OposDivAlg(_1467721, _1467723))))], (36039 ^ _782652) ^ [_1467874, _1467876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467876)), -(c_Divides_OposDivAlg(_1467874, _1467876) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467874), _1467876)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1467874, _1467876)))], (36049 ^ _782652) ^ [_1468049, _1468051] : [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), _1468049))), 36052 ^ _782652 : [(36053 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468051)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468049))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468051), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468049)) = 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), _1468051)))], (36059 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468051)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468049)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468051), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468049)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468049)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1468051), 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), _1468049)))))]]], (36065 ^ _782652) ^ [_1468367, _1468369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468367)), 36068 ^ _782652 : [(36069 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1468369), _1468367)), -(c_Divides_OposDivAlg(_1468369, _1468367) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468369))], (36075 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1468369), _1468367))), -(c_Divides_OposDivAlg(_1468369, _1468367) = hAPP(c_Divides_Oadjust(_1468367), c_Divides_OposDivAlg(_1468369, 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)))), _1468367))))]]], (36107 ^ _782652) ^ [_1468986, _1468988] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468986))), 36110 ^ _782652 : [(36111 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468988)), -(c_Divides_Odivmod__int(_1468986, _1468988) = c_Divides_OnegDivAlg(_1468986, _1468988))], (36117 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468988))), -(c_Divides_Odivmod__int(_1468986, _1468988) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1468986), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1468988))))]]], (36081 ^ _782652) ^ [_1468616, _1468618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468616)), 36084 ^ _782652 : [(36085 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468618)), -(c_Divides_Odivmod__int(_1468616, _1468618) = c_Divides_OposDivAlg(_1468616, _1468618))], (36091 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468618))), 36094 ^ _782652 : [(36095 ^ _782652) ^ [] : [_1468616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1468616, _1468618) = 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)))], (36101 ^ _782652) ^ [] : [-(_1468616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1468616, _1468618) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1468616), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1468618))))]]]]], (36123 ^ _782652) ^ [_1469214, _1469216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1469214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1469214), _1469216)), -(c_Divides_Odivmod__nat(_1469216, _1469214) = 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), _1469216), _1469214)), _1469214))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1469216), _1469214), _1469214)))], (36133 ^ _782652) ^ [_1469434, _1469436] : [_1469434 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1469434, _1469436) = 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)))], (36139 ^ _782652) ^ [_1469512, _1469514] : [-(_1469512 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36142 ^ _782652 : [(36143 ^ _782652) ^ [] : [_1469514 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1469512, _1469514) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1469512))], (36149 ^ _782652) ^ [] : [-(_1469514 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1469512, _1469514) = 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, _1469514))), 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)), _1469514)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1469512))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1469514), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1469512), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1469512, _1469514)), 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), _1469514))))), c_Divides_Opdivmod(_1469512, _1469514)))))]]], (36155 ^ _782652) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (36157 ^ _782652) ^ [_1469890, _1469892, _1469894, _1469896, _1469898, _1469900] : [-(hAPP(c_Product__Type_Oapsnd(_1469890, _1469892, _1469894, _1469896), hAPP(hAPP(c_Product__Type_OPair(_1469894, _1469890), _1469898), _1469900)) = hAPP(hAPP(c_Product__Type_OPair(_1469894, _1469892), _1469898), hAPP(_1469896, _1469900)))], (36159 ^ _782652) ^ [_1469952] : [-(c_Divides_Odivmod__nat(_1469952, 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)), _1469952))], (36161 ^ _782652) ^ [_1469981, _1469983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1469981), _1469983)), -(c_Divides_Odivmod__nat(_1469981, _1469983) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1469981))], (36167 ^ _782652) ^ [_1470080, _1470082] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1470080), _1470082)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1470080), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1470082)))], (36169 ^ _782652) ^ [_1470123, _1470125] : [-(c_Divides_Odivmod__nat(_1470123, _1470125) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1470123), _1470125)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1470123, _1470125)))], (36171 ^ _782652) ^ [_1470167, _1470169, _1470171] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1470167), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1470169)), _1470171)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1470167, _1470169), hAPP(c_Divides_OnegateSnd, _1470171))))], (36177 ^ _782652) ^ [_1470293, _1470295] : [36178 ^ _782652 : [(36179 ^ _782652) ^ [] : [_1470293 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36181 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1470295), _1470293))]], -(c_Divides_Odivmod__nat(_1470295, _1470293) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1470295))], (36185 ^ _782652) ^ [_1470424, _1470426] : [-(c_Divides_Odivmod__nat(_1470426, _1470424) = 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), _1470426), _1470424), _1470424))), -(_1470424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1470426), _1470424)))], (36195 ^ _782652) ^ [_1470489, _1470491] : [-(c_Divides_Opdivmod(_1470489, _1470491) = 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), _1470489)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1470491))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1470489), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1470491))))], (36197 ^ _782652) ^ [_1470554, _1470556] : [_1470554 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1470556, _1470554) = 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), _1470556)))], (36203 ^ _782652) ^ [_1470643, _1470645] : [-(_1470643 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1470645, _1470643) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1470645), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1470643)))], (36209 ^ _782652) ^ [_1470702, _1470704] : [_1470702 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1470702, _1470704) = 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)))], (36215 ^ _782652) ^ [_1470780, _1470782] : [-(_1470780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36218 ^ _782652 : [(36219 ^ _782652) ^ [] : [_1470782 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1470780, _1470782) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1470780))], (36225 ^ _782652) ^ [] : [-(_1470782 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1470780, _1470782) = 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, _1470782))), 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, _1470780)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1470782))), c_Divides_Opdivmod(_1470780, _1470782)), 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), _1470782))))), c_Divides_Opdivmod(_1470780, _1470782)))))]]], (36231 ^ _782652) ^ [_1471092, _1471094, _1471096, _1471098, _1471100, _1471102, _1471104] : [c_Equiv__Relations_Oequiv(_1471092, _1471094, _1471096), c_Equiv__Relations_Ocongruent(_1471092, tc_fun(_1471098, tc_HOL_Obool), _1471096, _1471100), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1471092, tc_fun(_1471098, tc_HOL_Obool)), _1471102), _1471100) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1471092, tc_fun(_1471098, tc_HOL_Obool)), _1471104), _1471100), hBOOL(hAPP(hAPP(c_member(tc_fun(_1471092, tc_HOL_Obool)), _1471102), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471092), _1471094), _1471096))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1471092, tc_HOL_Obool)), _1471104), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471092), _1471094), _1471096))), 36253 ^ _782652 : [(36254 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471092), 36252 ^ [_1471092, _1471094, _1471096, _1471098, _1471100, _1471102, _1471104]), _1471094)))], (36257 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471092), 36255 ^ [_1471092, _1471094, _1471096, _1471098, _1471100, _1471102, _1471104]), _1471094)))], (36259 ^ _782652) ^ [] : [-(hAPP(_1471100, 36252 ^ [_1471092, _1471094, _1471096, _1471098, _1471100, _1471102, _1471104]) = hAPP(_1471100, 36255 ^ [_1471092, _1471094, _1471096, _1471098, _1471100, _1471102, _1471104]))], (36261 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1471092, _1471092)), hAPP(hAPP(c_Product__Type_OPair(_1471092, _1471092), 36252 ^ [_1471092, _1471094, _1471096, _1471098, _1471100, _1471102, _1471104]), 36255 ^ [_1471092, _1471094, _1471096, _1471098, _1471100, _1471102, _1471104])), _1471096))]], -(_1471102 = _1471104)], (36265 ^ _782652) ^ [_1472062, _1472064, _1472066, _1472068, _1472070] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1472062, _1472064), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1472066), _1472068))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1472064)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1472070), _1472062), _1472064), 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), _1472070), _1472066)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1472070), _1472068)), _1472064))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1472070), _1472068), _1472064)))))], (36275 ^ _782652) ^ [_1472331, _1472333, _1472335, _1472337, _1472339] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1472331, _1472333), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1472335), _1472337))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1472333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1472339)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1472331, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1472333), _1472339)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1472335), _1472339)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1472333), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1472335, _1472339))), _1472337)))))], (36289 ^ _782652) ^ [_1472638, _1472640, _1472642, _1472644] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1472638, _1472640), _1472642)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1472638, _1472640), _1472644)), -(_1472642 = _1472644)], (36299 ^ _782652) ^ [_1472795, _1472797, _1472799] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1472795, _1472797), _1472799)), -(c_Divides_Odivmod__nat(_1472795, _1472797) = _1472799)], (36305 ^ _782652) ^ [_1472890, _1472892] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1472890, _1472892), c_Divides_Odivmod__nat(_1472890, _1472892))))], (36307 ^ _782652) ^ [_1472923, _1472925] : [-(c_Divides_Odivmod__nat(_1472923, _1472925) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1472923, _1472925)))], (36309 ^ _782652) ^ [_1472957, _1472959, _1472961, _1472963] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1472957, _1472959), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1472961), _1472963))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1472957, _1472959) = _1472963)], (36315 ^ _782652) ^ [_1473068, _1473070, _1473072, _1473074] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1473068, _1473070), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1473072), _1473074))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1473068), _1473070) = _1473072)], (36321 ^ _782652) ^ [_1473183, _1473185] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1473183, _1473185), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1473183), _1473185)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1473183, _1473185)))))], (36323 ^ _782652) ^ [_1473229, _1473231, _1473233, _1473235, _1473237, _1473239, _1473241] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1473229, _1473231), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1473233), _1473235))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1473237, _1473231), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1473239), _1473241))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1473231)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1473229), _1473237), _1473231), 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), _1473233), _1473239)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1473235), _1473241)), _1473231))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1473235), _1473241), _1473231)))))], (36337 ^ _782652) ^ [_1473590, _1473592] : [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), _1473590), _1473592))), 36340 ^ _782652 : [(36341 ^ _782652) ^ [] : [36342 ^ _782652 : [(36343 ^ _782652) ^ [] : [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), _1473590), _1473592)))], (36345 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1473592), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1473590, _1473592) = 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), _1473590), _1473592)))], (36349 ^ _782652) ^ [] : [-(c_Divides_OnegDivAlg(_1473590, _1473592) = hAPP(c_Divides_Oadjust(_1473592), c_Divides_OnegDivAlg(_1473590, 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)))), _1473592)))), -(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), _1473590), _1473592)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1473592), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (36359 ^ _782652) ^ [_1473937, _1473939] : [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), _1473937), _1473939))), 36362 ^ _782652 : [(36363 ^ _782652) ^ [] : [36364 ^ _782652 : [(36365 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1473937), _1473939))], (36367 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1473939), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1473937, _1473939) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1473937))], (36371 ^ _782652) ^ [] : [-(c_Divides_OposDivAlg(_1473937, _1473939) = hAPP(c_Divides_Oadjust(_1473939), c_Divides_OposDivAlg(_1473937, 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)))), _1473939)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1473937), _1473939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1473939), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (36381 ^ _782652) ^ [_1474260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474260)), 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), _1474260)) = 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), _1474260))))))], (36387 ^ _782652) ^ [_1474395, _1474397, _1474399, _1474401, _1474403] : [-(hAPP(c_Product__Type_Osnd(_1474395, _1474397), hAPP(c_Product__Type_Oapsnd(_1474399, _1474397, _1474395, _1474401), _1474403)) = hAPP(_1474401, hAPP(c_Product__Type_Osnd(_1474395, _1474399), _1474403)))], (36389 ^ _782652) ^ [_1474476, _1474478, _1474480, _1474482, _1474484, _1474486] : [hAPP(c_Product__Type_Oapsnd(_1474476, _1474478, _1474480, _1474482), _1474484) = hAPP(c_Product__Type_Oapsnd(_1474476, _1474478, _1474480, _1474486), _1474484), -(hAPP(_1474482, hAPP(c_Product__Type_Osnd(_1474480, _1474476), _1474484)) = hAPP(_1474486, hAPP(c_Product__Type_Osnd(_1474480, _1474476), _1474484)))], (36395 ^ _782652) ^ [_1474625, _1474627, _1474629, _1474631, _1474633, _1474635] : [hAPP(_1474631, hAPP(c_Product__Type_Osnd(_1474629, _1474625), _1474633)) = hAPP(_1474635, hAPP(c_Product__Type_Osnd(_1474629, _1474625), _1474633)), -(hAPP(c_Product__Type_Oapsnd(_1474625, _1474627, _1474629, _1474631), _1474633) = hAPP(c_Product__Type_Oapsnd(_1474625, _1474627, _1474629, _1474635), _1474633))], (36401 ^ _782652) ^ [_1474780, _1474782, _1474784] : [-(hAPP(c_Product__Type_Osnd(_1474780, _1474782), _1474784) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1474780, _1474782, _1474782), hAPP(c_COMBK(tc_fun(_1474782, _1474782), _1474780), c_COMBI(_1474782))), _1474784))], (36413 ^ _782652) ^ [_1475038, _1475040, _1475042] : [36415 ^ _782652 : [(36416 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1475040, 36414 ^ [_1475038, _1475040, _1475042]), _1475042)))], (36418 ^ _782652) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1475038, _1475040), 36414 ^ [_1475038, _1475040, _1475042]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1475038, _1475040), _1475042)))], (36403 ^ _782652) ^ [_1474852, _1474854, _1474856] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1474852, _1474854), _1474856)), 36406 ^ _782652 : [(36407 ^ _782652) ^ [_1474937] : [hBOOL(hAPP(hAPP(_1474854, _1474937), _1474856)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1474852, _1474854), _1474937)))]]], (36432 ^ _782652) ^ [_1475428, _1475430, _1475432] : [36434 ^ _782652 : [(36435 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1475430, 36433 ^ [_1475428, _1475430, _1475432]), _1475432)))], (36437 ^ _782652) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1475428, _1475430), 36433 ^ [_1475428, _1475430, _1475432]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1475428, _1475430), _1475432)))], (36422 ^ _782652) ^ [_1475242, _1475244, _1475246] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1475242, _1475244), _1475246)), 36425 ^ _782652 : [(36426 ^ _782652) ^ [_1475327] : [hBOOL(hAPP(hAPP(_1475244, _1475327), _1475246)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1475242, _1475244), _1475327)))]]], (36441 ^ _782652) ^ [_1475614, _1475616, _1475618, _1475620] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1475614, _1475616), _1475618)), hBOOL(hAPP(hAPP(_1475616, _1475620), _1475618)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1475614, _1475616), _1475620)))], (36451 ^ _782652) ^ [_1475781, _1475783, _1475785, _1475787, _1475789] : [hAPP(c_Product__Type_Osnd(_1475781, _1475783), hAPP(hAPP(c_Product__Type_OPair(_1475781, _1475783), _1475785), _1475787)) = _1475789, -(_1475787 = _1475789)], (36457 ^ _782652) ^ [_1475894, _1475896, _1475898, _1475900] : [-(hAPP(c_Product__Type_Osnd(_1475894, _1475896), hAPP(hAPP(c_Product__Type_OPair(_1475894, _1475896), _1475898), _1475900)) = _1475900)], (36459 ^ _782652) ^ [_1475938, _1475940] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1475938, _1475940) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1475938, _1475940)))], (36461 ^ _782652) ^ [_1475973, _1475975, _1475977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475973, tc_fun(_1475973, tc_HOL_Obool))), _1475975), _1475977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475973, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1475973, _1475977)), c_Wellfounded_Oaccp(_1475973, _1475975))))], (36467 ^ _782652) ^ [_1476110, _1476112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476110), 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)), _1476112)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1476110, _1476112) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1476110, _1476112)))], (36477 ^ _782652) ^ [_1476273, _1476275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476275)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1476273, _1476275) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1476273, _1476275)))], (36487 ^ _782652) ^ [_1476430] : [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), _1476430))), -(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), _1476430)) = 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), _1476430))))], (36493 ^ _782652) ^ [_1476547, _1476549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476549), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1476547, _1476549) = 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), _1476547), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1476549)))))], (36503 ^ _782652) ^ [_1476728, _1476730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476728), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1476730), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1476728, _1476730) = 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), _1476728), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1476730)))))], (36513 ^ _782652) ^ [_1476915, _1476917] : [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), _1476915), _1476917))), 36516 ^ _782652 : [(36517 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476917), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1476915, _1476917) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1476915), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1476917)))], (36523 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476917), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36526 ^ _782652 : [(36527 ^ _782652) ^ [] : [36528 ^ _782652 : [(36529 ^ _782652) ^ [] : [_1476915 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36531 ^ _782652) ^ [] : [_1476917 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1476915, _1476917) = 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)))], (36535 ^ _782652) ^ [] : [-(c_Nitpick_Onorm__frac(_1476915, _1476917) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1476915), _1476917)), 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), _1476915))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1476917)))), -(_1476915 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1476917 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (36545 ^ _782652) ^ [_1477407, _1477409, _1477411] : [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), _1477407), _1477409))), -(hBOOL(hAPP(hAPP(_1477411, _1477407), _1477409))), 36552 ^ _782652 : [(36553 ^ _782652) ^ [] : [-(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), 36550 ^ [_1477407, _1477409, _1477411]), 36551 ^ [_1477407, _1477409, _1477411]))))], (36565 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1477411, 36550 ^ [_1477407, _1477409, _1477411]), 36551 ^ [_1477407, _1477409, _1477411]))], (36555 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1477411, 36550 ^ [_1477407, _1477409, _1477411]), 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)))), 36551 ^ [_1477407, _1477409, _1477411])))), -(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), 36550 ^ [_1477407, _1477409, _1477411]), 36551 ^ [_1477407, _1477409, _1477411])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36551 ^ [_1477407, _1477409, _1477411]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (36569 ^ _782652) ^ [_1477902, _1477904, _1477906] : [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), _1477902), _1477904))), -(hBOOL(hAPP(hAPP(_1477906, _1477902), _1477904))), 36576 ^ _782652 : [(36577 ^ _782652) ^ [] : [-(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), 36574 ^ [_1477902, _1477904, _1477906]), 36575 ^ [_1477902, _1477904, _1477906]))))], (36589 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1477906, 36574 ^ [_1477902, _1477904, _1477906]), 36575 ^ [_1477902, _1477904, _1477906]))], (36579 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1477906, 36574 ^ [_1477902, _1477904, _1477906]), 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)))), 36575 ^ [_1477902, _1477904, _1477906])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36574 ^ [_1477902, _1477904, _1477906]), 36575 ^ [_1477902, _1477904, _1477906]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36575 ^ [_1477902, _1477904, _1477906]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (36593 ^ _782652) ^ [_1478388, _1478390] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1478388, _1478390) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1478388, _1478390)))], (36595 ^ _782652) ^ [_1478423, _1478425] : [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), _1478423), _1478425))), 36598 ^ _782652 : [(36599 ^ _782652) ^ [] : [_1478425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1478423, _1478425) = _1478423)], (36605 ^ _782652) ^ [] : [-(_1478425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1478423, _1478425) = c_Nitpick_Onat__gcd(_1478425, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1478423, _1478425)))]]], (36611 ^ _782652) ^ [_1478662, _1478664, _1478666, _1478668] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478662, _1478662)), hAPP(hAPP(c_Product__Type_OPair(_1478662, _1478662), _1478664), _1478666)), hAPP(c_Wellfounded_Omeasure(_1478662), _1478668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1478668, _1478664)), hAPP(_1478668, _1478666))))], (36617 ^ _782652) ^ [_1478809, _1478811, _1478813, _1478815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1478815, _1478811)), hAPP(_1478815, _1478813))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1478809, _1478809)), hAPP(hAPP(c_Product__Type_OPair(_1478809, _1478809), _1478811), _1478813)), hAPP(c_Wellfounded_Omeasure(_1478809), _1478815))))], (36623 ^ _782652) ^ [_1478977, _1478979] : [c_Relation_Oirrefl(_1478977, _1478979), 36626 ^ _782652 : [(36627 ^ _782652) ^ [_1479059] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478977, _1478977)), hAPP(hAPP(c_Product__Type_OPair(_1478977, _1478977), _1479059), _1479059)), _1478979))]]], (36629 ^ _782652) ^ [_1479099, _1479101] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1479099, _1479099)), hAPP(hAPP(c_Product__Type_OPair(_1479099, _1479099), 36630 ^ [_1479099, _1479101]), 36630 ^ [_1479099, _1479101])), _1479101))), -(c_Relation_Oirrefl(_1479099, _1479101))], (36636 ^ _782652) ^ [_1479170, _1479172, _1479174] : [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), _1479170), _1479172))), -(hBOOL(hAPP(hAPP(_1479174, _1479170), _1479172))), 36643 ^ _782652 : [(36644 ^ _782652) ^ [] : [-(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), 36641 ^ [_1479170, _1479172, _1479174]), 36642 ^ [_1479170, _1479172, _1479174]))))], (36652 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1479174, 36641 ^ [_1479170, _1479172, _1479174]), 36642 ^ [_1479170, _1479172, _1479174]))], (36646 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36642 ^ [_1479170, _1479172, _1479174]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1479174, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 36641 ^ [_1479170, _1479172, _1479174])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 36642 ^ [_1479170, _1479172, _1479174]))))]]], (36656 ^ _782652) ^ [_1479643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1479643)), 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), _1479643)) = 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), _1479643))))))], (36662 ^ _782652) ^ [_1479776] : [-(hAPP(c_Int_Onat, _1479776) = 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, _1479776)), 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)))))))], (36664 ^ _782652) ^ [_1479835, _1479837, _1479839, _1479841] : [_1479835 = _1479837, 36667 ^ _782652 : [(36668 ^ _782652) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1479839, _1479841), _1479835) = hAPP(c_Product__Type_Ofst(_1479839, _1479841), _1479837))], (36670 ^ _782652) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1479839, _1479841), _1479835) = hAPP(c_Product__Type_Osnd(_1479839, _1479841), _1479837))]]], (36672 ^ _782652) ^ [_1479986, _1479988, _1479990, _1479992] : [-(_1479986 = _1479988), hAPP(c_Product__Type_Ofst(_1479990, _1479992), _1479986) = hAPP(c_Product__Type_Ofst(_1479990, _1479992), _1479988), hAPP(c_Product__Type_Osnd(_1479990, _1479992), _1479986) = hAPP(c_Product__Type_Osnd(_1479990, _1479992), _1479988)], (36682 ^ _782652) ^ [_1480173, _1480175, _1480177, _1480179] : [hAPP(c_Product__Type_Ofst(_1480173, _1480175), _1480177) = hAPP(c_Product__Type_Ofst(_1480173, _1480175), _1480179), hAPP(c_Product__Type_Osnd(_1480173, _1480175), _1480177) = hAPP(c_Product__Type_Osnd(_1480173, _1480175), _1480179), -(_1480177 = _1480179)], (36692 ^ _782652) ^ [_1480358, _1480360, _1480362, _1480364] : [-(hAPP(c_Product__Type_Ofst(_1480358, _1480360), hAPP(hAPP(c_Product__Type_OPair(_1480358, _1480360), _1480362), _1480364)) = _1480362)], (36694 ^ _782652) ^ [_1480402, _1480404, _1480406, _1480408, _1480410] : [hAPP(c_Product__Type_Ofst(_1480402, _1480404), hAPP(hAPP(c_Product__Type_OPair(_1480402, _1480404), _1480406), _1480408)) = _1480410, -(_1480406 = _1480410)], (36700 ^ _782652) ^ [_1480530, _1480532] : [hAPP(c_Int_ORep__Integ, _1480530) = hAPP(c_Int_ORep__Integ, _1480532), -(_1480530 = _1480532)], (36706 ^ _782652) ^ [_1480615, _1480617] : [_1480615 = _1480617, -(hAPP(c_Int_ORep__Integ, _1480615) = hAPP(c_Int_ORep__Integ, _1480617))], (36712 ^ _782652) ^ [_1480706, _1480708, _1480710] : [-(hAPP(c_Product__Type_Ofst(_1480706, _1480708), _1480710) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1480706, _1480708, _1480706), c_COMBK(_1480706, _1480708)), _1480710))], (36714 ^ _782652) ^ [_1480752, _1480754, _1480756, _1480758, _1480760] : [-(hAPP(c_Product__Type_Ofst(_1480752, _1480754), hAPP(c_Product__Type_Oapsnd(_1480756, _1480754, _1480752, _1480758), _1480760)) = hAPP(c_Product__Type_Ofst(_1480752, _1480756), _1480760))], (36716 ^ _782652) ^ [_1480803, _1480805, _1480807] : [-(_1480803 = hAPP(hAPP(c_Product__Type_OPair(_1480805, _1480807), hAPP(c_Product__Type_Ofst(_1480805, _1480807), _1480803)), hAPP(c_Product__Type_Osnd(_1480805, _1480807), _1480803)))], (36718 ^ _782652) ^ [_1480851, _1480853, _1480855] : [-(hAPP(hAPP(c_Product__Type_OPair(_1480851, _1480853), hAPP(c_Product__Type_Ofst(_1480851, _1480853), _1480855)), hAPP(c_Product__Type_Osnd(_1480851, _1480853), _1480855)) = _1480855)], (36720 ^ _782652) ^ [_1480899, _1480901, _1480903, _1480905, _1480907] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1480899, _1480901, _1480903), _1480905), _1480907) = hAPP(hAPP(_1480905, hAPP(c_Product__Type_Ofst(_1480899, _1480901), _1480907)), hAPP(c_Product__Type_Osnd(_1480899, _1480901), _1480907)))], (36722 ^ _782652) ^ [_1480958, _1480960] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1480958), _1480960) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1480958, _1480960)))], (36724 ^ _782652) ^ [_1480995, _1480997, _1480999, _1481001, _1481003, _1481005] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1480995, _1480997), _1480997, _1480999), hAPP(hAPP(c_COMBB(_1481001, tc_fun(_1480997, _1480999), tc_prod(_1480995, _1480997)), _1481003), hAPP(hAPP(c_COMBB(_1480995, _1481001, tc_prod(_1480995, _1480997)), _1481005), c_Product__Type_Ofst(_1480995, _1480997)))), c_Product__Type_Osnd(_1480995, _1480997)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1480995, _1480997, _1480999), hAPP(hAPP(c_COMBB(_1481001, tc_fun(_1480997, _1480999), _1480995), _1481003), _1481005)))], (36726 ^ _782652) ^ [_1481096, _1481098, _1481100, _1481102, _1481104] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1481096, _1481098, _1481100), _1481102), _1481104) = hAPP(hAPP(_1481102, hAPP(c_Product__Type_Ofst(_1481096, _1481098), _1481104)), hAPP(c_Product__Type_Osnd(_1481096, _1481098), _1481104)))], (36728 ^ _782652) ^ [_1481155, _1481157, _1481159, _1481161, _1481163] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1481155, _1481157, _1481159), _1481161), _1481163) = hAPP(hAPP(_1481161, hAPP(c_Product__Type_Ofst(_1481155, _1481157), _1481163)), hAPP(c_Product__Type_Osnd(_1481155, _1481157), _1481163)))], (36730 ^ _782652) ^ [_1481214, _1481216, _1481218] : [-(c_HOL_OThe(tc_prod(_1481214, _1481216), hAPP(c_Product__Type_Oprod_Oprod__case(_1481214, _1481216, tc_HOL_Obool), _1481218)) = c_HOL_OThe(tc_prod(_1481214, _1481216), hAPP(hAPP(c_COMBS(tc_prod(_1481214, _1481216), _1481216, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1481214, tc_fun(_1481216, tc_HOL_Obool), tc_prod(_1481214, _1481216)), _1481218), c_Product__Type_Ofst(_1481214, _1481216))), c_Product__Type_Osnd(_1481214, _1481216))))], (36732 ^ _782652) ^ [_1481295, _1481297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481295), 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)), _1481297)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1481295), _1481297) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1481295, _1481297)))], (36742 ^ _782652) ^ [_1481462, _1481464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1481462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1481464)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1481462), _1481464) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1481462, _1481464)))], (36752 ^ _782652) ^ [_1481623] : [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), _1481623))), -(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), _1481623)) = 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), _1481623))))], (36758 ^ _782652) ^ [_1481738, _1481740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1481738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481740), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1481738), _1481740) = 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), _1481738), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1481740)))))], (36768 ^ _782652) ^ [_1481923, _1481925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481923), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1481925), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1481923), _1481925) = 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), _1481923), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1481925)))))], (36778 ^ _782652) ^ [_1482114, _1482116, _1482118, _1482120, _1482122] : [-(c_Product__Type_Oprod_Oprod__size(_1482114, _1482116, _1482118, _1482120, _1482122) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1482118, hAPP(c_Product__Type_Ofst(_1482114, _1482116), _1482122))), hAPP(_1482120, hAPP(c_Product__Type_Osnd(_1482114, _1482116), _1482122)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36780 ^ _782652) ^ [_1482181, _1482183, _1482185, _1482187, _1482189] : [hBOOL(hAPP(hAPP(_1482181, _1482183), _1482185)), -(hBOOL(hAPP(hAPP(_1482181, hAPP(c_Product__Type_Osnd(_1482187, _1482189), hAPP(hAPP(c_Product__Type_OPair(_1482187, _1482189), _1482185), _1482183))), hAPP(c_Product__Type_Ofst(_1482187, _1482189), hAPP(hAPP(c_Product__Type_OPair(_1482187, _1482189), _1482185), _1482183)))))], (36786 ^ _782652) ^ [_1482344, _1482346, _1482348, _1482350, _1482352, _1482354] : [hBOOL(hAPP(_1482344, _1482346)), hBOOL(hAPP(_1482348, _1482350)), 36793 ^ _782652 : [(36794 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1482344, hAPP(c_Product__Type_Ofst(_1482352, _1482354), hAPP(hAPP(c_Product__Type_OPair(_1482352, _1482354), _1482346), _1482350)))))], (36796 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1482348, hAPP(c_Product__Type_Osnd(_1482352, _1482354), hAPP(hAPP(c_Product__Type_OPair(_1482352, _1482354), _1482346), _1482350)))))]]], (36798 ^ _782652) ^ [_1482591, _1482593] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1482591), _1482593) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1482591, _1482593)))], (36832 ^ _782652) ^ [_1483182, _1483184, _1483186] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1483182, _1483184), _1483186))), _1483182 = 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), _1483186)), _1483184)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1483186)), 36839 ^ _782652 : [(36840 ^ _782652) ^ [] : [-(_1483184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36842 ^ _782652) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1483186) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 36843 ^ _782652 : [(36844 ^ _782652) ^ [] : [_1483184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36846 ^ _782652) ^ [] : [36847 ^ _782652 : [(36848 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1483184)))], (36850 ^ _782652) ^ [] : [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), _1483186))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1483186)), _1483184))]], 36855 ^ _782652 : [(36856 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1483184))], (36858 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1483184), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1483186))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1483186)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (36800 ^ _782652) ^ [_1482646, _1482648, _1482650] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1482646, _1482648), _1482650)), 36803 ^ _782652 : [(36804 ^ _782652) ^ [] : [-(_1482646 = 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), _1482650)), _1482648)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1482650)))], (36806 ^ _782652) ^ [] : [_1482648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1482650) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36812 ^ _782652) ^ [] : [-(_1482648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36815 ^ _782652 : [(36816 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1482648)), 36819 ^ _782652 : [(36820 ^ _782652) ^ [] : [-(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), _1482650))))], (36822 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1482650)), _1482648)))]]], (36824 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1482648))), 36827 ^ _782652 : [(36828 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1482648), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1482650))))], (36830 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1482650)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (36866 ^ _782652) ^ [_1483791, _1483793, _1483795] : [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), _1483791), _1483793))), -(hBOOL(hAPP(hAPP(_1483795, _1483791), _1483793))), 36873 ^ _782652 : [(36874 ^ _782652) ^ [] : [-(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), 36871 ^ [_1483791, _1483793, _1483795]), 36872 ^ [_1483791, _1483793, _1483795]))))], (36882 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1483795, 36871 ^ [_1483791, _1483793, _1483795]), 36872 ^ [_1483791, _1483793, _1483795]))], (36876 ^ _782652) ^ [] : [-(36872 ^ [_1483791, _1483793, _1483795] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1483795, 36872 ^ [_1483791, _1483793, _1483795]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 36871 ^ [_1483791, _1483793, _1483795], 36872 ^ [_1483791, _1483793, _1483795]))))]]], (36886 ^ _782652) ^ [_1484213, _1484215, _1484217, _1484219] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1484213, _1484215), _1484217), _1484219) = hAPP(c_Set_OCollect(tc_prod(_1484215, _1484215)), hAPP(c_Product__Type_Oprod_Oprod__case(_1484215, _1484215, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1484215, tc_fun(tc_prod(_1484213, _1484213), tc_HOL_Obool), tc_fun(_1484215, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484215, tc_fun(tc_fun(tc_prod(_1484213, _1484213), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484213, _1484213), tc_HOL_Obool), tc_fun(_1484215, tc_HOL_Obool)), _1484215), c_COMBC(_1484215, tc_fun(tc_prod(_1484213, _1484213), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484215, tc_prod(_1484213, _1484213)), tc_fun(_1484215, tc_fun(tc_fun(tc_prod(_1484213, _1484213), tc_HOL_Obool), tc_HOL_Obool)), _1484215), hAPP(c_COMBB(tc_prod(_1484213, _1484213), tc_fun(tc_fun(tc_prod(_1484213, _1484213), tc_HOL_Obool), tc_HOL_Obool), _1484215), c_member(tc_prod(_1484213, _1484213)))), hAPP(hAPP(c_COMBC(_1484215, tc_fun(_1484215, _1484213), tc_fun(_1484215, tc_prod(_1484213, _1484213))), hAPP(hAPP(c_COMBB(tc_fun(_1484213, tc_prod(_1484213, _1484213)), tc_fun(tc_fun(_1484215, _1484213), tc_fun(_1484215, tc_prod(_1484213, _1484213))), _1484215), c_COMBB(_1484213, tc_prod(_1484213, _1484213), _1484215)), hAPP(hAPP(c_COMBB(_1484213, tc_fun(_1484213, tc_prod(_1484213, _1484213)), _1484215), c_Product__Type_OPair(_1484213, _1484213)), _1484219))), _1484219)))), _1484217))))], (36888 ^ _782652) ^ [_1484454, _1484456, _1484458, _1484460, _1484462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1484454, _1484456)), hAPP(_1484454, _1484458))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1484460, _1484460)), hAPP(hAPP(c_Product__Type_OPair(_1484460, _1484460), _1484456), _1484458)), _1484462)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484460, _1484460)), hAPP(hAPP(c_Product__Type_OPair(_1484460, _1484460), _1484456), _1484458)), c_Wellfounded_Omlex__prod(_1484460, _1484454, _1484462))))], (36898 ^ _782652) ^ [_1484728, _1484730, _1484732, _1484734, _1484736, _1484738] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484728, _1484728)), hAPP(hAPP(c_Product__Type_OPair(_1484728, _1484728), _1484730), _1484732)), hAPP(hAPP(c_Relation_Oinv__image(_1484734, _1484728), _1484736), _1484738))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484734, _1484734)), hAPP(hAPP(c_Product__Type_OPair(_1484734, _1484734), hAPP(_1484738, _1484730)), hAPP(_1484738, _1484732))), _1484736)))], (36904 ^ _782652) ^ [_1484915, _1484917, _1484919, _1484921, _1484923, _1484925] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484921, _1484921)), hAPP(hAPP(c_Product__Type_OPair(_1484921, _1484921), hAPP(_1484925, _1484917)), hAPP(_1484925, _1484919))), _1484923)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484915, _1484915)), hAPP(hAPP(c_Product__Type_OPair(_1484915, _1484915), _1484917), _1484919)), hAPP(hAPP(c_Relation_Oinv__image(_1484921, _1484915), _1484923), _1484925))))], (36910 ^ _782652) ^ [_1485108, _1485110, _1485112, _1485114, _1485116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1485108, _1485110)), hAPP(_1485108, _1485112))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1485114, _1485114)), hAPP(hAPP(c_Product__Type_OPair(_1485114, _1485114), _1485110), _1485112)), c_Wellfounded_Omlex__prod(_1485114, _1485108, _1485116))))], (36916 ^ _782652) ^ [_1485259, _1485261] : [-(c_FunDef_Orp__inv__image(_1485259, _1485261) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool), tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool), tc_fun(tc_fun(_1485261, _1485259), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool), tc_fun(tc_fun(_1485261, _1485259), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool), tc_fun(tc_fun(_1485261, _1485259), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1485261, _1485259), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)), tc_fun(tc_fun(_1485261, _1485259), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool), tc_fun(tc_fun(_1485261, _1485259), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool), tc_fun(tc_fun(_1485261, _1485259), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool))))), tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1485261, _1485259), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)), tc_fun(tc_fun(_1485261, _1485259), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool))), tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1485261, _1485259), tc_fun(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1485261, _1485259), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)), tc_fun(tc_fun(_1485261, _1485259), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)))), tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool)), c_COMBS(tc_fun(_1485261, _1485259), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1485261, _1485259), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)), tc_fun(tc_fun(_1485261, _1485259), tc_fun(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)))), tc_fun(tc_prod(_1485259, _1485259), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool))), tc_fun(_1485261, _1485259)), c_Product__Type_OPair(tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool), tc_fun(tc_prod(_1485261, _1485261), tc_HOL_Obool)))), c_Relation_Oinv__image(_1485259, _1485261))))), c_Relation_Oinv__image(_1485259, _1485261))))], (36918 ^ _782652) ^ [_1485772] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1485772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1485772)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36920 ^ _782652) ^ [_1485807, _1485809, _1485811, _1485813, _1485815, _1485817] : [-(c_Product__Type_Oprod_Oprod__rec(_1485807, _1485809, _1485811, _1485813, hAPP(hAPP(c_Product__Type_OPair(_1485807, _1485809), _1485815), _1485817)) = hAPP(hAPP(_1485813, _1485815), _1485817))], (36922 ^ _782652) ^ [_1485876, _1485878] : [c_Code__Numeral_OSuc__code__numeral(_1485876) = c_Code__Numeral_OSuc__code__numeral(_1485878), -(_1485876 = _1485878)], (36928 ^ _782652) ^ [_1485957, _1485959] : [_1485957 = _1485959, -(c_Code__Numeral_OSuc__code__numeral(_1485957) = c_Code__Numeral_OSuc__code__numeral(_1485959))], (36934 ^ _782652) ^ [_1486053] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1486053)], (36936 ^ _782652) ^ [_1486087] : [c_Code__Numeral_OSuc__code__numeral(_1486087) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (36938 ^ _782652) ^ [_1486112] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1486112)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1486112)], (36940 ^ _782652) ^ [_1486143] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1486143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1486143)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36942 ^ _782652) ^ [_1486180, _1486182] : [class_Int_Onumber__ring(_1486180), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1486182)), -(hBOOL(hAPP(hAPP(c_member(_1486180), hAPP(c_Int_Onumber__class_Onumber__of(_1486180), _1486182)), c_Nat_Osemiring__1__class_ONats(_1486180))))], (36952 ^ _782652) ^ [_1486372, _1486374, _1486376, _1486378, _1486380, _1486382, _1486384, _1486386] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1486372, _1486374), tc_prod(_1486372, _1486374))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1486372, _1486374), tc_prod(_1486372, _1486374)), hAPP(hAPP(c_Product__Type_OPair(_1486372, _1486374), _1486376), _1486378)), hAPP(hAPP(c_Product__Type_OPair(_1486372, _1486374), _1486380), _1486382))), c_Wellfounded_Olex__prod(_1486372, _1486374, _1486384, _1486386))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486372, _1486372)), hAPP(hAPP(c_Product__Type_OPair(_1486372, _1486372), _1486376), _1486380)), _1486384))), 36959 ^ _782652 : [(36960 ^ _782652) ^ [] : [-(_1486376 = _1486380)], (36962 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486374, _1486374)), hAPP(hAPP(c_Product__Type_OPair(_1486374, _1486374), _1486378), _1486382)), _1486386)))]]], (36964 ^ _782652) ^ [_1486697, _1486699, _1486701, _1486703, _1486705, _1486707, _1486709, _1486711] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1486697, _1486699), tc_prod(_1486697, _1486699))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1486697, _1486699), tc_prod(_1486697, _1486699)), hAPP(hAPP(c_Product__Type_OPair(_1486697, _1486699), _1486701), _1486703)), hAPP(hAPP(c_Product__Type_OPair(_1486697, _1486699), _1486705), _1486707))), c_Wellfounded_Olex__prod(_1486697, _1486699, _1486709, _1486711)))), 36965 ^ _782652 : [(36966 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486697, _1486697)), hAPP(hAPP(c_Product__Type_OPair(_1486697, _1486697), _1486701), _1486705)), _1486709))], (36968 ^ _782652) ^ [] : [_1486701 = _1486705, hBOOL(hAPP(hAPP(c_member(tc_prod(_1486699, _1486699)), hAPP(hAPP(c_Product__Type_OPair(_1486699, _1486699), _1486703), _1486707)), _1486711))]]], (36976 ^ _782652) ^ [_1487072] : [class_Rings_Osemiring__1(_1487072), -(hBOOL(hAPP(hAPP(c_member(_1487072), c_Groups_Ozero__class_Ozero(_1487072)), c_Nat_Osemiring__1__class_ONats(_1487072))))], (36982 ^ _782652) ^ [_1487167, _1487169, _1487171] : [class_Rings_Osemiring__1(_1487167), hBOOL(hAPP(hAPP(c_member(_1487167), _1487169), c_Nat_Osemiring__1__class_ONats(_1487167))), hBOOL(hAPP(hAPP(c_member(_1487167), _1487171), c_Nat_Osemiring__1__class_ONats(_1487167))), -(hBOOL(hAPP(hAPP(c_member(_1487167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1487167), _1487169), _1487171)), c_Nat_Osemiring__1__class_ONats(_1487167))))], (36996 ^ _782652) ^ [_1487422, _1487424, _1487426] : [class_Rings_Osemiring__1(_1487422), hBOOL(hAPP(hAPP(c_member(_1487422), _1487424), c_Nat_Osemiring__1__class_ONats(_1487422))), hBOOL(hAPP(hAPP(c_member(_1487422), _1487426), c_Nat_Osemiring__1__class_ONats(_1487422))), -(hBOOL(hAPP(hAPP(c_member(_1487422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1487422), _1487424), _1487426)), c_Nat_Osemiring__1__class_ONats(_1487422))))], (37010 ^ _782652) ^ [_1487677] : [class_Rings_Osemiring__1(_1487677), -(hBOOL(hAPP(hAPP(c_member(_1487677), c_Groups_Oone__class_Oone(_1487677)), c_Nat_Osemiring__1__class_ONats(_1487677))))], (37016 ^ _782652) ^ [_1487772, _1487774] : [class_Rings_Osemiring__1(_1487772), -(hBOOL(hAPP(hAPP(c_member(_1487772), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1487772), _1487774)), c_Nat_Osemiring__1__class_ONats(_1487772))))], (37022 ^ _782652) ^ [] : [-(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))], (37024 ^ _782652) ^ [_1487893, _1487895, _1487897, _1487899, _1487901, _1487903, _1487905] : [hBOOL(hAPP(_1487893, _1487895)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1487897, _1487897)), hAPP(hAPP(c_Product__Type_OPair(_1487897, _1487897), _1487899), _1487901)), hAPP(_1487903, _1487895))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1487905, _1487897), tc_prod(_1487905, _1487897))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1487905, _1487897), tc_prod(_1487905, _1487897)), hAPP(hAPP(c_Product__Type_OPair(_1487905, _1487897), _1487895), _1487899)), hAPP(hAPP(c_Product__Type_OPair(_1487905, _1487897), _1487895), _1487901))), c_Recdef_Osame__fst(_1487905, _1487897, _1487893, _1487903))))], (37034 ^ _782652) ^ [_1488213, _1488215] : [c_Equiv__Relations_Oequiv(_1488213, c_Orderings_Otop__class_Otop(tc_fun(_1488213, tc_HOL_Obool)), _1488215), -(c_Equiv__Relations_Oequivp(_1488213, hAPP(hAPP(c_COMBC(_1488213, tc_fun(tc_prod(_1488213, _1488213), tc_HOL_Obool), tc_fun(_1488213, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488213, tc_fun(tc_fun(tc_prod(_1488213, _1488213), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1488213, _1488213), tc_HOL_Obool), tc_fun(_1488213, tc_HOL_Obool)), _1488213), c_COMBC(_1488213, tc_fun(tc_prod(_1488213, _1488213), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488213, tc_prod(_1488213, _1488213)), tc_fun(_1488213, tc_fun(tc_fun(tc_prod(_1488213, _1488213), tc_HOL_Obool), tc_HOL_Obool)), _1488213), hAPP(c_COMBB(tc_prod(_1488213, _1488213), tc_fun(tc_fun(tc_prod(_1488213, _1488213), tc_HOL_Obool), tc_HOL_Obool), _1488213), c_member(tc_prod(_1488213, _1488213)))), c_Product__Type_OPair(_1488213, _1488213)))), _1488215)))], (37040 ^ _782652) ^ [_1488534, _1488536] : [c_Equiv__Relations_Oequivp(_1488534, hAPP(hAPP(c_COMBC(_1488534, tc_fun(tc_prod(_1488534, _1488534), tc_HOL_Obool), tc_fun(_1488534, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488534, tc_fun(tc_fun(tc_prod(_1488534, _1488534), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1488534, _1488534), tc_HOL_Obool), tc_fun(_1488534, tc_HOL_Obool)), _1488534), c_COMBC(_1488534, tc_fun(tc_prod(_1488534, _1488534), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488534, tc_prod(_1488534, _1488534)), tc_fun(_1488534, tc_fun(tc_fun(tc_prod(_1488534, _1488534), tc_HOL_Obool), tc_HOL_Obool)), _1488534), hAPP(c_COMBB(tc_prod(_1488534, _1488534), tc_fun(tc_fun(tc_prod(_1488534, _1488534), tc_HOL_Obool), tc_HOL_Obool), _1488534), c_member(tc_prod(_1488534, _1488534)))), c_Product__Type_OPair(_1488534, _1488534)))), _1488536)), -(c_Equiv__Relations_Oequiv(_1488534, c_Orderings_Otop__class_Otop(tc_fun(_1488534, tc_HOL_Obool)), _1488536))], (37046 ^ _782652) ^ [_1488861, _1488863, _1488865, _1488867, _1488869, _1488871, _1488873] : [-(hAPP(c_Product__Type_Oapsnd(_1488861, _1488863, _1488865, _1488867), hAPP(c_Product__Type_Oapfst(_1488869, _1488865, _1488861, _1488871), _1488873)) = hAPP(hAPP(c_Product__Type_OPair(_1488865, _1488863), hAPP(_1488871, hAPP(c_Product__Type_Ofst(_1488869, _1488861), _1488873))), hAPP(_1488867, hAPP(c_Product__Type_Osnd(_1488869, _1488861), _1488873))))], (37048 ^ _782652) ^ [_1488939, _1488941, _1488943, _1488945, _1488947, _1488949] : [-(hAPP(c_Product__Type_Oapfst(_1488939, _1488941, _1488943, _1488945), hAPP(hAPP(c_Product__Type_OPair(_1488939, _1488943), _1488947), _1488949)) = hAPP(hAPP(c_Product__Type_OPair(_1488941, _1488943), hAPP(_1488945, _1488947)), _1488949))], (37050 ^ _782652) ^ [_1489028, _1489030, _1489032, _1489034, _1489036, _1489038] : [hAPP(c_Product__Type_Oapfst(_1489028, _1489030, _1489032, _1489034), _1489036) = hAPP(c_Product__Type_Oapfst(_1489028, _1489030, _1489032, _1489038), _1489036), -(hAPP(_1489034, hAPP(c_Product__Type_Ofst(_1489028, _1489032), _1489036)) = hAPP(_1489038, hAPP(c_Product__Type_Ofst(_1489028, _1489032), _1489036)))], (37056 ^ _782652) ^ [_1489177, _1489179, _1489181, _1489183, _1489185, _1489187] : [hAPP(_1489183, hAPP(c_Product__Type_Ofst(_1489177, _1489181), _1489185)) = hAPP(_1489187, hAPP(c_Product__Type_Ofst(_1489177, _1489181), _1489185)), -(hAPP(c_Product__Type_Oapfst(_1489177, _1489179, _1489181, _1489183), _1489185) = hAPP(c_Product__Type_Oapfst(_1489177, _1489179, _1489181, _1489187), _1489185))], (37062 ^ _782652) ^ [_1489332, _1489334, _1489336, _1489338, _1489340] : [-(hAPP(c_Product__Type_Ofst(_1489332, _1489334), hAPP(c_Product__Type_Oapfst(_1489336, _1489332, _1489334, _1489338), _1489340)) = hAPP(_1489338, hAPP(c_Product__Type_Ofst(_1489336, _1489334), _1489340)))], (37064 ^ _782652) ^ [_1489386] : [-(c_Equiv__Relations_Oequivp(_1489386, c_fequal))], (37082 ^ _782652) ^ [_1489722, _1489724] : [-(c_Equiv__Relations_Oequivp(_1489722, _1489724)), 37087 ^ _782652 : [(37088 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1489724, 37083 ^ [_1489722, _1489724]), 37084 ^ [_1489722, _1489724])))], (37090 ^ _782652) ^ [] : [hAPP(_1489724, 37083 ^ [_1489722, _1489724]) = hAPP(_1489724, 37084 ^ [_1489722, _1489724])]], 37091 ^ _782652 : [(37092 ^ _782652) ^ [] : [-(hAPP(_1489724, 37083 ^ [_1489722, _1489724]) = hAPP(_1489724, 37084 ^ [_1489722, _1489724]))], (37094 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1489724, 37083 ^ [_1489722, _1489724]), 37084 ^ [_1489722, _1489724]))]]], (37066 ^ _782652) ^ [_1489424, _1489426] : [c_Equiv__Relations_Oequivp(_1489424, _1489426), 37069 ^ _782652 : [(37070 ^ _782652) ^ [_1489518, _1489520] : [hBOOL(hAPP(hAPP(_1489426, _1489520), _1489518)), -(hAPP(_1489426, _1489520) = hAPP(_1489426, _1489518))], (37076 ^ _782652) ^ [_1489617, _1489619] : [hAPP(_1489426, _1489619) = hAPP(_1489426, _1489617), -(hBOOL(hAPP(hAPP(_1489426, _1489619), _1489617)))]]], (37098 ^ _782652) ^ [_1490051, _1490053, _1490055] : [c_Equiv__Relations_Oequivp(_1490051, _1490053), -(hBOOL(hAPP(hAPP(_1490053, _1490055), _1490055)))], (37104 ^ _782652) ^ [_1490140, _1490142, _1490144, _1490146] : [c_Equiv__Relations_Oequivp(_1490140, _1490142), hBOOL(hAPP(hAPP(_1490142, _1490144), _1490146)), -(hBOOL(hAPP(hAPP(_1490142, _1490146), _1490144)))], (37114 ^ _782652) ^ [_1490297, _1490299, _1490301, _1490303, _1490305] : [c_Equiv__Relations_Oequivp(_1490297, _1490299), hBOOL(hAPP(hAPP(_1490299, _1490301), _1490303)), hBOOL(hAPP(hAPP(_1490299, _1490303), _1490305)), -(hBOOL(hAPP(hAPP(_1490299, _1490301), _1490305)))], (37128 ^ _782652) ^ [_1490526, _1490528, _1490530, _1490532, _1490534] : [-(hAPP(c_Product__Type_Osnd(_1490526, _1490528), hAPP(c_Product__Type_Oapfst(_1490530, _1490526, _1490528, _1490532), _1490534)) = hAPP(c_Product__Type_Osnd(_1490530, _1490528), _1490534))], (37130 ^ _782652) ^ [_1490577, _1490579, _1490581, _1490583, _1490585, _1490587, _1490589] : [-(hAPP(c_Product__Type_Oapsnd(_1490577, _1490579, _1490581, _1490583), hAPP(c_Product__Type_Oapfst(_1490585, _1490581, _1490577, _1490587), _1490589)) = hAPP(c_Product__Type_Oapfst(_1490585, _1490581, _1490579, _1490587), hAPP(c_Product__Type_Oapsnd(_1490577, _1490579, _1490585, _1490583), _1490589)))], (37132 ^ _782652) ^ [_1490644, _1490646, _1490648, _1490650, _1490652, _1490654, _1490656] : [-(hAPP(c_Product__Type_Oapfst(_1490644, _1490646, _1490648, _1490650), hAPP(c_Product__Type_Oapsnd(_1490652, _1490648, _1490644, _1490654), _1490656)) = hAPP(hAPP(c_Product__Type_OPair(_1490646, _1490648), hAPP(_1490650, hAPP(c_Product__Type_Ofst(_1490644, _1490652), _1490656))), hAPP(_1490654, hAPP(c_Product__Type_Osnd(_1490644, _1490652), _1490656))))], (37134 ^ _782652) ^ [_1490722, _1490724, _1490726, _1490728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1490722), _1490724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1490726), _1490728)), -(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), _1490722), _1490726)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1490724), _1490728))), c_FunDef_Opair__less)))], (37144 ^ _782652) ^ [_1490925, _1490927, _1490929, _1490931, _1490933] : [hBOOL(hAPP(hAPP(c_member(_1490925), _1490927), hAPP(c_Relation_OImage(_1490929, _1490925, _1490931), _1490933))), 37148 ^ _782652 : [(37149 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490929, _1490925)), hAPP(hAPP(c_Product__Type_OPair(_1490929, _1490925), 37147 ^ [_1490925, _1490927, _1490929, _1490931, _1490933]), _1490927)), _1490931)))], (37151 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490929), 37147 ^ [_1490925, _1490927, _1490929, _1490931, _1490933]), _1490933)))]]], (37153 ^ _782652) ^ [_1491149, _1491151, _1491153] : [-(c_Wellfounded_Omlex__prod(_1491149, _1491151, _1491153) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1491149), _1491149), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1491149, c_Wellfounded_Oless__than, _1491153)), hAPP(hAPP(c_COMBS(_1491149, _1491149, tc_prod(tc_Nat_Onat, _1491149)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1491149, tc_prod(tc_Nat_Onat, _1491149)), _1491149), c_Product__Type_OPair(tc_Nat_Onat, _1491149)), _1491151)), c_COMBI(_1491149))))], (37155 ^ _782652) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (37157 ^ _782652) ^ [_1491249] : [-(c_Wellfounded_Omeasure(_1491249) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1491249), c_Wellfounded_Oless__than))], (37159 ^ _782652) ^ [_1491295, _1491297] : [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), _1491295), _1491297)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491295), _1491297)))], (37165 ^ _782652) ^ [_1491400, _1491402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491400), _1491402)), -(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), _1491400), _1491402)), c_Wellfounded_Oless__than)))], (37171 ^ _782652) ^ [_1491511, _1491513, _1491515, _1491517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491511), _1491513)), -(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), _1491511), _1491515)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1491513), _1491517))), c_FunDef_Opair__less)))], (37177 ^ _782652) ^ [_1491648, _1491650, _1491652, _1491654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1491648), _1491650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1491652), _1491654)), -(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), _1491648), _1491652)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1491650), _1491654))), c_FunDef_Opair__leq)))], (37187 ^ _782652) ^ [_1491851, _1491853, _1491855, _1491857] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1491851), _1491853)), 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)), _1491851), _1491855)), 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)), _1491853), _1491857)), 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)), _1491853), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1491855), _1491857))), c_FunDef_Omin__strict)))], (37201 ^ _782652) ^ [_1492132, _1492134, _1492136, _1492138] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1492132), _1492134)), 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)), _1492136), _1492132)), 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)), _1492138), _1492134)), 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)), _1492136), _1492138)), _1492134)), c_FunDef_Omax__strict)))], (37215 ^ _782652) ^ [_1492413] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1492413)), -(_1492413 = 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))), _1492413)), c_FunDef_Omax__strict)))], (37225 ^ _782652) ^ [_1492519] : [-(_1492519 = 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)), _1492519), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (37231 ^ _782652) ^ [_1492564, _1492566, _1492568, _1492570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1492564), _1492566)), -(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), _1492564), _1492568)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1492566), _1492570))), c_FunDef_Opair__leq)))], (37237 ^ _782652) ^ [_1492701, _1492703, _1492705, _1492707] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1492701), _1492703)), 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)), _1492705), _1492701)), 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)), _1492707), _1492703)), 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)), _1492705), _1492707)), _1492703)), c_FunDef_Omax__weak)))], (37251 ^ _782652) ^ [_1492982, _1492984, _1492986, _1492988] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1492982), _1492984)), 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)), _1492982), _1492986)), 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)), _1492984), _1492988)), 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)), _1492984), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1492986), _1492988))), c_FunDef_Omin__weak)))], (37265 ^ _782652) ^ [_1493263, _1493265, _1493267, _1493269] : [-(hAPP(c_Relation_OField(_1493263), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1493263, _1493263)), hAPP(hAPP(c_Product__Type_OPair(_1493263, _1493263), _1493265), _1493267)), _1493269)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493263, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1493263), _1493265), hAPP(hAPP(c_Set_Oinsert(_1493263), _1493267), c_Orderings_Obot__class_Obot(tc_fun(_1493263, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1493263), _1493269)))], (37267 ^ _782652) ^ [_1493354] : [-(hAPP(c_Relation_OField(_1493354), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1493354, _1493354), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1493354, tc_HOL_Obool)))], (37269 ^ _782652) ^ [_1493395, _1493397, _1493399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493395, _1493395), tc_HOL_Obool)), _1493397), _1493399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493395, tc_HOL_Obool)), hAPP(c_Relation_OField(_1493395), _1493397)), hAPP(c_Relation_OField(_1493395), _1493399))))], (37275 ^ _782652) ^ [_1493540, _1493542, _1493544] : [-(hAPP(c_Relation_OField(_1493540), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1493540, _1493540), tc_HOL_Obool)), _1493542), _1493544)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493540, tc_HOL_Obool)), hAPP(c_Relation_OField(_1493540), _1493542)), hAPP(c_Relation_OField(_1493540), _1493544)))], (37277 ^ _782652) ^ [_1493607, _1493609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1493607, _1493607)), _1493609)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493607), hAPP(c_Relation_OField(_1493607), _1493609))))], (37283 ^ _782652) ^ [_1493716] : [-(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)), _1493716), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (37285 ^ _782652) ^ [_1493750] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1493750)), -(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))), _1493750)), c_FunDef_Omax__weak)))], (37291 ^ _782652) ^ [] : [-(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)))))], (37293 ^ _782652) ^ [] : [-(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)))))], (37295 ^ _782652) ^ [_1493881, _1493883] : [-(c_Relation_OId__on(_1493881, _1493883) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1493881, tc_fun(tc_prod(_1493881, _1493881), tc_HOL_Obool)), _1493883), hAPP(hAPP(c_COMBC(_1493881, tc_fun(tc_prod(_1493881, _1493881), tc_HOL_Obool), tc_fun(tc_prod(_1493881, _1493881), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1493881, _1493881), tc_fun(tc_fun(tc_prod(_1493881, _1493881), tc_HOL_Obool), tc_fun(tc_prod(_1493881, _1493881), tc_HOL_Obool)), _1493881), c_Set_Oinsert(tc_prod(_1493881, _1493881))), hAPP(hAPP(c_COMBS(_1493881, _1493881, tc_prod(_1493881, _1493881)), c_Product__Type_OPair(_1493881, _1493881)), c_COMBI(_1493881)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1493881, _1493881), tc_HOL_Obool)))))], (37297 ^ _782652) ^ [_1494005, _1494007] : [-(c_Relation_OId__on(_1494005, _1494007) = hAPP(c_Product__Type_Oprod_Oprod__case(_1494005, _1494005, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1494005, tc_HOL_Obool, tc_fun(_1494005, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494005, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1494005, tc_HOL_Obool)), _1494005), c_COMBC(_1494005, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494005, tc_HOL_Obool), tc_fun(_1494005, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1494005), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1494005), c_fconj)), c_fequal))), _1494007)))], (37299 ^ _782652) ^ [_1494099] : [-(c_Relation_OId__on(_1494099, c_Orderings_Obot__class_Obot(tc_fun(_1494099, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1494099, _1494099), tc_HOL_Obool)))], (37301 ^ _782652) ^ [_1494138, _1494140, _1494142] : [-(hAPP(c_Relation_OImage(_1494138, _1494138, c_Relation_OId__on(_1494138, _1494140)), _1494142) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494138, tc_HOL_Obool)), _1494140), _1494142))], (37303 ^ _782652) ^ [_1494186, _1494188, _1494190, _1494192] : [_1494186 = _1494188, hBOOL(hAPP(hAPP(c_member(_1494190), _1494186), _1494192)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494190, _1494190)), hAPP(hAPP(c_Product__Type_OPair(_1494190, _1494190), _1494186), _1494188)), c_Relation_OId__on(_1494190, _1494192))))], (37313 ^ _782652) ^ [_1494402, _1494404, _1494406, _1494408] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494402, _1494402)), hAPP(hAPP(c_Product__Type_OPair(_1494402, _1494402), _1494404), _1494406)), c_Relation_OId__on(_1494402, _1494408))), 37316 ^ _782652 : [(37317 ^ _782652) ^ [] : [-(_1494404 = _1494406)], (37319 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494402), _1494404), _1494408)))]]], (37321 ^ _782652) ^ [_1494563, _1494565, _1494567, _1494569] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494563, _1494563)), hAPP(hAPP(c_Product__Type_OPair(_1494563, _1494563), _1494565), _1494567)), c_Relation_OId__on(_1494563, _1494569)))), _1494565 = _1494567, hBOOL(hAPP(hAPP(c_member(_1494563), _1494565), _1494569))], (37331 ^ _782652) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (37333 ^ _782652) ^ [_1494778, _1494780, _1494782, _1494784, _1494786, _1494788] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1494778, tc_HOL_Obool), tc_fun(_1494778, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1494778, tc_HOL_Obool), tc_fun(_1494778, tc_HOL_Obool)), _1494780), _1494782)), c_Wellfounded_Omax__ext(_1494778, _1494784))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1494778, tc_HOL_Obool), tc_fun(_1494778, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1494778, tc_HOL_Obool), tc_fun(_1494778, tc_HOL_Obool)), _1494786), _1494788)), c_Wellfounded_Omax__ext(_1494778, _1494784))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1494778, tc_HOL_Obool), tc_fun(_1494778, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1494778, tc_HOL_Obool), tc_fun(_1494778, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494778, tc_HOL_Obool)), _1494780), _1494786)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1494778, tc_HOL_Obool)), _1494782), _1494788))), c_Wellfounded_Omax__ext(_1494778, _1494784))))], (37343 ^ _782652) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (37345 ^ _782652) ^ [_1495210, _1495212, _1495214, _1495216] : [c_Wellfounded_Omax__extp(_1495210, hAPP(hAPP(c_COMBC(_1495210, tc_fun(tc_prod(_1495210, _1495210), tc_HOL_Obool), tc_fun(_1495210, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495210, tc_fun(tc_fun(tc_prod(_1495210, _1495210), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495210, _1495210), tc_HOL_Obool), tc_fun(_1495210, tc_HOL_Obool)), _1495210), c_COMBC(_1495210, tc_fun(tc_prod(_1495210, _1495210), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495210, tc_prod(_1495210, _1495210)), tc_fun(_1495210, tc_fun(tc_fun(tc_prod(_1495210, _1495210), tc_HOL_Obool), tc_HOL_Obool)), _1495210), hAPP(c_COMBB(tc_prod(_1495210, _1495210), tc_fun(tc_fun(tc_prod(_1495210, _1495210), tc_HOL_Obool), tc_HOL_Obool), _1495210), c_member(tc_prod(_1495210, _1495210)))), c_Product__Type_OPair(_1495210, _1495210)))), _1495212), _1495214, _1495216), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1495210, tc_HOL_Obool), tc_fun(_1495210, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1495210, tc_HOL_Obool), tc_fun(_1495210, tc_HOL_Obool)), _1495214), _1495216)), c_Wellfounded_Omax__ext(_1495210, _1495212))))], (37351 ^ _782652) ^ [_1495595, _1495597, _1495599, _1495601] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1495595, tc_HOL_Obool), tc_fun(_1495595, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1495595, tc_HOL_Obool), tc_fun(_1495595, tc_HOL_Obool)), _1495599), _1495601)), c_Wellfounded_Omax__ext(_1495595, _1495597))), -(c_Wellfounded_Omax__extp(_1495595, hAPP(hAPP(c_COMBC(_1495595, tc_fun(tc_prod(_1495595, _1495595), tc_HOL_Obool), tc_fun(_1495595, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495595, tc_fun(tc_fun(tc_prod(_1495595, _1495595), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495595, _1495595), tc_HOL_Obool), tc_fun(_1495595, tc_HOL_Obool)), _1495595), c_COMBC(_1495595, tc_fun(tc_prod(_1495595, _1495595), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495595, tc_prod(_1495595, _1495595)), tc_fun(_1495595, tc_fun(tc_fun(tc_prod(_1495595, _1495595), tc_HOL_Obool), tc_HOL_Obool)), _1495595), hAPP(c_COMBB(tc_prod(_1495595, _1495595), tc_fun(tc_fun(tc_prod(_1495595, _1495595), tc_HOL_Obool), tc_HOL_Obool), _1495595), c_member(tc_prod(_1495595, _1495595)))), c_Product__Type_OPair(_1495595, _1495595)))), _1495597), _1495599, _1495601))], (37357 ^ _782652) ^ [] : [-(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)))], (37359 ^ _782652) ^ [] : [-(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)))], (37361 ^ _782652) ^ [_1496022, _1496024, _1496026, _1496028] : [c_FunDef_Oreduction__pair(_1496022, _1496024), -(c_FunDef_Oreduction__pair(_1496026, hAPP(hAPP(c_FunDef_Orp__inv__image(_1496022, _1496026), _1496024), _1496028)))], (37367 ^ _782652) ^ [_1496136, _1496138] : [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)), _1496136), 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)), _1496138), 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)), _1496136), _1496138)), c_Int_Ointrel)))], (37373 ^ _782652) ^ [_1496267, _1496269] : [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)), _1496267), _1496269)), 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)), _1496267), 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)), _1496269), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (37379 ^ _782652) ^ [_1496425, _1496427, _1496429, _1496431] : [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), _1496425), _1496427)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1496429), _1496431))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1496425), _1496431) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1496429), _1496427))], (37385 ^ _782652) ^ [_1496572, _1496574, _1496576, _1496578] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1496572), _1496578) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1496576), _1496574), -(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), _1496572), _1496574)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1496576), _1496578))), c_Int_Ointrel)))], (37391 ^ _782652) ^ [_1496725, _1496727, _1496729] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1496725, _1496725)), _1496727), c_Relation_OId__on(_1496725, _1496729))), 37395 ^ _782652 : [(37396 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1496725), 37394 ^ [_1496725, _1496727, _1496729]), _1496729)))], (37398 ^ _782652) ^ [] : [-(_1496727 = hAPP(hAPP(c_Product__Type_OPair(_1496725, _1496725), 37394 ^ [_1496725, _1496727, _1496729]), 37394 ^ [_1496725, _1496727, _1496729]))]]], (37400 ^ _782652) ^ [] : [-(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))], (37402 ^ _782652) ^ [_1496942, _1496944, _1496946] : [class_Rings_Oring__1(_1496942), -(hAPP(c_Int_Oring__1__class_Oof__int(_1496942), 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), _1496944), _1496946)), 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(_1496942), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1496942), _1496944)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1496942), _1496946)))], (37408 ^ _782652) ^ [] : [-(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))))))], (37410 ^ _782652) ^ [_1497119, _1497121, _1497123, _1497125] : [-(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), _1497119), _1497121)), 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), _1497123), _1497125)), 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), _1497119), _1497123)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1497121), _1497125))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1497119), _1497125)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1497121), _1497123)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37412 ^ _782652) ^ [_1497244] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1497244)) = _1497244)], (37414 ^ _782652) ^ [_1497273, _1497275] : [-(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), _1497273), _1497275)), 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), _1497275), _1497273)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37416 ^ _782652) ^ [] : [-(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))))))], (37418 ^ _782652) ^ [_1497355] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1497355) = 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), _1497355), 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))))))], (37420 ^ _782652) ^ [_1497399, _1497401, _1497403, _1497405] : [-(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), _1497399), _1497401)), 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), _1497403), _1497405)), 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), _1497399), _1497403)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1497401), _1497405))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37422 ^ _782652) ^ [_1497500, _1497502] : [-(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), _1497500), _1497502)), 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), _1497500), _1497502))], (37424 ^ _782652) ^ [_1497552] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1497552) = 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, _1497552)), 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))))))))], (37426 ^ _782652) ^ [_1497611, _1497613, _1497615, _1497617] : [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), _1497611), _1497613)), 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), _1497615), _1497617)), 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), _1497611), _1497617)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1497615), _1497613))))], (37432 ^ _782652) ^ [_1497804, _1497806, _1497808, _1497810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1497804), _1497810)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1497808), _1497806))), -(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), _1497804), _1497806)), 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), _1497808), _1497810)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (37438 ^ _782652) ^ [_1498024, _1498026, _1498028, _1498030] : [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), _1498024), _1498026)), 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), _1498028), _1498030)), 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), _1498024), _1498030)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1498028), _1498026))))], (37444 ^ _782652) ^ [_1498217, _1498219, _1498221, _1498223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1498217), _1498223)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1498221), _1498219))), -(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), _1498217), _1498219)), 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), _1498221), _1498223)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (37452 ^ _782652) ^ [_1498416] : [-(_1498416 = 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), 37449 ^ [_1498416]), 37450 ^ [_1498416])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37454 ^ _782652) ^ [] : [-(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))], (37456 ^ _782652) ^ [_1498485, _1498487, _1498489, _1498491] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1498485, _1498487, _1498489, c_Code__Numeral_OSuc__code__numeral(_1498491)) = hAPP(_1498489, _1498491))], (37458 ^ _782652) ^ [_1498524] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1498524)), c_Int_OInteg)))], (37460 ^ _782652) ^ [_1498555, _1498557, _1498559] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1498555, _1498557, _1498559, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1498557)], (37462 ^ _782652) ^ [] : [-(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))], (37464 ^ _782652) ^ [_1498623, _1498625, _1498627] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1498623, hAPP(hAPP(c_COMBC(_1498623, tc_fun(tc_prod(_1498623, _1498623), tc_HOL_Obool), tc_fun(_1498623, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498623, tc_fun(tc_fun(tc_prod(_1498623, _1498623), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1498623, _1498623), tc_HOL_Obool), tc_fun(_1498623, tc_HOL_Obool)), _1498623), c_COMBC(_1498623, tc_fun(tc_prod(_1498623, _1498623), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498623, tc_prod(_1498623, _1498623)), tc_fun(_1498623, tc_fun(tc_fun(tc_prod(_1498623, _1498623), tc_HOL_Obool), tc_HOL_Obool)), _1498623), hAPP(c_COMBB(tc_prod(_1498623, _1498623), tc_fun(tc_fun(tc_prod(_1498623, _1498623), tc_HOL_Obool), tc_HOL_Obool), _1498623), c_member(tc_prod(_1498623, _1498623)))), c_Product__Type_OPair(_1498623, _1498623)))), _1498625)), _1498627)), -(hBOOL(hAPP(hAPP(c_member(_1498623), _1498627), c_Wellfounded_Oacc(_1498623, _1498625))))], (37470 ^ _782652) ^ [_1498964, _1498966, _1498968] : [hBOOL(hAPP(hAPP(c_member(_1498964), _1498968), c_Wellfounded_Oacc(_1498964, _1498966))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1498964, hAPP(hAPP(c_COMBC(_1498964, tc_fun(tc_prod(_1498964, _1498964), tc_HOL_Obool), tc_fun(_1498964, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498964, tc_fun(tc_fun(tc_prod(_1498964, _1498964), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1498964, _1498964), tc_HOL_Obool), tc_fun(_1498964, tc_HOL_Obool)), _1498964), c_COMBC(_1498964, tc_fun(tc_prod(_1498964, _1498964), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498964, tc_prod(_1498964, _1498964)), tc_fun(_1498964, tc_fun(tc_fun(tc_prod(_1498964, _1498964), tc_HOL_Obool), tc_HOL_Obool)), _1498964), hAPP(c_COMBB(tc_prod(_1498964, _1498964), tc_fun(tc_fun(tc_prod(_1498964, _1498964), tc_HOL_Obool), tc_HOL_Obool), _1498964), c_member(tc_prod(_1498964, _1498964)))), c_Product__Type_OPair(_1498964, _1498964)))), _1498966)), _1498968)))], (37476 ^ _782652) ^ [_1499311, _1499313, _1499315, _1499317, _1499319] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1499311, _1499313, _1499315), _1499317), _1499319) = hAPP(c_Set_OCollect(tc_prod(_1499311, _1499315)), hAPP(c_Product__Type_Oprod_Oprod__case(_1499311, _1499315, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1499315, tc_fun(_1499313, tc_HOL_Obool)), tc_fun(_1499315, tc_HOL_Obool), _1499311), hAPP(c_COMBB(tc_fun(_1499313, tc_HOL_Obool), tc_HOL_Obool, _1499315), c_HOL_OEx(_1499313))), hAPP(hAPP(c_COMBC(_1499311, tc_fun(_1499315, tc_fun(_1499313, tc_HOL_Obool)), tc_fun(_1499315, tc_fun(_1499313, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1499313, tc_HOL_Obool), tc_fun(_1499313, tc_HOL_Obool)), tc_fun(tc_fun(_1499315, tc_fun(_1499313, tc_HOL_Obool)), tc_fun(_1499315, tc_fun(_1499313, tc_HOL_Obool))), _1499311), c_COMBB(tc_fun(_1499313, tc_HOL_Obool), tc_fun(_1499313, tc_HOL_Obool), _1499315)), hAPP(hAPP(c_COMBB(tc_fun(_1499313, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1499313, tc_HOL_Obool), tc_fun(_1499313, tc_HOL_Obool)), _1499311), c_COMBS(_1499313, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499313, tc_HOL_Obool), tc_fun(_1499313, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1499311), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1499313), c_fconj)), hAPP(hAPP(c_COMBC(_1499311, tc_fun(tc_prod(_1499311, _1499313), tc_HOL_Obool), tc_fun(_1499313, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499313, tc_fun(tc_fun(tc_prod(_1499311, _1499313), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499311, _1499313), tc_HOL_Obool), tc_fun(_1499313, tc_HOL_Obool)), _1499311), c_COMBC(_1499313, tc_fun(tc_prod(_1499311, _1499313), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499313, tc_prod(_1499311, _1499313)), tc_fun(_1499313, tc_fun(tc_fun(tc_prod(_1499311, _1499313), tc_HOL_Obool), tc_HOL_Obool)), _1499311), hAPP(c_COMBB(tc_prod(_1499311, _1499313), tc_fun(tc_fun(tc_prod(_1499311, _1499313), tc_HOL_Obool), tc_HOL_Obool), _1499313), c_member(tc_prod(_1499311, _1499313)))), c_Product__Type_OPair(_1499311, _1499313)))), _1499317))))), hAPP(hAPP(c_COMBC(_1499315, tc_fun(tc_prod(_1499313, _1499315), tc_HOL_Obool), tc_fun(_1499313, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499313, tc_fun(tc_fun(tc_prod(_1499313, _1499315), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1499313, _1499315), tc_HOL_Obool), tc_fun(_1499313, tc_HOL_Obool)), _1499315), c_COMBC(_1499313, tc_fun(tc_prod(_1499313, _1499315), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499313, tc_prod(_1499313, _1499315)), tc_fun(_1499313, tc_fun(tc_fun(tc_prod(_1499313, _1499315), tc_HOL_Obool), tc_HOL_Obool)), _1499315), hAPP(c_COMBB(tc_prod(_1499313, _1499315), tc_fun(tc_fun(tc_prod(_1499313, _1499315), tc_HOL_Obool), tc_HOL_Obool), _1499313), c_member(tc_prod(_1499313, _1499315)))), hAPP(c_COMBC(_1499313, _1499315, tc_prod(_1499313, _1499315)), c_Product__Type_OPair(_1499313, _1499315))))), _1499319))))))], (37478 ^ _782652) ^ [_1499759, _1499761, _1499763, _1499765, _1499767, _1499769, _1499771, _1499773] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499759, _1499761)), hAPP(hAPP(c_Product__Type_OPair(_1499759, _1499761), _1499763), _1499765)), _1499767)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1499761, _1499769)), hAPP(hAPP(c_Product__Type_OPair(_1499761, _1499769), _1499765), _1499771)), _1499773)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1499759, _1499769)), hAPP(hAPP(c_Product__Type_OPair(_1499759, _1499769), _1499763), _1499771)), hAPP(hAPP(c_Relation_Orel__comp(_1499759, _1499761, _1499769), _1499767), _1499773))))], (37488 ^ _782652) ^ [_1500046, _1500048, _1500050, _1500052, _1500054, _1500056, _1500058] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500046, _1500048, _1500050), _1500052), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500054, tc_fun(tc_prod(_1500048, _1500050), tc_HOL_Obool)), _1500056), _1500058)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500054, tc_fun(tc_prod(_1500046, _1500050), tc_HOL_Obool)), _1500056), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1500048, _1500050), tc_HOL_Obool), tc_fun(tc_prod(_1500046, _1500050), tc_HOL_Obool), _1500054), hAPP(c_Relation_Orel__comp(_1500046, _1500048, _1500050), _1500052)), _1500058)))], (37490 ^ _782652) ^ [_1500150, _1500152, _1500154, _1500156, _1500158, _1500160, _1500162] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500150, _1500152, _1500154), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500156, tc_fun(tc_prod(_1500150, _1500152), tc_HOL_Obool)), _1500158), _1500160)), _1500162) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500156, tc_fun(tc_prod(_1500150, _1500154), tc_HOL_Obool)), _1500158), hAPP(hAPP(c_COMBC(_1500156, tc_fun(tc_prod(_1500152, _1500154), tc_HOL_Obool), tc_fun(tc_prod(_1500150, _1500154), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1500150, _1500152), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1500152, _1500154), tc_HOL_Obool), tc_fun(tc_prod(_1500150, _1500154), tc_HOL_Obool)), _1500156), c_Relation_Orel__comp(_1500150, _1500152, _1500154)), _1500160)), _1500162)))], (37492 ^ _782652) ^ [_1500282, _1500284, _1500286, _1500288] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500282, _1500284, _1500286), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500282, _1500284), tc_HOL_Obool))), _1500288) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500282, _1500286), tc_HOL_Obool)))], (37494 ^ _782652) ^ [_1500337, _1500339, _1500341, _1500343] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500337, _1500339, _1500341), _1500343), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500339, _1500341), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500337, _1500341), tc_HOL_Obool)))], (37496 ^ _782652) ^ [_1500392, _1500394, _1500396, _1500398, _1500400, _1500402] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500392, _1500394, _1500396), _1500398), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500394, _1500396), tc_HOL_Obool)), _1500400), _1500402)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500392, _1500396), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1500392, _1500394, _1500396), _1500398), _1500400)), hAPP(hAPP(c_Relation_Orel__comp(_1500392, _1500394, _1500396), _1500398), _1500402)))], (37498 ^ _782652) ^ [_1500483, _1500485, _1500487, _1500489, _1500491, _1500493] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500483, _1500485, _1500487), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500483, _1500485), tc_HOL_Obool)), _1500489), _1500491)), _1500493) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500483, _1500487), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1500483, _1500485, _1500487), _1500489), _1500493)), hAPP(hAPP(c_Relation_Orel__comp(_1500483, _1500485, _1500487), _1500491), _1500493)))], (37500 ^ _782652) ^ [_1500574, _1500576, _1500578, _1500580, _1500582, _1500584, _1500586] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1500574, _1500576, _1500578), hAPP(hAPP(c_Relation_Orel__comp(_1500574, _1500580, _1500576), _1500582), _1500584)), _1500586) = hAPP(hAPP(c_Relation_Orel__comp(_1500574, _1500580, _1500578), _1500582), hAPP(hAPP(c_Relation_Orel__comp(_1500580, _1500576, _1500578), _1500584), _1500586)))], (37502 ^ _782652) ^ [_1500649, _1500651, _1500653, _1500655, _1500657, _1500659, _1500661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500649, _1500651), tc_HOL_Obool)), _1500653), _1500655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500651, _1500657), tc_HOL_Obool)), _1500659), _1500661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500649, _1500657), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1500649, _1500651, _1500657), _1500653), _1500659)), hAPP(hAPP(c_Relation_Orel__comp(_1500649, _1500651, _1500657), _1500655), _1500661))))], (37512 ^ _782652) ^ [_1500916, _1500918, _1500920, _1500922] : [hAPP(hAPP(c_Relation_Orel__comp(_1500916, _1500916, _1500916), _1500918), _1500920) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500916, _1500916), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1500916, _1500916, _1500916), _1500922), _1500920) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500916, _1500916), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1500916, _1500916, _1500916), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500916, _1500916), tc_HOL_Obool)), _1500918), _1500922)), _1500920) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500916, _1500916), tc_HOL_Obool)))], (37522 ^ _782652) ^ [_1501189, _1501191, _1501193, _1501195] : [hAPP(hAPP(c_Relation_Orel__comp(_1501189, _1501189, _1501189), _1501191), _1501193) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501189, _1501189), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1501189, _1501189, _1501189), _1501191), _1501195) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501189, _1501189), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1501189, _1501189, _1501189), _1501191), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501189, _1501189), tc_HOL_Obool)), _1501193), _1501195)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501189, _1501189), tc_HOL_Obool)))], (37532 ^ _782652) ^ [_1501462, _1501464, _1501466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501462, _1501462), tc_HOL_Obool)), _1501464), _1501466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501462, tc_HOL_Obool)), c_Wellfounded_Oacc(_1501462, _1501466)), c_Wellfounded_Oacc(_1501462, _1501464))))], (37548 ^ _782652) ^ [_1501870, _1501872, _1501874] : [37550 ^ _782652 : [(37551 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501870, _1501870)), hAPP(hAPP(c_Product__Type_OPair(_1501870, _1501870), 37549 ^ [_1501870, _1501872, _1501874]), _1501872)), _1501874)))], (37553 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1501870), 37549 ^ [_1501870, _1501872, _1501874]), c_Wellfounded_Oacc(_1501870, _1501874)))]], -(hBOOL(hAPP(hAPP(c_member(_1501870), _1501872), c_Wellfounded_Oacc(_1501870, _1501874))))], (37538 ^ _782652) ^ [_1501617, _1501619, _1501621] : [hBOOL(hAPP(hAPP(c_member(_1501617), _1501619), c_Wellfounded_Oacc(_1501617, _1501621))), 37541 ^ _782652 : [(37542 ^ _782652) ^ [_1501731] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501617, _1501617)), hAPP(hAPP(c_Product__Type_OPair(_1501617, _1501617), _1501731), _1501619)), _1501621)), -(hBOOL(hAPP(hAPP(c_member(_1501617), _1501731), c_Wellfounded_Oacc(_1501617, _1501621))))]]], (37557 ^ _782652) ^ [_1502110, _1502112, _1502114, _1502116] : [hBOOL(hAPP(hAPP(c_member(_1502110), _1502112), c_Wellfounded_Oacc(_1502110, _1502114))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1502110, _1502110)), hAPP(hAPP(c_Product__Type_OPair(_1502110, _1502110), _1502116), _1502112)), _1502114)), -(hBOOL(hAPP(hAPP(c_member(_1502110), _1502116), c_Wellfounded_Oacc(_1502110, _1502114))))], (37567 ^ _782652) ^ [_1502325, _1502327, _1502329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502325, _1502325), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1502325, _1502325, _1502325), _1502327), _1502329)), _1502327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1502325, tc_HOL_Obool), tc_fun(_1502325, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1502325, tc_HOL_Obool), tc_fun(_1502325, tc_HOL_Obool), tc_fun(_1502325, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1502325, _1502327)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1502325, tc_HOL_Obool), tc_fun(_1502325, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1502325, _1502329)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1502325, tc_HOL_Obool), tc_fun(_1502325, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1502325, tc_HOL_Obool), tc_fun(_1502325, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1502325, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1502325, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1502325, tc_HOL_Obool), tc_fun(_1502325, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1502325, _1502327))))], (37573 ^ _782652) ^ [_1502696, _1502698, _1502700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502696, _1502696), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1502696, _1502696, _1502696), _1502698), _1502700)), _1502698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1502696, tc_HOL_Obool), tc_fun(_1502696, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1502696, tc_HOL_Obool), tc_fun(_1502696, tc_HOL_Obool), tc_fun(_1502696, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1502696, _1502698)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1502696, tc_HOL_Obool), tc_fun(_1502696, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1502696, _1502700)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1502696, tc_HOL_Obool), tc_fun(_1502696, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1502696, tc_HOL_Obool), tc_fun(_1502696, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1502696, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1502696, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1502696, tc_HOL_Obool), tc_fun(_1502696, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1502696, _1502698))))], (37579 ^ _782652) ^ [_1503067, _1503069, _1503071, _1503073, _1503075] : [c_Typedef_Otype__definition(_1503067, _1503069, _1503071, _1503073, _1503075), -(hAPP(c_Set_Oimage(_1503069, _1503067, _1503073), _1503075) = c_Orderings_Otop__class_Otop(tc_fun(_1503067, tc_HOL_Obool)))], (37585 ^ _782652) ^ [_1503180, _1503182, _1503184, _1503186, _1503188] : [c_Typedef_Otype__definition(_1503180, _1503182, _1503184, _1503186, _1503188), -(hAPP(c_Set_Oimage(_1503180, _1503182, _1503184), c_Orderings_Otop__class_Otop(tc_fun(_1503180, tc_HOL_Obool))) = _1503188)], (37591 ^ _782652) ^ [_1503293, _1503295, _1503297, _1503299, _1503301, _1503303, _1503305] : [c_Typedef_Otype__definition(_1503293, _1503295, _1503297, _1503299, _1503301), hBOOL(hAPP(hAPP(c_member(_1503295), _1503303), _1503301)), hBOOL(hAPP(hAPP(c_member(_1503295), _1503305), _1503301)), 37602 ^ _782652 : [(37603 ^ _782652) ^ [] : [hAPP(_1503299, _1503303) = hAPP(_1503299, _1503305), -(_1503303 = _1503305)], (37609 ^ _782652) ^ [] : [_1503303 = _1503305, -(hAPP(_1503299, _1503303) = hAPP(_1503299, _1503305))]]], (37615 ^ _782652) ^ [_1503706, _1503708, _1503710, _1503712, _1503714, _1503716, _1503718] : [c_Typedef_Otype__definition(_1503706, _1503708, _1503710, _1503712, _1503714), 37618 ^ _782652 : [(37619 ^ _782652) ^ [] : [hAPP(_1503710, _1503716) = hAPP(_1503710, _1503718), -(_1503716 = _1503718)], (37625 ^ _782652) ^ [] : [_1503716 = _1503718, -(hAPP(_1503710, _1503716) = hAPP(_1503710, _1503718))]]], (37631 ^ _782652) ^ [_1503967, _1503969, _1503971, _1503973, _1503975, _1503977] : [c_Typedef_Otype__definition(_1503967, _1503969, _1503971, _1503973, _1503975), -(hAPP(_1503973, hAPP(_1503971, _1503977)) = _1503977)], (37637 ^ _782652) ^ [_1504070, _1504072, _1504074, _1504076, _1504078, _1504080] : [c_Typedef_Otype__definition(_1504070, _1504072, _1504074, _1504076, _1504078), -(hBOOL(hAPP(hAPP(c_member(_1504072), hAPP(_1504074, _1504080)), _1504078)))], (37643 ^ _782652) ^ [_1504181, _1504183, _1504185, _1504187, _1504189, _1504191] : [c_Typedef_Otype__definition(_1504181, _1504183, _1504185, _1504187, _1504189), hBOOL(hAPP(hAPP(c_member(_1504183), _1504191), _1504189)), -(hAPP(_1504185, hAPP(_1504187, _1504191)) = _1504191)], (37653 ^ _782652) ^ [_1504388, _1504390, _1504392, _1504394, _1504396, _1504398, _1504400] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1504388, _1504390, _1504392, hAPP(hAPP(c_COMBC(_1504388, tc_fun(tc_prod(_1504388, _1504390), tc_HOL_Obool), tc_fun(_1504390, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504390, tc_fun(tc_fun(tc_prod(_1504388, _1504390), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504388, _1504390), tc_HOL_Obool), tc_fun(_1504390, tc_HOL_Obool)), _1504388), c_COMBC(_1504390, tc_fun(tc_prod(_1504388, _1504390), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504390, tc_prod(_1504388, _1504390)), tc_fun(_1504390, tc_fun(tc_fun(tc_prod(_1504388, _1504390), tc_HOL_Obool), tc_HOL_Obool)), _1504388), hAPP(c_COMBB(tc_prod(_1504388, _1504390), tc_fun(tc_fun(tc_prod(_1504388, _1504390), tc_HOL_Obool), tc_HOL_Obool), _1504390), c_member(tc_prod(_1504388, _1504390)))), c_Product__Type_OPair(_1504388, _1504390)))), _1504394), hAPP(hAPP(c_COMBC(_1504390, tc_fun(tc_prod(_1504390, _1504392), tc_HOL_Obool), tc_fun(_1504392, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504392, tc_fun(tc_fun(tc_prod(_1504390, _1504392), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504390, _1504392), tc_HOL_Obool), tc_fun(_1504392, tc_HOL_Obool)), _1504390), c_COMBC(_1504392, tc_fun(tc_prod(_1504390, _1504392), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504392, tc_prod(_1504390, _1504392)), tc_fun(_1504392, tc_fun(tc_fun(tc_prod(_1504390, _1504392), tc_HOL_Obool), tc_HOL_Obool)), _1504390), hAPP(c_COMBB(tc_prod(_1504390, _1504392), tc_fun(tc_fun(tc_prod(_1504390, _1504392), tc_HOL_Obool), tc_HOL_Obool), _1504392), c_member(tc_prod(_1504390, _1504392)))), c_Product__Type_OPair(_1504390, _1504392)))), _1504396)), _1504398), _1504400)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504388, _1504392)), hAPP(hAPP(c_Product__Type_OPair(_1504388, _1504392), _1504398), _1504400)), hAPP(hAPP(c_Relation_Orel__comp(_1504388, _1504390, _1504392), _1504394), _1504396))))], (37659 ^ _782652) ^ [_1505023, _1505025, _1505027, _1505029, _1505031, _1505033, _1505035] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1505023, _1505027)), hAPP(hAPP(c_Product__Type_OPair(_1505023, _1505027), _1505033), _1505035)), hAPP(hAPP(c_Relation_Orel__comp(_1505023, _1505025, _1505027), _1505029), _1505031))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1505023, _1505025, _1505027, hAPP(hAPP(c_COMBC(_1505023, tc_fun(tc_prod(_1505023, _1505025), tc_HOL_Obool), tc_fun(_1505025, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505025, tc_fun(tc_fun(tc_prod(_1505023, _1505025), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1505023, _1505025), tc_HOL_Obool), tc_fun(_1505025, tc_HOL_Obool)), _1505023), c_COMBC(_1505025, tc_fun(tc_prod(_1505023, _1505025), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505025, tc_prod(_1505023, _1505025)), tc_fun(_1505025, tc_fun(tc_fun(tc_prod(_1505023, _1505025), tc_HOL_Obool), tc_HOL_Obool)), _1505023), hAPP(c_COMBB(tc_prod(_1505023, _1505025), tc_fun(tc_fun(tc_prod(_1505023, _1505025), tc_HOL_Obool), tc_HOL_Obool), _1505025), c_member(tc_prod(_1505023, _1505025)))), c_Product__Type_OPair(_1505023, _1505025)))), _1505029), hAPP(hAPP(c_COMBC(_1505025, tc_fun(tc_prod(_1505025, _1505027), tc_HOL_Obool), tc_fun(_1505027, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505027, tc_fun(tc_fun(tc_prod(_1505025, _1505027), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1505025, _1505027), tc_HOL_Obool), tc_fun(_1505027, tc_HOL_Obool)), _1505025), c_COMBC(_1505027, tc_fun(tc_prod(_1505025, _1505027), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505027, tc_prod(_1505025, _1505027)), tc_fun(_1505027, tc_fun(tc_fun(tc_prod(_1505025, _1505027), tc_HOL_Obool), tc_HOL_Obool)), _1505025), hAPP(c_COMBB(tc_prod(_1505025, _1505027), tc_fun(tc_fun(tc_prod(_1505025, _1505027), tc_HOL_Obool), tc_HOL_Obool), _1505027), c_member(tc_prod(_1505025, _1505027)))), c_Product__Type_OPair(_1505025, _1505027)))), _1505031)), _1505033), _1505035)))], (37665 ^ _782652) ^ [_1505664, _1505666, _1505668] : [c_Wellfounded_Owf(_1505664, _1505666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1505664, _1505664), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1505664, _1505664, _1505664), _1505666), _1505668)), _1505666)), -(c_FunDef_Oreduction__pair(_1505664, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1505664, _1505664), tc_HOL_Obool), tc_fun(tc_prod(_1505664, _1505664), tc_HOL_Obool)), _1505666), _1505668)))], (37675 ^ _782652) ^ [_1505906, _1505908, _1505910, _1505912] : [c_Wellfounded_Omax__extp(_1505906, _1505908, _1505910, _1505912), 37678 ^ _782652 : [(37679 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505906), _1505910)))], (37681 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505906), _1505912)))], (37683 ^ _782652) ^ [] : [_1505912 = c_Orderings_Obot__class_Obot(tc_fun(_1505906, tc_HOL_Obool))], (37685 ^ _782652) ^ [_1506122] : [hBOOL(hAPP(hAPP(c_member(_1505906), _1506122), _1505910)), 37689 ^ _782652 : [(37690 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505906), 37688 ^ [_1505906, _1505908, _1505910, _1505912, _1506122]), _1505912)))], (37692 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1505908, _1506122), 37688 ^ [_1505906, _1505908, _1505910, _1505912, _1506122])))]]]]], (37694 ^ _782652) ^ [_1506306, _1506308, _1506310, _1506312] : [-(c_Wellfounded_Omax__extp(_1506306, _1506308, _1506310, _1506312)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506306), _1506310)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506306), _1506312)), -(_1506312 = c_Orderings_Obot__class_Obot(tc_fun(_1506306, tc_HOL_Obool))), 37708 ^ _782652 : [(37709 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1506306), 37707 ^ [_1506306, _1506308, _1506310, _1506312]), _1506310)))], (37711 ^ _782652) ^ [_1506651] : [hBOOL(hAPP(hAPP(c_member(_1506306), _1506651), _1506312)), hBOOL(hAPP(hAPP(_1506308, 37707 ^ [_1506306, _1506308, _1506310, _1506312]), _1506651))]]], (37719 ^ _782652) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (37721 ^ _782652) ^ [_1506837, _1506839, _1506841, _1506843, _1506845, _1506847, _1506849, _1506851] : [hBOOL(hAPP(hAPP(_1506837, _1506839), _1506841)), hBOOL(hAPP(hAPP(_1506843, _1506841), _1506845)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1506847, _1506849, _1506851, _1506837, _1506843), _1506839), _1506845)))], (37731 ^ _782652) ^ [_1507032] : [-(c_Wellfounded_Owf(_1507032, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507032, _1507032), tc_HOL_Obool))))], (37733 ^ _782652) ^ [_1507063, _1507065, _1507067, _1507069] : [c_Wellfounded_Owf(_1507063, _1507065), -(c_Wellfounded_Owf(_1507067, hAPP(hAPP(c_Relation_Oinv__image(_1507063, _1507067), _1507065), _1507069)))], (37739 ^ _782652) ^ [_1507162, _1507164, _1507166, _1507168] : [c_Wellfounded_Owf(_1507162, _1507164), c_Wellfounded_Owf(_1507166, _1507168), -(c_Wellfounded_Owf(tc_prod(_1507162, _1507166), c_Wellfounded_Olex__prod(_1507162, _1507166, _1507164, _1507168)))], (37749 ^ _782652) ^ [_1507315, _1507317] : [-(c_Wellfounded_Owf(_1507315, hAPP(c_Wellfounded_Omeasure(_1507315), _1507317)))], (37751 ^ _782652) ^ [_1507360, _1507362] : [c_Wellfounded_Owf(_1507360, _1507362), -(c_Wellfounded_Owf(_1507360, hAPP(hAPP(c_Relation_Orel__comp(_1507360, _1507360, _1507360), _1507362), _1507362)))], (37757 ^ _782652) ^ [_1507453, _1507455] : [c_Wellfounded_Owf(_1507453, hAPP(hAPP(c_Relation_Orel__comp(_1507453, _1507453, _1507453), _1507455), _1507455)), -(c_Wellfounded_Owf(_1507453, _1507455))], (37763 ^ _782652) ^ [_1507552, _1507554, _1507556] : [c_Wellfounded_Owf(_1507552, _1507554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507552, _1507552), tc_HOL_Obool)), _1507556), _1507554)), -(c_Wellfounded_Owf(_1507552, _1507556))], (37773 ^ _782652) ^ [_1507711, _1507713] : [c_Wellfounded_Owf(_1507711, _1507713), -(c_Wellfounded_Owf(tc_fun(_1507711, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1507711, _1507713)))], (37779 ^ _782652) ^ [] : [-(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)))))], (37781 ^ _782652) ^ [_1507848, _1507850, _1507852, _1507854, _1507856, _1507858, _1507860] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1507848, _1507850, _1507852, _1507854, _1507856), _1507858), _1507860)), 37785 ^ _782652 : [(37786 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1507854, _1507858), 37784 ^ [_1507848, _1507850, _1507852, _1507854, _1507856, _1507858, _1507860])))], (37788 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1507856, 37784 ^ [_1507848, _1507850, _1507852, _1507854, _1507856, _1507858, _1507860]), _1507860)))]]], (37790 ^ _782652) ^ [_1508038, _1508040, _1508042, _1508044, _1508046, _1508048, _1508050] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1508038, _1508040, _1508042, _1508044, _1508046), _1508048), _1508050))), 37791 ^ _782652 : [(37792 ^ _782652) ^ [_1508109] : [hBOOL(hAPP(hAPP(_1508044, _1508048), _1508109)), hBOOL(hAPP(hAPP(_1508046, _1508109), _1508050))]]], (37800 ^ _782652) ^ [_1508258] : [-(c_Wellfounded_Owf(tc_fun(_1508258, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1508258)))], (37802 ^ _782652) ^ [_1508286, _1508288, _1508290] : [c_Wellfounded_Owf(_1508286, _1508288), -(c_Wellfounded_Owf(_1508286, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1508286, _1508286), tc_HOL_Obool)), _1508290), _1508288)))], (37808 ^ _782652) ^ [_1508393, _1508395, _1508397] : [c_Wellfounded_Owf(_1508393, _1508395), -(c_Wellfounded_Owf(_1508393, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1508393, _1508393), tc_HOL_Obool)), _1508395), _1508397)))], (37814 ^ _782652) ^ [_1508500, _1508502, _1508504] : [c_Wellfounded_Owf(_1508500, _1508502), -(c_Wellfounded_Owf(_1508500, c_Wellfounded_Omlex__prod(_1508500, _1508504, _1508502)))], (37820 ^ _782652) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (37822 ^ _782652) ^ [_1508605, _1508607] : [c_Wellfounded_Owf(_1508605, _1508607), -(c_Wellfounded_Owf(tc_fun(_1508605, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1508605, _1508607)))], (37828 ^ _782652) ^ [_1508694, _1508696, _1508698] : [c_Wellfounded_Owf(_1508694, _1508696), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508694, _1508694)), hAPP(hAPP(c_Product__Type_OPair(_1508694, _1508694), _1508698), _1508698)), _1508696))], (37834 ^ _782652) ^ [_1508812, _1508814, _1508816, _1508818] : [c_Wellfounded_Owf(_1508812, _1508814), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508812, _1508812)), hAPP(hAPP(c_Product__Type_OPair(_1508812, _1508812), _1508816), _1508818)), _1508814)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1508812, _1508812)), hAPP(hAPP(c_Product__Type_OPair(_1508812, _1508812), _1508818), _1508816)), _1508814))], (37844 ^ _782652) ^ [_1509026, _1509028, _1509030, _1509032] : [c_Wellfounded_Owf(_1509026, _1509028), hBOOL(hAPP(hAPP(c_member(tc_prod(_1509026, _1509026)), hAPP(hAPP(c_Product__Type_OPair(_1509026, _1509026), _1509030), _1509032)), _1509028)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1509026, _1509026)), hAPP(hAPP(c_Product__Type_OPair(_1509026, _1509026), _1509032), _1509030)), _1509028))], (37854 ^ _782652) ^ [_1509240, _1509242, _1509244] : [c_Wellfounded_Owf(_1509240, _1509242), hBOOL(hAPP(hAPP(c_member(tc_prod(_1509240, _1509240)), hAPP(hAPP(c_Product__Type_OPair(_1509240, _1509240), _1509244), _1509244)), _1509242))], (37860 ^ _782652) ^ [_1509358] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1509358)))], (37862 ^ _782652) ^ [_1509383] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1509383)))], (37864 ^ _782652) ^ [_1509408, _1509410, _1509412] : [c_Wellfounded_Owf(_1509408, _1509410), -(hBOOL(hAPP(hAPP(c_member(_1509408), _1509412), c_Wellfounded_Oacc(_1509408, _1509410))))], (37870 ^ _782652) ^ [_1509522, _1509524] : [c_Wellfounded_Owf(_1509522, _1509524), 37873 ^ _782652 : [(37874 ^ _782652) ^ [_1509591] : [-(hBOOL(hAPP(hAPP(c_member(_1509522), _1509591), c_Wellfounded_Oacc(_1509522, _1509524))))]]], (37876 ^ _782652) ^ [_1509624, _1509626] : [hBOOL(hAPP(hAPP(c_member(_1509624), 37877 ^ [_1509624, _1509626]), c_Wellfounded_Oacc(_1509624, _1509626))), -(c_Wellfounded_Owf(_1509624, _1509626))], (37883 ^ _782652) ^ [_1509757, _1509759] : [hAPP(hAPP(c_Relation_Orel__comp(_1509757, _1509757, _1509757), _1509759), _1509759) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509757, _1509757), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1509757, _1509759))], (37889 ^ _782652) ^ [_1509888, _1509890, _1509892] : [c_Wellfounded_Owf(_1509888, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509888, _1509888), tc_HOL_Obool)), _1509890), _1509892)), -(c_Wellfounded_Owf(_1509888, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509888, _1509888), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509888, _1509888), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509888, _1509888, _1509888), _1509890), _1509890)), hAPP(hAPP(c_Relation_Orel__comp(_1509888, _1509888, _1509888), _1509892), _1509890))), _1509892)))], (37895 ^ _782652) ^ [_1510087, _1510089, _1510091] : [c_Wellfounded_Owf(_1510087, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510087, _1510087), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510087, _1510087), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510087, _1510087, _1510087), _1510089), _1510089)), hAPP(hAPP(c_Relation_Orel__comp(_1510087, _1510087, _1510087), _1510091), _1510089))), _1510091)), -(c_Wellfounded_Owf(_1510087, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510087, _1510087), tc_HOL_Obool)), _1510089), _1510091)))], (37901 ^ _782652) ^ [_1510307, _1510309] : [c_Wellfounded_Owf(_1510307, _1510309), 37905 ^ _782652 : [(37906 ^ _782652) ^ [_1510443] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1510307, _1510307)), hAPP(hAPP(c_Product__Type_OPair(_1510307, _1510307), hAPP(_1510443, hAPP(c_Nat_OSuc, 37904 ^ [_1510307, _1510309, _1510443]))), hAPP(_1510443, 37904 ^ [_1510307, _1510309, _1510443]))), _1510309))]]], (37908 ^ _782652) ^ [_1510510, _1510512] : [37910 ^ _782652 : [(37911 ^ _782652) ^ [_1510535] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1510510, _1510510)), hAPP(hAPP(c_Product__Type_OPair(_1510510, _1510510), hAPP(37909 ^ [_1510510, _1510512], hAPP(c_Nat_OSuc, _1510535))), hAPP(37909 ^ [_1510510, _1510512], _1510535))), _1510512)))]], -(c_Wellfounded_Owf(_1510510, _1510512))], (37915 ^ _782652) ^ [_1510611, _1510613, _1510615] : [c_Wellfounded_Owf(_1510611, _1510613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510611, tc_HOL_Obool)), _1510615), hAPP(c_Relation_OImage(_1510611, _1510611, _1510613), _1510615))), -(_1510615 = c_Orderings_Obot__class_Obot(tc_fun(_1510611, tc_HOL_Obool)))], (37925 ^ _782652) ^ [_1510788, _1510790, _1510792] : [c_Wellfounded_Owf(_1510788, _1510790), c_Wellfounded_Owf(_1510788, _1510792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510788, _1510788), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510788, _1510788, _1510788), _1510790), _1510792)), _1510790)), -(c_Wellfounded_Owf(_1510788, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1510788, _1510788), tc_HOL_Obool)), _1510790), _1510792)))], (37939 ^ _782652) ^ [_1511049] : [class_Orderings_Owellorder(_1511049), -(c_Wellfounded_Owf(_1511049, hAPP(c_Set_OCollect(tc_prod(_1511049, _1511049)), hAPP(c_Product__Type_Oprod_Oprod__case(_1511049, _1511049, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1511049)))))], (37945 ^ _782652) ^ [_1511171, _1511173] : [c_FunDef_Oreduction__pair(_1511171, _1511173), 37948 ^ _782652 : [(37949 ^ _782652) ^ [] : [-(c_Wellfounded_Owf(_1511171, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool), tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool)), _1511173)))], (37951 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1511171, _1511171, _1511171), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool), tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool)), _1511173)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool), tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool)), _1511173))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool), tc_fun(tc_prod(_1511171, _1511171), tc_HOL_Obool)), _1511173))))]]], (37953 ^ _782652) ^ [_1511460, _1511462] : [-(c_FunDef_Oreduction__pair(_1511460, _1511462)), c_Wellfounded_Owf(_1511460, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool), tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool)), _1511462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1511460, _1511460, _1511460), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool), tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool)), _1511462)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool), tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool)), _1511462))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool), tc_fun(tc_prod(_1511460, _1511460), tc_HOL_Obool)), _1511462)))], (37963 ^ _782652) ^ [_1511781, _1511783, _1511785, _1511787] : [c_FunDef_Oreduction__pair(_1511781, _1511783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511781, _1511781), tc_HOL_Obool)), _1511785), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1511781, _1511781), tc_HOL_Obool), tc_fun(tc_prod(_1511781, _1511781), tc_HOL_Obool)), _1511783))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1511781, _1511781), tc_HOL_Obool)), _1511787), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1511781, _1511781), tc_HOL_Obool), tc_fun(tc_prod(_1511781, _1511781), tc_HOL_Obool)), _1511783))), c_Wellfounded_Owf(_1511781, _1511787), -(c_Wellfounded_Owf(_1511781, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1511781, _1511781), tc_HOL_Obool)), _1511785), _1511787)))], (37981 ^ _782652) ^ [_1512182, _1512184] : [c_Wellfounded_Owf(_1512182, _1512184), -(c_Wellfounded_Owf(tc_List_Olist(_1512182), c_List_Olenlex(_1512182, _1512184)))], (37987 ^ _782652) ^ [_1512269, _1512271, _1512273, _1512275] : [37989 ^ _782652 : [(37990 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1512269, 37988 ^ [_1512269, _1512271, _1512273, _1512275])))], (37992 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1512271, hAPP(_1512273, 37988 ^ [_1512269, _1512271, _1512273, _1512275]))), hAPP(_1512271, 37988 ^ [_1512269, _1512271, _1512273, _1512275])))]], -(c_Wellfounded_Owf(_1512275, hAPP(c_Set_OCollect(tc_prod(_1512275, _1512275)), hAPP(c_Product__Type_Oprod_Oprod__case(_1512275, _1512275, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1512275, tc_HOL_Obool), tc_fun(_1512275, tc_HOL_Obool), _1512275), hAPP(c_COMBS(_1512275, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512275), c_fconj), _1512269))), hAPP(hAPP(c_COMBC(_1512275, tc_fun(_1512275, _1512275), tc_fun(_1512275, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512275, tc_HOL_Obool), tc_fun(tc_fun(_1512275, _1512275), tc_fun(_1512275, tc_HOL_Obool)), _1512275), c_COMBB(_1512275, tc_HOL_Obool, _1512275)), c_fequal)), _1512273))))))], (37996 ^ _782652) ^ [_1512662, _1512664, _1512666, _1512668] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1512662), _1512664)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512662), _1512666)), -(_1512666 = c_Orderings_Obot__class_Obot(tc_fun(_1512662, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1512662, tc_HOL_Obool), tc_fun(_1512662, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1512662, tc_HOL_Obool), tc_fun(_1512662, tc_HOL_Obool)), _1512664), _1512666)), c_Wellfounded_Omax__ext(_1512662, _1512668)))), 38010 ^ _782652 : [(38011 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512662), 38009 ^ [_1512662, _1512664, _1512666, _1512668]), _1512664)))], (38013 ^ _782652) ^ [_1513067] : [hBOOL(hAPP(hAPP(c_member(_1512662), _1513067), _1512666)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512662, _1512662)), hAPP(hAPP(c_Product__Type_OPair(_1512662, _1512662), 38009 ^ [_1512662, _1512664, _1512666, _1512668]), _1513067)), _1512668))]]], (38021 ^ _782652) ^ [] : [-(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))))], (38023 ^ _782652) ^ [_1513311, _1513313] : [c_Wellfounded_Owf(_1513311, _1513313), -(c_Wellfounded_Owf(tc_List_Olist(_1513311), c_List_Olex(_1513311, _1513313)))], (38029 ^ _782652) ^ [_1513398, _1513400, _1513402] : [c_Wellfounded_Owf(_1513398, _1513400), -(c_Wellfounded_Owf(tc_List_Olist(_1513398), hAPP(c_List_Olexn(_1513398, _1513400), _1513402)))], (38035 ^ _782652) ^ [_1513493, _1513495] : [-(c_List_Olex(_1513493, _1513495) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1513493), tc_List_Olist(_1513493)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1513493, _1513495)))], (38037 ^ _782652) ^ [_1513543, _1513545] : [-(hAPP(c_List_Olexn(_1513543, _1513545), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1513543), tc_List_Olist(_1513543)), tc_HOL_Obool)))], (38039 ^ _782652) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (38041 ^ _782652) ^ [_1513604, _1513606, _1513608, _1513610] : [38043 ^ _782652 : [(38044 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1513604, 38042 ^ [_1513604, _1513606, _1513608, _1513610])))], (38046 ^ _782652) ^ [] : [c_Wellfounded_Owf(_1513606, hAPP(_1513608, 38042 ^ [_1513604, _1513606, _1513608, _1513610]))]], -(c_Wellfounded_Owf(tc_prod(_1513610, _1513606), c_Recdef_Osame__fst(_1513610, _1513606, _1513604, _1513608)))], (38050 ^ _782652) ^ [_1513789] : [-(c_Nitpick_Ozero__frac(_1513789) = c_Nitpick_OAbs__Frac(_1513789, 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))))], (38052 ^ _782652) ^ [_1513817, _1513819, _1513821] : [-(hAPP(c_Relation_ORange(_1513817, _1513819), hAPP(c_Set_OCollect(tc_prod(_1513817, _1513819)), hAPP(c_Product__Type_Oprod_Oprod__case(_1513817, _1513819, tc_HOL_Obool), _1513821))) = hAPP(c_Set_OCollect(_1513819), hAPP(hAPP(c_COMBB(tc_fun(_1513817, tc_HOL_Obool), tc_HOL_Obool, _1513819), c_HOL_OEx(_1513817)), hAPP(c_COMBC(_1513817, _1513819, tc_HOL_Obool), _1513821))))], (38054 ^ _782652) ^ [_1513892, _1513894, _1513896, _1513898, _1513900] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513892, _1513894)), hAPP(hAPP(c_Product__Type_OPair(_1513892, _1513894), _1513896), _1513898)), _1513900)), -(hBOOL(hAPP(hAPP(c_member(_1513894), _1513898), hAPP(c_Relation_ORange(_1513892, _1513894), _1513900))))], (38060 ^ _782652) ^ [_1514039, _1514041] : [-(hAPP(c_Relation_ORange(_1514039, _1514039), c_Relation_OId__on(_1514039, _1514041)) = _1514041)], (38062 ^ _782652) ^ [_1514073, _1514075, _1514077, _1514079] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514073, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514073, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1514075, _1514073), _1514077)), hAPP(c_Relation_ORange(_1514075, _1514073), _1514079))), hAPP(c_Relation_ORange(_1514075, _1514073), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1514075, _1514073), tc_HOL_Obool)), _1514077), _1514079)))))], (38064 ^ _782652) ^ [_1514155, _1514157] : [-(hAPP(c_Relation_ORange(_1514155, _1514157), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1514155, _1514157), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1514157, tc_HOL_Obool)))], (38066 ^ _782652) ^ [_1514217, _1514219, _1514221] : [hAPP(c_Relation_ORange(_1514217, _1514219), _1514221) = c_Orderings_Obot__class_Obot(tc_fun(_1514219, tc_HOL_Obool)), -(_1514221 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1514217, _1514219), tc_HOL_Obool)))], (38072 ^ _782652) ^ [_1514330, _1514332, _1514334] : [_1514334 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1514330, _1514332), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1514330, _1514332), _1514334) = c_Orderings_Obot__class_Obot(tc_fun(_1514332, tc_HOL_Obool)))], (38078 ^ _782652) ^ [_1514449, _1514451, _1514453, _1514455] : [-(hAPP(c_Relation_ORange(_1514449, _1514451), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1514449, _1514451), tc_HOL_Obool)), _1514453), _1514455)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1514451, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1514449, _1514451), _1514453)), hAPP(c_Relation_ORange(_1514449, _1514451), _1514455)))], (38080 ^ _782652) ^ [_1514521, _1514523, _1514525] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1514521, _1514523)), _1514525)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1514523), hAPP(c_Relation_ORange(_1514521, _1514523), _1514525))))], (38086 ^ _782652) ^ [_1514634, _1514636, _1514638] : [-(hAPP(c_Set_Oimage(tc_prod(_1514634, _1514636), _1514636, c_Product__Type_Osnd(_1514634, _1514636)), _1514638) = hAPP(c_Relation_ORange(_1514634, _1514636), _1514638))], (38088 ^ _782652) ^ [_1514701, _1514703, _1514705, _1514707] : [hBOOL(hAPP(hAPP(c_member(_1514701), _1514703), hAPP(c_Relation_ORange(_1514705, _1514701), _1514707))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1514705, _1514701)), hAPP(hAPP(c_Product__Type_OPair(_1514705, _1514701), 38091 ^ [_1514701, _1514703, _1514705, _1514707]), _1514703)), _1514707)))], (38095 ^ _782652) ^ [_1514858, _1514860, _1514862, _1514864] : [38096 ^ _782652 : [(38097 ^ _782652) ^ [_1514933] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1514862, _1514858)), hAPP(hAPP(c_Product__Type_OPair(_1514862, _1514858), _1514933), _1514860)), _1514864))]], -(hBOOL(hAPP(hAPP(c_member(_1514858), _1514860), hAPP(c_Relation_ORange(_1514862, _1514858), _1514864))))], (38101 ^ _782652) ^ [_1515018, _1515020, _1515022, _1515024, _1515026] : [-(hAPP(c_Relation_ORange(_1515018, _1515020), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1515018, _1515020)), hAPP(hAPP(c_Product__Type_OPair(_1515018, _1515020), _1515022), _1515024)), _1515026)) = hAPP(hAPP(c_Set_Oinsert(_1515020), _1515024), hAPP(c_Relation_ORange(_1515018, _1515020), _1515026)))], (38103 ^ _782652) ^ [_1515089, _1515091, _1515093, _1515095] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515089, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1515091, _1515089), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1515091, _1515089), tc_HOL_Obool)), _1515093), _1515095))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1515089, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1515091, _1515089), _1515093)), hAPP(c_Relation_ORange(_1515091, _1515089), _1515095)))))], (38105 ^ _782652) ^ [_1515171] : [-(c_Nitpick_Oone__frac(_1515171) = c_Nitpick_OAbs__Frac(_1515171, 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))))], (38107 ^ _782652) ^ [_1515199, _1515201] : [-(c_Nitpick_Onumber__of__frac(_1515199, _1515201) = c_Nitpick_OAbs__Frac(_1515199, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1515201), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38109 ^ _782652) ^ [_1515257, _1515259, _1515261, _1515263] : [hBOOL(hAPP(c_Predicate_ORangeP(_1515257, _1515259, hAPP(hAPP(c_COMBC(_1515257, tc_fun(tc_prod(_1515257, _1515259), tc_HOL_Obool), tc_fun(_1515259, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515259, tc_fun(tc_fun(tc_prod(_1515257, _1515259), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1515257, _1515259), tc_HOL_Obool), tc_fun(_1515259, tc_HOL_Obool)), _1515257), c_COMBC(_1515259, tc_fun(tc_prod(_1515257, _1515259), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515259, tc_prod(_1515257, _1515259)), tc_fun(_1515259, tc_fun(tc_fun(tc_prod(_1515257, _1515259), tc_HOL_Obool), tc_HOL_Obool)), _1515257), hAPP(c_COMBB(tc_prod(_1515257, _1515259), tc_fun(tc_fun(tc_prod(_1515257, _1515259), tc_HOL_Obool), tc_HOL_Obool), _1515259), c_member(tc_prod(_1515257, _1515259)))), c_Product__Type_OPair(_1515257, _1515259)))), _1515261)), _1515263)), -(hBOOL(hAPP(hAPP(c_member(_1515259), _1515263), hAPP(c_Relation_ORange(_1515257, _1515259), _1515261))))], (38115 ^ _782652) ^ [_1515608, _1515610, _1515612, _1515614] : [hBOOL(hAPP(hAPP(c_member(_1515610), _1515614), hAPP(c_Relation_ORange(_1515608, _1515610), _1515612))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1515608, _1515610, hAPP(hAPP(c_COMBC(_1515608, tc_fun(tc_prod(_1515608, _1515610), tc_HOL_Obool), tc_fun(_1515610, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515610, tc_fun(tc_fun(tc_prod(_1515608, _1515610), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1515608, _1515610), tc_HOL_Obool), tc_fun(_1515610, tc_HOL_Obool)), _1515608), c_COMBC(_1515610, tc_fun(tc_prod(_1515608, _1515610), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515610, tc_prod(_1515608, _1515610)), tc_fun(_1515610, tc_fun(tc_fun(tc_prod(_1515608, _1515610), tc_HOL_Obool), tc_HOL_Obool)), _1515608), hAPP(c_COMBB(tc_prod(_1515608, _1515610), tc_fun(tc_fun(tc_prod(_1515608, _1515610), tc_HOL_Obool), tc_HOL_Obool), _1515610), c_member(tc_prod(_1515608, _1515610)))), c_Product__Type_OPair(_1515608, _1515610)))), _1515612)), _1515614)))], (38121 ^ _782652) ^ [_1515965, _1515967, _1515969, _1515971, _1515973] : [hBOOL(hAPP(hAPP(_1515965, _1515967), _1515969)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1515971, _1515973, _1515965), _1515969)))], (38127 ^ _782652) ^ [_1516091, _1516093, _1516095, _1516097] : [hBOOL(hAPP(c_Predicate_ORangeP(_1516091, _1516093, _1516095), _1516097)), -(hBOOL(hAPP(hAPP(_1516095, 38130 ^ [_1516091, _1516093, _1516095, _1516097]), _1516097)))], (38134 ^ _782652) ^ [_1516206, _1516208, _1516210, _1516212] : [38135 ^ _782652 : [(38136 ^ _782652) ^ [_1516260] : [hBOOL(hAPP(hAPP(_1516210, _1516260), _1516212))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1516206, _1516208, _1516210), _1516212)))], (38140 ^ _782652) ^ [_1516324, _1516326, _1516328] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1516324), _1516326), _1516328) = c_Nitpick_OAbs__Frac(_1516324, c_Nitpick_Onorm__frac(_1516326, _1516328)))], (38142 ^ _782652) ^ [_1516365, _1516367, _1516369, _1516371] : [hBOOL(hAPP(hAPP(c_member(_1516365), _1516367), hAPP(c_Relation_ORange(_1516369, _1516365), _1516371))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516369, _1516365)), hAPP(hAPP(c_Product__Type_OPair(_1516369, _1516365), 38145 ^ [_1516365, _1516367, _1516369, _1516371]), _1516367)), _1516371)))], (38149 ^ _782652) ^ [_1516530, _1516532, _1516534] : [c_Wellfounded_Owf(_1516530, _1516532), c_Wellfounded_Owf(_1516530, _1516534), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1516530, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1516530, _1516530), _1516532)), hAPP(c_Relation_ORange(_1516530, _1516530), _1516534)) = c_Orderings_Obot__class_Obot(tc_fun(_1516530, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1516530, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516530, _1516530), tc_HOL_Obool)), _1516532), _1516534)))], (38163 ^ _782652) ^ [_1516801, _1516803, _1516805, _1516807, _1516809] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516801, _1516803)), hAPP(hAPP(c_Product__Type_OPair(_1516801, _1516803), _1516805), _1516807)), _1516809)), -(hBOOL(hAPP(hAPP(c_member(_1516801), _1516805), hAPP(c_Relation_ODomain(_1516801, _1516803), _1516809))))], (38169 ^ _782652) ^ [_1516948, _1516950] : [-(hAPP(c_Relation_ODomain(_1516948, _1516948), c_Relation_OId__on(_1516948, _1516950)) = _1516950)], (38171 ^ _782652) ^ [_1516982, _1516984] : [-(hAPP(c_Relation_ODomain(_1516982, _1516984), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516982, _1516984), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1516982, tc_HOL_Obool)))], (38173 ^ _782652) ^ [_1517044, _1517046, _1517048] : [hAPP(c_Relation_ODomain(_1517044, _1517046), _1517048) = c_Orderings_Obot__class_Obot(tc_fun(_1517044, tc_HOL_Obool)), -(_1517048 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517044, _1517046), tc_HOL_Obool)))], (38179 ^ _782652) ^ [_1517157, _1517159, _1517161] : [_1517161 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1517157, _1517159), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1517157, _1517159), _1517161) = c_Orderings_Obot__class_Obot(tc_fun(_1517157, tc_HOL_Obool)))], (38185 ^ _782652) ^ [_1517276, _1517278, _1517280, _1517282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517276, _1517278), tc_HOL_Obool)), _1517280), _1517282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517276, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1517276, _1517278), _1517280)), hAPP(c_Relation_ODomain(_1517276, _1517278), _1517282))))], (38191 ^ _782652) ^ [_1517427, _1517429, _1517431, _1517433] : [-(hAPP(c_Relation_ODomain(_1517427, _1517429), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517427, _1517429), tc_HOL_Obool)), _1517431), _1517433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517427, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1517427, _1517429), _1517431)), hAPP(c_Relation_ODomain(_1517427, _1517429), _1517433)))], (38193 ^ _782652) ^ [_1517499, _1517501, _1517503] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1517499, _1517501)), _1517503)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1517499), hAPP(c_Relation_ODomain(_1517499, _1517501), _1517503))))], (38199 ^ _782652) ^ [_1517612, _1517614, _1517616] : [-(hAPP(c_Set_Oimage(tc_prod(_1517612, _1517614), _1517612, c_Product__Type_Ofst(_1517612, _1517614)), _1517616) = hAPP(c_Relation_ODomain(_1517612, _1517614), _1517616))], (38201 ^ _782652) ^ [_1517679, _1517681, _1517683, _1517685] : [hBOOL(hAPP(hAPP(c_member(_1517679), _1517681), hAPP(c_Relation_ODomain(_1517679, _1517683), _1517685))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517679, _1517683)), hAPP(hAPP(c_Product__Type_OPair(_1517679, _1517683), _1517681), 38204 ^ [_1517679, _1517681, _1517683, _1517685])), _1517685)))], (38208 ^ _782652) ^ [_1517836, _1517838, _1517840, _1517842] : [38209 ^ _782652 : [(38210 ^ _782652) ^ [_1517911] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517836, _1517840)), hAPP(hAPP(c_Product__Type_OPair(_1517836, _1517840), _1517838), _1517911)), _1517842))]], -(hBOOL(hAPP(hAPP(c_member(_1517836), _1517838), hAPP(c_Relation_ODomain(_1517836, _1517840), _1517842))))], (38214 ^ _782652) ^ [_1517996, _1517998, _1518000, _1518002, _1518004] : [-(hAPP(c_Relation_ODomain(_1517996, _1517998), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1517996, _1517998)), hAPP(hAPP(c_Product__Type_OPair(_1517996, _1517998), _1518000), _1518002)), _1518004)) = hAPP(hAPP(c_Set_Oinsert(_1517996), _1518000), hAPP(c_Relation_ODomain(_1517996, _1517998), _1518004)))], (38216 ^ _782652) ^ [_1518067, _1518069, _1518071, _1518073] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1518067, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1518067, _1518069), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518067, _1518069), tc_HOL_Obool)), _1518071), _1518073))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1518067, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1518067, _1518069), _1518071)), hAPP(c_Relation_ODomain(_1518067, _1518069), _1518073)))))], (38218 ^ _782652) ^ [_1518149, _1518151, _1518153, _1518155] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1518149, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1518149, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1518149, _1518151), _1518153)), hAPP(c_Relation_ODomain(_1518149, _1518151), _1518155))), hAPP(c_Relation_ODomain(_1518149, _1518151), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1518149, _1518151), tc_HOL_Obool)), _1518153), _1518155)))))], (38220 ^ _782652) ^ [_1518231, _1518233] : [-(hAPP(c_Relation_OField(_1518231), _1518233) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1518231, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1518231, _1518231), _1518233)), hAPP(c_Relation_ORange(_1518231, _1518231), _1518233)))], (38222 ^ _782652) ^ [_1518284, _1518286, _1518288] : [-(hAPP(c_Relation_ODomain(_1518284, _1518286), hAPP(c_Set_OCollect(tc_prod(_1518284, _1518286)), hAPP(c_Product__Type_Oprod_Oprod__case(_1518284, _1518286, tc_HOL_Obool), _1518288))) = hAPP(c_Set_OCollect(_1518284), hAPP(hAPP(c_COMBB(tc_fun(_1518286, tc_HOL_Obool), tc_HOL_Obool, _1518284), c_HOL_OEx(_1518286)), _1518288)))], (38224 ^ _782652) ^ [_1518373, _1518375, _1518377, _1518379] : [hBOOL(hAPP(c_Predicate_ODomainP(_1518373, _1518375, hAPP(hAPP(c_COMBC(_1518373, tc_fun(tc_prod(_1518373, _1518375), tc_HOL_Obool), tc_fun(_1518375, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518375, tc_fun(tc_fun(tc_prod(_1518373, _1518375), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518373, _1518375), tc_HOL_Obool), tc_fun(_1518375, tc_HOL_Obool)), _1518373), c_COMBC(_1518375, tc_fun(tc_prod(_1518373, _1518375), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518375, tc_prod(_1518373, _1518375)), tc_fun(_1518375, tc_fun(tc_fun(tc_prod(_1518373, _1518375), tc_HOL_Obool), tc_HOL_Obool)), _1518373), hAPP(c_COMBB(tc_prod(_1518373, _1518375), tc_fun(tc_fun(tc_prod(_1518373, _1518375), tc_HOL_Obool), tc_HOL_Obool), _1518375), c_member(tc_prod(_1518373, _1518375)))), c_Product__Type_OPair(_1518373, _1518375)))), _1518377)), _1518379)), -(hBOOL(hAPP(hAPP(c_member(_1518373), _1518379), hAPP(c_Relation_ODomain(_1518373, _1518375), _1518377))))], (38230 ^ _782652) ^ [_1518724, _1518726, _1518728, _1518730] : [hBOOL(hAPP(hAPP(c_member(_1518724), _1518730), hAPP(c_Relation_ODomain(_1518724, _1518726), _1518728))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1518724, _1518726, hAPP(hAPP(c_COMBC(_1518724, tc_fun(tc_prod(_1518724, _1518726), tc_HOL_Obool), tc_fun(_1518726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518726, tc_fun(tc_fun(tc_prod(_1518724, _1518726), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518724, _1518726), tc_HOL_Obool), tc_fun(_1518726, tc_HOL_Obool)), _1518724), c_COMBC(_1518726, tc_fun(tc_prod(_1518724, _1518726), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518726, tc_prod(_1518724, _1518726)), tc_fun(_1518726, tc_fun(tc_fun(tc_prod(_1518724, _1518726), tc_HOL_Obool), tc_HOL_Obool)), _1518724), hAPP(c_COMBB(tc_prod(_1518724, _1518726), tc_fun(tc_fun(tc_prod(_1518724, _1518726), tc_HOL_Obool), tc_HOL_Obool), _1518726), c_member(tc_prod(_1518724, _1518726)))), c_Product__Type_OPair(_1518724, _1518726)))), _1518728)), _1518730)))], (38236 ^ _782652) ^ [_1519081, _1519083, _1519085, _1519087] : [hBOOL(hAPP(hAPP(c_member(_1519081), _1519083), hAPP(c_Relation_ODomain(_1519081, _1519085), _1519087))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1519081, _1519085)), hAPP(hAPP(c_Product__Type_OPair(_1519081, _1519085), _1519083), 38239 ^ [_1519081, _1519083, _1519085, _1519087])), _1519087)))], (38243 ^ _782652) ^ [_1519246, _1519248, _1519250, _1519252, _1519254, _1519256] : [-(hAPP(c_Set_Oimage(_1519246, tc_prod(_1519248, _1519250), hAPP(hAPP(c_COMBS(_1519246, _1519250, tc_prod(_1519248, _1519250)), hAPP(hAPP(c_COMBB(_1519248, tc_fun(_1519250, tc_prod(_1519248, _1519250)), _1519246), c_Product__Type_OPair(_1519248, _1519250)), _1519252)), _1519254)), _1519256) = hAPP(hAPP(c_Product__Type_OSigma(_1519248, _1519250), hAPP(c_Set_Oimage(_1519246, _1519248, _1519252), _1519256)), hAPP(hAPP(c_COMBB(tc_fun(_1519246, tc_HOL_Obool), tc_fun(_1519250, tc_HOL_Obool), _1519248), c_Set_Oimage(_1519246, _1519250, _1519254)), hAPP(hAPP(c_COMBC(_1519248, tc_fun(_1519246, tc_HOL_Obool), tc_fun(_1519246, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519246, tc_HOL_Obool), tc_fun(tc_fun(_1519246, tc_HOL_Obool), tc_fun(_1519246, tc_HOL_Obool)), _1519248), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1519246, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1519248, tc_HOL_Obool), tc_fun(_1519246, tc_HOL_Obool), _1519248), c_Set_Ovimage(_1519246, _1519248, _1519252)), hAPP(hAPP(c_COMBC(_1519248, tc_fun(_1519248, tc_HOL_Obool), tc_fun(_1519248, tc_HOL_Obool)), c_Set_Oinsert(_1519248)), c_Orderings_Obot__class_Obot(tc_fun(_1519248, tc_HOL_Obool)))))), _1519256))))], (38245 ^ _782652) ^ [_1519443, _1519445, _1519447, _1519449, _1519451] : [hBOOL(hAPP(hAPP(_1519443, _1519445), _1519447)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1519449, _1519451, _1519443), _1519445)))], (38251 ^ _782652) ^ [_1519548, _1519550, _1519552, _1519554, _1519556, _1519558] : [hBOOL(hAPP(hAPP(c_member(_1519548), _1519550), _1519552)), hBOOL(hAPP(hAPP(c_member(_1519554), _1519556), hAPP(_1519558, _1519550))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1519548, _1519554)), hAPP(hAPP(c_Product__Type_OPair(_1519548, _1519554), _1519550), _1519556)), hAPP(hAPP(c_Product__Type_OSigma(_1519548, _1519554), _1519552), _1519558))))], (38261 ^ _782652) ^ [_1519783, _1519785, _1519787] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1519783, _1519785), c_Orderings_Obot__class_Obot(tc_fun(_1519783, tc_HOL_Obool))), _1519787) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519783, _1519785), tc_HOL_Obool)))], (38263 ^ _782652) ^ [_1519832, _1519834, _1519836, _1519838, _1519840, _1519842] : [hBOOL(hAPP(hAPP(c_member(_1519832), _1519834), _1519836)), 38266 ^ _782652 : [(38267 ^ _782652) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1519838, _1519832), _1519840), hAPP(c_COMBK(tc_fun(_1519832, tc_HOL_Obool), _1519838), _1519836)) = hAPP(hAPP(c_Product__Type_OSigma(_1519838, _1519832), _1519842), hAPP(c_COMBK(tc_fun(_1519832, tc_HOL_Obool), _1519838), _1519836)), -(_1519840 = _1519842)], (38273 ^ _782652) ^ [] : [_1519840 = _1519842, -(hAPP(hAPP(c_Product__Type_OSigma(_1519838, _1519832), _1519840), hAPP(c_COMBK(tc_fun(_1519832, tc_HOL_Obool), _1519838), _1519836)) = hAPP(hAPP(c_Product__Type_OSigma(_1519838, _1519832), _1519842), hAPP(c_COMBK(tc_fun(_1519832, tc_HOL_Obool), _1519838), _1519836)))]]], (38279 ^ _782652) ^ [_1520185, _1520187, _1520189, _1520191] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1520185, _1520187)), hAPP(hAPP(c_Product__Type_OSigma(_1520185, _1520187), _1520189), hAPP(c_COMBK(tc_fun(_1520187, tc_HOL_Obool), _1520185), _1520191))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1520185), _1520189)), hAPP(c_Finite__Set_Ocard(_1520187), _1520191)))], (38281 ^ _782652) ^ [_1520256, _1520258, _1520260, _1520262, _1520264, _1520266] : [class_Groups_Ocomm__monoid__add(_1520256), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1520258, _1520256), hAPP(hAPP(c_COMBC(_1520258, tc_fun(_1520260, tc_HOL_Obool), _1520256), hAPP(hAPP(c_COMBB(tc_fun(_1520260, _1520256), tc_fun(tc_fun(_1520260, tc_HOL_Obool), _1520256), _1520258), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1520260, _1520256)), _1520262)), _1520264)), _1520266) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1520258, _1520260), _1520256), hAPP(c_Product__Type_Oprod_Oprod__case(_1520258, _1520260, _1520256), _1520262)), hAPP(hAPP(c_Product__Type_OSigma(_1520258, _1520260), _1520266), hAPP(c_COMBK(tc_fun(_1520260, tc_HOL_Obool), _1520258), _1520264))))], (38297 ^ _782652) ^ [_1520684, _1520686, _1520688, _1520690] : [38298 ^ _782652 : [(38299 ^ _782652) ^ [] : [_1520688 = c_Orderings_Obot__class_Obot(tc_fun(_1520684, tc_HOL_Obool))], (38301 ^ _782652) ^ [] : [_1520690 = c_Orderings_Obot__class_Obot(tc_fun(_1520686, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1520684, _1520686), _1520688), hAPP(c_COMBK(tc_fun(_1520686, tc_HOL_Obool), _1520684), _1520690)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520684, _1520686), tc_HOL_Obool)))], (38287 ^ _782652) ^ [_1520522, _1520524, _1520526, _1520528] : [hAPP(hAPP(c_Product__Type_OSigma(_1520522, _1520524), _1520526), hAPP(c_COMBK(tc_fun(_1520524, tc_HOL_Obool), _1520522), _1520528)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520522, _1520524), tc_HOL_Obool)), -(_1520526 = c_Orderings_Obot__class_Obot(tc_fun(_1520522, tc_HOL_Obool))), -(_1520528 = c_Orderings_Obot__class_Obot(tc_fun(_1520524, tc_HOL_Obool)))], (38305 ^ _782652) ^ [_1520877, _1520879, _1520881] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1520877, _1520879), _1520881), hAPP(c_COMBK(tc_fun(_1520879, tc_HOL_Obool), _1520877), c_Orderings_Obot__class_Obot(tc_fun(_1520879, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520877, _1520879), tc_HOL_Obool)))], (38307 ^ _782652) ^ [_1520935, _1520937, _1520939] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1520935, _1520937), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1520935, _1520937), c_Orderings_Otop__class_Otop(tc_fun(_1520935, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1520937, tc_HOL_Obool), _1520935), _1520939))) = hAPP(hAPP(c_Product__Type_OSigma(_1520935, _1520937), c_Orderings_Otop__class_Otop(tc_fun(_1520935, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1520937, tc_HOL_Obool), _1520935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1520937, tc_HOL_Obool)), _1520939))))], (38309 ^ _782652) ^ [_1521027, _1521029, _1521031] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1521027, _1521029), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1521027, _1521029), _1521031), hAPP(c_COMBK(tc_fun(_1521029, tc_HOL_Obool), _1521027), c_Orderings_Otop__class_Otop(tc_fun(_1521029, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1521027, _1521029), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1521027, tc_HOL_Obool)), _1521031)), hAPP(c_COMBK(tc_fun(_1521029, tc_HOL_Obool), _1521027), c_Orderings_Otop__class_Otop(tc_fun(_1521029, tc_HOL_Obool)))))], (38311 ^ _782652) ^ [_1521119, _1521121, _1521123, _1521125, _1521127, _1521129] : [class_Groups_Ocomm__monoid__mult(_1521119), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1521121, _1521119), hAPP(hAPP(c_COMBC(_1521121, tc_fun(_1521123, tc_HOL_Obool), _1521119), hAPP(hAPP(c_COMBB(tc_fun(_1521123, _1521119), tc_fun(tc_fun(_1521123, tc_HOL_Obool), _1521119), _1521121), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1521123, _1521119)), _1521125)), _1521127)), _1521129) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1521121, _1521123), _1521119), hAPP(c_Product__Type_Oprod_Oprod__case(_1521121, _1521123, _1521119), _1521125)), hAPP(hAPP(c_Product__Type_OSigma(_1521121, _1521123), _1521129), hAPP(c_COMBK(tc_fun(_1521123, tc_HOL_Obool), _1521121), _1521127))))], (38317 ^ _782652) ^ [_1521364, _1521366, _1521368, _1521370, _1521372] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1521364, _1521366), _1521368), hAPP(hAPP(c_COMBS(_1521364, tc_fun(_1521366, tc_HOL_Obool), tc_fun(_1521366, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1521366, tc_HOL_Obool), tc_fun(tc_fun(_1521366, tc_HOL_Obool), tc_fun(_1521366, tc_HOL_Obool)), _1521364), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521366, tc_HOL_Obool))), _1521370)), _1521372)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521364, _1521366), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1521364, _1521366), _1521368), _1521370)), hAPP(hAPP(c_Product__Type_OSigma(_1521364, _1521366), _1521368), _1521372)))], (38319 ^ _782652) ^ [_1521479, _1521481, _1521483, _1521485, _1521487] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1521479, _1521481), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521479, tc_HOL_Obool)), _1521483), _1521485)), hAPP(c_COMBK(tc_fun(_1521481, tc_HOL_Obool), _1521479), _1521487)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521479, _1521481), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1521479, _1521481), _1521483), hAPP(c_COMBK(tc_fun(_1521481, tc_HOL_Obool), _1521479), _1521487))), hAPP(hAPP(c_Product__Type_OSigma(_1521479, _1521481), _1521485), hAPP(c_COMBK(tc_fun(_1521481, tc_HOL_Obool), _1521479), _1521487))))], (38321 ^ _782652) ^ [_1521589, _1521591, _1521593, _1521595, _1521597] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1521589, _1521591), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521589, tc_HOL_Obool)), _1521593), _1521595)), _1521597) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521589, _1521591), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1521589, _1521591), _1521593), _1521597)), hAPP(hAPP(c_Product__Type_OSigma(_1521589, _1521591), _1521595), _1521597)))], (38323 ^ _782652) ^ [_1521672, _1521674, _1521676, _1521678, _1521680, _1521682, _1521684, _1521686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521672, _1521674), tc_HOL_Obool)), _1521676), hAPP(hAPP(c_Product__Type_OSigma(_1521672, _1521674), _1521678), hAPP(c_COMBK(tc_fun(_1521674, tc_HOL_Obool), _1521672), _1521680)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521674, _1521682), tc_HOL_Obool)), _1521684), hAPP(hAPP(c_Product__Type_OSigma(_1521674, _1521682), _1521680), hAPP(c_COMBK(tc_fun(_1521682, tc_HOL_Obool), _1521674), _1521686)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521672, _1521682), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1521672, _1521674, _1521682), _1521676), _1521684)), hAPP(hAPP(c_Product__Type_OSigma(_1521672, _1521682), _1521678), hAPP(c_COMBK(tc_fun(_1521682, tc_HOL_Obool), _1521672), _1521686)))))], (38333 ^ _782652) ^ [_1522031, _1522033, _1522035, _1522037] : [-(hAPP(c_Set_Oimage(tc_prod(_1522031, _1522033), tc_prod(_1522033, _1522031), hAPP(c_Product__Type_Oprod_Oprod__case(_1522031, _1522033, tc_prod(_1522033, _1522031)), hAPP(c_COMBC(_1522033, _1522031, tc_prod(_1522033, _1522031)), c_Product__Type_OPair(_1522033, _1522031)))), hAPP(hAPP(c_Product__Type_OSigma(_1522031, _1522033), _1522035), hAPP(c_COMBK(tc_fun(_1522033, tc_HOL_Obool), _1522031), _1522037))) = hAPP(hAPP(c_Product__Type_OSigma(_1522033, _1522031), _1522037), hAPP(c_COMBK(tc_fun(_1522031, tc_HOL_Obool), _1522033), _1522035)))], (38335 ^ _782652) ^ [_1522132, _1522134, _1522136, _1522138] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522132), _1522134)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1522136), _1522138)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522132, _1522136)), hAPP(hAPP(c_Product__Type_OSigma(_1522132, _1522136), _1522134), hAPP(c_COMBK(tc_fun(_1522136, tc_HOL_Obool), _1522132), _1522138)))))], (38345 ^ _782652) ^ [_1522335, _1522337, _1522339] : [c_Equiv__Relations_Oequiv(_1522335, _1522337, _1522339), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522335, _1522335), tc_HOL_Obool)), _1522339), hAPP(hAPP(c_Product__Type_OSigma(_1522335, _1522335), _1522337), hAPP(c_COMBK(tc_fun(_1522335, tc_HOL_Obool), _1522335), _1522337)))))], (38351 ^ _782652) ^ [_1522478, _1522480, _1522482, _1522484, _1522486] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1522478, _1522480), _1522482), hAPP(hAPP(c_COMBS(_1522478, tc_fun(_1522480, tc_HOL_Obool), tc_fun(_1522480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522480, tc_HOL_Obool), tc_fun(tc_fun(_1522480, tc_HOL_Obool), tc_fun(_1522480, tc_HOL_Obool)), _1522478), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522480, tc_HOL_Obool))), _1522484)), _1522486)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522478, _1522480), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1522478, _1522480), _1522482), _1522484)), hAPP(hAPP(c_Product__Type_OSigma(_1522478, _1522480), _1522482), _1522486)))], (38353 ^ _782652) ^ [_1522593, _1522595, _1522597, _1522599, _1522601] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1522593, _1522595), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522593, tc_HOL_Obool)), _1522597), _1522599)), hAPP(c_COMBK(tc_fun(_1522595, tc_HOL_Obool), _1522593), _1522601)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522593, _1522595), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1522593, _1522595), _1522597), hAPP(c_COMBK(tc_fun(_1522595, tc_HOL_Obool), _1522593), _1522601))), hAPP(hAPP(c_Product__Type_OSigma(_1522593, _1522595), _1522599), hAPP(c_COMBK(tc_fun(_1522595, tc_HOL_Obool), _1522593), _1522601))))], (38355 ^ _782652) ^ [_1522703, _1522705, _1522707, _1522709, _1522711] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1522703, _1522705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522703, tc_HOL_Obool)), _1522707), _1522709)), _1522711) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522703, _1522705), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1522703, _1522705), _1522707), _1522711)), hAPP(hAPP(c_Product__Type_OSigma(_1522703, _1522705), _1522709), _1522711)))], (38357 ^ _782652) ^ [_1522786, _1522788] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522786, _1522786), tc_HOL_Obool)), c_Relation_OId__on(_1522786, _1522788)), hAPP(hAPP(c_Product__Type_OSigma(_1522786, _1522786), _1522788), hAPP(c_COMBK(tc_fun(_1522786, tc_HOL_Obool), _1522786), _1522788)))))], (38359 ^ _782652) ^ [_1522845, _1522847, _1522849, _1522851, _1522853] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1522845, _1522847), _1522849), hAPP(hAPP(c_COMBS(_1522845, tc_fun(_1522847, tc_HOL_Obool), tc_fun(_1522847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522847, tc_HOL_Obool), tc_fun(tc_fun(_1522847, tc_HOL_Obool), tc_fun(_1522847, tc_HOL_Obool)), _1522845), c_Groups_Ominus__class_Ominus(tc_fun(_1522847, tc_HOL_Obool))), _1522851)), _1522853)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1522845, _1522847), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1522845, _1522847), _1522849), _1522851)), hAPP(hAPP(c_Product__Type_OSigma(_1522845, _1522847), _1522849), _1522853)))], (38361 ^ _782652) ^ [_1522960, _1522962, _1522964, _1522966, _1522968] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1522960, _1522962), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1522960, tc_HOL_Obool)), _1522964), _1522966)), hAPP(c_COMBK(tc_fun(_1522962, tc_HOL_Obool), _1522960), _1522968)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1522960, _1522962), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1522960, _1522962), _1522964), hAPP(c_COMBK(tc_fun(_1522962, tc_HOL_Obool), _1522960), _1522968))), hAPP(hAPP(c_Product__Type_OSigma(_1522960, _1522962), _1522966), hAPP(c_COMBK(tc_fun(_1522962, tc_HOL_Obool), _1522960), _1522968))))], (38363 ^ _782652) ^ [_1523070, _1523072, _1523074, _1523076, _1523078] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1523070, _1523072), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1523070, tc_HOL_Obool)), _1523074), _1523076)), _1523078) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1523070, _1523072), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1523070, _1523072), _1523074), _1523078)), hAPP(hAPP(c_Product__Type_OSigma(_1523070, _1523072), _1523076), _1523078)))], (38365 ^ _782652) ^ [_1523174, _1523176, _1523178, _1523180] : [hBOOL(hAPP(c_Predicate_ODomainP(_1523174, _1523176, _1523178), _1523180)), -(hBOOL(hAPP(hAPP(_1523178, _1523180), 38368 ^ [_1523174, _1523176, _1523178, _1523180])))], (38372 ^ _782652) ^ [_1523289, _1523291, _1523293, _1523295] : [38373 ^ _782652 : [(38374 ^ _782652) ^ [_1523343] : [hBOOL(hAPP(hAPP(_1523293, _1523295), _1523343))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1523289, _1523291, _1523293), _1523295)))], (38378 ^ _782652) ^ [_1523407, _1523409] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1523407, _1523409), c_Orderings_Otop__class_Otop(tc_fun(_1523407, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1523409, tc_HOL_Obool), _1523407), c_Orderings_Otop__class_Otop(tc_fun(_1523409, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1523407, _1523409), tc_HOL_Obool)))], (38380 ^ _782652) ^ [_1523495, _1523497, _1523499, _1523501, _1523503, _1523505] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523495, _1523497)), hAPP(hAPP(c_Product__Type_OPair(_1523495, _1523497), _1523499), _1523501)), hAPP(hAPP(c_Product__Type_OSigma(_1523495, _1523497), _1523503), _1523505))), 38383 ^ _782652 : [(38384 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1523495), _1523499), _1523503)))], (38386 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1523497), _1523501), hAPP(_1523505, _1523499))))]]], (38388 ^ _782652) ^ [_1523692, _1523694, _1523696, _1523698, _1523700, _1523702] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523692, _1523694)), hAPP(hAPP(c_Product__Type_OPair(_1523692, _1523694), _1523696), _1523698)), hAPP(hAPP(c_Product__Type_OSigma(_1523692, _1523694), _1523700), _1523702)))), hBOOL(hAPP(hAPP(c_member(_1523692), _1523696), _1523700)), hBOOL(hAPP(hAPP(c_member(_1523694), _1523698), hAPP(_1523702, _1523696)))], (38398 ^ _782652) ^ [_1523929, _1523931, _1523933, _1523935, _1523937, _1523939] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523929, _1523931)), hAPP(hAPP(c_Product__Type_OPair(_1523929, _1523931), _1523933), _1523935)), hAPP(hAPP(c_Product__Type_OSigma(_1523929, _1523931), _1523937), _1523939))), -(hBOOL(hAPP(hAPP(c_member(_1523929), _1523933), _1523937)))], (38404 ^ _782652) ^ [_1524084, _1524086, _1524088, _1524090, _1524092, _1524094] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524084, _1524086)), hAPP(hAPP(c_Product__Type_OPair(_1524084, _1524086), _1524088), _1524090)), hAPP(hAPP(c_Product__Type_OSigma(_1524084, _1524086), _1524092), _1524094))), -(hBOOL(hAPP(hAPP(c_member(_1524086), _1524090), hAPP(_1524094, _1524088))))], (38410 ^ _782652) ^ [_1524245, _1524247, _1524249, _1524251, _1524253, _1524255] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524245, _1524247)), hAPP(hAPP(c_Product__Type_OPair(_1524245, _1524247), _1524249), _1524251)), hAPP(hAPP(c_Product__Type_OSigma(_1524245, _1524247), _1524253), _1524255))), 38413 ^ _782652 : [(38414 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524245), _1524249), _1524253)))], (38416 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524247), _1524251), hAPP(_1524255, _1524249))))]]], (38418 ^ _782652) ^ [_1524450, _1524452, _1524454, _1524456] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1524450, _1524452)), hAPP(hAPP(c_Product__Type_OSigma(_1524450, _1524452), hAPP(hAPP(c_Set_Oinsert(_1524450), _1524454), c_Orderings_Obot__class_Obot(tc_fun(_1524450, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1524452, tc_HOL_Obool), _1524450), _1524456))) = hAPP(c_Finite__Set_Ocard(_1524452), _1524456))], (38420 ^ _782652) ^ [_1524523, _1524525, _1524527, _1524529, _1524531, _1524533] : [hBOOL(hAPP(hAPP(c_member(_1524523), _1524525), _1524527)), 38423 ^ _782652 : [(38424 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524529, _1524523), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1524529, _1524523), _1524531), hAPP(c_COMBK(tc_fun(_1524523, tc_HOL_Obool), _1524529), _1524527))), hAPP(hAPP(c_Product__Type_OSigma(_1524529, _1524523), _1524533), hAPP(c_COMBK(tc_fun(_1524523, tc_HOL_Obool), _1524529), _1524527)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524529, tc_HOL_Obool)), _1524531), _1524533)))], (38430 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524529, tc_HOL_Obool)), _1524531), _1524533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524529, _1524523), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1524529, _1524523), _1524531), hAPP(c_COMBK(tc_fun(_1524523, tc_HOL_Obool), _1524529), _1524527))), hAPP(hAPP(c_Product__Type_OSigma(_1524529, _1524523), _1524533), hAPP(c_COMBK(tc_fun(_1524523, tc_HOL_Obool), _1524529), _1524527)))))]]], (38436 ^ _782652) ^ [_1524945, _1524947, _1524949, _1524951, _1524953, _1524955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524945, _1524947), tc_HOL_Obool)), _1524949), hAPP(hAPP(c_Product__Type_OSigma(_1524945, _1524947), _1524951), hAPP(c_COMBK(tc_fun(_1524947, tc_HOL_Obool), _1524945), _1524953)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524947, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1524945, _1524947, _1524949), _1524955)), _1524953)))], (38442 ^ _782652) ^ [_1525126, _1525128, _1525130, _1525132] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1525126, _1525128)), hAPP(hAPP(c_Product__Type_OSigma(_1525126, _1525128), _1525130), hAPP(c_COMBK(tc_fun(_1525128, tc_HOL_Obool), _1525126), _1525132)))), -(_1525132 = c_Orderings_Obot__class_Obot(tc_fun(_1525128, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1525126), _1525130)))], (38452 ^ _782652) ^ [_1525290, _1525292, _1525294, _1525296] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1525290, _1525292)), hAPP(hAPP(c_Product__Type_OSigma(_1525290, _1525292), _1525294), hAPP(c_COMBK(tc_fun(_1525292, tc_HOL_Obool), _1525290), _1525296)))), -(_1525294 = c_Orderings_Obot__class_Obot(tc_fun(_1525290, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1525292), _1525296)))], (38462 ^ _782652) ^ [_1525454, _1525456, _1525458, _1525460] : [-(hAPP(c_Set_OCollect(tc_prod(_1525454, _1525456)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525454, _1525456, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1525454, tc_fun(_1525456, tc_HOL_Obool), tc_fun(_1525456, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1525456, tc_HOL_Obool), tc_fun(_1525456, tc_HOL_Obool)), _1525454), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525456)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525454), c_fconj), _1525458))), _1525460))) = hAPP(hAPP(c_Product__Type_OSigma(_1525454, _1525456), hAPP(c_Set_OCollect(_1525454), _1525458)), hAPP(c_COMBK(tc_fun(_1525456, tc_HOL_Obool), _1525454), hAPP(c_Set_OCollect(_1525456), _1525460))))], (38464 ^ _782652) ^ [_1525575, _1525577, _1525579, _1525581] : [-(hAPP(c_Set_OCollect(tc_prod(_1525575, _1525577)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525575, _1525577, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1525575, tc_fun(_1525577, tc_HOL_Obool), tc_fun(_1525577, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1525577, tc_HOL_Obool), tc_fun(_1525577, tc_HOL_Obool)), _1525575), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525577)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525575), c_fconj), _1525579))), _1525581))) = hAPP(hAPP(c_Product__Type_OSigma(_1525575, _1525577), hAPP(c_Set_OCollect(_1525575), _1525579)), hAPP(hAPP(c_COMBB(tc_fun(_1525577, tc_HOL_Obool), tc_fun(_1525577, tc_HOL_Obool), _1525575), c_Set_OCollect(_1525577)), _1525581)))], (38466 ^ _782652) ^ [_1525715, _1525717, _1525719, _1525721] : [_1525715 = c_Orderings_Obot__class_Obot(tc_fun(_1525717, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1525719, _1525717), _1525719, c_Product__Type_Ofst(_1525719, _1525717)), hAPP(hAPP(c_Product__Type_OSigma(_1525719, _1525717), _1525721), hAPP(c_COMBK(tc_fun(_1525717, tc_HOL_Obool), _1525719), _1525715))) = c_Orderings_Obot__class_Obot(tc_fun(_1525719, tc_HOL_Obool)))], (38472 ^ _782652) ^ [_1525872, _1525874, _1525876, _1525878] : [-(_1525872 = c_Orderings_Obot__class_Obot(tc_fun(_1525874, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1525876, _1525874), _1525876, c_Product__Type_Ofst(_1525876, _1525874)), hAPP(hAPP(c_Product__Type_OSigma(_1525876, _1525874), _1525878), hAPP(c_COMBK(tc_fun(_1525874, tc_HOL_Obool), _1525876), _1525872))) = _1525878)], (38478 ^ _782652) ^ [_1525965, _1525967, _1525969, _1525971] : [_1525965 = c_Orderings_Obot__class_Obot(tc_fun(_1525967, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1525967, _1525969), _1525969, c_Product__Type_Osnd(_1525967, _1525969)), hAPP(hAPP(c_Product__Type_OSigma(_1525967, _1525969), _1525965), hAPP(c_COMBK(tc_fun(_1525969, tc_HOL_Obool), _1525967), _1525971))) = c_Orderings_Obot__class_Obot(tc_fun(_1525969, tc_HOL_Obool)))], (38484 ^ _782652) ^ [_1526122, _1526124, _1526126, _1526128] : [-(_1526122 = c_Orderings_Obot__class_Obot(tc_fun(_1526124, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1526124, _1526126), _1526126, c_Product__Type_Osnd(_1526124, _1526126)), hAPP(hAPP(c_Product__Type_OSigma(_1526124, _1526126), _1526122), hAPP(c_COMBK(tc_fun(_1526126, tc_HOL_Obool), _1526124), _1526128))) = _1526128)], (38490 ^ _782652) ^ [_1526200, _1526202, _1526204, _1526206, _1526208, _1526210] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1526200, _1526202), hAPP(hAPP(c_Set_Oinsert(_1526200), _1526204), _1526206)), hAPP(c_COMBK(tc_fun(_1526202, tc_HOL_Obool), _1526200), hAPP(hAPP(c_Set_Oinsert(_1526202), _1526208), _1526210))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1526200, _1526202)), hAPP(hAPP(c_Product__Type_OPair(_1526200, _1526202), _1526204), _1526208)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1526200, _1526202), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1526200, _1526202), _1526206), hAPP(c_COMBK(tc_fun(_1526202, tc_HOL_Obool), _1526200), hAPP(hAPP(c_Set_Oinsert(_1526202), _1526208), _1526210)))), hAPP(hAPP(c_Product__Type_OSigma(_1526200, _1526202), hAPP(hAPP(c_Set_Oinsert(_1526200), _1526204), _1526206)), hAPP(c_COMBK(tc_fun(_1526202, tc_HOL_Obool), _1526200), _1526210)))))], (38492 ^ _782652) ^ [_1526353, _1526355, _1526357, _1526359] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526353), _1526355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526353, _1526353), tc_HOL_Obool)), _1526357), hAPP(hAPP(c_Product__Type_OSigma(_1526353, _1526353), _1526355), hAPP(c_COMBK(tc_fun(_1526353, tc_HOL_Obool), _1526353), _1526355)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1526353, tc_HOL_Obool)), _1526359), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1526353), _1526355), _1526357))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1526353), _1526359)))], (38506 ^ _782652) ^ [_1526660, _1526662, _1526664, _1526666, _1526668, _1526670, _1526672, _1526674] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1526660, _1526662), tc_fun(tc_prod(_1526664, _1526666), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1526660, _1526662), _1526668), hAPP(c_COMBK(tc_fun(_1526662, tc_HOL_Obool), _1526660), _1526670))), hAPP(c_Product__Type_Oprod_Oprod__case(_1526660, _1526662, tc_fun(tc_prod(_1526664, _1526666), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1526660, tc_fun(_1526662, tc_fun(_1526664, tc_fun(_1526666, tc_HOL_Obool))), tc_fun(_1526662, tc_fun(tc_prod(_1526664, _1526666), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1526664, tc_fun(_1526666, tc_HOL_Obool)), tc_fun(tc_prod(_1526664, _1526666), tc_HOL_Obool)), tc_fun(tc_fun(_1526662, tc_fun(_1526664, tc_fun(_1526666, tc_HOL_Obool))), tc_fun(_1526662, tc_fun(tc_prod(_1526664, _1526666), tc_HOL_Obool))), _1526660), c_COMBB(tc_fun(_1526664, tc_fun(_1526666, tc_HOL_Obool)), tc_fun(tc_prod(_1526664, _1526666), tc_HOL_Obool), _1526662)), hAPP(hAPP(c_COMBB(tc_fun(_1526664, tc_HOL_Obool), tc_fun(tc_fun(_1526664, tc_fun(_1526666, tc_HOL_Obool)), tc_fun(tc_prod(_1526664, _1526666), tc_HOL_Obool)), _1526660), c_Product__Type_OSigma(_1526664, _1526666)), _1526672))), hAPP(hAPP(c_COMBB(tc_fun(_1526666, tc_HOL_Obool), tc_fun(_1526664, tc_fun(_1526666, tc_HOL_Obool)), _1526662), c_COMBK(tc_fun(_1526666, tc_HOL_Obool), _1526664)), _1526674)))) = hAPP(hAPP(c_Product__Type_OSigma(_1526664, _1526666), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1526660, tc_fun(_1526664, tc_HOL_Obool)), _1526668), _1526672)), hAPP(c_COMBK(tc_fun(_1526666, tc_HOL_Obool), _1526664), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1526662, tc_fun(_1526666, tc_HOL_Obool)), _1526670), _1526674))))], (38508 ^ _782652) ^ [_1526934, _1526936, _1526938, _1526940] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1526934, _1526936), _1526938), _1526940) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1526934, tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool)), _1526938), hAPP(hAPP(c_COMBS(_1526934, tc_fun(_1526936, tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool)), tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526936, tc_HOL_Obool), tc_fun(tc_fun(_1526936, tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool)), tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool)), _1526934), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1526936, tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool))), _1526940)), hAPP(hAPP(c_COMBC(_1526934, tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool), tc_fun(_1526936, tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1526936, tc_fun(tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool), tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool), tc_fun(_1526936, tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool))), _1526934), c_COMBC(_1526936, tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool), tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1526936, tc_prod(_1526934, _1526936)), tc_fun(_1526936, tc_fun(tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool), tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool))), _1526934), hAPP(c_COMBB(tc_prod(_1526934, _1526936), tc_fun(tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool), tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool)), _1526936), c_Set_Oinsert(tc_prod(_1526934, _1526936)))), c_Product__Type_OPair(_1526934, _1526936)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526934, _1526936), tc_HOL_Obool))))))], (38510 ^ _782652) ^ [_1527214, _1527216, _1527218] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527214), _1527216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527214, _1527214), tc_HOL_Obool)), _1527218), hAPP(hAPP(c_Product__Type_OSigma(_1527214, _1527214), _1527216), hAPP(c_COMBK(tc_fun(_1527214, tc_HOL_Obool), _1527214), _1527216)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1527214, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1527214), _1527216), _1527218))))], (38520 ^ _782652) ^ [_1527447, _1527449, _1527451, _1527453, _1527455, _1527457, _1527459] : [class_Rings_Osemiring__0(_1527447), c_Fun_Oinj__on(tc_prod(_1527449, _1527451), _1527447, hAPP(c_Product__Type_Oprod_Oprod__case(_1527449, _1527451, _1527447), hAPP(hAPP(c_COMBC(_1527449, tc_fun(_1527451, _1527447), tc_fun(_1527451, _1527447)), hAPP(hAPP(c_COMBB(tc_fun(_1527447, _1527447), tc_fun(tc_fun(_1527451, _1527447), tc_fun(_1527451, _1527447)), _1527449), c_COMBB(_1527447, _1527447, _1527451)), hAPP(hAPP(c_COMBB(_1527447, tc_fun(_1527447, _1527447), _1527449), c_Groups_Otimes__class_Otimes(_1527447)), _1527453))), _1527455)), hAPP(hAPP(c_Product__Type_OSigma(_1527449, _1527451), _1527457), hAPP(c_COMBK(tc_fun(_1527451, tc_HOL_Obool), _1527449), _1527459))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1527447), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527449, _1527447), _1527453), _1527457)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527451, _1527447), _1527455), _1527459)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527447, _1527447), c_Fun_Oid(_1527447)), hAPP(c_Set_OCollect(_1527447), hAPP(hAPP(c_COMBB(tc_fun(_1527449, tc_HOL_Obool), tc_HOL_Obool, _1527447), c_HOL_OEx(_1527449)), hAPP(hAPP(c_COMBB(tc_fun(_1527449, tc_fun(_1527451, tc_HOL_Obool)), tc_fun(_1527449, tc_HOL_Obool), _1527447), hAPP(c_COMBB(tc_fun(_1527451, tc_HOL_Obool), tc_HOL_Obool, _1527449), c_HOL_OEx(_1527451))), hAPP(hAPP(c_COMBC(_1527447, tc_fun(_1527449, tc_fun(_1527451, tc_HOL_Obool)), tc_fun(_1527449, tc_fun(_1527451, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1527449, tc_fun(tc_fun(_1527451, tc_HOL_Obool), tc_fun(_1527451, tc_HOL_Obool))), tc_fun(tc_fun(_1527449, tc_fun(_1527451, tc_HOL_Obool)), tc_fun(_1527449, tc_fun(_1527451, tc_HOL_Obool))), _1527447), c_COMBS(_1527449, tc_fun(_1527451, tc_HOL_Obool), tc_fun(_1527451, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1527449, tc_fun(_1527451, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1527449, tc_fun(tc_fun(_1527451, tc_HOL_Obool), tc_fun(_1527451, tc_HOL_Obool))), _1527447), hAPP(c_COMBB(tc_fun(_1527451, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1527451, tc_HOL_Obool), tc_fun(_1527451, tc_HOL_Obool)), _1527449), c_COMBS(_1527451, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1527449, tc_fun(_1527451, tc_HOL_Obool)), tc_fun(_1527449, tc_fun(_1527451, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1527447), hAPP(c_COMBB(tc_fun(_1527451, tc_HOL_Obool), tc_fun(_1527451, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1527449), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527451), c_fconj))), hAPP(hAPP(c_COMBC(_1527447, tc_fun(_1527449, tc_fun(_1527451, _1527447)), tc_fun(_1527449, tc_fun(_1527451, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1527451, _1527447), tc_fun(_1527451, tc_HOL_Obool)), tc_fun(tc_fun(_1527449, tc_fun(_1527451, _1527447)), tc_fun(_1527449, tc_fun(_1527451, tc_HOL_Obool))), _1527447), c_COMBB(tc_fun(_1527451, _1527447), tc_fun(_1527451, tc_HOL_Obool), _1527449)), hAPP(hAPP(c_COMBB(tc_fun(_1527447, tc_HOL_Obool), tc_fun(tc_fun(_1527451, _1527447), tc_fun(_1527451, tc_HOL_Obool)), _1527447), c_COMBB(_1527447, tc_HOL_Obool, _1527451)), c_fequal))), hAPP(hAPP(c_COMBC(_1527449, tc_fun(_1527451, _1527447), tc_fun(_1527451, _1527447)), hAPP(hAPP(c_COMBB(tc_fun(_1527447, _1527447), tc_fun(tc_fun(_1527451, _1527447), tc_fun(_1527451, _1527447)), _1527449), c_COMBB(_1527447, _1527447, _1527451)), hAPP(hAPP(c_COMBB(_1527447, tc_fun(_1527447, _1527447), _1527449), c_Groups_Otimes__class_Otimes(_1527447)), _1527453))), _1527455)))))), hAPP(hAPP(c_COMBC(_1527449, tc_fun(_1527451, tc_HOL_Obool), tc_fun(_1527451, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1527451, tc_HOL_Obool), tc_fun(_1527451, tc_HOL_Obool)), _1527449), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1527451)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527449), c_fconj), hAPP(hAPP(c_COMBC(_1527449, tc_fun(_1527449, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527449)), _1527457)))), hAPP(hAPP(c_COMBC(_1527451, tc_fun(_1527451, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527451)), _1527459))))))))], (38531 ^ _782652) ^ [_1528722, _1528724, _1528726, _1528728] : [-(c_Fun_Oinj__on(_1528722, tc_prod(_1528724, _1528722), 38529 ^ [_1528722, _1528724, _1528726, _1528728], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528724, tc_fun(_1528722, tc_HOL_Obool)), _1528726), _1528728)))], (38533 ^ _782652) ^ [_1528776, _1528778, _1528780, _1528782] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528778, _1528776), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1528776, tc_prod(_1528778, _1528776), 38529 ^ [_1528776, _1528778, _1528780, _1528782]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1528778, tc_fun(_1528776, tc_HOL_Obool)), _1528780), _1528782))), hAPP(hAPP(c_Product__Type_OSigma(_1528778, _1528776), _1528780), _1528782))))], (38535 ^ _782652) ^ [_1528862, _1528864, _1528866, _1528868, _1528870, _1528872] : [class_Groups_Ocomm__monoid__mult(_1528862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1528864), _1528866)), 38545 ^ _782652 : [(38546 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1528864), 38544 ^ [_1528862, _1528864, _1528866, _1528868, _1528870, _1528872]), _1528866)))], (38548 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1528868), hAPP(_1528870, 38544 ^ [_1528862, _1528864, _1528866, _1528868, _1528870, _1528872])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1528862, _1528864, c_Groups_Otimes__class_Otimes(_1528862)), hAPP(hAPP(c_COMBS(_1528864, tc_fun(_1528868, tc_HOL_Obool), _1528862), hAPP(hAPP(c_COMBC(_1528864, _1528862, tc_fun(tc_fun(_1528868, tc_HOL_Obool), _1528862)), hAPP(hAPP(c_COMBB(tc_fun(_1528868, _1528862), tc_fun(_1528862, tc_fun(tc_fun(_1528868, tc_HOL_Obool), _1528862)), _1528864), c_Finite__Set_Ofold__image(_1528862, _1528868, c_Groups_Otimes__class_Otimes(_1528862))), _1528872)), c_Groups_Oone__class_Oone(_1528862))), _1528870)), c_Groups_Oone__class_Oone(_1528862)), _1528866) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1528862, tc_prod(_1528864, _1528868), c_Groups_Otimes__class_Otimes(_1528862)), hAPP(c_Product__Type_Oprod_Oprod__case(_1528864, _1528868, _1528862), _1528872)), c_Groups_Oone__class_Oone(_1528862)), hAPP(hAPP(c_Product__Type_OSigma(_1528864, _1528868), _1528866), _1528870)))], (38552 ^ _782652) ^ [_1529419, _1529421] : [-(hAPP(c_Set_Oimage(_1529419, _1529419, c_Fun_Oid(_1529419)), _1529421) = _1529421)], (38554 ^ _782652) ^ [_1529453, _1529455] : [-(c_Product__Type_Oapsnd(_1529453, _1529453, _1529455, c_Fun_Oid(_1529453)) = c_Fun_Oid(tc_prod(_1529455, _1529453)))], (38556 ^ _782652) ^ [_1529490, _1529492] : [-(hAPP(c_Set_Ovimage(_1529490, _1529490, c_Fun_Oid(_1529490)), _1529492) = _1529492)], (38558 ^ _782652) ^ [_1529524, _1529526] : [-(hAPP(c_Fun_Oid(_1529524), _1529526) = _1529526)], (38560 ^ _782652) ^ [_1529554, _1529556] : [-(hAPP(c_Fun_Oid(_1529554), _1529556) = _1529556)], (38562 ^ _782652) ^ [_1529584, _1529586] : [-(c_Fun_Oinj__on(_1529584, _1529584, c_Fun_Oid(_1529584), _1529586))], (38564 ^ _782652) ^ [_1529613, _1529615] : [-(c_Product__Type_Oapfst(_1529613, _1529613, _1529615, c_Fun_Oid(_1529613)) = c_Fun_Oid(tc_prod(_1529613, _1529615)))], (38566 ^ _782652) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (38568 ^ _782652) ^ [_1529668] : [-(hAPP(c_Set_Oimage(_1529668, _1529668, c_Fun_Oid(_1529668)), c_Orderings_Otop__class_Otop(tc_fun(_1529668, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1529668, tc_HOL_Obool)))], (38570 ^ _782652) ^ [_1529710, _1529712] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1529710, _1529712, tc_prod(_1529710, _1529712)), c_Product__Type_OPair(_1529710, _1529712)) = c_Fun_Oid(tc_prod(_1529710, _1529712)))], (38572 ^ _782652) ^ [_1529753, _1529755, _1529757, _1529759] : [class_Groups_Ocomm__monoid__add(_1529753), c_Fun_Oinj__on(_1529755, _1529753, _1529757, _1529759), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1529755, _1529753), _1529757), _1529759) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1529753, _1529753), c_Fun_Oid(_1529753)), hAPP(c_Set_Oimage(_1529755, _1529753, _1529757), _1529759)))], (38582 ^ _782652) ^ [_1529946, _1529948, _1529950, _1529952] : [class_Groups_Ocomm__monoid__mult(_1529946), c_Fun_Oinj__on(_1529948, _1529946, _1529950, _1529952), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1529948, _1529946), _1529950), _1529952) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1529946, _1529946), c_Fun_Oid(_1529946)), hAPP(c_Set_Oimage(_1529948, _1529946, _1529950), _1529952)))], (38592 ^ _782652) ^ [_1530139, _1530141, _1530143, _1530145, _1530147, _1530149] : [class_Groups_Ocomm__monoid__mult(_1530139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530141), _1530143)), 38602 ^ _782652 : [(38603 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530141), 38601 ^ [_1530139, _1530141, _1530143, _1530145, _1530147, _1530149]), _1530143)))], (38605 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530145), hAPP(_1530147, 38601 ^ [_1530139, _1530141, _1530143, _1530145, _1530147, _1530149])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1530141, _1530139), hAPP(hAPP(c_COMBS(_1530141, tc_fun(_1530145, tc_HOL_Obool), _1530139), hAPP(hAPP(c_COMBB(tc_fun(_1530145, _1530139), tc_fun(tc_fun(_1530145, tc_HOL_Obool), _1530139), _1530141), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1530145, _1530139)), _1530149)), _1530147)), _1530143) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1530141, _1530145), _1530139), hAPP(c_Product__Type_Oprod_Oprod__case(_1530141, _1530145, _1530139), _1530149)), hAPP(hAPP(c_Product__Type_OSigma(_1530141, _1530145), _1530143), _1530147)))], (38609 ^ _782652) ^ [_1530616, _1530618, _1530620, _1530622, _1530624, _1530626] : [class_Groups_Ocomm__monoid__add(_1530616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1530618), _1530620)), 38619 ^ _782652 : [(38620 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530618), 38618 ^ [_1530616, _1530618, _1530620, _1530622, _1530624, _1530626]), _1530620)))], (38622 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1530622), hAPP(_1530624, 38618 ^ [_1530616, _1530618, _1530620, _1530622, _1530624, _1530626])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530618, _1530616), hAPP(hAPP(c_COMBS(_1530618, tc_fun(_1530622, tc_HOL_Obool), _1530616), hAPP(hAPP(c_COMBB(tc_fun(_1530622, _1530616), tc_fun(tc_fun(_1530622, tc_HOL_Obool), _1530616), _1530618), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530622, _1530616)), _1530626)), _1530624)), _1530620) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1530618, _1530622), _1530616), hAPP(c_Product__Type_Oprod_Oprod__case(_1530618, _1530622, _1530616), _1530626)), hAPP(hAPP(c_Product__Type_OSigma(_1530618, _1530622), _1530620), _1530624)))], (38626 ^ _782652) ^ [_1531093, _1531095, _1531097, _1531099] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1531093), _1531095)), 38632 ^ _782652 : [(38633 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531093), 38631 ^ [_1531093, _1531095, _1531097, _1531099]), _1531095)))], (38635 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1531097), hAPP(_1531099, 38631 ^ [_1531093, _1531095, _1531097, _1531099])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1531093, _1531097)), hAPP(hAPP(c_Product__Type_OSigma(_1531093, _1531097), _1531095), _1531099)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1531093, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1531097, tc_HOL_Obool), tc_Nat_Onat, _1531093), c_Finite__Set_Ocard(_1531097)), _1531099)), _1531095))], (38639 ^ _782652) ^ [_1531430, _1531432, _1531434, _1531436] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1531430), _1531432)), 38645 ^ _782652 : [(38646 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531430), 38644 ^ [_1531430, _1531432, _1531434, _1531436]), _1531432)))], (38648 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1531434), hAPP(_1531436, 38644 ^ [_1531430, _1531432, _1531434, _1531436])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1531430, _1531434)), hAPP(hAPP(c_Product__Type_OSigma(_1531430, _1531434), _1531432), _1531436))))], (38652 ^ _782652) ^ [_1531717, _1531719, _1531721, _1531723, _1531725] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531717, _1531719)), _1531721), hAPP(hAPP(c_Product__Type_OSigma(_1531717, _1531719), _1531723), _1531725))), 38656 ^ _782652 : [(38657 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531717), 38655 ^ [_1531717, _1531719, _1531721, _1531723, _1531725]), _1531723)))], (38660 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531719), 38658 ^ [_1531717, _1531719, _1531721, _1531723, _1531725]), hAPP(_1531725, 38655 ^ [_1531717, _1531719, _1531721, _1531723, _1531725]))))], (38662 ^ _782652) ^ [] : [-(_1531721 = hAPP(hAPP(c_Product__Type_OPair(_1531717, _1531719), 38655 ^ [_1531717, _1531719, _1531721, _1531723, _1531725]), 38658 ^ [_1531717, _1531719, _1531721, _1531723, _1531725]))]]], (38664 ^ _782652) ^ [_1532019, _1532021, _1532023, _1532025, _1532027, _1532029] : [hAPP(c_Set_Oimage(_1532019, _1532021, _1532023), c_Orderings_Otop__class_Otop(tc_fun(_1532019, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1532021, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1532025, _1532027, _1532029), c_Orderings_Otop__class_Otop(tc_fun(_1532025, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1532027, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1532019, _1532025), tc_prod(_1532021, _1532027), c_Product__Type_Omap__pair(_1532019, _1532021, _1532025, _1532027, _1532023, _1532029)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1532019, _1532025), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1532021, _1532027), tc_HOL_Obool)))], (38674 ^ _782652) ^ [_1532304, _1532306, _1532308, _1532310, _1532312, _1532314, _1532316, _1532318, _1532320] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532304, _1532306)), hAPP(hAPP(c_Product__Type_OPair(_1532304, _1532306), _1532308), _1532310)), _1532312)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532314, _1532316)), hAPP(hAPP(c_Product__Type_OPair(_1532314, _1532316), hAPP(_1532318, _1532308)), hAPP(_1532320, _1532310))), hAPP(c_Set_Oimage(tc_prod(_1532304, _1532306), tc_prod(_1532314, _1532316), c_Product__Type_Omap__pair(_1532304, _1532314, _1532306, _1532316, _1532318, _1532320)), _1532312))))], (38680 ^ _782652) ^ [_1532523, _1532525, _1532527, _1532529, _1532531, _1532533, _1532535, _1532537] : [-(hAPP(c_Product__Type_Omap__pair(_1532523, _1532525, _1532527, _1532529, _1532531, _1532533), hAPP(hAPP(c_Product__Type_OPair(_1532523, _1532527), _1532535), _1532537)) = hAPP(hAPP(c_Product__Type_OPair(_1532525, _1532529), hAPP(_1532531, _1532535)), hAPP(_1532533, _1532537)))], (38682 ^ _782652) ^ [_1532594, _1532596, _1532598] : [-(hAPP(c_Product__Type_Omap__pair(_1532594, _1532594, _1532596, _1532596, c_COMBI(_1532594), c_COMBI(_1532596)), _1532598) = _1532598)], (38684 ^ _782652) ^ [_1532635, _1532637, _1532639, _1532641, _1532643, _1532645, _1532647] : [-(hAPP(c_Product__Type_Osnd(_1532635, _1532637), hAPP(c_Product__Type_Omap__pair(_1532639, _1532635, _1532641, _1532637, _1532643, _1532645), _1532647)) = hAPP(_1532645, hAPP(c_Product__Type_Osnd(_1532639, _1532641), _1532647)))], (38686 ^ _782652) ^ [_1532695, _1532697, _1532699, _1532701, _1532703, _1532705, _1532707] : [-(hAPP(c_Product__Type_Ofst(_1532695, _1532697), hAPP(c_Product__Type_Omap__pair(_1532699, _1532695, _1532701, _1532697, _1532703, _1532705), _1532707)) = hAPP(_1532703, hAPP(c_Product__Type_Ofst(_1532699, _1532701), _1532707)))], (38688 ^ _782652) ^ [_1532755, _1532757] : [-(c_Product__Type_Omap__pair(_1532755, _1532755, _1532757, _1532757, c_COMBI(_1532755), c_COMBI(_1532757)) = c_Fun_Oid(tc_prod(_1532755, _1532757)))], (38690 ^ _782652) ^ [_1532796, _1532798, _1532800, _1532802] : [-(c_Product__Type_Oapsnd(_1532796, _1532798, _1532800, _1532802) = c_Product__Type_Omap__pair(_1532800, _1532800, _1532796, _1532798, c_Fun_Oid(_1532800), _1532802))], (38692 ^ _782652) ^ [_1532839, _1532841, _1532843, _1532845] : [-(c_Product__Type_Oapfst(_1532839, _1532841, _1532843, _1532845) = c_Product__Type_Omap__pair(_1532839, _1532841, _1532843, _1532843, _1532845, c_Fun_Oid(_1532843)))], (38694 ^ _782652) ^ [_1532882, _1532884] : [-(c_Product__Type_Omap__pair(_1532882, _1532882, _1532884, _1532884, c_Fun_Oid(_1532882), c_Fun_Oid(_1532884)) = c_Fun_Oid(tc_prod(_1532882, _1532884)))], (38696 ^ _782652) ^ [_1532923, _1532925, _1532927, _1532929, _1532931, _1532933] : [-(c_Product__Type_Omap__pair(_1532923, _1532925, _1532927, _1532929, _1532931, _1532933) = hAPP(c_Product__Type_Oprod_Oprod__case(_1532923, _1532927, tc_prod(_1532925, _1532929)), hAPP(hAPP(c_COMBC(_1532923, tc_fun(_1532927, _1532929), tc_fun(_1532927, tc_prod(_1532925, _1532929))), hAPP(hAPP(c_COMBB(tc_fun(_1532929, tc_prod(_1532925, _1532929)), tc_fun(tc_fun(_1532927, _1532929), tc_fun(_1532927, tc_prod(_1532925, _1532929))), _1532923), c_COMBB(_1532929, tc_prod(_1532925, _1532929), _1532927)), hAPP(hAPP(c_COMBB(_1532925, tc_fun(_1532929, tc_prod(_1532925, _1532929)), _1532923), c_Product__Type_OPair(_1532925, _1532929)), _1532931))), _1532933)))], (38698 ^ _782652) ^ [_1533046, _1533048, _1533050, _1533052, _1533054, _1533056, _1533058, _1533060, _1533062, _1533064] : [hAPP(c_Set_Oimage(_1533046, _1533048, _1533050), _1533052) = _1533054, hAPP(c_Set_Oimage(_1533056, _1533058, _1533060), _1533062) = _1533064, -(hAPP(c_Set_Oimage(tc_prod(_1533046, _1533056), tc_prod(_1533048, _1533058), c_Product__Type_Omap__pair(_1533046, _1533048, _1533056, _1533058, _1533050, _1533060)), hAPP(hAPP(c_Product__Type_OSigma(_1533046, _1533056), _1533052), hAPP(c_COMBK(tc_fun(_1533056, tc_HOL_Obool), _1533046), _1533062))) = hAPP(hAPP(c_Product__Type_OSigma(_1533048, _1533058), _1533054), hAPP(c_COMBK(tc_fun(_1533058, tc_HOL_Obool), _1533048), _1533064)))], (38708 ^ _782652) ^ [_1533347, _1533349, _1533351, _1533353] : [c_Wellfounded_Owf(_1533347, _1533349), c_Fun_Oinj__on(_1533347, _1533351, _1533353, c_Orderings_Otop__class_Otop(tc_fun(_1533347, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1533351, hAPP(c_Set_Oimage(tc_prod(_1533347, _1533347), tc_prod(_1533351, _1533351), c_Product__Type_Omap__pair(_1533347, _1533351, _1533347, _1533351, _1533353, _1533353)), _1533349)))], (38718 ^ _782652) ^ [_1533538, _1533540, _1533542, _1533544, _1533546, _1533548, _1533550, _1533552] : [c_Fun_Oinj__on(_1533538, _1533540, _1533542, _1533544), c_Fun_Oinj__on(_1533546, _1533548, _1533550, _1533552), -(c_Fun_Oinj__on(tc_prod(_1533538, _1533546), tc_prod(_1533540, _1533548), c_Product__Type_Omap__pair(_1533538, _1533540, _1533546, _1533548, _1533542, _1533550), hAPP(hAPP(c_Product__Type_OSigma(_1533538, _1533546), _1533544), hAPP(c_COMBK(tc_fun(_1533546, tc_HOL_Obool), _1533538), _1533552))))], (38728 ^ _782652) ^ [_1533765, _1533767, _1533769, _1533771, _1533773, _1533775, _1533777, _1533779] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1533765, _1533767)), _1533769), hAPP(c_Set_Oimage(tc_prod(_1533771, _1533773), tc_prod(_1533765, _1533767), c_Product__Type_Omap__pair(_1533771, _1533765, _1533773, _1533767, _1533775, _1533777)), _1533779))), 38733 ^ _782652 : [(38734 ^ _782652) ^ [] : [-(_1533769 = hAPP(hAPP(c_Product__Type_OPair(_1533765, _1533767), hAPP(_1533775, 38731 ^ [_1533765, _1533767, _1533769, _1533771, _1533773, _1533775, _1533777, _1533779])), hAPP(_1533777, 38732 ^ [_1533765, _1533767, _1533769, _1533771, _1533773, _1533775, _1533777, _1533779])))], (38736 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533771, _1533773)), hAPP(hAPP(c_Product__Type_OPair(_1533771, _1533773), 38731 ^ [_1533765, _1533767, _1533769, _1533771, _1533773, _1533775, _1533777, _1533779]), 38732 ^ [_1533765, _1533767, _1533769, _1533771, _1533773, _1533775, _1533777, _1533779])), _1533779)))]]], (38738 ^ _782652) ^ [_1534116, _1534118, _1534120] : [c_Relation_Orefl__on(_1534116, _1534118, _1534120), 38741 ^ _782652 : [(38742 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534116, _1534116), tc_HOL_Obool)), _1534120), hAPP(hAPP(c_Product__Type_OSigma(_1534116, _1534116), _1534118), hAPP(c_COMBK(tc_fun(_1534116, tc_HOL_Obool), _1534116), _1534118)))))], (38744 ^ _782652) ^ [_1534298] : [hBOOL(hAPP(hAPP(c_member(_1534116), _1534298), _1534118)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534116, _1534116)), hAPP(hAPP(c_Product__Type_OPair(_1534116, _1534116), _1534298), _1534298)), _1534120)))]]], (38750 ^ _782652) ^ [_1534433, _1534435, _1534437] : [-(c_Relation_Orefl__on(_1534433, _1534435, _1534437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534433, _1534433), tc_HOL_Obool)), _1534437), hAPP(hAPP(c_Product__Type_OSigma(_1534433, _1534433), _1534435), hAPP(c_COMBK(tc_fun(_1534433, tc_HOL_Obool), _1534433), _1534435)))), 38756 ^ _782652 : [(38757 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1534433), 38755 ^ [_1534433, _1534435, _1534437]), _1534435)))], (38759 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1534433, _1534433)), hAPP(hAPP(c_Product__Type_OPair(_1534433, _1534433), 38755 ^ [_1534433, _1534435, _1534437]), 38755 ^ [_1534433, _1534435, _1534437])), _1534437))]]], (38763 ^ _782652) ^ [_1534797, _1534799] : [c_Wellfounded_OwfP(_1534797, _1534799), -(c_Wellfounded_Owf(_1534797, hAPP(c_Set_OCollect(tc_prod(_1534797, _1534797)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534797, _1534797, tc_HOL_Obool), _1534799))))], (38769 ^ _782652) ^ [_1534900, _1534902] : [c_Wellfounded_Owf(_1534900, hAPP(c_Set_OCollect(tc_prod(_1534900, _1534900)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534900, _1534900, tc_HOL_Obool), _1534902))), -(c_Wellfounded_OwfP(_1534900, _1534902))], (38775 ^ _782652) ^ [_1535009] : [-(c_Wellfounded_OwfP(_1535009, hAPP(c_COMBK(tc_fun(_1535009, tc_HOL_Obool), _1535009), hAPP(c_COMBK(tc_HOL_Obool, _1535009), c_fFalse))))], (38777 ^ _782652) ^ [_1535047, _1535049] : [-(c_Relation_Orefl__on(_1535047, _1535049, c_Relation_OId__on(_1535047, _1535049)))], (38779 ^ _782652) ^ [_1535091, _1535093] : [c_Wellfounded_OwfP(_1535091, _1535093), 38782 ^ _782652 : [(38783 ^ _782652) ^ [_1535155] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1535091, _1535093), _1535155)))]]], (38785 ^ _782652) ^ [_1535183, _1535185] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1535183, _1535185), 38786 ^ [_1535183, _1535185])), -(c_Wellfounded_OwfP(_1535183, _1535185))], (38792 ^ _782652) ^ [_1535301, _1535303, _1535305] : [c_Wellfounded_OwfP(_1535301, _1535303), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1535301, _1535303), _1535305)))], (38798 ^ _782652) ^ [_1535390, _1535392, _1535394] : [c_Wellfounded_OwfP(_1535390, _1535392), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1535390, tc_fun(_1535390, tc_HOL_Obool))), _1535394), _1535392)), -(c_Wellfounded_OwfP(_1535390, _1535394))], (38808 ^ _782652) ^ [_1535549] : [-(c_Relation_Orefl__on(_1535549, c_Orderings_Obot__class_Obot(tc_fun(_1535549, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1535549, _1535549), tc_HOL_Obool))))], (38810 ^ _782652) ^ [_1535586, _1535588, _1535590, _1535592, _1535594] : [c_Relation_Orefl__on(_1535586, _1535588, _1535590), c_Relation_Orefl__on(_1535586, _1535592, _1535594), -(c_Relation_Orefl__on(_1535586, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535586, tc_HOL_Obool)), _1535588), _1535592), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1535586, _1535586), tc_HOL_Obool)), _1535590), _1535594)))], (38820 ^ _782652) ^ [_1535783, _1535785, _1535787, _1535789, _1535791] : [c_Relation_Orefl__on(_1535783, _1535785, _1535787), c_Relation_Orefl__on(_1535783, _1535789, _1535791), -(c_Relation_Orefl__on(_1535783, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535783, tc_HOL_Obool)), _1535785), _1535789), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1535783, _1535783), tc_HOL_Obool)), _1535787), _1535791)))], (38830 ^ _782652) ^ [_1535980, _1535982, _1535984, _1535986] : [c_Relation_Orefl__on(_1535980, _1535982, _1535984), hBOOL(hAPP(hAPP(c_member(_1535980), _1535986), _1535982)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1535980, _1535980)), hAPP(hAPP(c_Product__Type_OPair(_1535980, _1535980), _1535986), _1535986)), _1535984)))], (38840 ^ _782652) ^ [_1536171, _1536173, _1536175, _1536177, _1536179] : [c_Relation_Orefl__on(_1536171, _1536173, _1536175), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536171, _1536171)), hAPP(hAPP(c_Product__Type_OPair(_1536171, _1536171), _1536177), _1536179)), _1536175)), -(hBOOL(hAPP(hAPP(c_member(_1536171), _1536177), _1536173)))], (38850 ^ _782652) ^ [_1536366, _1536368, _1536370, _1536372, _1536374] : [c_Relation_Orefl__on(_1536366, _1536368, _1536370), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536366, _1536366)), hAPP(hAPP(c_Product__Type_OPair(_1536366, _1536366), _1536372), _1536374)), _1536370)), -(hBOOL(hAPP(hAPP(c_member(_1536366), _1536374), _1536368)))], (38860 ^ _782652) ^ [_1536561, _1536563] : [c_Wellfounded_Owf(_1536561, _1536563), -(c_Wellfounded_OwfP(_1536561, c_FunDef_Oin__rel(_1536561, _1536561, _1536563)))], (38866 ^ _782652) ^ [_1536661, _1536663] : [c_Wellfounded_OwfP(_1536661, hAPP(hAPP(c_COMBC(_1536661, tc_fun(tc_prod(_1536661, _1536661), tc_HOL_Obool), tc_fun(_1536661, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536661, tc_fun(tc_fun(tc_prod(_1536661, _1536661), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1536661, _1536661), tc_HOL_Obool), tc_fun(_1536661, tc_HOL_Obool)), _1536661), c_COMBC(_1536661, tc_fun(tc_prod(_1536661, _1536661), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536661, tc_prod(_1536661, _1536661)), tc_fun(_1536661, tc_fun(tc_fun(tc_prod(_1536661, _1536661), tc_HOL_Obool), tc_HOL_Obool)), _1536661), hAPP(c_COMBB(tc_prod(_1536661, _1536661), tc_fun(tc_fun(tc_prod(_1536661, _1536661), tc_HOL_Obool), tc_HOL_Obool), _1536661), c_member(tc_prod(_1536661, _1536661)))), c_Product__Type_OPair(_1536661, _1536661)))), _1536663)), -(c_Wellfounded_Owf(_1536661, _1536663))], (38872 ^ _782652) ^ [_1536970, _1536972] : [c_Wellfounded_Owf(_1536970, _1536972), -(c_Wellfounded_OwfP(_1536970, hAPP(hAPP(c_COMBC(_1536970, tc_fun(tc_prod(_1536970, _1536970), tc_HOL_Obool), tc_fun(_1536970, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536970, tc_fun(tc_fun(tc_prod(_1536970, _1536970), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1536970, _1536970), tc_HOL_Obool), tc_fun(_1536970, tc_HOL_Obool)), _1536970), c_COMBC(_1536970, tc_fun(tc_prod(_1536970, _1536970), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536970, tc_prod(_1536970, _1536970)), tc_fun(_1536970, tc_fun(tc_fun(tc_prod(_1536970, _1536970), tc_HOL_Obool), tc_HOL_Obool)), _1536970), hAPP(c_COMBB(tc_prod(_1536970, _1536970), tc_fun(tc_fun(tc_prod(_1536970, _1536970), tc_HOL_Obool), tc_HOL_Obool), _1536970), c_member(tc_prod(_1536970, _1536970)))), c_Product__Type_OPair(_1536970, _1536970)))), _1536972)))], (38878 ^ _782652) ^ [_1537300, _1537302] : [c_Predicate_Oreflp(_1537300, _1537302), -(c_Relation_Orefl__on(_1537300, c_Orderings_Otop__class_Otop(tc_fun(_1537300, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1537300, _1537300)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537300, _1537300, tc_HOL_Obool), _1537302))))], (38884 ^ _782652) ^ [_1537415, _1537417] : [c_Relation_Orefl__on(_1537415, c_Orderings_Otop__class_Otop(tc_fun(_1537415, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1537415, _1537415)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537415, _1537415, tc_HOL_Obool), _1537417))), -(c_Predicate_Oreflp(_1537415, _1537417))], (38890 ^ _782652) ^ [_1537536, _1537538, _1537540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537536, _1537536), tc_HOL_Obool)), _1537538), hAPP(hAPP(c_Product__Type_OSigma(_1537536, _1537536), _1537540), hAPP(c_COMBK(tc_fun(_1537536, tc_HOL_Obool), _1537536), _1537540)))), 38896 ^ _782652 : [(38897 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537536), 38895 ^ [_1537536, _1537538, _1537540]), _1537540)))], (38899 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537536, _1537536)), hAPP(hAPP(c_Product__Type_OPair(_1537536, _1537536), 38895 ^ [_1537536, _1537538, _1537540]), 38895 ^ [_1537536, _1537538, _1537540])), _1537538))]], -(c_Relation_Orefl__on(_1537536, _1537540, _1537538))], (38903 ^ _782652) ^ [_1537883, _1537885] : [c_Wellfounded_OwfP(_1537883, _1537885), -(c_Wellfounded_Oacyclic(_1537883, hAPP(c_Set_OCollect(tc_prod(_1537883, _1537883)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537883, _1537883, tc_HOL_Obool), _1537885))))], (38909 ^ _782652) ^ [_1537990, _1537992, _1537994] : [c_Wellfounded_Oacyclic(_1537990, _1537992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537990, _1537990), tc_HOL_Obool)), _1537994), _1537992)), -(c_Wellfounded_Oacyclic(_1537990, _1537994))], (38919 ^ _782652) ^ [_1538149, _1538151, _1538153] : [c_Predicate_Oreflp(_1538149, _1538151), -(hBOOL(hAPP(hAPP(_1538151, _1538153), _1538153)))], (38925 ^ _782652) ^ [_1538238, _1538240] : [c_Wellfounded_Owf(_1538238, _1538240), -(c_Wellfounded_Oacyclic(_1538238, _1538240))], (38931 ^ _782652) ^ [_1538315, _1538317] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1538315, _1538315)), _1538317)), c_Wellfounded_Oacyclic(_1538315, _1538317), -(c_Wellfounded_Owf(_1538315, _1538317))], (38941 ^ _782652) ^ [_1538458, _1538460] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1538458, _1538458)), _1538460)), 38944 ^ _782652 : [(38945 ^ _782652) ^ [] : [c_Wellfounded_Owf(_1538458, _1538460), -(c_Wellfounded_Oacyclic(_1538458, _1538460))], (38951 ^ _782652) ^ [] : [c_Wellfounded_Oacyclic(_1538458, _1538460), -(c_Wellfounded_Owf(_1538458, _1538460))]]], (38957 ^ _782652) ^ [_1538694, _1538696] : [c_Nitpick_Owf_H(_1538694, _1538696), 38960 ^ _782652 : [(38961 ^ _782652) ^ [] : [-(c_Wellfounded_Oacyclic(_1538694, _1538696))], (38963 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1538694, _1538694)), _1538696))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (38969 ^ _782652) ^ [_1538814, _1538816] : [-(c_Nitpick_Owf_H(_1538814, _1538816)), c_Wellfounded_Oacyclic(_1538814, _1538816), 38974 ^ _782652 : [(38975 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1538814, _1538814)), _1538816))], (38977 ^ _782652) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (38981 ^ _782652) ^ [_1538991, _1538993] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1538991), c_Int_OInteg)), hBOOL(hAPP(_1538993, hAPP(c_Int_ORep__Integ, 38986 ^ [_1538991, _1538993]))), -(hBOOL(hAPP(_1538993, _1538991)))], (38992 ^ _782652) ^ [_1539173] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1539173), c_Int_OInteg)), -(_1539173 = hAPP(c_Int_ORep__Integ, 38995 ^ [_1539173]))], (39015 ^ _782652) ^ [_1539915, _1539917, _1539919] : [-(c_Relation_Orefl__on(_1539915, _1539917, _1539919)), 39019 ^ _782652 : [(39020 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539915, _1539915)), 39018 ^ [_1539915, _1539917, _1539919]), _1539919)))], (39022 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1539915, _1539915, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1539915, tc_fun(_1539915, tc_HOL_Obool), tc_fun(_1539915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1539915, tc_HOL_Obool), tc_fun(_1539915, tc_HOL_Obool)), _1539915), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1539915)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539915), c_fconj), hAPP(hAPP(c_COMBC(_1539915, tc_fun(_1539915, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539915)), _1539917)))), hAPP(hAPP(c_COMBC(_1539915, tc_fun(_1539915, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539915)), _1539917))), 39018 ^ [_1539915, _1539917, _1539919]))]], 39024 ^ _782652 : [(39025 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539915), 39023 ^ [_1539915, _1539917, _1539919]), _1539917)))], (39027 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539915, _1539915)), hAPP(hAPP(c_Product__Type_OPair(_1539915, _1539915), 39023 ^ [_1539915, _1539917, _1539919]), 39023 ^ [_1539915, _1539917, _1539919])), _1539919))]]], (38999 ^ _782652) ^ [_1539296, _1539298, _1539300] : [c_Relation_Orefl__on(_1539296, _1539298, _1539300), 39002 ^ _782652 : [(39003 ^ _782652) ^ [_1539507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539296, _1539296)), _1539507), _1539300)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1539296, _1539296, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1539296, tc_fun(_1539296, tc_HOL_Obool), tc_fun(_1539296, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1539296, tc_HOL_Obool), tc_fun(_1539296, tc_HOL_Obool)), _1539296), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1539296)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539296), c_fconj), hAPP(hAPP(c_COMBC(_1539296, tc_fun(_1539296, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539296)), _1539298)))), hAPP(hAPP(c_COMBC(_1539296, tc_fun(_1539296, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539296)), _1539298))), _1539507)))], (39009 ^ _782652) ^ [_1539780] : [hBOOL(hAPP(hAPP(c_member(_1539296), _1539780), _1539298)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539296, _1539296)), hAPP(hAPP(c_Product__Type_OPair(_1539296, _1539296), _1539780), _1539780)), _1539300)))]]], (39031 ^ _782652) ^ [_1540556, _1540558] : [39033 ^ _782652 : [(39034 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39032 ^ [_1540556, _1540558]), c_Int_OInteg)))], (39036 ^ _782652) ^ [] : [hBOOL(hAPP(_1540556, hAPP(c_Int_OAbs__Integ, 39032 ^ [_1540556, _1540558])))]], -(hBOOL(hAPP(_1540556, _1540558)))], (39041 ^ _782652) ^ [_1540723] : [-(_1540723 = hAPP(c_Int_OAbs__Integ, 39039 ^ [_1540723]))], (39043 ^ _782652) ^ [_1540751] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39039 ^ [_1540751]), c_Int_OInteg)))], (39055 ^ _782652) ^ [_1540987, _1540989, _1540991] : [39057 ^ _782652 : [(39058 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540987), 39056 ^ [_1540987, _1540989, _1540991]), _1540991)))], (39060 ^ _782652) ^ [] : [hBOOL(hAPP(_1540989, 39056 ^ [_1540987, _1540989, _1540991]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1540987, _1540989), _1540991)))], (39045 ^ _782652) ^ [_1540804, _1540806, _1540808] : [hBOOL(hAPP(c_Predicate_OPowp(_1540804, _1540806), _1540808)), 39048 ^ _782652 : [(39049 ^ _782652) ^ [_1540888] : [hBOOL(hAPP(hAPP(c_member(_1540804), _1540888), _1540808)), -(hBOOL(hAPP(_1540806, _1540888)))]]], (39064 ^ _782652) ^ [_1541167, _1541169, _1541171] : [hBOOL(hAPP(hAPP(c_member(_1541169), _1541167), c_Orderings_Obot__class_Obot(tc_fun(_1541169, tc_HOL_Obool)))), -(hBOOL(hAPP(_1541171, _1541167)))], (39070 ^ _782652) ^ [_1541289, _1541291] : [39072 ^ _782652 : [(39073 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541289), 39071 ^ [_1541289, _1541291]), c_Orderings_Otop__class_Otop(tc_fun(_1541289, tc_HOL_Obool)))))], (39075 ^ _782652) ^ [] : [hBOOL(hAPP(_1541291, 39071 ^ [_1541289, _1541291]))]], 39076 ^ _782652 : [(39077 ^ _782652) ^ [_1541441] : [-(hBOOL(hAPP(_1541291, _1541441)))]]], (39079 ^ _782652) ^ [_1541468, _1541470] : [hBOOL(hAPP(_1541470, 39080 ^ [_1541468, _1541470])), 39083 ^ _782652 : [(39084 ^ _782652) ^ [_1541575] : [hBOOL(hAPP(hAPP(c_member(_1541468), _1541575), c_Orderings_Otop__class_Otop(tc_fun(_1541468, tc_HOL_Obool)))), -(hBOOL(hAPP(_1541470, _1541575)))]]], (39100 ^ _782652) ^ [_1542085, _1542087, _1542089, _1542091] : [39102 ^ _782652 : [(39103 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542085, _1542085)), 39101 ^ [_1542085, _1542087, _1542089, _1542091]), _1542089)))], (39105 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1542085, _1542085, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1542085, tc_fun(_1542085, _1542087), tc_fun(_1542085, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542087, tc_HOL_Obool), tc_fun(tc_fun(_1542085, _1542087), tc_fun(_1542085, tc_HOL_Obool)), _1542085), c_COMBB(_1542087, tc_HOL_Obool, _1542085)), hAPP(hAPP(c_COMBB(_1542087, tc_fun(_1542087, tc_HOL_Obool), _1542085), c_fequal), _1542091))), _1542091)), 39101 ^ [_1542085, _1542087, _1542089, _1542091]))]], -(c_Equiv__Relations_Ocongruent(_1542085, _1542087, _1542089, _1542091))], (39090 ^ _782652) ^ [_1541709, _1541711, _1541713, _1541715] : [c_Equiv__Relations_Ocongruent(_1541709, _1541711, _1541713, _1541715), 39093 ^ _782652 : [(39094 ^ _782652) ^ [_1541854] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1541709, _1541709)), _1541854), _1541713)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1541709, _1541709, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1541709, tc_fun(_1541709, _1541711), tc_fun(_1541709, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541711, tc_HOL_Obool), tc_fun(tc_fun(_1541709, _1541711), tc_fun(_1541709, tc_HOL_Obool)), _1541709), c_COMBB(_1541711, tc_HOL_Obool, _1541709)), hAPP(hAPP(c_COMBB(_1541711, tc_fun(_1541711, tc_HOL_Obool), _1541709), c_fequal), _1541715))), _1541715)), _1541854)))]]], (39109 ^ _782652) ^ [_1542460, _1542462, _1542464] : [c_Wellfounded_OwfP(_1542460, hAPP(_1542462, 39110 ^ [_1542460, _1542462, _1542464])), 39117 ^ _782652 : [(39118 ^ _782652) ^ [] : [hAPP(_1542462, 39115 ^ [_1542460, _1542462, _1542464]) = hAPP(_1542462, 39116 ^ [_1542460, _1542462, _1542464])], (39120 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1542460, tc_HOL_Obool)), c_Predicate_ODomainP(_1542460, _1542460, hAPP(_1542462, 39115 ^ [_1542460, _1542462, _1542464]))), c_Predicate_ORangeP(_1542460, _1542460, hAPP(_1542462, 39116 ^ [_1542460, _1542462, _1542464]))) = c_Orderings_Obot__class_Obot(tc_fun(_1542460, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1542460, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542464, tc_fun(_1542460, tc_fun(_1542460, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1542464, tc_HOL_Obool))), _1542462)))], (39124 ^ _782652) ^ [_1542900, _1542902, _1542904, _1542906, _1542908, _1542910] : [39127 ^ _782652 : [(39128 ^ _782652) ^ [] : [-(_1542900 = hAPP(hAPP(c_Product__Type_OPair(_1542902, _1542904), 39125 ^ [_1542900, _1542902, _1542904, _1542906, _1542908, _1542910]), 39126 ^ [_1542900, _1542902, _1542904, _1542906, _1542908, _1542910]))], (39130 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1542906), _1542908), hAPP(hAPP(_1542910, 39125 ^ [_1542900, _1542902, _1542904, _1542906, _1542908, _1542910]), 39126 ^ [_1542900, _1542902, _1542904, _1542906, _1542908, _1542910])))]], -(hBOOL(hAPP(hAPP(c_member(_1542906), _1542908), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1542902, _1542904, tc_fun(_1542906, tc_HOL_Obool)), _1542910), _1542900))))], (39134 ^ _782652) ^ [_1543225, _1543227, _1543229, _1543231, _1543233, _1543235] : [hBOOL(hAPP(hAPP(c_member(_1543225), _1543227), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1543229, _1543231, tc_fun(_1543225, tc_HOL_Obool)), _1543233), _1543235))), 39139 ^ _782652 : [(39140 ^ _782652) ^ [] : [-(_1543235 = hAPP(hAPP(c_Product__Type_OPair(_1543229, _1543231), 39137 ^ [_1543225, _1543227, _1543229, _1543231, _1543233, _1543235]), 39138 ^ [_1543225, _1543227, _1543229, _1543231, _1543233, _1543235]))], (39142 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543225), _1543227), hAPP(hAPP(_1543233, 39137 ^ [_1543225, _1543227, _1543229, _1543231, _1543233, _1543235]), 39138 ^ [_1543225, _1543227, _1543229, _1543231, _1543233, _1543235]))))]]], (39144 ^ _782652) ^ [_1543494, _1543496, _1543498] : [39146 ^ _782652 : [(39147 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1543494)), 39145 ^ [_1543494, _1543496, _1543498]), _1543496)))], (39149 ^ _782652) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1543494, hAPP(c_Nat_OSuc, _1543498), 39145 ^ [_1543494, _1543496, _1543498])]], 39150 ^ _782652 : [(39151 ^ _782652) ^ [_1543667] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1543494)), _1543667), _1543496)), -(c_Hoare__Mirabelle_Otriple__valid(_1543494, _1543498, _1543667))]]], (39174 ^ _782652) ^ [_1544182, _1544184, _1544186] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1544182, _1544184, _1544186)), 39176 ^ _782652 : [(39184 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1544182)), 39182 ^ [_1544182, _1544184, _1544186]), _1544186)))], (39186 ^ _782652) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1544182, 39175 ^ [_1544182, _1544184, _1544186], 39182 ^ [_1544182, _1544184, _1544186])], (39177 ^ _782652) ^ [_1544328] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1544182)), _1544328), _1544184)), -(c_Hoare__Mirabelle_Otriple__valid(_1544182, 39175 ^ [_1544182, _1544184, _1544186], _1544328))]]], (39157 ^ _782652) ^ [_1543792, _1543794, _1543796] : [c_Hoare__Mirabelle_Ohoare__valids(_1543792, _1543794, _1543796), 39160 ^ _782652 : [(39161 ^ _782652) ^ [_1543901] : [39163 ^ _782652 : [(39164 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1543792)), 39162 ^ [_1543792, _1543794, _1543796, _1543901]), _1543794)))], (39166 ^ _782652) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1543792, _1543901, 39162 ^ [_1543792, _1543794, _1543796, _1543901])]], 39167 ^ _782652 : [(39168 ^ _782652) ^ [_1544073] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1543792)), _1544073), _1543796)), -(c_Hoare__Mirabelle_Otriple__valid(_1543792, _1543901, _1544073))]]]]], (39190 ^ _782652) ^ [_1544583, _1544585, _1544587, _1544589, _1544591, _1544593] : [-(hAPP(c_Set_Ovimage(_1544583, tc_prod(_1544585, _1544587), _1544589), hAPP(hAPP(c_Product__Type_OSigma(_1544585, _1544587), _1544591), hAPP(c_COMBK(tc_fun(_1544587, tc_HOL_Obool), _1544585), _1544593))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1544583, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1544583, _1544585, hAPP(c_Fun_Ocomp(tc_prod(_1544585, _1544587), _1544585, _1544583, c_Product__Type_Ofst(_1544585, _1544587)), _1544589)), _1544591)), hAPP(c_Set_Ovimage(_1544583, _1544587, hAPP(c_Fun_Ocomp(tc_prod(_1544585, _1544587), _1544587, _1544583, c_Product__Type_Osnd(_1544585, _1544587)), _1544589)), _1544593)))], (39192 ^ _782652) ^ [_1544697, _1544699, _1544701] : [-(c_Hilbert__Choice_OEps(tc_prod(_1544697, _1544699), hAPP(c_Product__Type_Oprod_Oprod__case(_1544697, _1544699, tc_HOL_Obool), _1544701)) = c_Hilbert__Choice_OEps(tc_prod(_1544697, _1544699), hAPP(hAPP(c_COMBS(tc_prod(_1544697, _1544699), _1544699, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1544697, tc_fun(_1544699, tc_HOL_Obool), tc_prod(_1544697, _1544699)), _1544701), c_Product__Type_Ofst(_1544697, _1544699))), c_Product__Type_Osnd(_1544697, _1544699))))], (39194 ^ _782652) ^ [_1544778, _1544780] : [39196 ^ _782652 : [(39197 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1544778, tc_HOL_Obool)), 39195 ^ [_1544778, _1544780]), hAPP(c_Relation_OImage(_1544778, _1544778, _1544780), 39195 ^ [_1544778, _1544780]))))], (39199 ^ _782652) ^ [] : [39195 ^ [_1544778, _1544780] = c_Orderings_Obot__class_Obot(tc_fun(_1544778, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1544778, _1544780))], (39203 ^ _782652) ^ [_1544975, _1544977, _1544979] : [-(hAPP(c_Fun_Ocomp(_1544975, _1544975, _1544977, c_Fun_Oid(_1544975)), _1544979) = _1544979)], (39205 ^ _782652) ^ [_1545012, _1545014, _1545016] : [-(hAPP(c_Fun_Ocomp(_1545012, _1545014, _1545012, _1545016), c_Fun_Oid(_1545012)) = _1545016)], (39207 ^ _782652) ^ [_1545049, _1545051, _1545053, _1545055, _1545057, _1545059, _1545061] : [hAPP(c_Fun_Ocomp(_1545049, _1545051, _1545053, _1545055), _1545057) = hAPP(c_Fun_Ocomp(_1545051, _1545051, _1545053, c_Fun_Oid(_1545051)), _1545059), -(hAPP(_1545055, hAPP(_1545057, _1545061)) = hAPP(_1545059, _1545061))], (39213 ^ _782652) ^ [_1545190, _1545192, _1545194, _1545196, _1545198, _1545200, _1545202] : [-(hAPP(c_Product__Type_Oapsnd(_1545190, _1545192, _1545194, _1545196), hAPP(c_Product__Type_Oapsnd(_1545198, _1545190, _1545194, _1545200), _1545202)) = hAPP(c_Product__Type_Oapsnd(_1545198, _1545192, _1545194, hAPP(c_Fun_Ocomp(_1545190, _1545192, _1545198, _1545196), _1545200)), _1545202))], (39215 ^ _782652) ^ [_1545257, _1545259, _1545261, _1545263] : [c_Finite__Set_Ofun__left__comm__idem(_1545257, _1545259, _1545261), -(hAPP(c_Fun_Ocomp(_1545259, _1545259, _1545259, hAPP(_1545261, _1545263)), hAPP(_1545261, _1545263)) = hAPP(_1545261, _1545263))], (39221 ^ _782652) ^ [_1545374, _1545376] : [-(c_Hilbert__Choice_OEps(_1545374, hAPP(c_fequal, _1545376)) = _1545376)], (39223 ^ _782652) ^ [_1545405, _1545407] : [-(c_Hilbert__Choice_OEps(_1545405, hAPP(hAPP(c_COMBC(_1545405, _1545405, tc_HOL_Obool), c_fequal), _1545407)) = _1545407)], (39225 ^ _782652) ^ [_1545458, _1545460] : [hBOOL(hAPP(_1545458, c_Hilbert__Choice_OEps(_1545460, _1545458))), -(hBOOL(hAPP(_1545458, 39228 ^ [_1545458, _1545460])))], (39232 ^ _782652) ^ [_1545557, _1545559] : [39233 ^ _782652 : [(39234 ^ _782652) ^ [_1545603] : [hBOOL(hAPP(_1545557, _1545603))]], -(hBOOL(hAPP(_1545557, c_Hilbert__Choice_OEps(_1545559, _1545557))))], (39238 ^ _782652) ^ [_1545663, _1545665] : [39239 ^ _782652 : [(39240 ^ _782652) ^ [_1545709] : [hBOOL(hAPP(_1545663, _1545709))]], -(hBOOL(hAPP(_1545663, c_Hilbert__Choice_OEps(_1545665, _1545663))))], (39244 ^ _782652) ^ [_1545767, _1545769, _1545771, _1545773, _1545775, _1545777, _1545779, _1545781, _1545783, _1545785, _1545787] : [hAPP(_1545767, hAPP(_1545769, _1545771)) = hAPP(_1545773, hAPP(_1545775, _1545777)), -(hAPP(hAPP(c_Fun_Ocomp(_1545779, _1545781, _1545783, _1545767), _1545769), _1545771) = hAPP(hAPP(c_Fun_Ocomp(_1545785, _1545781, _1545787, _1545773), _1545775), _1545777))], (39250 ^ _782652) ^ [_1545930, _1545932, _1545934, _1545936, _1545938, _1545940, _1545942] : [-(hAPP(c_Fun_Ocomp(_1545930, _1545932, _1545934, _1545936), hAPP(c_Fun_Ocomp(_1545938, _1545930, _1545934, _1545940), _1545942)) = hAPP(c_Fun_Ocomp(_1545938, _1545932, _1545934, hAPP(c_Fun_Ocomp(_1545930, _1545932, _1545938, _1545936), _1545940)), _1545942))], (39252 ^ _782652) ^ [_1545997, _1545999, _1546001, _1546003, _1546005, _1546007] : [-(hAPP(hAPP(c_Fun_Ocomp(_1545997, _1545999, _1546001, _1546003), _1546005), _1546007) = hAPP(_1546003, hAPP(_1546005, _1546007)))], (39254 ^ _782652) ^ [_1546047, _1546049, _1546051, _1546053, _1546055, _1546057, _1546059, _1546061, _1546063] : [hAPP(c_Fun_Ocomp(_1546047, _1546049, _1546051, _1546053), _1546055) = hAPP(c_Fun_Ocomp(_1546057, _1546049, _1546051, _1546059), _1546061), -(hAPP(_1546053, hAPP(_1546055, _1546063)) = hAPP(_1546059, hAPP(_1546061, _1546063)))], (39260 ^ _782652) ^ [_1546194, _1546196, _1546198, _1546200, _1546202, _1546204, _1546206, _1546208] : [hAPP(c_Fun_Ocomp(_1546194, _1546196, _1546198, _1546200), _1546202) = hAPP(c_Fun_Ocomp(_1546204, _1546196, _1546198, _1546206), _1546208), 39263 ^ _782652 : [(39264 ^ _782652) ^ [_1546309] : [-(hAPP(_1546200, hAPP(_1546202, _1546309)) = hAPP(_1546206, hAPP(_1546208, _1546309)))]]], (39266 ^ _782652) ^ [_1546348, _1546350] : [39267 ^ _782652 : [(39268 ^ _782652) ^ [_1546394] : [hBOOL(hAPP(_1546348, _1546394))]], -(hBOOL(hAPP(_1546348, c_Hilbert__Choice_OEps(_1546350, _1546348))))], (39272 ^ _782652) ^ [_1546452, _1546454, _1546456] : [hBOOL(hAPP(_1546452, _1546454)), -(hBOOL(hAPP(_1546452, c_Hilbert__Choice_OEps(_1546456, _1546452))))], (39278 ^ _782652) ^ [_1546545, _1546547, _1546549, _1546551, _1546553, _1546555] : [-(hAPP(hAPP(c_Fun_Ocomp(_1546545, _1546547, _1546549, _1546551), _1546553), _1546555) = hAPP(_1546551, hAPP(_1546553, _1546555)))], (39280 ^ _782652) ^ [_1546595, _1546597, _1546599, _1546601, _1546603, _1546605] : [-(hAPP(hAPP(c_Fun_Ocomp(_1546595, _1546597, _1546599, hAPP(c_COMBK(_1546597, _1546595), _1546601)), _1546603), _1546605) = _1546601)], (39282 ^ _782652) ^ [_1546645, _1546647, _1546649, _1546651, _1546653, _1546655, _1546657] : [hAPP(c_Fun_Ocomp(_1546645, _1546647, _1546649, _1546651), _1546653) = _1546655, -(hAPP(_1546651, hAPP(_1546653, _1546657)) = hAPP(_1546655, _1546657))], (39288 ^ _782652) ^ [_1546766, _1546768, _1546770, _1546772, _1546774, _1546776] : [-(hAPP(c_Set_Ovimage(_1546766, _1546768, hAPP(c_Fun_Ocomp(_1546770, _1546768, _1546766, _1546772), _1546774)), _1546776) = hAPP(c_Set_Ovimage(_1546766, _1546770, _1546774), hAPP(c_Set_Ovimage(_1546770, _1546768, _1546772), _1546776)))], (39290 ^ _782652) ^ [_1546828, _1546830, _1546832, _1546834, _1546836, _1546838, _1546840] : [-(hAPP(c_Fun_Ocomp(_1546828, _1546830, _1546832, _1546834), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1546832, _1546828), _1546836), _1546838), _1546840)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1546832, _1546830), hAPP(c_Fun_Ocomp(_1546828, _1546830, _1546832, _1546834), _1546836)), _1546838), hAPP(_1546834, _1546840)))], (39292 ^ _782652) ^ [_1546906, _1546908, _1546910] : [39293 ^ _782652 : [(39294 ^ _782652) ^ [_1546960] : [hBOOL(hAPP(_1546906, _1546960))]], _1546908 = c_Hilbert__Choice_OEps(_1546910, _1546906), -(hBOOL(hAPP(_1546906, _1546908)))], (39302 ^ _782652) ^ [_1547066, _1547068, _1547070, _1547072, _1547074, _1547076, _1547078] : [-(hAPP(c_Product__Type_Oapfst(_1547066, _1547068, _1547070, _1547072), hAPP(c_Product__Type_Oapfst(_1547074, _1547066, _1547070, _1547076), _1547078)) = hAPP(c_Product__Type_Oapfst(_1547074, _1547068, _1547070, hAPP(c_Fun_Ocomp(_1547066, _1547068, _1547074, _1547072), _1547076)), _1547078))], (39304 ^ _782652) ^ [_1547133, _1547135, _1547137, _1547139, _1547141] : [c_Fun_Oinj__on(_1547133, _1547135, _1547137, c_Orderings_Otop__class_Otop(tc_fun(_1547133, tc_HOL_Obool))), c_Fun_Oinj__on(_1547139, _1547133, _1547141, c_Orderings_Otop__class_Otop(tc_fun(_1547139, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1547139, _1547135, hAPP(c_Fun_Ocomp(_1547133, _1547135, _1547139, _1547137), _1547141), c_Orderings_Otop__class_Otop(tc_fun(_1547139, tc_HOL_Obool))))], (39314 ^ _782652) ^ [_1547332, _1547334, _1547336, _1547338, _1547340, _1547342] : [c_Fun_Oinj__on(_1547332, _1547334, hAPP(c_Fun_Ocomp(_1547336, _1547334, _1547332, _1547338), _1547340), _1547342), -(c_Fun_Oinj__on(_1547332, _1547336, _1547340, _1547342))], (39320 ^ _782652) ^ [_1547441, _1547443, _1547445, _1547447, _1547449] : [hAPP(c_Set_Oimage(_1547441, _1547443, _1547445), c_Orderings_Otop__class_Otop(tc_fun(_1547441, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1547443, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1547443, _1547447, _1547449), c_Orderings_Otop__class_Otop(tc_fun(_1547443, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1547447, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1547441, _1547447, hAPP(c_Fun_Ocomp(_1547443, _1547447, _1547441, _1547449), _1547445)), c_Orderings_Otop__class_Otop(tc_fun(_1547441, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1547447, tc_HOL_Obool)))], (39330 ^ _782652) ^ [_1547700, _1547702, _1547704, _1547706, _1547708, _1547710] : [-(hAPP(c_Set_Oimage(_1547700, _1547702, hAPP(c_Fun_Ocomp(_1547704, _1547702, _1547700, _1547706), _1547708)), _1547710) = hAPP(c_Set_Oimage(_1547704, _1547702, _1547706), hAPP(c_Set_Oimage(_1547700, _1547704, _1547708), _1547710)))], (39332 ^ _782652) ^ [_1547762, _1547764, _1547766, _1547768, _1547770, _1547772] : [c_Fun_Oinj__on(_1547762, _1547764, _1547766, _1547768), 39335 ^ _782652 : [(39336 ^ _782652) ^ [] : [c_Fun_Oinj__on(_1547764, _1547770, _1547772, hAPP(c_Set_Oimage(_1547762, _1547764, _1547766), _1547768)), -(c_Fun_Oinj__on(_1547762, _1547770, hAPP(c_Fun_Ocomp(_1547764, _1547770, _1547762, _1547772), _1547766), _1547768))], (39342 ^ _782652) ^ [] : [c_Fun_Oinj__on(_1547762, _1547770, hAPP(c_Fun_Ocomp(_1547764, _1547770, _1547762, _1547772), _1547766), _1547768), -(c_Fun_Oinj__on(_1547764, _1547770, _1547772, hAPP(c_Set_Oimage(_1547762, _1547764, _1547766), _1547768)))]]], (39348 ^ _782652) ^ [_1548054, _1548056, _1548058, _1548060, _1548062, _1548064] : [c_Fun_Oinj__on(_1548054, _1548056, _1548058, _1548060), c_Fun_Oinj__on(_1548056, _1548062, _1548064, hAPP(c_Set_Oimage(_1548054, _1548056, _1548058), _1548060)), -(c_Fun_Oinj__on(_1548054, _1548062, hAPP(c_Fun_Ocomp(_1548056, _1548062, _1548054, _1548064), _1548058), _1548060))], (39358 ^ _782652) ^ [_1548241, _1548243, _1548245, _1548247, _1548249, _1548251] : [c_Fun_Oinj__on(_1548241, _1548243, hAPP(c_Fun_Ocomp(_1548245, _1548243, _1548241, _1548247), _1548249), _1548251), -(c_Fun_Oinj__on(_1548245, _1548243, _1548247, hAPP(c_Set_Oimage(_1548241, _1548245, _1548249), _1548251)))], (39364 ^ _782652) ^ [_1548364, _1548366, _1548368, _1548370, _1548372, _1548374, _1548376, _1548378, _1548380, _1548382, _1548384] : [-(hAPP(c_Product__Type_Omap__pair(_1548364, _1548366, _1548368, _1548370, _1548372, _1548374), hAPP(c_Product__Type_Omap__pair(_1548376, _1548364, _1548378, _1548368, _1548380, _1548382), _1548384)) = hAPP(c_Product__Type_Omap__pair(_1548376, _1548366, _1548378, _1548370, hAPP(c_Fun_Ocomp(_1548364, _1548366, _1548376, _1548372), _1548380), hAPP(c_Fun_Ocomp(_1548368, _1548370, _1548378, _1548374), _1548382)), _1548384))], (39366 ^ _782652) ^ [_1548453, _1548455, _1548457, _1548459, _1548461, _1548463, _1548465, _1548467, _1548469, _1548471] : [-(c_Product__Type_Omap__pair(_1548453, _1548455, _1548457, _1548459, hAPP(c_Fun_Ocomp(_1548461, _1548455, _1548453, _1548463), _1548465), hAPP(c_Fun_Ocomp(_1548467, _1548459, _1548457, _1548469), _1548471)) = hAPP(c_Fun_Ocomp(tc_prod(_1548461, _1548467), tc_prod(_1548455, _1548459), tc_prod(_1548453, _1548457), c_Product__Type_Omap__pair(_1548461, _1548455, _1548467, _1548459, _1548463, _1548469)), c_Product__Type_Omap__pair(_1548453, _1548461, _1548457, _1548467, _1548465, _1548471)))], (39368 ^ _782652) ^ [_1548548, _1548550, _1548552, _1548554, _1548556, _1548558, _1548560, _1548562, _1548564, _1548566] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1548548, _1548550), tc_prod(_1548552, _1548554), tc_prod(_1548556, _1548558), c_Product__Type_Omap__pair(_1548548, _1548552, _1548550, _1548554, _1548560, _1548562)), c_Product__Type_Omap__pair(_1548556, _1548548, _1548558, _1548550, _1548564, _1548566)) = c_Product__Type_Omap__pair(_1548556, _1548552, _1548558, _1548554, hAPP(c_Fun_Ocomp(_1548548, _1548552, _1548556, _1548560), _1548564), hAPP(c_Fun_Ocomp(_1548550, _1548554, _1548558, _1548562), _1548566)))], (39370 ^ _782652) ^ [_1548643, _1548645, _1548647, _1548649, _1548651, _1548653] : [class_Groups_Ocomm__monoid__add(_1548643), c_Fun_Oinj__on(_1548645, _1548647, _1548649, _1548651), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1548647, _1548643), _1548653), hAPP(c_Set_Oimage(_1548645, _1548647, _1548649), _1548651)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1548645, _1548643), hAPP(c_Fun_Ocomp(_1548647, _1548643, _1548645, _1548653), _1548649)), _1548651))], (39380 ^ _782652) ^ [_1548856, _1548858, _1548860, _1548862, _1548864, _1548866] : [class_Groups_Ocomm__monoid__mult(_1548856), c_Fun_Oinj__on(_1548858, _1548860, _1548862, _1548864), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1548860, _1548856), _1548866), hAPP(c_Set_Oimage(_1548858, _1548860, _1548862), _1548864)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1548858, _1548856), hAPP(c_Fun_Ocomp(_1548860, _1548856, _1548858, _1548866), _1548862)), _1548864))], (39390 ^ _782652) ^ [_1549069, _1549071, _1549073, _1549075, _1549077, _1549079, _1549081, _1549083] : [class_Groups_Ocomm__monoid__mult(_1549069), c_Fun_Oinj__on(_1549071, _1549073, _1549075, _1549077), _1549079 = hAPP(c_Set_Oimage(_1549071, _1549073, _1549075), _1549077), _1549081 = hAPP(c_Fun_Ocomp(_1549073, _1549069, _1549071, _1549083), _1549075), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549073, _1549069), _1549083), _1549079) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549071, _1549069), _1549081), _1549077))], (39408 ^ _782652) ^ [_1549418, _1549420, _1549422] : [-(c_Hilbert__Choice_OEps(tc_prod(_1549418, _1549420), _1549422) = c_Hilbert__Choice_OEps(tc_prod(_1549418, _1549420), hAPP(c_Product__Type_Oprod_Oprod__case(_1549418, _1549420, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1549420, tc_prod(_1549418, _1549420)), tc_fun(_1549420, tc_HOL_Obool), _1549418), hAPP(c_COMBB(tc_prod(_1549418, _1549420), tc_HOL_Obool, _1549420), _1549422)), c_Product__Type_OPair(_1549418, _1549420)))))], (39410 ^ _782652) ^ [_1549496, _1549498, _1549500, _1549502] : [-(c_Hilbert__Choice_OEps(tc_prod(_1549496, _1549498), hAPP(c_Product__Type_Oprod_Oprod__case(_1549496, _1549498, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549496, tc_fun(_1549498, tc_HOL_Obool), tc_fun(_1549498, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1549498, tc_HOL_Obool), tc_fun(_1549498, tc_HOL_Obool)), _1549496), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1549498)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549496), c_fconj), hAPP(c_fequal, _1549500)))), hAPP(c_fequal, _1549502)))) = hAPP(hAPP(c_Product__Type_OPair(_1549496, _1549498), _1549500), _1549502))], (39412 ^ _782652) ^ [_1549602, _1549604, _1549606, _1549608, _1549610] : [class_Groups_Ocomm__monoid__add(_1549602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549604), _1549606)), c_Fun_Oinj__on(_1549604, _1549604, _1549608, _1549606), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549604, _1549602), _1549610), hAPP(c_Set_Oimage(_1549604, _1549604, _1549608), _1549606)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549604, _1549602), hAPP(c_Fun_Ocomp(_1549604, _1549602, _1549604, _1549610), _1549608)), _1549606))], (39426 ^ _782652) ^ [_1549877, _1549879, _1549881, _1549883, _1549885] : [class_Groups_Ocomm__monoid__mult(_1549877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549879), _1549881)), c_Fun_Oinj__on(_1549879, _1549879, _1549883, _1549881), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549879, _1549877), _1549885), hAPP(c_Set_Oimage(_1549879, _1549879, _1549883), _1549881)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549879, _1549877), hAPP(c_Fun_Ocomp(_1549879, _1549877, _1549879, _1549885), _1549883)), _1549881))], (39440 ^ _782652) ^ [_1550152, _1550154, _1550156, _1550158, _1550160, _1550162, _1550164] : [c_Fun_Oinj__on(_1550152, _1550154, _1550156, hAPP(c_Set_Oimage(_1550158, _1550152, _1550160), _1550162)), c_Fun_Oinj__on(_1550158, _1550152, _1550160, _1550162), hBOOL(hAPP(hAPP(c_member(_1550154), _1550164), hAPP(c_Set_Oimage(_1550152, _1550154, _1550156), hAPP(c_Set_Oimage(_1550158, _1550152, _1550160), _1550162)))), -(hAPP(c_Fun_Othe__inv__into(_1550158, _1550154, _1550162, hAPP(c_Fun_Ocomp(_1550152, _1550154, _1550158, _1550156), _1550160)), _1550164) = hAPP(hAPP(c_Fun_Ocomp(_1550152, _1550158, _1550154, c_Fun_Othe__inv__into(_1550158, _1550152, _1550162, _1550160)), c_Fun_Othe__inv__into(_1550152, _1550154, hAPP(c_Set_Oimage(_1550158, _1550152, _1550160), _1550162), _1550156)), _1550164))], (39454 ^ _782652) ^ [_1550515, _1550517, _1550519, _1550521, _1550523, _1550525, _1550527] : [class_Groups_Oab__semigroup__mult(_1550515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550517), _1550519)), c_Fun_Oinj__on(_1550517, _1550521, _1550523, _1550519), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1550515, _1550521, c_Groups_Otimes__class_Otimes(_1550515)), _1550525), _1550527), hAPP(c_Set_Oimage(_1550517, _1550521, _1550523), _1550519)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1550515, _1550517, c_Groups_Otimes__class_Otimes(_1550515)), hAPP(c_Fun_Ocomp(_1550521, _1550515, _1550517, _1550525), _1550523)), _1550527), _1550519))], (39468 ^ _782652) ^ [_1550826, _1550828, _1550830, _1550832] : [class_Orderings_Oord(_1550826), -(c_Hilbert__Choice_OLeastM(_1550828, _1550826, _1550830, _1550832) = c_Hilbert__Choice_OEps(_1550828, hAPP(hAPP(c_COMBS(_1550828, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550828), c_fconj), _1550832)), hAPP(hAPP(c_COMBB(tc_fun(_1550828, tc_HOL_Obool), tc_HOL_Obool, _1550828), c_HOL_OAll(_1550828)), hAPP(hAPP(c_COMBB(tc_fun(_1550828, tc_HOL_Obool), tc_fun(_1550828, tc_HOL_Obool), _1550828), hAPP(c_COMBS(_1550828, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550828), c_fimplies), _1550832))), hAPP(hAPP(c_COMBC(_1550828, tc_fun(_1550828, _1550826), tc_fun(_1550828, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1550826, tc_HOL_Obool), tc_fun(tc_fun(_1550828, _1550826), tc_fun(_1550828, tc_HOL_Obool)), _1550828), c_COMBB(_1550826, tc_HOL_Obool, _1550828)), hAPP(hAPP(c_COMBB(_1550826, tc_fun(_1550826, tc_HOL_Obool), _1550828), c_Orderings_Oord__class_Oless__eq(_1550826)), _1550830))), _1550830))))))], (39474 ^ _782652) ^ [_1551171, _1551173, _1551175, _1551177] : [class_Orderings_Oord(_1551171), -(hAPP(c_Hilbert__Choice_OGreatestM(_1551173, _1551171, _1551175), _1551177) = c_Hilbert__Choice_OEps(_1551173, hAPP(hAPP(c_COMBS(_1551173, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551173), c_fconj), _1551177)), hAPP(hAPP(c_COMBB(tc_fun(_1551173, tc_HOL_Obool), tc_HOL_Obool, _1551173), c_HOL_OAll(_1551173)), hAPP(hAPP(c_COMBB(tc_fun(_1551173, tc_HOL_Obool), tc_fun(_1551173, tc_HOL_Obool), _1551173), hAPP(c_COMBS(_1551173, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1551173), c_fimplies), _1551177))), hAPP(hAPP(c_COMBB(_1551171, tc_fun(_1551173, tc_HOL_Obool), _1551173), hAPP(c_COMBC(_1551173, _1551171, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1551171, tc_fun(_1551171, tc_HOL_Obool), _1551173), c_Orderings_Oord__class_Oless__eq(_1551171)), _1551175))), _1551175))))))], (39480 ^ _782652) ^ [_1551476, _1551478, _1551480, _1551482, _1551484, _1551486] : [c_Finite__Set_Ofolding(_1551476, _1551478, _1551480, _1551482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551476), _1551484)), hBOOL(hAPP(hAPP(c_member(_1551476), _1551486), _1551484)), -(hAPP(_1551482, _1551484) = hAPP(c_Fun_Ocomp(_1551478, _1551478, _1551478, hAPP(_1551482, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1551476, tc_HOL_Obool)), _1551484), hAPP(hAPP(c_Set_Oinsert(_1551476), _1551486), c_Orderings_Obot__class_Obot(tc_fun(_1551476, tc_HOL_Obool)))))), hAPP(_1551480, _1551486)))], (39494 ^ _782652) ^ [_1551789, _1551791, _1551793, _1551795, _1551797, _1551799, _1551801, _1551803, _1551805, _1551807, _1551809] : [c_Finite__Set_Ofolding(_1551789, _1551791, _1551793, _1551795), -(hAPP(c_Fun_Ocomp(_1551797, _1551799, _1551801, _1551803), hAPP(c_Fun_Ocomp(_1551805, _1551797, _1551801, _1551807), _1551809)) = hAPP(c_Fun_Ocomp(_1551805, _1551799, _1551801, hAPP(c_Fun_Ocomp(_1551797, _1551799, _1551805, _1551803), _1551807)), _1551809))], (39500 ^ _782652) ^ [_1551952, _1551954, _1551956, _1551958, _1551960, _1551962] : [c_Finite__Set_Ofolding(_1551952, _1551954, _1551956, _1551958), -(hAPP(c_Fun_Ocomp(_1551954, _1551954, _1551954, hAPP(_1551956, _1551960)), hAPP(_1551956, _1551962)) = hAPP(c_Fun_Ocomp(_1551954, _1551954, _1551954, hAPP(_1551956, _1551962)), hAPP(_1551956, _1551960)))], (39506 ^ _782652) ^ [_1552097, _1552099, _1552101, _1552103, _1552105, _1552107, _1552109, _1552111] : [c_Finite__Set_Ofolding(_1552097, _1552099, _1552101, _1552103), -(hAPP(c_Fun_Ocomp(_1552099, _1552099, _1552105, hAPP(_1552101, _1552107)), hAPP(c_Fun_Ocomp(_1552099, _1552099, _1552105, hAPP(_1552101, _1552109)), _1552111)) = hAPP(c_Fun_Ocomp(_1552099, _1552099, _1552105, hAPP(_1552101, _1552109)), hAPP(c_Fun_Ocomp(_1552099, _1552099, _1552105, hAPP(_1552101, _1552107)), _1552111)))], (39512 ^ _782652) ^ [_1552278, _1552280, _1552282, _1552284, _1552286, _1552288] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1552278, tc_fun(_1552280, tc_HOL_Obool)), _1552282), hAPP(c_Fun_Ocomp(_1552284, tc_fun(_1552280, tc_HOL_Obool), _1552278, _1552286), _1552288)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1552284, tc_fun(_1552280, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1552278, _1552284, _1552288), _1552282)), _1552286))], (39514 ^ _782652) ^ [_1552353, _1552355, _1552357, _1552359, _1552361, _1552363] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1552353, _1552355), _1552353, tc_prod(_1552357, _1552359), c_Product__Type_Ofst(_1552353, _1552355)), c_Product__Type_Omap__pair(_1552357, _1552353, _1552359, _1552355, _1552361, _1552363)) = hAPP(c_Fun_Ocomp(_1552357, _1552353, tc_prod(_1552357, _1552359), _1552361), c_Product__Type_Ofst(_1552357, _1552359)))], (39516 ^ _782652) ^ [_1552424, _1552426, _1552428, _1552430, _1552432, _1552434] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1552424, _1552426), _1552426, tc_prod(_1552428, _1552430), c_Product__Type_Osnd(_1552424, _1552426)), c_Product__Type_Omap__pair(_1552428, _1552424, _1552430, _1552426, _1552432, _1552434)) = hAPP(c_Fun_Ocomp(_1552430, _1552426, tc_prod(_1552428, _1552430), _1552434), c_Product__Type_Osnd(_1552428, _1552430)))], (39518 ^ _782652) ^ [_1552495, _1552497, _1552499, _1552501] : [hBOOL(hAPP(_1552495, _1552497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1552499, c_Hilbert__Choice_OLeastM(_1552501, tc_Nat_Onat, _1552499, _1552495))), hAPP(_1552499, _1552497))))], (39524 ^ _782652) ^ [_1552612, _1552614, _1552616, _1552618] : [hBOOL(hAPP(_1552612, _1552614)), 39527 ^ _782652 : [(39528 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1552612, c_Hilbert__Choice_OLeastM(_1552616, tc_Nat_Onat, _1552618, _1552612))))], (39530 ^ _782652) ^ [_1552742] : [hBOOL(hAPP(_1552612, _1552742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1552618, c_Hilbert__Choice_OLeastM(_1552616, tc_Nat_Onat, _1552618, _1552612))), hAPP(_1552618, _1552742))))]]], (39536 ^ _782652) ^ [_1552867, _1552869, _1552871, _1552873, _1552875, _1552877, _1552879] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1552867, _1552869, _1552871), hAPP(c_Fun_Ocomp(_1552873, tc_fun(_1552869, _1552871), _1552867, _1552875), _1552877)), _1552879) = hAPP(hAPP(_1552875, hAPP(_1552877, hAPP(c_Product__Type_Ofst(_1552867, _1552869), _1552879))), hAPP(c_Product__Type_Osnd(_1552867, _1552869), _1552879)))], (39538 ^ _782652) ^ [_1552944, _1552946, _1552948, _1552950, _1552952, _1552954, _1552956, _1552958] : [c_Finite__Set_Ofolding(_1552944, _1552946, _1552948, _1552950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552944), _1552952)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552944), _1552954)), -(hAPP(c_Fun_Ocomp(_1552946, _1552946, _1552956, hAPP(_1552950, _1552954)), hAPP(c_Fun_Ocomp(_1552946, _1552946, _1552956, hAPP(_1552950, _1552952)), _1552958)) = hAPP(c_Fun_Ocomp(_1552946, _1552946, _1552956, hAPP(_1552950, _1552952)), hAPP(c_Fun_Ocomp(_1552946, _1552946, _1552956, hAPP(_1552950, _1552954)), _1552958)))], (39552 ^ _782652) ^ [_1553269, _1553271, _1553273, _1553275, _1553277, _1553279] : [c_Finite__Set_Ofolding(_1553269, _1553271, _1553273, _1553275), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553269), _1553277)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553269), _1553279)), -(hAPP(c_Fun_Ocomp(_1553271, _1553271, _1553271, hAPP(_1553275, _1553279)), hAPP(_1553275, _1553277)) = hAPP(c_Fun_Ocomp(_1553271, _1553271, _1553271, hAPP(_1553275, _1553277)), hAPP(_1553275, _1553279)))], (39566 ^ _782652) ^ [_1553550, _1553552, _1553554, _1553556, _1553558, _1553560, _1553562, _1553564] : [c_Finite__Set_Ofolding(_1553550, _1553552, _1553554, _1553556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553550), _1553558)), -(hAPP(c_Fun_Ocomp(_1553552, _1553552, _1553560, hAPP(_1553554, _1553562)), hAPP(c_Fun_Ocomp(_1553552, _1553552, _1553560, hAPP(_1553556, _1553558)), _1553564)) = hAPP(c_Fun_Ocomp(_1553552, _1553552, _1553560, hAPP(_1553556, _1553558)), hAPP(c_Fun_Ocomp(_1553552, _1553552, _1553560, hAPP(_1553554, _1553562)), _1553564)))], (39576 ^ _782652) ^ [_1553803, _1553805, _1553807, _1553809, _1553811, _1553813] : [c_Finite__Set_Ofolding(_1553803, _1553805, _1553807, _1553809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553803), _1553811)), -(hAPP(c_Fun_Ocomp(_1553805, _1553805, _1553805, hAPP(_1553807, _1553813)), hAPP(_1553809, _1553811)) = hAPP(c_Fun_Ocomp(_1553805, _1553805, _1553805, hAPP(_1553809, _1553811)), hAPP(_1553807, _1553813)))], (39586 ^ _782652) ^ [_1554016, _1554018, _1554020, _1554022] : [c_Finite__Set_Ofolding(_1554016, _1554018, _1554020, _1554022), -(hAPP(_1554022, c_Orderings_Obot__class_Obot(tc_fun(_1554016, tc_HOL_Obool))) = c_Fun_Oid(_1554018))], (39592 ^ _782652) ^ [_1554121, _1554123, _1554125, _1554127, _1554129, _1554131] : [c_Finite__Set_Ofolding(_1554121, _1554123, _1554125, _1554127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554121), _1554129)), -(hBOOL(hAPP(hAPP(c_member(_1554121), _1554131), _1554129))), -(hAPP(_1554127, hAPP(hAPP(c_Set_Oinsert(_1554121), _1554131), _1554129)) = hAPP(c_Fun_Ocomp(_1554123, _1554123, _1554123, hAPP(_1554127, _1554129)), hAPP(_1554125, _1554131)))], (39606 ^ _782652) ^ [_1554357, _1554359, _1554361, _1554363, _1554365, _1554367] : [c_Finite__Set_Ofolding(_1554357, _1554359, _1554361, _1554363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554357), _1554365)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554357), _1554367)), -(hAPP(c_Fun_Ocomp(_1554359, _1554359, _1554359, hAPP(_1554363, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1554357, tc_HOL_Obool)), _1554365), _1554367))), hAPP(_1554363, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1554357, tc_HOL_Obool)), _1554365), _1554367))) = hAPP(c_Fun_Ocomp(_1554359, _1554359, _1554359, hAPP(_1554363, _1554365)), hAPP(_1554363, _1554367)))], (39620 ^ _782652) ^ [_1554682, _1554684, _1554686, _1554688, _1554690, _1554692] : [c_Finite__Set_Ofolding(_1554682, _1554684, _1554686, _1554688), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554682), _1554690)), -(hAPP(_1554688, hAPP(hAPP(c_Set_Oinsert(_1554682), _1554692), _1554690)) = hAPP(c_Fun_Ocomp(_1554684, _1554684, _1554684, hAPP(_1554688, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1554682, tc_HOL_Obool)), _1554690), hAPP(hAPP(c_Set_Oinsert(_1554682), _1554692), c_Orderings_Obot__class_Obot(tc_fun(_1554682, tc_HOL_Obool)))))), hAPP(_1554686, _1554692)))], (39630 ^ _782652) ^ [_1554937, _1554939, _1554941, _1554943, _1554945, _1554947] : [c_Finite__Set_Ofolding(_1554937, _1554939, _1554941, _1554943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554937), _1554945)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554937), _1554947)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1554937, tc_HOL_Obool)), _1554945), _1554947) = c_Orderings_Obot__class_Obot(tc_fun(_1554937, tc_HOL_Obool)), -(hAPP(_1554943, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1554937, tc_HOL_Obool)), _1554945), _1554947)) = hAPP(c_Fun_Ocomp(_1554939, _1554939, _1554939, hAPP(_1554943, _1554945)), hAPP(_1554943, _1554947)))], (39648 ^ _782652) ^ [_1555310, _1555312, _1555314, _1555316, _1555318] : [c_Hoare__Mirabelle_Ohoare__valids(_1555310, _1555312, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1555310)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1555310), c_Hoare__Mirabelle_Opeek__and(_1555310, _1555314, _1555316)), _1555318), _1555314)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1555310), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1555310, _1555312, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1555310)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1555310), _1555314), c_Com_Ocom_OWhile(_1555316, _1555318)), c_Hoare__Mirabelle_Opeek__and(_1555310, _1555314, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1555316)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1555310), tc_HOL_Obool)))))], (39654 ^ _782652) ^ [_1555537, _1555539, _1555541, _1555543, _1555545, _1555547, _1555549] : [c_Hoare__Mirabelle_Ohoare__derivs(_1555537, _1555539, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1555537)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1555537), c_Hoare__Mirabelle_Opeek__and(_1555537, _1555541, _1555543)), _1555545), _1555547)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1555537), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1555537, _1555539, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1555537)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1555537), c_Hoare__Mirabelle_Opeek__and(_1555537, _1555541, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1555543))), _1555549), _1555547)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1555537), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1555537, _1555539, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1555537)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1555537), _1555541), c_Com_Ocom_OCond(_1555543, _1555545, _1555549)), _1555547)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1555537), tc_HOL_Obool)))))], (39664 ^ _782652) ^ [_1555890, _1555892, _1555894, _1555896, _1555898] : [c_Hoare__Mirabelle_Ohoare__derivs(_1555890, _1555892, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1555890)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1555890), c_Hoare__Mirabelle_Opeek__and(_1555890, _1555894, _1555896)), _1555898), _1555894)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1555890), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1555890, _1555892, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1555890)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1555890), _1555894), c_Com_Ocom_OWhile(_1555896, _1555898)), c_Hoare__Mirabelle_Opeek__and(_1555890, _1555894, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1555896)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1555890), tc_HOL_Obool)))))], (39670 ^ _782652) ^ [_1556117, _1556119, _1556121, _1556123] : [hBOOL(hAPP(_1556117, _1556119)), -(hBOOL(hAPP(_1556117, c_Hilbert__Choice_OLeastM(_1556121, tc_Nat_Onat, _1556123, _1556117))))], (39676 ^ _782652) ^ [_1556240, _1556242, _1556244, _1556246, _1556248] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1556240, _1556242, _1556244), _1556246), _1556248)), 39679 ^ _782652 : [(39680 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1556242, _1556246), _1556248)))], (39682 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1556244, _1556248)))]]], (39684 ^ _782652) ^ [_1556377, _1556379, _1556381, _1556383, _1556385] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1556377, _1556379, _1556381), _1556383), _1556385))), hBOOL(hAPP(hAPP(_1556379, _1556383), _1556385)), hBOOL(hAPP(_1556381, _1556385))], (39694 ^ _782652) ^ [_1556552] : [class_Orderings_Oord(_1556552), -(c_Hilbert__Choice_OGreatest(_1556552) = c_Hilbert__Choice_OGreatestM(_1556552, _1556552, c_COMBI(_1556552)))], (39700 ^ _782652) ^ [_1556641, _1556643, _1556645, _1556647, _1556649, _1556651, _1556653, _1556655] : [c_Finite__Set_Ofolding__image(_1556641, _1556643, _1556645, _1556647, _1556649), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556643), _1556651)), c_Fun_Oinj__on(_1556643, _1556643, _1556653, _1556651), -(hAPP(hAPP(_1556649, _1556655), hAPP(c_Set_Oimage(_1556643, _1556643, _1556653), _1556651)) = hAPP(hAPP(_1556649, hAPP(c_Fun_Ocomp(_1556643, _1556641, _1556643, _1556655), _1556653)), _1556651))], (39714 ^ _782652) ^ [_1556930, _1556932, _1556934, _1556936, _1556938, _1556940] : [class_Groups_Ocomm__monoid__add(_1556930), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556932), _1556934)), 39724 ^ _782652 : [(39725 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556932), 39723 ^ [_1556930, _1556932, _1556934, _1556936, _1556938, _1556940]), _1556934)))], (39728 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556932), 39726 ^ [_1556930, _1556932, _1556934, _1556936, _1556938, _1556940]), _1556934)))], (39730 ^ _782652) ^ [] : [39723 ^ [_1556930, _1556932, _1556934, _1556936, _1556938, _1556940] = 39726 ^ [_1556930, _1556932, _1556934, _1556936, _1556938, _1556940]], (39732 ^ _782652) ^ [] : [-(hAPP(_1556936, 39723 ^ [_1556930, _1556932, _1556934, _1556936, _1556938, _1556940]) = hAPP(_1556936, 39726 ^ [_1556930, _1556932, _1556934, _1556936, _1556938, _1556940]))], (39734 ^ _782652) ^ [] : [hAPP(_1556938, hAPP(_1556936, 39723 ^ [_1556930, _1556932, _1556934, _1556936, _1556938, _1556940])) = c_Groups_Ozero__class_Ozero(_1556930)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1556940, _1556930), _1556938), hAPP(c_Set_Oimage(_1556932, _1556940, _1556936), _1556934)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1556932, _1556930), hAPP(c_Fun_Ocomp(_1556940, _1556930, _1556932, _1556938), _1556936)), _1556934))], (39738 ^ _782652) ^ [_1557667, _1557669, _1557671, _1557673, _1557675, _1557677, _1557679, _1557681] : [c_Finite__Set_Ofolding__image(_1557667, _1557669, _1557671, _1557673, _1557675), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557669), _1557677)), -(hAPP(hAPP(_1557675, hAPP(hAPP(c_COMBS(_1557669, _1557667, _1557667), hAPP(hAPP(c_COMBB(_1557667, tc_fun(_1557667, _1557667), _1557669), _1557671), _1557679)), _1557681)), _1557677) = hAPP(hAPP(_1557671, hAPP(hAPP(_1557675, _1557679), _1557677)), hAPP(hAPP(_1557675, _1557681), _1557677)))], (39748 ^ _782652) ^ [_1557928, _1557930, _1557932, _1557934, _1557936, _1557938, _1557940] : [c_Finite__Set_Ofolding__image(_1557928, _1557930, _1557932, _1557934, _1557936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557930), _1557938)), -(hAPP(hAPP(_1557936, _1557940), _1557938) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1557928, _1557930, _1557932), _1557940), _1557934), _1557938))], (39758 ^ _782652) ^ [_1558129, _1558131, _1558133, _1558135, _1558137, _1558139] : [c_Finite__Set_Ofolding__idem(_1558129, _1558131, _1558133, _1558135), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558129), _1558137)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558129), _1558139)), -(hAPP(_1558135, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1558129, tc_HOL_Obool)), _1558137), _1558139)) = hAPP(c_Fun_Ocomp(_1558131, _1558131, _1558131, hAPP(_1558135, _1558137)), hAPP(_1558135, _1558139)))], (39772 ^ _782652) ^ [_1558410, _1558412, _1558414, _1558416, _1558418, _1558420] : [c_Finite__Set_Ofolding__idem(_1558410, _1558412, _1558414, _1558416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558410), _1558418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558410, tc_HOL_Obool)), _1558420), _1558418)), -(hAPP(c_Fun_Ocomp(_1558412, _1558412, _1558412, hAPP(_1558416, _1558418)), hAPP(_1558416, _1558420)) = hAPP(_1558416, _1558418))], (39786 ^ _782652) ^ [_1558681, _1558683, _1558685, _1558687, _1558689, _1558691] : [c_Finite__Set_Ofolding__idem(_1558681, _1558683, _1558685, _1558687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558681), _1558689)), -(hAPP(_1558687, hAPP(hAPP(c_Set_Oinsert(_1558681), _1558691), _1558689)) = hAPP(c_Fun_Ocomp(_1558683, _1558683, _1558683, hAPP(_1558687, _1558689)), hAPP(_1558685, _1558691)))], (39796 ^ _782652) ^ [_1558888, _1558890, _1558892, _1558894, _1558896] : [c_Finite__Set_Ofolding__idem(_1558888, _1558890, _1558892, _1558894), -(hAPP(c_Fun_Ocomp(_1558890, _1558890, _1558890, hAPP(_1558892, _1558896)), hAPP(_1558892, _1558896)) = hAPP(_1558892, _1558896))], (39802 ^ _782652) ^ [_1559009, _1559011, _1559013, _1559015, _1559017, _1559019, _1559021] : [c_Finite__Set_Ofolding__idem(_1559009, _1559011, _1559013, _1559015), -(hAPP(c_Fun_Ocomp(_1559011, _1559011, _1559017, hAPP(_1559013, _1559019)), hAPP(c_Fun_Ocomp(_1559011, _1559011, _1559017, hAPP(_1559013, _1559019)), _1559021)) = hAPP(c_Fun_Ocomp(_1559011, _1559011, _1559017, hAPP(_1559013, _1559019)), _1559021))], (39808 ^ _782652) ^ [_1559166, _1559168, _1559170, _1559172, _1559174, _1559176] : [c_Finite__Set_Ofolding__idem(_1559166, _1559168, _1559170, _1559172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559166), _1559174)), hBOOL(hAPP(hAPP(c_member(_1559166), _1559176), _1559174)), -(hAPP(c_Fun_Ocomp(_1559168, _1559168, _1559168, hAPP(_1559172, _1559174)), hAPP(_1559170, _1559176)) = hAPP(_1559172, _1559174))], (39822 ^ _782652) ^ [_1559431, _1559433, _1559435, _1559437, _1559439, _1559441, _1559443, _1559445] : [class_Groups_Ocomm__monoid__mult(_1559431), c_Fun_Oinj__on(_1559433, _1559435, _1559437, _1559439), _1559441 = hAPP(c_Set_Oimage(_1559433, _1559435, _1559437), _1559439), 39836 ^ _782652 : [(39837 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559433), 39835 ^ [_1559431, _1559433, _1559435, _1559437, _1559439, _1559441, _1559443, _1559445]), _1559439)))], (39839 ^ _782652) ^ [] : [hAPP(_1559443, 39835 ^ [_1559431, _1559433, _1559435, _1559437, _1559439, _1559441, _1559443, _1559445]) = hAPP(hAPP(c_Fun_Ocomp(_1559435, _1559431, _1559433, _1559445), _1559437), 39835 ^ [_1559431, _1559433, _1559435, _1559437, _1559439, _1559441, _1559443, _1559445])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1559435, _1559431), _1559445), _1559441) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1559433, _1559431), _1559443), _1559439))], (39843 ^ _782652) ^ [_1559939, _1559941, _1559943, _1559945, _1559947, _1559949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1559939, tc_HOL_Obool)), _1559941), _1559943)), 39849 ^ _782652 : [(39850 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559939), 39848 ^ [_1559939, _1559941, _1559943, _1559945, _1559947, _1559949]), _1559941)))], (39852 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1559945, tc_HOL_Obool)), hAPP(_1559947, 39848 ^ [_1559939, _1559941, _1559943, _1559945, _1559947, _1559949])), hAPP(_1559949, 39848 ^ [_1559939, _1559941, _1559943, _1559945, _1559947, _1559949])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559939, _1559945), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1559939, _1559945), _1559941), _1559947)), hAPP(hAPP(c_Product__Type_OSigma(_1559939, _1559945), _1559943), _1559949))))], (39856 ^ _782652) ^ [_1560329, _1560331, _1560333] : [-(hBOOL(hAPP(hAPP(c_member(_1560329), _1560331), c_Wellfounded_Oacc(_1560329, _1560333)))), 39860 ^ _782652 : [(39861 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560329, _1560329)), hAPP(hAPP(c_Product__Type_OPair(_1560329, _1560329), 39859 ^ [_1560329, _1560331, _1560333]), _1560331)), _1560333)))], (39863 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1560329), 39859 ^ [_1560329, _1560331, _1560333]), c_Wellfounded_Oacc(_1560329, _1560333)))]]], (39865 ^ _782652) ^ [_1560556, _1560558, _1560560] : [39867 ^ _782652 : [(39868 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560556, _1560556)), hAPP(hAPP(c_Product__Type_OPair(_1560556, _1560556), 39866 ^ [_1560556, _1560558, _1560560]), _1560558)), _1560560)))], (39870 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1560556), 39866 ^ [_1560556, _1560558, _1560560]), c_Wellfounded_Oacc(_1560556, _1560560)))]], -(hBOOL(hAPP(hAPP(c_member(_1560556), _1560558), c_Wellfounded_Oacc(_1560556, _1560560))))], (39874 ^ _782652) ^ [_1560815, _1560817, _1560819, _1560821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1560815, tc_HOL_Obool), tc_fun(_1560815, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1560815, tc_HOL_Obool), tc_fun(_1560815, tc_HOL_Obool)), _1560817), _1560819)), c_Wellfounded_Omax__ext(_1560815, _1560821))), 39877 ^ _782652 : [(39878 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560815), _1560817)))], (39880 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560815), _1560819)))], (39882 ^ _782652) ^ [] : [_1560819 = c_Orderings_Obot__class_Obot(tc_fun(_1560815, tc_HOL_Obool))], (39884 ^ _782652) ^ [_1561109] : [hBOOL(hAPP(hAPP(c_member(_1560815), _1561109), _1560817)), 39888 ^ _782652 : [(39889 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560815), 39887 ^ [_1560815, _1560817, _1560819, _1560821, _1561109]), _1560819)))], (39891 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560815, _1560815)), hAPP(hAPP(c_Product__Type_OPair(_1560815, _1560815), _1561109), 39887 ^ [_1560815, _1560817, _1560819, _1560821, _1561109])), _1560821)))]]]]], (39893 ^ _782652) ^ [_1561321, _1561323, _1561325, _1561327] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1561321, tc_HOL_Obool), tc_fun(_1561321, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1561321, tc_HOL_Obool), tc_fun(_1561321, tc_HOL_Obool)), _1561323), _1561325)), c_Wellfounded_Omax__ext(_1561321, _1561327)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561321), _1561323)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561321), _1561325)), -(_1561325 = c_Orderings_Obot__class_Obot(tc_fun(_1561321, tc_HOL_Obool))), 39907 ^ _782652 : [(39908 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561321), 39906 ^ [_1561321, _1561323, _1561325, _1561327]), _1561323)))], (39910 ^ _782652) ^ [_1561726] : [hBOOL(hAPP(hAPP(c_member(_1561321), _1561726), _1561325)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1561321, _1561321)), hAPP(hAPP(c_Product__Type_OPair(_1561321, _1561321), 39906 ^ [_1561321, _1561323, _1561325, _1561327]), _1561726)), _1561327))]]], (39918 ^ _782652) ^ [_1561954, _1561956, _1561958] : [c_Wellfounded_Owf(_1561954, _1561956), hBOOL(hAPP(hAPP(c_member(tc_prod(_1561954, _1561954)), hAPP(hAPP(c_Product__Type_OPair(_1561954, _1561954), hAPP(_1561958, hAPP(c_Nat_OSuc, 39921 ^ [_1561954, _1561956, _1561958]))), hAPP(_1561958, 39921 ^ [_1561954, _1561956, _1561958]))), _1561956))], (39925 ^ _782652) ^ [_1562155, _1562157, _1562159] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1562155, _1562157, _1562159)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1562159)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39927 ^ _782652) ^ [_1562198, _1562200, _1562202] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1562198, _1562200, _1562202)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1562202)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39929 ^ _782652) ^ [_1562239, _1562241, _1562243, _1562245, _1562247, _1562249, _1562251, _1562253] : [class_Groups_Ocomm__monoid__add(_1562239), c_Fun_Oinj__on(_1562241, _1562243, _1562245, _1562247), _1562249 = hAPP(c_Set_Oimage(_1562241, _1562243, _1562245), _1562247), 39943 ^ _782652 : [(39944 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562241), 39942 ^ [_1562239, _1562241, _1562243, _1562245, _1562247, _1562249, _1562251, _1562253]), _1562247)))], (39946 ^ _782652) ^ [] : [hAPP(_1562251, 39942 ^ [_1562239, _1562241, _1562243, _1562245, _1562247, _1562249, _1562251, _1562253]) = hAPP(_1562253, hAPP(_1562245, 39942 ^ [_1562239, _1562241, _1562243, _1562245, _1562247, _1562249, _1562251, _1562253]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562243, _1562239), _1562253), _1562249) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562241, _1562239), _1562251), _1562247))], (39950 ^ _782652) ^ [_1562731, _1562733, _1562735] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1562731, _1562733, _1562735))), -(hBOOL(hAPP(c_Com_OWT, _1562735)))], (39956 ^ _782652) ^ [_1562850, _1562852, _1562854, _1562856, _1562858, _1562860] : [c_Com_Ocom_OCond(_1562850, _1562852, _1562854) = c_Com_Ocom_OLocal(_1562856, _1562858, _1562860)], (39958 ^ _782652) ^ [_1562915, _1562917, _1562919, _1562921, _1562923, _1562925] : [c_Com_Ocom_OLocal(_1562915, _1562917, _1562919) = c_Com_Ocom_OCond(_1562921, _1562923, _1562925)], (39960 ^ _782652) ^ [_1562977, _1562979, _1562981, _1562983, _1562985] : [c_Com_Ocom_OWhile(_1562977, _1562979) = c_Com_Ocom_OLocal(_1562981, _1562983, _1562985)], (39962 ^ _782652) ^ [_1563036, _1563038, _1563040, _1563042, _1563044] : [c_Com_Ocom_OLocal(_1563036, _1563038, _1563040) = c_Com_Ocom_OWhile(_1563042, _1563044)], (39964 ^ _782652) ^ [_1563101, _1563103, _1563105, _1563107, _1563109, _1563111] : [c_Com_Ocom_OLocal(_1563101, _1563103, _1563105) = c_Com_Ocom_OLocal(_1563107, _1563109, _1563111), 39967 ^ _782652 : [(39968 ^ _782652) ^ [] : [-(_1563101 = _1563107)], (39970 ^ _782652) ^ [] : [-(_1563103 = _1563109)], (39972 ^ _782652) ^ [] : [-(_1563105 = _1563111)]]], (39974 ^ _782652) ^ [_1563248, _1563250, _1563252, _1563254, _1563256, _1563258] : [-(c_Com_Ocom_OLocal(_1563248, _1563250, _1563252) = c_Com_Ocom_OLocal(_1563254, _1563256, _1563258)), _1563248 = _1563254, _1563250 = _1563256, _1563252 = _1563258], (39988 ^ _782652) ^ [_1563489, _1563491, _1563493] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1563489, _1563491, _1563493))), -(hBOOL(hAPP(c_Com_OWT, _1563493)))], (39994 ^ _782652) ^ [_1563580, _1563582, _1563584] : [hBOOL(hAPP(c_Com_OWT, _1563584)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1563580, _1563582, _1563584))))], (40000 ^ _782652) ^ [_1563677, _1563679, _1563681] : [hBOOL(hAPP(c_Com_OWT, _1563677)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1563679, _1563681, _1563677))))], (40006 ^ _782652) ^ [_1563790, _1563792, _1563794, _1563796] : [hAPP(c_Com_Ocom_OBODY, _1563790) = c_Com_Ocom_OLocal(_1563792, _1563794, _1563796)], (40008 ^ _782652) ^ [_1563844, _1563846, _1563848, _1563850] : [c_Com_Ocom_OLocal(_1563844, _1563846, _1563848) = hAPP(c_Com_Ocom_OBODY, _1563850)], (40010 ^ _782652) ^ [_1563895, _1563897, _1563899] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1563895, _1563897, _1563899)], (40012 ^ _782652) ^ [_1563941, _1563943, _1563945] : [c_Com_Ocom_OLocal(_1563941, _1563943, _1563945) = c_Com_Ocom_OSKIP], (40014 ^ _782652) ^ [_1563993, _1563995, _1563997, _1563999, _1564001] : [c_Com_Ocom_OSemi(_1563993, _1563995) = c_Com_Ocom_OLocal(_1563997, _1563999, _1564001)], (40016 ^ _782652) ^ [_1564052, _1564054, _1564056, _1564058, _1564060] : [c_Com_Ocom_OLocal(_1564052, _1564054, _1564056) = c_Com_Ocom_OSemi(_1564058, _1564060)], (40018 ^ _782652) ^ [_1564090, _1564092, _1564094, _1564096, _1564098, _1564100, _1564102] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1564090, _1564092, _1564094, _1564096), _1564098), _1564100), _1564102) = hAPP(hAPP(_1564100, hAPP(c_Product__Type_Ofst(_1564092, _1564094), hAPP(_1564098, _1564102))), hAPP(c_Product__Type_Osnd(_1564092, _1564094), hAPP(_1564098, _1564102))))], (40020 ^ _782652) ^ [_1564163, _1564165, _1564167, _1564169, _1564171, _1564173, _1564175, _1564177] : [class_Groups_Ocomm__monoid__add(_1564163), class_Orderings_Oord(_1564165), _1564167 = _1564169, _1564171 = _1564173, 40038 ^ _782652 : [(40039 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1564165), _1564169), 40037 ^ [_1564163, _1564165, _1564167, _1564169, _1564171, _1564173, _1564175, _1564177])))], (40041 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1564165), 40037 ^ [_1564163, _1564165, _1564167, _1564169, _1564171, _1564173, _1564175, _1564177]), _1564173)))], (40043 ^ _782652) ^ [] : [hAPP(_1564175, 40037 ^ [_1564163, _1564165, _1564167, _1564169, _1564171, _1564173, _1564175, _1564177]) = hAPP(_1564177, 40037 ^ [_1564163, _1564165, _1564167, _1564169, _1564171, _1564173, _1564175, _1564177])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1564165, _1564163), _1564175), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1564165, _1564167), _1564171)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1564165, _1564163), _1564177), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1564165, _1564169), _1564173)))], (40047 ^ _782652) ^ [_1564807, _1564809] : [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), _1564807), _1564809)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1564807), _1564809)))], (40053 ^ _782652) ^ [_1564912, _1564914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1564912), _1564914)), -(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), _1564912), _1564914)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40059 ^ _782652) ^ [_1565023, _1565025, _1565027, _1565029, _1565031] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1565023, _1565025, _1565023, _1565027), hAPP(c_Product__Type_OPair(_1565025, _1565023), _1565029)), _1565031) = hAPP(_1565031, _1565029))], (40061 ^ _782652) ^ [_1565074, _1565076, _1565078, _1565080] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1565074, _1565076, _1565078, tc_prod(_1565076, _1565078)), _1565080), c_Product__Type_OPair(_1565076, _1565078)) = _1565080)], (40063 ^ _782652) ^ [_1565120, _1565122, _1565124, _1565126, _1565128, _1565130, _1565132, _1565134, _1565136] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1565120, _1565122, _1565124, _1565126), hAPP(hAPP(c_Product__Type_Oscomp(_1565120, _1565128, _1565130, tc_prod(_1565122, _1565124)), _1565132), _1565134)), _1565136) = hAPP(hAPP(c_Product__Type_Oscomp(_1565120, _1565128, _1565130, _1565126), _1565132), hAPP(hAPP(c_COMBC(_1565128, tc_fun(_1565122, tc_fun(_1565124, _1565126)), tc_fun(_1565130, _1565126)), hAPP(hAPP(c_COMBB(tc_fun(_1565130, tc_prod(_1565122, _1565124)), tc_fun(tc_fun(_1565122, tc_fun(_1565124, _1565126)), tc_fun(_1565130, _1565126)), _1565128), c_Product__Type_Oscomp(_1565130, _1565122, _1565124, _1565126)), _1565134)), _1565136)))], (40065 ^ _782652) ^ [_1565247, _1565249] : [c_Wellfounded_Owf(_1565247, _1565249), -(c_Wellfounded_Owf(_1565247, c_Transitive__Closure_Otrancl(_1565247, _1565249)))], (40071 ^ _782652) ^ [_1565330, _1565332, _1565334, _1565336, _1565338, _1565340, _1565342] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1565330, _1565332, _1565334, _1565336), _1565338), _1565340), _1565342) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1565332, _1565334, _1565336), _1565340), hAPP(_1565338, _1565342)))], (40073 ^ _782652) ^ [_1565392, _1565394, _1565396, _1565398, _1565400, _1565402, _1565404] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1565392, _1565394, _1565396, _1565398), _1565400), _1565402), _1565404) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1565394, _1565396, _1565398), _1565402), hAPP(_1565400, _1565404)))], (40075 ^ _782652) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (40077 ^ _782652) ^ [_1565487, _1565489] : [c_Wellfounded_Oacyclic(_1565487, _1565489), 40080 ^ _782652 : [(40081 ^ _782652) ^ [_1565572] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565487, _1565487)), hAPP(hAPP(c_Product__Type_OPair(_1565487, _1565487), _1565572), _1565572)), c_Transitive__Closure_Otrancl(_1565487, _1565489)))]]], (40083 ^ _782652) ^ [_1565615, _1565617] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565615, _1565615)), hAPP(hAPP(c_Product__Type_OPair(_1565615, _1565615), 40084 ^ [_1565615, _1565617]), 40084 ^ [_1565615, _1565617])), c_Transitive__Closure_Otrancl(_1565615, _1565617)))), -(c_Wellfounded_Oacyclic(_1565615, _1565617))], (40090 ^ _782652) ^ [_1565689, _1565691, _1565693, _1565695] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565689, _1565689)), hAPP(hAPP(c_Product__Type_OPair(_1565689, _1565689), _1565691), _1565693)), _1565695)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565689, _1565689)), hAPP(hAPP(c_Product__Type_OPair(_1565689, _1565689), _1565691), _1565693)), c_Transitive__Closure_Otrancl(_1565689, _1565695))))], (40096 ^ _782652) ^ [_1565852, _1565854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565852, _1565852), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1565852, _1565854)), hAPP(hAPP(c_Product__Type_OSigma(_1565852, _1565852), hAPP(c_Relation_OField(_1565852), _1565854)), hAPP(c_COMBK(tc_fun(_1565852, tc_HOL_Obool), _1565852), hAPP(c_Relation_OField(_1565852), _1565854))))))], (40098 ^ _782652) ^ [_1565921, _1565923, _1565925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565921, _1565921), tc_HOL_Obool)), _1565923), _1565925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565921, _1565921), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1565921, _1565921, _1565921), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1565921, _1565921), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1565921, _1565923)), _1565925)), _1565923)), _1565925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565921, _1565921), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1565921, _1565923)), _1565925)))], (40108 ^ _782652) ^ [_1566192, _1566194, _1566196] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566192, _1566192)), _1566194), _1566196)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566192, _1566192)), _1566194), c_Transitive__Closure_Otrancl(_1566192, _1566196))))], (40114 ^ _782652) ^ [_1566317] : [-(c_Transitive__Closure_Otrancl(_1566317, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1566317, _1566317), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1566317, _1566317), tc_HOL_Obool)))], (40116 ^ _782652) ^ [_1566359, _1566361] : [-(hAPP(c_Relation_ODomain(_1566359, _1566359), c_Transitive__Closure_Otrancl(_1566359, _1566361)) = hAPP(c_Relation_ODomain(_1566359, _1566359), _1566361))], (40118 ^ _782652) ^ [_1566399, _1566401] : [-(hAPP(c_Relation_ORange(_1566399, _1566399), c_Transitive__Closure_Otrancl(_1566399, _1566401)) = hAPP(c_Relation_ORange(_1566399, _1566399), _1566401))], (40120 ^ _782652) ^ [_1566454, _1566456] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1566454, _1566454)), c_Transitive__Closure_Otrancl(_1566454, _1566456))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1566454, _1566454)), _1566456)))], (40126 ^ _782652) ^ [_1566561, _1566563] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1566561, _1566561)), _1566563)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1566561, _1566561)), c_Transitive__Closure_Otrancl(_1566561, _1566563))))], (40132 ^ _782652) ^ [_1566674, _1566676, _1566678, _1566680, _1566682] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566674, _1566674)), hAPP(hAPP(c_Product__Type_OPair(_1566674, _1566674), _1566676), _1566678)), c_Transitive__Closure_Otrancl(_1566674, _1566680))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566674, _1566674)), hAPP(hAPP(c_Product__Type_OPair(_1566674, _1566674), _1566678), _1566682)), c_Transitive__Closure_Otrancl(_1566674, _1566680))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566674, _1566674)), hAPP(hAPP(c_Product__Type_OPair(_1566674, _1566674), _1566676), _1566682)), c_Transitive__Closure_Otrancl(_1566674, _1566680))))], (40142 ^ _782652) ^ [_1566947, _1566949, _1566951, _1566953, _1566955] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566947, _1566947)), hAPP(hAPP(c_Product__Type_OPair(_1566947, _1566947), _1566949), _1566951)), c_Transitive__Closure_Otrancl(_1566947, _1566953))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566947, _1566947)), hAPP(hAPP(c_Product__Type_OPair(_1566947, _1566947), _1566951), _1566955)), _1566953)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566947, _1566947)), hAPP(hAPP(c_Product__Type_OPair(_1566947, _1566947), _1566949), _1566955)), c_Transitive__Closure_Otrancl(_1566947, _1566953))))], (40152 ^ _782652) ^ [_1567214, _1567216, _1567218, _1567220, _1567222] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567214, _1567214)), hAPP(hAPP(c_Product__Type_OPair(_1567214, _1567214), _1567216), _1567218)), _1567220)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567214, _1567214)), hAPP(hAPP(c_Product__Type_OPair(_1567214, _1567214), _1567218), _1567222)), c_Transitive__Closure_Otrancl(_1567214, _1567220))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567214, _1567214)), hAPP(hAPP(c_Product__Type_OPair(_1567214, _1567214), _1567216), _1567222)), c_Transitive__Closure_Otrancl(_1567214, _1567220))))], (40162 ^ _782652) ^ [_1567481, _1567483, _1567485, _1567487, _1567489] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567481, _1567481)), hAPP(hAPP(c_Product__Type_OPair(_1567481, _1567481), _1567483), _1567485)), _1567487)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567481, _1567481)), hAPP(hAPP(c_Product__Type_OPair(_1567481, _1567481), _1567485), _1567489)), _1567487)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567481, _1567481)), hAPP(hAPP(c_Product__Type_OPair(_1567481, _1567481), _1567483), _1567489)), c_Transitive__Closure_Otrancl(_1567481, _1567487))))], (40172 ^ _782652) ^ [_1567742, _1567744, _1567746, _1567748] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567742, _1567742)), _1567744), c_Transitive__Closure_Otrancl(_1567742, _1567746))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567742, _1567742), tc_HOL_Obool)), _1567746), _1567748)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567742, _1567742)), _1567744), c_Transitive__Closure_Otrancl(_1567742, _1567748))))], (40182 ^ _782652) ^ [_1567957, _1567959] : [-(c_Transitive__Closure_Otrancl(_1567957, _1567959) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567957, _1567957), tc_HOL_Obool)), _1567959), hAPP(hAPP(c_Relation_Orel__comp(_1567957, _1567957, _1567957), c_Transitive__Closure_Otrancl(_1567957, _1567959)), _1567959)))], (40184 ^ _782652) ^ [_1568012, _1568014, _1568016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568012, _1568012), tc_HOL_Obool)), _1568014), hAPP(hAPP(c_Product__Type_OSigma(_1568012, _1568012), _1568016), hAPP(c_COMBK(tc_fun(_1568012, tc_HOL_Obool), _1568012), _1568016)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568012, _1568012), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1568012, _1568014)), hAPP(hAPP(c_Product__Type_OSigma(_1568012, _1568012), _1568016), hAPP(c_COMBK(tc_fun(_1568012, tc_HOL_Obool), _1568012), _1568016)))))], (40190 ^ _782652) ^ [_1568239, _1568241, _1568243, _1568245, _1568247] : [_1568239 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1568241, _1568243, _1568239, _1568245), _1568247) = hAPP(c_Product__Type_OPair(_1568241, _1568243), _1568247))], (40196 ^ _782652) ^ [_1568344, _1568346, _1568348, _1568350, _1568352] : [-(_1568344 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1568346, _1568348, _1568344, _1568350), _1568352) = hAPP(hAPP(c_Product__Type_Oscomp(_1568348, _1568346, _1568348, tc_prod(_1568346, _1568348)), hAPP(_1568350, _1568352)), c_Random_Oiterate(_1568346, _1568348, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1568344), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1568350)))], (40202 ^ _782652) ^ [_1568424, _1568426, _1568428, _1568430] : [-(c_Transitive__Closure_Otrancl(_1568424, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1568424, _1568424)), hAPP(hAPP(c_Product__Type_OPair(_1568424, _1568424), _1568426), _1568428)), _1568430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568424, _1568424), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1568424, _1568430)), hAPP(c_Set_OCollect(tc_prod(_1568424, _1568424)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568424, _1568424, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1568424, tc_fun(_1568424, tc_HOL_Obool), tc_fun(_1568424, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1568424, tc_HOL_Obool), tc_fun(_1568424, tc_HOL_Obool)), _1568424), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1568424)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1568424), c_fconj), hAPP(hAPP(c_COMBC(_1568424, tc_fun(tc_prod(_1568424, _1568424), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1568424, _1568424), tc_fun(tc_fun(tc_prod(_1568424, _1568424), tc_HOL_Obool), tc_HOL_Obool), _1568424), c_member(tc_prod(_1568424, _1568424))), hAPP(hAPP(c_COMBC(_1568424, _1568424, tc_prod(_1568424, _1568424)), c_Product__Type_OPair(_1568424, _1568424)), _1568426))), c_Transitive__Closure_Ortrancl(_1568424, _1568430))))), hAPP(hAPP(c_COMBC(_1568424, tc_fun(tc_prod(_1568424, _1568424), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1568424, _1568424), tc_fun(tc_fun(tc_prod(_1568424, _1568424), tc_HOL_Obool), tc_HOL_Obool), _1568424), c_member(tc_prod(_1568424, _1568424))), hAPP(c_Product__Type_OPair(_1568424, _1568424), _1568428))), c_Transitive__Closure_Ortrancl(_1568424, _1568430)))))))], (40204 ^ _782652) ^ [_1568692, _1568694, _1568696, _1568698] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1568692, tc_fun(_1568692, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1568692, tc_fun(tc_prod(_1568692, _1568692), tc_HOL_Obool), tc_fun(_1568692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568692, tc_fun(tc_fun(tc_prod(_1568692, _1568692), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568692, _1568692), tc_HOL_Obool), tc_fun(_1568692, tc_HOL_Obool)), _1568692), c_COMBC(_1568692, tc_fun(tc_prod(_1568692, _1568692), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568692, tc_prod(_1568692, _1568692)), tc_fun(_1568692, tc_fun(tc_fun(tc_prod(_1568692, _1568692), tc_HOL_Obool), tc_HOL_Obool)), _1568692), hAPP(c_COMBB(tc_prod(_1568692, _1568692), tc_fun(tc_fun(tc_prod(_1568692, _1568692), tc_HOL_Obool), tc_HOL_Obool), _1568692), c_member(tc_prod(_1568692, _1568692)))), c_Product__Type_OPair(_1568692, _1568692)))), _1568694)), c_fequal), _1568696), _1568698)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568692, _1568692)), hAPP(hAPP(c_Product__Type_OPair(_1568692, _1568692), _1568696), _1568698)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568692, _1568692), tc_HOL_Obool)), _1568694), c_Relation_OId(_1568692)))))], (40210 ^ _782652) ^ [_1569113, _1569115, _1569117, _1569119] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569113, _1569113)), hAPP(hAPP(c_Product__Type_OPair(_1569113, _1569113), _1569117), _1569119)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569113, _1569113), tc_HOL_Obool)), _1569115), c_Relation_OId(_1569113)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1569113, tc_fun(_1569113, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1569113, tc_fun(tc_prod(_1569113, _1569113), tc_HOL_Obool), tc_fun(_1569113, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569113, tc_fun(tc_fun(tc_prod(_1569113, _1569113), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1569113, _1569113), tc_HOL_Obool), tc_fun(_1569113, tc_HOL_Obool)), _1569113), c_COMBC(_1569113, tc_fun(tc_prod(_1569113, _1569113), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569113, tc_prod(_1569113, _1569113)), tc_fun(_1569113, tc_fun(tc_fun(tc_prod(_1569113, _1569113), tc_HOL_Obool), tc_HOL_Obool)), _1569113), hAPP(c_COMBB(tc_prod(_1569113, _1569113), tc_fun(tc_fun(tc_prod(_1569113, _1569113), tc_HOL_Obool), tc_HOL_Obool), _1569113), c_member(tc_prod(_1569113, _1569113)))), c_Product__Type_OPair(_1569113, _1569113)))), _1569115)), c_fequal), _1569117), _1569119)))], (40216 ^ _782652) ^ [_1569540, _1569542, _1569544] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569540, _1569540)), _1569542), _1569544)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569540, _1569540)), _1569542), c_Transitive__Closure_Ortrancl(_1569540, _1569544))))], (40222 ^ _782652) ^ [_1569665, _1569667, _1569669] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569665, _1569665)), hAPP(hAPP(c_Product__Type_OPair(_1569665, _1569665), _1569667), _1569667)), c_Transitive__Closure_Ortrancl(_1569665, _1569669))))], (40224 ^ _782652) ^ [_1569714, _1569716] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569714, _1569714)), hAPP(hAPP(c_Product__Type_OPair(_1569714, _1569714), _1569716), _1569716)), c_Relation_OId(_1569714))))], (40226 ^ _782652) ^ [_1569760, _1569762, _1569764, _1569766] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569760, _1569760)), hAPP(hAPP(c_Product__Type_OPair(_1569760, _1569760), _1569762), _1569764)), c_Transitive__Closure_Otrancl(_1569760, _1569766))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569760, _1569760)), hAPP(hAPP(c_Product__Type_OPair(_1569760, _1569760), _1569762), _1569764)), c_Transitive__Closure_Ortrancl(_1569760, _1569766))))], (40232 ^ _782652) ^ [_1569929, _1569931] : [-(c_Transitive__Closure_Ortrancl(_1569929, c_Transitive__Closure_Otrancl(_1569929, _1569931)) = c_Transitive__Closure_Ortrancl(_1569929, _1569931))], (40234 ^ _782652) ^ [_1569963, _1569965] : [-(c_Transitive__Closure_Otrancl(_1569963, c_Transitive__Closure_Ortrancl(_1569963, _1569965)) = c_Transitive__Closure_Ortrancl(_1569963, _1569965))], (40236 ^ _782652) ^ [_1569997, _1569999] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569997, _1569997), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569997, _1569999)), c_Relation_OId(_1569997)) = c_Transitive__Closure_Ortrancl(_1569997, _1569999))], (40238 ^ _782652) ^ [_1570044, _1570046] : [-(c_Transitive__Closure_Otrancl(_1570044, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570044, _1570044), tc_HOL_Obool)), _1570046), c_Relation_OId(_1570044))) = c_Transitive__Closure_Ortrancl(_1570044, _1570046))], (40240 ^ _782652) ^ [_1570091, _1570093] : [-(c_Transitive__Closure_Otrancl(_1570091, _1570093) = hAPP(hAPP(c_Relation_Orel__comp(_1570091, _1570091, _1570091), c_Transitive__Closure_Ortrancl(_1570091, _1570093)), _1570093))], (40242 ^ _782652) ^ [_1570132, _1570134] : [-(c_Transitive__Closure_Otrancl(_1570132, _1570134) = hAPP(hAPP(c_Relation_Orel__comp(_1570132, _1570132, _1570132), _1570134), c_Transitive__Closure_Ortrancl(_1570132, _1570134)))], (40244 ^ _782652) ^ [_1570173, _1570175] : [-(hAPP(c_Relation_ODomain(_1570173, _1570173), c_Transitive__Closure_Ortrancl(_1570173, _1570175)) = c_Orderings_Otop__class_Otop(tc_fun(_1570173, tc_HOL_Obool)))], (40246 ^ _782652) ^ [_1570212, _1570214] : [-(hAPP(c_Relation_ORange(_1570212, _1570212), c_Transitive__Closure_Ortrancl(_1570212, _1570214)) = c_Orderings_Otop__class_Otop(tc_fun(_1570212, tc_HOL_Obool)))], (40248 ^ _782652) ^ [_1570251] : [-(c_Transitive__Closure_Ortrancl(_1570251, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1570251, _1570251), tc_HOL_Obool))) = c_Relation_OId(_1570251))], (40250 ^ _782652) ^ [_1570287, _1570289] : [-(c_Transitive__Closure_Ortrancl(_1570287, _1570289) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570287, _1570287), tc_HOL_Obool)), c_Relation_OId(_1570287)), hAPP(hAPP(c_Relation_Orel__comp(_1570287, _1570287, _1570287), c_Transitive__Closure_Ortrancl(_1570287, _1570289)), _1570289)))], (40252 ^ _782652) ^ [_1570344, _1570346, _1570348, _1570350] : [40253 ^ _782652 : [(40254 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570344, _1570344)), _1570346), c_Transitive__Closure_Ortrancl(_1570344, _1570348)))], (40256 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570344, _1570344)), _1570346), c_Transitive__Closure_Ortrancl(_1570344, _1570350)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570344, _1570344)), _1570346), c_Transitive__Closure_Ortrancl(_1570344, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570344, _1570344), tc_HOL_Obool)), _1570348), _1570350)))))], (40260 ^ _782652) ^ [_1570569, _1570571] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1570569, _1570569, _1570569), _1570571), c_Transitive__Closure_Ortrancl(_1570569, _1570571)) = hAPP(hAPP(c_Relation_Orel__comp(_1570569, _1570569, _1570569), c_Transitive__Closure_Ortrancl(_1570569, _1570571)), _1570571))], (40262 ^ _782652) ^ [_1570620, _1570622] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1570620, _1570620, _1570620), c_Transitive__Closure_Ortrancl(_1570620, _1570622)), c_Transitive__Closure_Ortrancl(_1570620, _1570622)) = c_Transitive__Closure_Ortrancl(_1570620, _1570622))], (40264 ^ _782652) ^ [_1570664, _1570666, _1570668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570664, _1570664), tc_HOL_Obool)), c_Relation_OId(_1570664)), _1570666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570664, _1570664), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1570664, _1570664, _1570664), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1570664, _1570664), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1570664, _1570668)), _1570666)), _1570668)), _1570666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570664, _1570664), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1570664, _1570668)), _1570666)))], (40274 ^ _782652) ^ [_1570939, _1570941, _1570943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570939, _1570939), tc_HOL_Obool)), _1570941), c_Transitive__Closure_Ortrancl(_1570939, _1570943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570939, _1570939), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1570939, _1570941)), c_Transitive__Closure_Ortrancl(_1570939, _1570943))))], (40280 ^ _782652) ^ [_1571088, _1571090, _1571092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571088, _1571088), tc_HOL_Obool)), _1571090), _1571092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571088, _1571088), tc_HOL_Obool)), _1571092), c_Transitive__Closure_Ortrancl(_1571088, _1571090))), -(c_Transitive__Closure_Ortrancl(_1571088, _1571092) = c_Transitive__Closure_Ortrancl(_1571088, _1571090))], (40290 ^ _782652) ^ [_1571291, _1571293, _1571295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571291, _1571291), tc_HOL_Obool)), _1571293), _1571295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571291, _1571291), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1571291, _1571293)), c_Transitive__Closure_Ortrancl(_1571291, _1571295))))], (40296 ^ _782652) ^ [_1571434, _1571436] : [-(c_Transitive__Closure_Ortrancl(_1571434, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571434, _1571434), tc_HOL_Obool)), _1571436), c_Relation_OId(_1571434))) = c_Transitive__Closure_Ortrancl(_1571434, _1571436))], (40298 ^ _782652) ^ [_1571481, _1571483, _1571485] : [-(c_Transitive__Closure_Ortrancl(_1571481, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571481, _1571481), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1571481, _1571483)), c_Transitive__Closure_Ortrancl(_1571481, _1571485))) = c_Transitive__Closure_Ortrancl(_1571481, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571481, _1571481), tc_HOL_Obool)), _1571483), _1571485)))], (40300 ^ _782652) ^ [_1571548, _1571550] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571548, _1571548), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1571548, _1571550)), c_Relation_OId(_1571548)) = c_Transitive__Closure_Ortrancl(_1571548, _1571550))], (40302 ^ _782652) ^ [_1571595, _1571597, _1571599] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571595, _1571595), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571595, _1571595), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1571595, _1571597)), c_Transitive__Closure_Ortrancl(_1571595, _1571599))), c_Transitive__Closure_Ortrancl(_1571595, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571595, _1571595), tc_HOL_Obool)), _1571597), _1571599)))))], (40304 ^ _782652) ^ [_1571672, _1571674, _1571676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571672, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1571672, _1571672, _1571674), _1571676)), _1571676)), -(hAPP(c_Relation_OImage(_1571672, _1571672, c_Transitive__Closure_Ortrancl(_1571672, _1571674)), _1571676) = _1571676)], (40310 ^ _782652) ^ [_1571805, _1571807] : [-(c_Transitive__Closure_Ortrancl(_1571805, c_Transitive__Closure_Ortrancl(_1571805, _1571807)) = c_Transitive__Closure_Ortrancl(_1571805, _1571807))], (40312 ^ _782652) ^ [_1571839, _1571841, _1571843, _1571845, _1571847] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571839, _1571839)), hAPP(hAPP(c_Product__Type_OPair(_1571839, _1571839), _1571841), _1571843)), c_Transitive__Closure_Ortrancl(_1571839, _1571845))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571839, _1571839)), hAPP(hAPP(c_Product__Type_OPair(_1571839, _1571839), _1571843), _1571847)), c_Transitive__Closure_Ortrancl(_1571839, _1571845))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571839, _1571839)), hAPP(hAPP(c_Product__Type_OPair(_1571839, _1571839), _1571841), _1571847)), c_Transitive__Closure_Ortrancl(_1571839, _1571845))))], (40322 ^ _782652) ^ [_1572112, _1572114, _1572116, _1572118, _1572120] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572112, _1572112)), hAPP(hAPP(c_Product__Type_OPair(_1572112, _1572112), _1572114), _1572116)), c_Transitive__Closure_Ortrancl(_1572112, _1572118))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572112, _1572112)), hAPP(hAPP(c_Product__Type_OPair(_1572112, _1572112), _1572116), _1572120)), _1572118)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572112, _1572112)), hAPP(hAPP(c_Product__Type_OPair(_1572112, _1572112), _1572114), _1572120)), c_Transitive__Closure_Ortrancl(_1572112, _1572118))))], (40332 ^ _782652) ^ [_1572379, _1572381, _1572383, _1572385, _1572387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572379, _1572379)), hAPP(hAPP(c_Product__Type_OPair(_1572379, _1572379), _1572381), _1572383)), _1572385)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572379, _1572379)), hAPP(hAPP(c_Product__Type_OPair(_1572379, _1572379), _1572383), _1572387)), c_Transitive__Closure_Ortrancl(_1572379, _1572385))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572379, _1572379)), hAPP(hAPP(c_Product__Type_OPair(_1572379, _1572379), _1572381), _1572387)), c_Transitive__Closure_Ortrancl(_1572379, _1572385))))], (40342 ^ _782652) ^ [_1572646, _1572648] : [-(c_Transitive__Closure_Ortrancl(_1572646, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1572646, _1572646), tc_HOL_Obool)), _1572648), c_Relation_OId(_1572646))) = c_Transitive__Closure_Ortrancl(_1572646, _1572648))], (40344 ^ _782652) ^ [_1572693, _1572695] : [-(c_Relation_Orefl__on(_1572693, c_Orderings_Otop__class_Otop(tc_fun(_1572693, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1572693, _1572695)))], (40346 ^ _782652) ^ [_1572727, _1572729] : [-(hAPP(c_Relation_OImage(_1572727, _1572727, c_Relation_OId(_1572727)), _1572729) = _1572729)], (40348 ^ _782652) ^ [_1572761, _1572763, _1572765] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1572761, _1572761, _1572763), c_Relation_OId(_1572761)), _1572765) = _1572765)], (40350 ^ _782652) ^ [_1572800, _1572802, _1572804] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1572800, _1572802, _1572802), _1572804), c_Relation_OId(_1572802)) = _1572804)], (40352 ^ _782652) ^ [_1572857, _1572859, _1572861] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572857, _1572857)), hAPP(hAPP(c_Product__Type_OPair(_1572857, _1572857), _1572859), _1572861)), c_Relation_OId(_1572857))), -(_1572859 = _1572861)], (40358 ^ _782652) ^ [_1572974, _1572976, _1572978] : [_1572976 = _1572978, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572974, _1572974)), hAPP(hAPP(c_Product__Type_OPair(_1572974, _1572974), _1572976), _1572978)), c_Relation_OId(_1572974))))], (40364 ^ _782652) ^ [_1573097, _1573099, _1573101, _1573103, _1573105] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573097, _1573097)), hAPP(hAPP(c_Product__Type_OPair(_1573097, _1573097), _1573099), _1573101)), c_Transitive__Closure_Ortrancl(_1573097, _1573103))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1573097, _1573097)), hAPP(hAPP(c_Product__Type_OPair(_1573097, _1573097), _1573101), _1573105)), c_Transitive__Closure_Otrancl(_1573097, _1573103))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573097, _1573097)), hAPP(hAPP(c_Product__Type_OPair(_1573097, _1573097), _1573099), _1573105)), c_Transitive__Closure_Otrancl(_1573097, _1573103))))], (40374 ^ _782652) ^ [_1573370, _1573372, _1573374, _1573376, _1573378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573370, _1573370)), hAPP(hAPP(c_Product__Type_OPair(_1573370, _1573370), _1573372), _1573374)), c_Transitive__Closure_Otrancl(_1573370, _1573376))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1573370, _1573370)), hAPP(hAPP(c_Product__Type_OPair(_1573370, _1573370), _1573374), _1573378)), c_Transitive__Closure_Ortrancl(_1573370, _1573376))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573370, _1573370)), hAPP(hAPP(c_Product__Type_OPair(_1573370, _1573370), _1573372), _1573378)), c_Transitive__Closure_Otrancl(_1573370, _1573376))))], (40384 ^ _782652) ^ [_1573643, _1573645, _1573647, _1573649, _1573651] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573643, _1573643)), hAPP(hAPP(c_Product__Type_OPair(_1573643, _1573643), _1573645), _1573647)), c_Transitive__Closure_Ortrancl(_1573643, _1573649))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1573643, _1573643)), hAPP(hAPP(c_Product__Type_OPair(_1573643, _1573643), _1573647), _1573651)), _1573649)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573643, _1573643)), hAPP(hAPP(c_Product__Type_OPair(_1573643, _1573643), _1573645), _1573651)), c_Transitive__Closure_Otrancl(_1573643, _1573649))))], (40394 ^ _782652) ^ [_1573910, _1573912, _1573914, _1573916] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573910, _1573910)), hAPP(hAPP(c_Product__Type_OPair(_1573910, _1573910), _1573912), _1573914)), c_Transitive__Closure_Ortrancl(_1573910, _1573916))), -(_1573912 = _1573914), 40401 ^ _782652 : [(40402 ^ _782652) ^ [] : [_1573912 = _1573914], (40404 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573910, _1573910)), hAPP(hAPP(c_Product__Type_OPair(_1573910, _1573910), _1573912), _1573914)), c_Transitive__Closure_Otrancl(_1573910, _1573916))))]]], (40406 ^ _782652) ^ [_1574172, _1574174, _1574176, _1574178, _1574180] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574172, _1574172)), hAPP(hAPP(c_Product__Type_OPair(_1574172, _1574172), _1574174), _1574176)), _1574178)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574172, _1574172)), hAPP(hAPP(c_Product__Type_OPair(_1574172, _1574172), _1574176), _1574180)), c_Transitive__Closure_Ortrancl(_1574172, _1574178))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574172, _1574172)), hAPP(hAPP(c_Product__Type_OPair(_1574172, _1574172), _1574174), _1574180)), c_Transitive__Closure_Otrancl(_1574172, _1574178))))], (40416 ^ _782652) ^ [_1574460, _1574462, _1574464, _1574466] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574460, _1574460)), hAPP(hAPP(c_Product__Type_OPair(_1574460, _1574460), _1574462), _1574464)), c_Transitive__Closure_Ortrancl(_1574460, _1574466))), -(_1574462 = _1574464), 40423 ^ _782652 : [(40424 ^ _782652) ^ [] : [_1574462 = _1574464], (40426 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574460, _1574460)), hAPP(hAPP(c_Product__Type_OPair(_1574460, _1574460), _1574462), _1574464)), c_Transitive__Closure_Otrancl(_1574460, _1574466))))]]], (40428 ^ _782652) ^ [_1574718, _1574720, _1574722, _1574724] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574718, _1574718)), hAPP(hAPP(c_Product__Type_OPair(_1574718, _1574718), _1574720), _1574722)), c_Transitive__Closure_Ortrancl(_1574718, _1574724)))), 40429 ^ _782652 : [(40430 ^ _782652) ^ [] : [_1574720 = _1574722], (40432 ^ _782652) ^ [] : [-(_1574720 = _1574722), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574718, _1574718)), hAPP(hAPP(c_Product__Type_OPair(_1574718, _1574718), _1574720), _1574722)), c_Transitive__Closure_Otrancl(_1574718, _1574724)))]]], (40440 ^ _782652) ^ [_1574984] : [-(hAPP(c_Relation_ODomain(_1574984, _1574984), c_Relation_OId(_1574984)) = c_Orderings_Otop__class_Otop(tc_fun(_1574984, tc_HOL_Obool)))], (40442 ^ _782652) ^ [_1575020] : [-(hAPP(c_Relation_ORange(_1575020, _1575020), c_Relation_OId(_1575020)) = c_Orderings_Otop__class_Otop(tc_fun(_1575020, tc_HOL_Obool)))], (40444 ^ _782652) ^ [_1575056] : [-(c_Relation_Orefl__on(_1575056, c_Orderings_Otop__class_Otop(tc_fun(_1575056, tc_HOL_Obool)), c_Relation_OId(_1575056)))], (40446 ^ _782652) ^ [] : [-(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))))], (40448 ^ _782652) ^ [_1575104, _1575106, _1575108, _1575110] : [-(hBOOL(hAPP(hAPP(c_member(_1575104), _1575106), hAPP(c_Relation_ODomain(_1575104, _1575104), _1575108)))), 40451 ^ _782652 : [(40452 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575104, _1575104)), hAPP(hAPP(c_Product__Type_OPair(_1575104, _1575104), _1575106), _1575110)), c_Transitive__Closure_Ortrancl(_1575104, _1575108))), -(_1575106 = _1575110)], (40458 ^ _782652) ^ [] : [_1575106 = _1575110, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575104, _1575104)), hAPP(hAPP(c_Product__Type_OPair(_1575104, _1575104), _1575106), _1575110)), c_Transitive__Closure_Ortrancl(_1575104, _1575108))))]]], (40464 ^ _782652) ^ [_1575400, _1575402, _1575404, _1575406] : [hBOOL(hAPP(hAPP(c_member(_1575400), _1575402), c_Wellfounded_Oacc(_1575400, _1575404))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575400, _1575400)), hAPP(hAPP(c_Product__Type_OPair(_1575400, _1575400), _1575406), _1575402)), c_Transitive__Closure_Ortrancl(_1575400, _1575404))), -(hBOOL(hAPP(hAPP(c_member(_1575400), _1575406), c_Wellfounded_Oacc(_1575400, _1575404))))], (40474 ^ _782652) ^ [_1575621, _1575623, _1575625, _1575627] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575621, _1575621)), hAPP(hAPP(c_Product__Type_OPair(_1575621, _1575621), _1575623), _1575625)), c_Transitive__Closure_Ortrancl(_1575621, _1575627))), hBOOL(hAPP(hAPP(c_member(_1575621), _1575625), c_Wellfounded_Oacc(_1575621, _1575627))), -(hBOOL(hAPP(hAPP(c_member(_1575621), _1575623), c_Wellfounded_Oacc(_1575621, _1575627))))], (40484 ^ _782652) ^ [_1575863, _1575865, _1575867, _1575869] : [c_Wellfounded_Owf(_1575863, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1575863, _1575863)), hAPP(hAPP(c_Product__Type_OPair(_1575863, _1575863), _1575865), _1575867)), _1575869)), 40487 ^ _782652 : [(40488 ^ _782652) ^ [] : [-(c_Wellfounded_Owf(_1575863, _1575869))], (40490 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575863, _1575863)), hAPP(hAPP(c_Product__Type_OPair(_1575863, _1575863), _1575867), _1575865)), c_Transitive__Closure_Ortrancl(_1575863, _1575869)))]]], (40492 ^ _782652) ^ [_1576058, _1576060, _1576062, _1576064] : [-(c_Wellfounded_Owf(_1576058, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1576058, _1576058)), hAPP(hAPP(c_Product__Type_OPair(_1576058, _1576058), _1576060), _1576062)), _1576064))), c_Wellfounded_Owf(_1576058, _1576064), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576058, _1576058)), hAPP(hAPP(c_Product__Type_OPair(_1576058, _1576058), _1576062), _1576060)), c_Transitive__Closure_Ortrancl(_1576058, _1576064))))], (40502 ^ _782652) ^ [_1576305, _1576307, _1576309, _1576311] : [c_Wellfounded_Oacyclic(_1576305, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1576305, _1576305)), hAPP(hAPP(c_Product__Type_OPair(_1576305, _1576305), _1576307), _1576309)), _1576311)), 40505 ^ _782652 : [(40506 ^ _782652) ^ [] : [-(c_Wellfounded_Oacyclic(_1576305, _1576311))], (40508 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576305, _1576305)), hAPP(hAPP(c_Product__Type_OPair(_1576305, _1576305), _1576309), _1576307)), c_Transitive__Closure_Ortrancl(_1576305, _1576311)))]]], (40510 ^ _782652) ^ [_1576500, _1576502, _1576504, _1576506] : [-(c_Wellfounded_Oacyclic(_1576500, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1576500, _1576500)), hAPP(hAPP(c_Product__Type_OPair(_1576500, _1576500), _1576502), _1576504)), _1576506))), c_Wellfounded_Oacyclic(_1576500, _1576506), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576500, _1576500)), hAPP(hAPP(c_Product__Type_OPair(_1576500, _1576500), _1576504), _1576502)), c_Transitive__Closure_Ortrancl(_1576500, _1576506))))], (40520 ^ _782652) ^ [_1576726, _1576728] : [-(c_Relation_Orefl__on(_1576726, c_Orderings_Otop__class_Otop(tc_fun(_1576726, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576726, _1576726), tc_HOL_Obool)), _1576728), c_Relation_OId(_1576726))))], (40522 ^ _782652) ^ [_1576773] : [-(c_Relation_OId(_1576773) = hAPP(c_Set_OCollect(tc_prod(_1576773, _1576773)), hAPP(hAPP(c_COMBB(tc_fun(_1576773, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1576773, _1576773)), c_HOL_OEx(_1576773)), hAPP(hAPP(c_COMBC(tc_prod(_1576773, _1576773), tc_fun(_1576773, tc_prod(_1576773, _1576773)), tc_fun(_1576773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1576773, _1576773), tc_HOL_Obool), tc_fun(tc_fun(_1576773, tc_prod(_1576773, _1576773)), tc_fun(_1576773, tc_HOL_Obool)), tc_prod(_1576773, _1576773)), c_COMBB(tc_prod(_1576773, _1576773), tc_HOL_Obool, _1576773)), c_fequal)), hAPP(hAPP(c_COMBS(_1576773, _1576773, tc_prod(_1576773, _1576773)), c_Product__Type_OPair(_1576773, _1576773)), c_COMBI(_1576773))))))], (40524 ^ _782652) ^ [_1576902, _1576904] : [-(c_Relation_Oirrefl(_1576902, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576902, _1576902), tc_HOL_Obool)), _1576904), c_Relation_OId(_1576902))))], (40526 ^ _782652) ^ [_1576958, _1576960] : [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), _1576958), _1576960)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1576958), _1576960)))], (40532 ^ _782652) ^ [_1577063, _1577065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1577063), _1577065)), -(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), _1577063), _1577065)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40538 ^ _782652) ^ [_1577174, _1577176, _1577178, _1577180, _1577182] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577174, _1577174)), hAPP(hAPP(c_Product__Type_OPair(_1577174, _1577174), _1577176), _1577178)), c_Transitive__Closure_Ortrancl(_1577174, _1577180))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1577174, _1577174), tc_HOL_Obool)), _1577180), hAPP(hAPP(c_Product__Type_OSigma(_1577174, _1577174), _1577182), hAPP(c_COMBK(tc_fun(_1577174, tc_HOL_Obool), _1577174), _1577182)))), -(_1577176 = _1577178), -(hBOOL(hAPP(hAPP(c_member(_1577174), _1577176), _1577182)))], (40552 ^ _782652) ^ [_1577457, _1577459] : [40553 ^ _782652 : [(40554 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1577457), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40556 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1577459), _1577457))]], -(c_Random_Olog(_1577457, _1577459) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40560 ^ _782652) ^ [_1577592, _1577594] : [-(c_Random_Olog(_1577592, _1577594) = 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(_1577592, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1577594), _1577592)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1577592), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1577594), _1577592)))], (40570 ^ _782652) ^ [_1577674, _1577676, _1577678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1577674), _1577676)), -(c_Random_Ominus__shift(_1577678, _1577674, _1577676) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1577678), _1577674)), _1577676))], (40576 ^ _782652) ^ [_1577789, _1577791, _1577793] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1577789), _1577791))), -(c_Random_Ominus__shift(_1577793, _1577789, _1577791) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1577789), _1577791))], (40582 ^ _782652) ^ [_1577853, _1577855] : [_1577853 = _1577855, -(c_Random_Oinc__shift(_1577853, _1577855) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40588 ^ _782652) ^ [_1577930, _1577932] : [-(_1577930 = _1577932), -(c_Random_Oinc__shift(_1577930, _1577932) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1577932), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40594 ^ _782652) ^ [_1577977, _1577979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1577977)), -(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(_1577977), _1577979))), _1577977)))], (40600 ^ _782652) ^ [_1578084, _1578086, _1578088] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1578084, _1578084), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1578084, _1578084), _1578086)), c_Transitive__Closure_Ortrancl(_1578084, _1578086)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1578084, _1578084), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578084, _1578084)), hAPP(hAPP(c_Product__Type_OPair(_1578084, _1578084), _1578088), _1578088)), c_Transitive__Closure_Otrancl(_1578084, _1578086)))], (40606 ^ _782652) ^ [_1578270, _1578272] : [-(c_Transitive__Closure_Ortrancl(_1578270, hAPP(c_Relation_Oconverse(_1578270, _1578270), _1578272)) = hAPP(c_Relation_Oconverse(_1578270, _1578270), c_Transitive__Closure_Ortrancl(_1578270, _1578272)))], (40608 ^ _782652) ^ [_1578313] : [-(hAPP(c_Relation_Oconverse(_1578313, _1578313), c_Relation_OId(_1578313)) = c_Relation_OId(_1578313))], (40610 ^ _782652) ^ [_1578346, _1578348, _1578350, _1578352] : [-(hAPP(c_Relation_Oconverse(_1578346, _1578348), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1578346, _1578348), tc_HOL_Obool)), _1578350), _1578352)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1578348, _1578346), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1578346, _1578348), _1578350)), hAPP(c_Relation_Oconverse(_1578346, _1578348), _1578352)))], (40612 ^ _782652) ^ [_1578421, _1578423] : [-(c_Transitive__Closure_Otrancl(_1578421, hAPP(c_Relation_Oconverse(_1578421, _1578421), _1578423)) = hAPP(c_Relation_Oconverse(_1578421, _1578421), c_Transitive__Closure_Otrancl(_1578421, _1578423)))], (40614 ^ _782652) ^ [_1578464, _1578466, _1578468, _1578470, _1578472] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578464, _1578466)), hAPP(hAPP(c_Product__Type_OPair(_1578464, _1578466), _1578468), _1578470)), hAPP(c_Relation_Oconverse(_1578466, _1578464), _1578472))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578466, _1578464)), hAPP(hAPP(c_Product__Type_OPair(_1578466, _1578464), _1578470), _1578468)), _1578472)))], (40620 ^ _782652) ^ [_1578635, _1578637, _1578639, _1578641, _1578643] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578635, _1578637)), hAPP(hAPP(c_Product__Type_OPair(_1578635, _1578637), _1578639), _1578641)), _1578643)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578637, _1578635)), hAPP(hAPP(c_Product__Type_OPair(_1578637, _1578635), _1578641), _1578639)), hAPP(c_Relation_Oconverse(_1578635, _1578637), _1578643))))], (40626 ^ _782652) ^ [_1578830, _1578832, _1578834, _1578836, _1578838] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578830, _1578832)), hAPP(hAPP(c_Product__Type_OPair(_1578830, _1578832), _1578834), _1578836)), hAPP(c_Relation_Oconverse(_1578832, _1578830), _1578838))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578832, _1578830)), hAPP(hAPP(c_Product__Type_OPair(_1578832, _1578830), _1578836), _1578834)), _1578838)))], (40632 ^ _782652) ^ [_1578997, _1578999, _1579001, _1579003, _1579005] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578999, _1578997)), hAPP(hAPP(c_Product__Type_OPair(_1578999, _1578997), _1579003), _1579001)), _1579005)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578997, _1578999)), hAPP(hAPP(c_Product__Type_OPair(_1578997, _1578999), _1579001), _1579003)), hAPP(c_Relation_Oconverse(_1578999, _1578997), _1579005))))], (40638 ^ _782652) ^ [_1579188, _1579190, _1579192] : [c_Relation_Orefl__on(_1579188, _1579190, hAPP(c_Relation_Oconverse(_1579188, _1579188), _1579192)), -(c_Relation_Orefl__on(_1579188, _1579190, _1579192))], (40644 ^ _782652) ^ [_1579279, _1579281, _1579283] : [c_Relation_Orefl__on(_1579279, _1579281, _1579283), -(c_Relation_Orefl__on(_1579279, _1579281, hAPP(c_Relation_Oconverse(_1579279, _1579279), _1579283)))], (40650 ^ _782652) ^ [_1579376, _1579378] : [-(hAPP(c_Relation_OField(_1579376), hAPP(c_Relation_Oconverse(_1579376, _1579376), _1579378)) = hAPP(c_Relation_OField(_1579376), _1579378))], (40652 ^ _782652) ^ [_1579435, _1579437, _1579439] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579435, _1579437)), hAPP(c_Relation_Oconverse(_1579437, _1579435), _1579439))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579437, _1579435)), _1579439)))], (40658 ^ _782652) ^ [_1579550, _1579552, _1579554] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579552, _1579550)), _1579554)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579550, _1579552)), hAPP(c_Relation_Oconverse(_1579552, _1579550), _1579554))))], (40664 ^ _782652) ^ [_1579671, _1579673, _1579675, _1579677] : [-(hAPP(c_Relation_Oconverse(_1579671, _1579673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1579671, _1579673), tc_HOL_Obool)), _1579675), _1579677)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1579673, _1579671), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1579671, _1579673), _1579675)), hAPP(c_Relation_Oconverse(_1579671, _1579673), _1579677)))], (40666 ^ _782652) ^ [_1579746, _1579748, _1579750] : [-(hAPP(c_Relation_Oconverse(_1579746, _1579748), hAPP(c_Relation_Oconverse(_1579748, _1579746), _1579750)) = _1579750)], (40668 ^ _782652) ^ [_1579785, _1579787, _1579789, _1579791] : [-(hAPP(c_Relation_Oconverse(_1579785, _1579785), hAPP(hAPP(c_Relation_Oinv__image(_1579787, _1579785), _1579789), _1579791)) = hAPP(hAPP(c_Relation_Oinv__image(_1579787, _1579785), hAPP(c_Relation_Oconverse(_1579787, _1579787), _1579789)), _1579791))], (40670 ^ _782652) ^ [_1579844, _1579846] : [-(hAPP(c_Relation_Oconverse(_1579844, _1579844), c_Relation_OId__on(_1579844, _1579846)) = c_Relation_OId__on(_1579844, _1579846))], (40672 ^ _782652) ^ [_1579881, _1579883, _1579885, _1579887, _1579889] : [-(hAPP(c_Relation_Oconverse(_1579881, _1579883), hAPP(hAPP(c_Relation_Orel__comp(_1579881, _1579885, _1579883), _1579887), _1579889)) = hAPP(hAPP(c_Relation_Orel__comp(_1579883, _1579885, _1579881), hAPP(c_Relation_Oconverse(_1579885, _1579883), _1579889)), hAPP(c_Relation_Oconverse(_1579881, _1579885), _1579887)))], (40674 ^ _782652) ^ [_1579950, _1579952, _1579954, _1579956, _1579958] : [-(hAPP(c_Relation_Oconverse(_1579950, _1579952), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1579954, tc_fun(tc_prod(_1579950, _1579952), tc_HOL_Obool)), _1579956), _1579958)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1579954, tc_fun(tc_prod(_1579952, _1579950), tc_HOL_Obool)), _1579956), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1579950, _1579952), tc_HOL_Obool), tc_fun(tc_prod(_1579952, _1579950), tc_HOL_Obool), _1579954), c_Relation_Oconverse(_1579950, _1579952)), _1579958)))], (40676 ^ _782652) ^ [_1580057, _1580059] : [c_Wellfounded_Oacyclic(_1580057, hAPP(c_Relation_Oconverse(_1580057, _1580057), _1580059)), -(c_Wellfounded_Oacyclic(_1580057, _1580059))], (40682 ^ _782652) ^ [_1580142, _1580144] : [c_Wellfounded_Oacyclic(_1580142, _1580144), -(c_Wellfounded_Oacyclic(_1580142, hAPP(c_Relation_Oconverse(_1580142, _1580142), _1580144)))], (40688 ^ _782652) ^ [_1580233, _1580235] : [c_Wellfounded_Owf(_1580233, hAPP(c_Relation_Oconverse(_1580233, _1580233), _1580235)), -(c_Wellfounded_Owf(_1580233, hAPP(c_Relation_Oconverse(_1580233, _1580233), c_Transitive__Closure_Otrancl(_1580233, _1580235))))], (40694 ^ _782652) ^ [_1580340, _1580342, _1580344] : [c_Equiv__Relations_Oequiv(_1580340, _1580342, _1580344), -(hAPP(hAPP(c_Relation_Orel__comp(_1580340, _1580340, _1580340), hAPP(c_Relation_Oconverse(_1580340, _1580340), _1580344)), _1580344) = _1580344)], (40700 ^ _782652) ^ [_1580453, _1580455, _1580457] : [-(hAPP(c_Relation_ORange(_1580453, _1580455), _1580457) = hAPP(c_Relation_ODomain(_1580455, _1580453), hAPP(c_Relation_Oconverse(_1580453, _1580455), _1580457)))], (40702 ^ _782652) ^ [_1580498, _1580500, _1580502] : [-(hAPP(c_Relation_ODomain(_1580498, _1580500), hAPP(c_Relation_Oconverse(_1580500, _1580498), _1580502)) = hAPP(c_Relation_ORange(_1580500, _1580498), _1580502))], (40704 ^ _782652) ^ [_1580543, _1580545, _1580547] : [-(hAPP(c_Relation_ORange(_1580543, _1580545), hAPP(c_Relation_Oconverse(_1580545, _1580543), _1580547)) = hAPP(c_Relation_ODomain(_1580545, _1580543), _1580547))], (40706 ^ _782652) ^ [_1580588, _1580590, _1580592, _1580594] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580588, _1580588)), hAPP(hAPP(c_Product__Type_OPair(_1580588, _1580588), _1580590), _1580592)), c_Transitive__Closure_Ortrancl(_1580588, hAPP(c_Relation_Oconverse(_1580588, _1580588), _1580594)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580588, _1580588)), hAPP(hAPP(c_Product__Type_OPair(_1580588, _1580588), _1580592), _1580590)), c_Transitive__Closure_Ortrancl(_1580588, _1580594))))], (40712 ^ _782652) ^ [_1580769, _1580771, _1580773, _1580775] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580769, _1580769)), hAPP(hAPP(c_Product__Type_OPair(_1580769, _1580769), _1580771), _1580773)), c_Transitive__Closure_Ortrancl(_1580769, _1580775))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580769, _1580769)), hAPP(hAPP(c_Product__Type_OPair(_1580769, _1580769), _1580773), _1580771)), c_Transitive__Closure_Ortrancl(_1580769, hAPP(c_Relation_Oconverse(_1580769, _1580769), _1580775)))))], (40718 ^ _782652) ^ [_1580950, _1580952, _1580954, _1580956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580950, _1580950)), hAPP(hAPP(c_Product__Type_OPair(_1580950, _1580950), _1580952), _1580954)), c_Transitive__Closure_Otrancl(_1580950, hAPP(c_Relation_Oconverse(_1580950, _1580950), _1580956)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580950, _1580950)), hAPP(hAPP(c_Product__Type_OPair(_1580950, _1580950), _1580952), _1580954)), hAPP(c_Relation_Oconverse(_1580950, _1580950), c_Transitive__Closure_Otrancl(_1580950, _1580956)))))], (40724 ^ _782652) ^ [_1581143, _1581145, _1581147, _1581149] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581143, _1581143)), hAPP(hAPP(c_Product__Type_OPair(_1581143, _1581143), _1581145), _1581147)), hAPP(c_Relation_Oconverse(_1581143, _1581143), c_Transitive__Closure_Otrancl(_1581143, _1581149)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581143, _1581143)), hAPP(hAPP(c_Product__Type_OPair(_1581143, _1581143), _1581145), _1581147)), c_Transitive__Closure_Otrancl(_1581143, hAPP(c_Relation_Oconverse(_1581143, _1581143), _1581149)))))], (40730 ^ _782652) ^ [_1581360, _1581362, _1581364, _1581366, _1581368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581360, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1581362, _1581360, _1581364), _1581366)), _1581368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581362, tc_HOL_Obool)), _1581366), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1581362, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1581360, _1581362, hAPP(c_Relation_Oconverse(_1581362, _1581360), _1581364)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1581360, tc_HOL_Obool)), _1581368))))))], (40736 ^ _782652) ^ [_1581551, _1581553, _1581555, _1581557, _1581559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581553, tc_HOL_Obool)), _1581557), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1581553, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1581551, _1581553, hAPP(c_Relation_Oconverse(_1581553, _1581551), _1581555)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1581551, tc_HOL_Obool)), _1581559))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581551, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1581553, _1581551, _1581555), _1581557)), _1581559)))], (40742 ^ _782652) ^ [_1581748, _1581750, _1581752] : [c_Relation_Orefl__on(_1581748, _1581750, _1581752), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1581748, _1581748), tc_HOL_Obool)), _1581752), hAPP(hAPP(c_Relation_Orel__comp(_1581748, _1581748, _1581748), hAPP(c_Relation_Oconverse(_1581748, _1581748), _1581752)), _1581752))))], (40748 ^ _782652) ^ [_1581887, _1581889, _1581891] : [hAPP(hAPP(c_Relation_Orel__comp(_1581887, _1581887, _1581887), hAPP(c_Relation_Oconverse(_1581887, _1581887), _1581889)), _1581889) = _1581889, hAPP(c_Relation_ODomain(_1581887, _1581887), _1581889) = _1581891, -(c_Equiv__Relations_Oequiv(_1581887, _1581891, _1581889))], (40758 ^ _782652) ^ [_1582066, _1582068] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1582066, _1582066)), _1582068)), c_Wellfounded_Oacyclic(_1582066, _1582068), -(c_Wellfounded_Owf(_1582066, hAPP(c_Relation_Oconverse(_1582066, _1582066), _1582068)))], (40768 ^ _782652) ^ [_1582221, _1582223, _1582225] : [-(hAPP(c_Relation_Oconverse(_1582221, _1582223), _1582225) = hAPP(c_Set_OCollect(tc_prod(_1582223, _1582221)), hAPP(c_Product__Type_Oprod_Oprod__case(_1582223, _1582221, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1582223, tc_fun(tc_prod(_1582221, _1582223), tc_HOL_Obool), tc_fun(_1582221, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582221, tc_fun(tc_fun(tc_prod(_1582221, _1582223), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1582221, _1582223), tc_HOL_Obool), tc_fun(_1582221, tc_HOL_Obool)), _1582223), c_COMBC(_1582221, tc_fun(tc_prod(_1582221, _1582223), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1582221, tc_prod(_1582221, _1582223)), tc_fun(_1582221, tc_fun(tc_fun(tc_prod(_1582221, _1582223), tc_HOL_Obool), tc_HOL_Obool)), _1582223), hAPP(c_COMBB(tc_prod(_1582221, _1582223), tc_fun(tc_fun(tc_prod(_1582221, _1582223), tc_HOL_Obool), tc_HOL_Obool), _1582221), c_member(tc_prod(_1582221, _1582223)))), hAPP(c_COMBC(_1582221, _1582223, tc_prod(_1582221, _1582223)), c_Product__Type_OPair(_1582221, _1582223))))), _1582225))))], (40770 ^ _782652) ^ [_1582397, _1582399, _1582401, _1582403, _1582405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582397, _1582397)), hAPP(hAPP(c_Product__Type_OPair(_1582397, _1582397), hAPP(_1582399, hAPP(c_Nat_OSuc, 40771 ^ [_1582397, _1582399, _1582401, _1582403, _1582405]))), hAPP(_1582399, 40771 ^ [_1582397, _1582399, _1582401, _1582403, _1582405]))), c_Transitive__Closure_Ortrancl(_1582397, _1582401))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582397, _1582397)), hAPP(hAPP(c_Product__Type_OPair(_1582397, _1582397), hAPP(_1582399, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1582403), _1582405))), hAPP(_1582399, _1582403))), c_Transitive__Closure_Ortrancl(_1582397, _1582401))))], (40777 ^ _782652) ^ [_1582708, _1582710, _1582712] : [c_Relation_Ototal__on(_1582708, _1582710, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1582708, _1582708), tc_HOL_Obool)), _1582712), c_Relation_OId(_1582708))), -(c_Relation_Ototal__on(_1582708, _1582710, _1582712))], (40783 ^ _782652) ^ [_1582819, _1582821, _1582823] : [c_Relation_Ototal__on(_1582819, _1582821, _1582823), -(c_Relation_Ototal__on(_1582819, _1582821, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1582819, _1582819), tc_HOL_Obool)), _1582823), c_Relation_OId(_1582819))))], (40789 ^ _782652) ^ [_1582936, _1582938] : [-(c_Relation_Ototal__on(_1582936, c_Orderings_Obot__class_Obot(tc_fun(_1582936, tc_HOL_Obool)), _1582938))], (40791 ^ _782652) ^ [_1582985, _1582987, _1582989] : [c_Relation_Ototal__on(_1582985, _1582987, hAPP(c_Relation_Oconverse(_1582985, _1582985), _1582989)), -(c_Relation_Ototal__on(_1582985, _1582987, _1582989))], (40797 ^ _782652) ^ [_1583076, _1583078, _1583080] : [c_Relation_Ototal__on(_1583076, _1583078, _1583080), -(c_Relation_Ototal__on(_1583076, _1583078, hAPP(c_Relation_Oconverse(_1583076, _1583076), _1583080)))], (40825 ^ _782652) ^ [_1583680, _1583682, _1583684] : [40827 ^ _782652 : [(40828 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1583680), 40826 ^ [_1583680, _1583682, _1583684]), _1583682)))], (40831 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1583680), 40829 ^ [_1583680, _1583682, _1583684]), _1583682)))], (40833 ^ _782652) ^ [] : [40826 ^ [_1583680, _1583682, _1583684] = 40829 ^ [_1583680, _1583682, _1583684]], (40835 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583680, _1583680)), hAPP(hAPP(c_Product__Type_OPair(_1583680, _1583680), 40826 ^ [_1583680, _1583682, _1583684]), 40829 ^ [_1583680, _1583682, _1583684])), _1583684))], (40837 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583680, _1583680)), hAPP(hAPP(c_Product__Type_OPair(_1583680, _1583680), 40829 ^ [_1583680, _1583682, _1583684]), 40826 ^ [_1583680, _1583682, _1583684])), _1583684))]], -(c_Relation_Ototal__on(_1583680, _1583682, _1583684))], (40803 ^ _782652) ^ [_1583191, _1583193, _1583195] : [c_Relation_Ototal__on(_1583191, _1583193, _1583195), 40806 ^ _782652 : [(40807 ^ _782652) ^ [_1583335] : [hBOOL(hAPP(hAPP(c_member(_1583191), _1583335), _1583193)), 40810 ^ _782652 : [(40811 ^ _782652) ^ [_1583475] : [hBOOL(hAPP(hAPP(c_member(_1583191), _1583475), _1583193)), -(_1583335 = _1583475), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583191, _1583191)), hAPP(hAPP(c_Product__Type_OPair(_1583191, _1583191), _1583335), _1583475)), _1583195))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583191, _1583191)), hAPP(hAPP(c_Product__Type_OPair(_1583191, _1583191), _1583475), _1583335)), _1583195)))]]]]], (40841 ^ _782652) ^ [_1584262, _1584264, _1584266] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584262, _1584262)), _1584264), c_Transitive__Closure_Ortrancl(_1584262, _1584266))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584262, _1584262)), _1584264), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1584262, _1584262), 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(_1584262, _1584262), tc_HOL_Obool), tc_fun(tc_prod(_1584262, _1584262), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1584262, _1584262), tc_HOL_Obool)), _1584266)))))], (40847 ^ _782652) ^ [_1584469, _1584471] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584469, _1584469)), hAPP(hAPP(c_Product__Type_OPair(_1584469, _1584469), 40848 ^ [_1584469, _1584471]), 40848 ^ [_1584469, _1584471])), c_Transitive__Closure_Otrancl(_1584469, _1584471)))), -(c_Wellfounded_Oacyclic(_1584469, _1584471))], (40854 ^ _782652) ^ [_1584541, _1584543, _1584545] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1584541, _1584541, _1584541), _1584543), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584541, _1584541), tc_HOL_Obool), _1584545), _1584543)) = hAPP(hAPP(c_Relation_Orel__comp(_1584541, _1584541, _1584541), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584541, _1584541), tc_HOL_Obool), _1584545), _1584543)), _1584543))], (40856 ^ _782652) ^ [_1584612, _1584614] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584612, _1584612), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1584614) = _1584614)], (40858 ^ _782652) ^ [_1584649, _1584651, _1584653, _1584655] : [-(hAPP(_1584649, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1584651, _1584651), _1584653), _1584649), _1584655)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1584651, _1584651), _1584653), _1584649), hAPP(_1584649, _1584655)))], (40860 ^ _782652) ^ [_1584708, _1584710, _1584712, _1584714] : [-(hAPP(hAPP(c_Nat_Ocompow(_1584708, _1584708), _1584710), hAPP(hAPP(c_Nat_Ocompow(_1584708, _1584708), _1584712), _1584714)) = hAPP(hAPP(c_Nat_Ocompow(_1584708, _1584708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1584712), _1584710)), _1584714))], (40862 ^ _782652) ^ [_1584770, _1584772, _1584774] : [c_Wellfounded_Owf(_1584770, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584770, _1584770), tc_HOL_Obool), _1584772), _1584774)), -(c_Wellfounded_Owf(_1584770, _1584774))], (40868 ^ _782652) ^ [_1584873, _1584875, _1584877, _1584879] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1584873, _1584875), tc_fun(_1584873, _1584875)), _1584877), c_Fun_Ocomp(_1584875, _1584875, _1584873, _1584879)) = c_Fun_Ocomp(_1584875, _1584875, _1584873, hAPP(hAPP(c_Nat_Ocompow(_1584875, _1584875), _1584877), _1584879)))], (40870 ^ _782652) ^ [_1584936, _1584938, _1584940, _1584942] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584936, _1584936)), _1584938), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584936, _1584936), tc_HOL_Obool), _1584940), _1584942))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584936, _1584936)), _1584938), c_Transitive__Closure_Ortrancl(_1584936, _1584942))))], (40876 ^ _782652) ^ [_1585105, _1585107, _1585109] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585105, _1585105)), _1585107), c_Transitive__Closure_Ortrancl(_1585105, _1585109))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585105, _1585105)), _1585107), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585105, _1585105), tc_HOL_Obool), 40879 ^ [_1585105, _1585107, _1585109]), _1585109))))], (40883 ^ _782652) ^ [_1585264, _1585266, _1585268] : [40884 ^ _782652 : [(40885 ^ _782652) ^ [_1585340] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585264, _1585264)), _1585266), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585264, _1585264), tc_HOL_Obool), _1585340), _1585268)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585264, _1585264)), _1585266), c_Transitive__Closure_Ortrancl(_1585264, _1585268))))], (40889 ^ _782652) ^ [_1585428, _1585430, _1585432] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585428, _1585428), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1585430)), _1585432) = hAPP(hAPP(c_Relation_Orel__comp(_1585428, _1585428, _1585428), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585428, _1585428), tc_HOL_Obool), _1585430), _1585432)), _1585432))], (40891 ^ _782652) ^ [_1585492, _1585494, _1585496, _1585498] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585492, _1585492), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1585494), _1585496)), _1585498) = hAPP(hAPP(c_Relation_Orel__comp(_1585492, _1585492, _1585492), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585492, _1585492), tc_HOL_Obool), _1585494), _1585498)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585492, _1585492), tc_HOL_Obool), _1585496), _1585498)))], (40893 ^ _782652) ^ [_1585573, _1585575] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585573, _1585573), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1585575) = c_Relation_OId(_1585573))], (40895 ^ _782652) ^ [_1585612, _1585614, _1585616, _1585618] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585612, _1585612)), hAPP(hAPP(c_Product__Type_OPair(_1585612, _1585612), _1585614), _1585616)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585612, _1585612), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1585618))), -(_1585614 = _1585616)], (40901 ^ _782652) ^ [_1585755, _1585757, _1585759] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585755, _1585755)), hAPP(hAPP(c_Product__Type_OPair(_1585755, _1585755), _1585757), _1585757)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585755, _1585755), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1585759))))], (40903 ^ _782652) ^ [_1585813, _1585815, _1585817, _1585819, _1585821, _1585823] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585813, _1585813)), hAPP(hAPP(c_Product__Type_OPair(_1585813, _1585813), _1585815), _1585817)), _1585819)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585813, _1585813)), hAPP(hAPP(c_Product__Type_OPair(_1585813, _1585813), _1585817), _1585821)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585813, _1585813), tc_HOL_Obool), _1585823), _1585819))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585813, _1585813)), hAPP(hAPP(c_Product__Type_OPair(_1585813, _1585813), _1585815), _1585821)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585813, _1585813), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1585823)), _1585819))))], (40913 ^ _782652) ^ [_1586126, _1586128, _1586130, _1586132, _1586134, _1586136] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586126, _1586126)), hAPP(hAPP(c_Product__Type_OPair(_1586126, _1586126), _1586128), _1586130)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586126, _1586126), tc_HOL_Obool), _1586132), _1586134))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586126, _1586126)), hAPP(hAPP(c_Product__Type_OPair(_1586126, _1586126), _1586130), _1586136)), _1586134)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586126, _1586126)), hAPP(hAPP(c_Product__Type_OPair(_1586126, _1586126), _1586128), _1586136)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586126, _1586126), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1586132)), _1586134))))], (40923 ^ _782652) ^ [_1586439, _1586441, _1586443] : [-(hAPP(hAPP(c_Nat_Ocompow(_1586439, _1586439), hAPP(c_Nat_OSuc, _1586441)), _1586443) = hAPP(c_Fun_Ocomp(_1586439, _1586439, _1586439, _1586443), hAPP(hAPP(c_Nat_Ocompow(_1586439, _1586439), _1586441), _1586443)))], (40925 ^ _782652) ^ [_1586495, _1586497, _1586499, _1586501] : [-(hAPP(hAPP(c_Nat_Ocompow(_1586495, _1586495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1586497), _1586499)), _1586501) = hAPP(c_Fun_Ocomp(_1586495, _1586495, _1586495, hAPP(hAPP(c_Nat_Ocompow(_1586495, _1586495), _1586497), _1586501)), hAPP(hAPP(c_Nat_Ocompow(_1586495, _1586495), _1586499), _1586501)))], (40927 ^ _782652) ^ [_1586565, _1586567] : [-(hAPP(hAPP(c_Nat_Ocompow(_1586565, _1586565), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1586567) = c_Fun_Oid(_1586565))], (40929 ^ _782652) ^ [_1586619, _1586621, _1586623] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586619, _1586619)), _1586621), c_Transitive__Closure_Otrancl(_1586619, _1586623))), 40933 ^ _782652 : [(40934 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 40932 ^ [_1586619, _1586621, _1586623])))], (40936 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586619, _1586619)), _1586621), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586619, _1586619), tc_HOL_Obool), 40932 ^ [_1586619, _1586621, _1586623]), _1586623))))]]], (40938 ^ _782652) ^ [_1586817, _1586819, _1586821] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586817, _1586817)), _1586819), c_Transitive__Closure_Otrancl(_1586817, _1586821)))), 40939 ^ _782652 : [(40940 ^ _782652) ^ [_1586896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1586896)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586817, _1586817)), _1586819), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586817, _1586817), tc_HOL_Obool), _1586896), _1586821)))]]], (40948 ^ _782652) ^ [_1587067, _1587069] : [-(c_Transitive__Closure_Ortrancl(_1587067, _1587069) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1587067, _1587067), 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(_1587067, _1587067), tc_HOL_Obool), tc_fun(tc_prod(_1587067, _1587067), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1587067, _1587067), tc_HOL_Obool)), _1587069)))], (40950 ^ _782652) ^ [_1587138] : [-(c_Nat_Ofunpow(_1587138) = c_Nat_Ocompow(_1587138, _1587138))], (40952 ^ _782652) ^ [_1587166, _1587168, _1587170, _1587172, _1587174] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587166, _1587166)), hAPP(hAPP(c_Product__Type_OPair(_1587166, _1587166), _1587168), _1587170)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587166, _1587166), tc_HOL_Obool), _1587172), _1587174))), 40957 ^ _782652 : [(40958 ^ _782652) ^ [] : [-(_1587172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40960 ^ _782652) ^ [] : [-(_1587168 = _1587170)]], 40963 ^ _782652 : [(40964 ^ _782652) ^ [] : [-(_1587172 = hAPP(c_Nat_OSuc, 40962 ^ [_1587166, _1587168, _1587170, _1587172, _1587174]))], (40966 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587166, _1587166)), hAPP(hAPP(c_Product__Type_OPair(_1587166, _1587166), _1587168), 40961 ^ [_1587166, _1587168, _1587170, _1587172, _1587174])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587166, _1587166), tc_HOL_Obool), 40962 ^ [_1587166, _1587168, _1587170, _1587172, _1587174]), _1587174))))], (40968 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587166, _1587166)), hAPP(hAPP(c_Product__Type_OPair(_1587166, _1587166), 40961 ^ [_1587166, _1587168, _1587170, _1587172, _1587174]), _1587170)), _1587174)))]]], (40970 ^ _782652) ^ [_1587608, _1587610, _1587612, _1587614, _1587616] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587608, _1587608)), hAPP(hAPP(c_Product__Type_OPair(_1587608, _1587608), _1587610), _1587612)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587608, _1587608), tc_HOL_Obool), _1587614), _1587616))), 40975 ^ _782652 : [(40976 ^ _782652) ^ [] : [-(_1587614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40978 ^ _782652) ^ [] : [-(_1587610 = _1587612)]], 40981 ^ _782652 : [(40982 ^ _782652) ^ [] : [-(_1587614 = hAPP(c_Nat_OSuc, 40980 ^ [_1587608, _1587610, _1587612, _1587614, _1587616]))], (40984 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587608, _1587608)), hAPP(hAPP(c_Product__Type_OPair(_1587608, _1587608), _1587610), 40979 ^ [_1587608, _1587610, _1587612, _1587614, _1587616])), _1587616)))], (40986 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587608, _1587608)), hAPP(hAPP(c_Product__Type_OPair(_1587608, _1587608), 40979 ^ [_1587608, _1587610, _1587612, _1587614, _1587616]), _1587612)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587608, _1587608), tc_HOL_Obool), 40980 ^ [_1587608, _1587610, _1587612, _1587614, _1587616]), _1587616))))]]], (40988 ^ _782652) ^ [_1588050, _1588052, _1588054, _1588056, _1588058] : [c_Relation_Osingle__valued(_1588050, _1588052, hAPP(c_Relation_Oconverse(_1588052, _1588050), _1588054)), -(hAPP(c_Relation_OImage(_1588052, _1588050, _1588054), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1588052, tc_HOL_Obool)), _1588056), _1588058)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1588050, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1588052, _1588050, _1588054), _1588056)), hAPP(c_Relation_OImage(_1588052, _1588050, _1588054), _1588058)))], (40994 ^ _782652) ^ [_1588233, _1588235, _1588237] : [c_Relation_Osingle__valued(_1588233, _1588233, _1588235), -(c_Relation_Osingle__valued(_1588233, _1588233, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588233, _1588233), tc_HOL_Obool), _1588237), _1588235)))], (41000 ^ _782652) ^ [_1588340] : [-(c_Relation_Osingle__valued(_1588340, _1588340, c_Relation_OId(_1588340)))], (41002 ^ _782652) ^ [_1588366, _1588368, _1588370, _1588372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588366, _1588368), tc_HOL_Obool)), _1588370), _1588372)), c_Relation_Osingle__valued(_1588366, _1588368, _1588372), -(c_Relation_Osingle__valued(_1588366, _1588368, _1588370))], (41012 ^ _782652) ^ [_1588533, _1588535, _1588537, _1588539, _1588541] : [c_Relation_Osingle__valued(_1588533, _1588535, _1588537), c_Relation_Osingle__valued(_1588535, _1588539, _1588541), -(c_Relation_Osingle__valued(_1588533, _1588539, hAPP(hAPP(c_Relation_Orel__comp(_1588533, _1588535, _1588539), _1588537), _1588541)))], (41022 ^ _782652) ^ [_1588700, _1588702] : [-(c_Relation_Osingle__valued(_1588700, _1588700, c_Relation_OId__on(_1588700, _1588702)))], (41024 ^ _782652) ^ [_1588729, _1588731, _1588733, _1588735, _1588737, _1588739] : [c_Relation_Osingle__valued(_1588729, _1588731, _1588733), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588729, _1588731)), hAPP(hAPP(c_Product__Type_OPair(_1588729, _1588731), _1588735), _1588737)), _1588733)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588729, _1588731)), hAPP(hAPP(c_Product__Type_OPair(_1588729, _1588731), _1588735), _1588739)), _1588733)), -(_1588737 = _1588739)], (41052 ^ _782652) ^ [_1589404, _1589406, _1589408] : [41055 ^ _782652 : [(41056 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589404, _1589406)), hAPP(hAPP(c_Product__Type_OPair(_1589404, _1589406), 41053 ^ [_1589404, _1589406, _1589408]), 41054 ^ [_1589404, _1589406, _1589408])), _1589408)))], (41059 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589404, _1589406)), hAPP(hAPP(c_Product__Type_OPair(_1589404, _1589406), 41053 ^ [_1589404, _1589406, _1589408]), 41057 ^ [_1589404, _1589406, _1589408])), _1589408)))], (41061 ^ _782652) ^ [] : [41054 ^ [_1589404, _1589406, _1589408] = 41057 ^ [_1589404, _1589406, _1589408]]], -(c_Relation_Osingle__valued(_1589404, _1589406, _1589408))], (41038 ^ _782652) ^ [_1589030, _1589032, _1589034] : [c_Relation_Osingle__valued(_1589030, _1589032, _1589034), 41041 ^ _782652 : [(41042 ^ _782652) ^ [_1589151, _1589153] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589030, _1589032)), hAPP(hAPP(c_Product__Type_OPair(_1589030, _1589032), _1589153), _1589151)), _1589034)), 41045 ^ _782652 : [(41046 ^ _782652) ^ [_1589277] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589030, _1589032)), hAPP(hAPP(c_Product__Type_OPair(_1589030, _1589032), _1589153), _1589277)), _1589034)), -(_1589151 = _1589277)]]]]], (41065 ^ _782652) ^ [_1589774, _1589776, _1589778, _1589780, _1589782] : [c_Relation_Osingle__valued(_1589774, _1589774, _1589776), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589774, _1589774)), hAPP(hAPP(c_Product__Type_OPair(_1589774, _1589774), _1589778), _1589780)), c_Transitive__Closure_Ortrancl(_1589774, _1589776))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589774, _1589774)), hAPP(hAPP(c_Product__Type_OPair(_1589774, _1589774), _1589778), _1589782)), c_Transitive__Closure_Ortrancl(_1589774, _1589776))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589774, _1589774)), hAPP(hAPP(c_Product__Type_OPair(_1589774, _1589774), _1589780), _1589782)), c_Transitive__Closure_Ortrancl(_1589774, _1589776)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589774, _1589774)), hAPP(hAPP(c_Product__Type_OPair(_1589774, _1589774), _1589782), _1589780)), c_Transitive__Closure_Ortrancl(_1589774, _1589776))))], (41083 ^ _782652) ^ [_1590164, _1590166, _1590168, _1590170, _1590172] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590164, _1590164)), hAPP(hAPP(c_Product__Type_OPair(_1590164, _1590164), _1590166), _1590168)), c_Transitive__Closure_Ortrancl(_1590164, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1590164, _1590164), tc_HOL_Obool)), _1590170), _1590172)))), 41089 ^ _782652 : [(41090 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590164, _1590164)), hAPP(hAPP(c_Product__Type_OPair(_1590164, _1590164), 41088 ^ [_1590164, _1590166, _1590168, _1590170, _1590172]), _1590168)), c_Transitive__Closure_Ortrancl(_1590164, _1590170))))], (41093 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590164, _1590164)), hAPP(hAPP(c_Product__Type_OPair(_1590164, _1590164), 41091 ^ [_1590164, _1590166, _1590168, _1590170, _1590172]), 41088 ^ [_1590164, _1590166, _1590168, _1590170, _1590172])), _1590172)))], (41095 ^ _782652) ^ [] : [41091 ^ [_1590164, _1590166, _1590168, _1590170, _1590172] = 41088 ^ [_1590164, _1590166, _1590168, _1590170, _1590172]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590164, _1590164)), hAPP(hAPP(c_Product__Type_OPair(_1590164, _1590164), _1590166), _1590168)), c_Transitive__Closure_Ortrancl(_1590164, _1590170))))], (41099 ^ _782652) ^ [_1590723, _1590725, _1590727, _1590729, _1590731] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590723, _1590723)), hAPP(hAPP(c_Product__Type_OPair(_1590723, _1590723), _1590725), _1590727)), c_Transitive__Closure_Ortrancl(_1590723, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1590723, _1590723), tc_HOL_Obool)), _1590729), _1590731)))), 41105 ^ _782652 : [(41106 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590723, _1590723)), hAPP(hAPP(c_Product__Type_OPair(_1590723, _1590723), _1590725), 41104 ^ [_1590723, _1590725, _1590727, _1590729, _1590731])), c_Transitive__Closure_Ortrancl(_1590723, _1590729))))], (41109 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590723, _1590723)), hAPP(hAPP(c_Product__Type_OPair(_1590723, _1590723), 41104 ^ [_1590723, _1590725, _1590727, _1590729, _1590731]), 41107 ^ [_1590723, _1590725, _1590727, _1590729, _1590731])), _1590731)))], (41111 ^ _782652) ^ [] : [41104 ^ [_1590723, _1590725, _1590727, _1590729, _1590731] = 41107 ^ [_1590723, _1590725, _1590727, _1590729, _1590731]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590723, _1590723)), hAPP(hAPP(c_Product__Type_OPair(_1590723, _1590723), _1590725), _1590727)), c_Transitive__Closure_Ortrancl(_1590723, _1590729))))], (41115 ^ _782652) ^ [_1591282, _1591284, _1591286, _1591288, _1591290] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591282, _1591282)), hAPP(hAPP(c_Product__Type_OPair(_1591282, _1591282), _1591284), _1591286)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591282, _1591282), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1591288)), _1591290))), 41119 ^ _782652 : [(41120 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591282, _1591282)), hAPP(hAPP(c_Product__Type_OPair(_1591282, _1591282), _1591284), 41118 ^ [_1591282, _1591284, _1591286, _1591288, _1591290])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591282, _1591282), tc_HOL_Obool), _1591288), _1591290))))], (41122 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591282, _1591282)), hAPP(hAPP(c_Product__Type_OPair(_1591282, _1591282), 41118 ^ [_1591282, _1591284, _1591286, _1591288, _1591290]), _1591286)), _1591290)))]]], (41124 ^ _782652) ^ [_1591594, _1591596, _1591598, _1591600, _1591602] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591594, _1591594)), hAPP(hAPP(c_Product__Type_OPair(_1591594, _1591594), _1591596), _1591598)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591594, _1591594), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1591600)), _1591602))), 41128 ^ _782652 : [(41129 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591594, _1591594)), hAPP(hAPP(c_Product__Type_OPair(_1591594, _1591594), _1591596), 41127 ^ [_1591594, _1591596, _1591598, _1591600, _1591602])), _1591602)))], (41131 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591594, _1591594)), hAPP(hAPP(c_Product__Type_OPair(_1591594, _1591594), 41127 ^ [_1591594, _1591596, _1591598, _1591600, _1591602]), _1591598)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591594, _1591594), tc_HOL_Obool), _1591600), _1591602))))]]], (41133 ^ _782652) ^ [_1591906, _1591908, _1591910, _1591912, _1591914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591906, _1591906)), hAPP(hAPP(c_Product__Type_OPair(_1591906, _1591906), _1591908), _1591910)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591906, _1591906), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1591912)), _1591914))), 41137 ^ _782652 : [(41138 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591906, _1591906)), hAPP(hAPP(c_Product__Type_OPair(_1591906, _1591906), _1591908), 41136 ^ [_1591906, _1591908, _1591910, _1591912, _1591914])), _1591914)))], (41140 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591906, _1591906)), hAPP(hAPP(c_Product__Type_OPair(_1591906, _1591906), 41136 ^ [_1591906, _1591908, _1591910, _1591912, _1591914]), _1591910)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591906, _1591906), tc_HOL_Obool), _1591912), _1591914))))]]], (41142 ^ _782652) ^ [_1592214, _1592216, _1592218, _1592220] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592214, _1592214)), hAPP(hAPP(c_Product__Type_OPair(_1592214, _1592214), _1592216), _1592218)), c_Transitive__Closure_Otrancl(_1592214, _1592220))), 41146 ^ _782652 : [(41147 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592214, _1592214)), hAPP(hAPP(c_Product__Type_OPair(_1592214, _1592214), _1592216), 41145 ^ [_1592214, _1592216, _1592218, _1592220])), _1592220)))], (41149 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592214, _1592214)), hAPP(hAPP(c_Product__Type_OPair(_1592214, _1592214), 41145 ^ [_1592214, _1592216, _1592218, _1592220]), _1592218)), c_Transitive__Closure_Ortrancl(_1592214, _1592220))))]]], (41151 ^ _782652) ^ [_1592474, _1592476, _1592478, _1592480] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592474, _1592474)), hAPP(hAPP(c_Product__Type_OPair(_1592474, _1592474), _1592476), _1592478)), c_Transitive__Closure_Otrancl(_1592474, _1592480))), 41155 ^ _782652 : [(41156 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592474, _1592474)), hAPP(hAPP(c_Product__Type_OPair(_1592474, _1592474), _1592476), 41154 ^ [_1592474, _1592476, _1592478, _1592480])), c_Transitive__Closure_Ortrancl(_1592474, _1592480))))], (41158 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592474, _1592474)), hAPP(hAPP(c_Product__Type_OPair(_1592474, _1592474), 41154 ^ [_1592474, _1592476, _1592478, _1592480]), _1592478)), _1592480)))]]], (41160 ^ _782652) ^ [_1592734, _1592736] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592734, _1592734)), _1592736), c_Relation_OId(_1592734))), -(_1592736 = hAPP(hAPP(c_Product__Type_OPair(_1592734, _1592734), 41163 ^ [_1592734, _1592736]), 41163 ^ [_1592734, _1592736]))], (41167 ^ _782652) ^ [_1592876, _1592878, _1592880, _1592882] : [41169 ^ _782652 : [(41170 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1592876), 41168 ^ [_1592876, _1592878, _1592880, _1592882])))], (41172 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41168 ^ [_1592876, _1592878, _1592880, _1592882]), _1592878)))], (41174 ^ _782652) ^ [] : [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(_1592880, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 41168 ^ [_1592876, _1592878, _1592880, _1592882]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1592880, 41168 ^ [_1592876, _1592878, _1592880, _1592882])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1592876), _1592878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1592880, _1592876)), _1592882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1592882), hAPP(_1592880, _1592878))), 41188 ^ _782652 : [(41189 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1592876), 41187 ^ [_1592876, _1592878, _1592880, _1592882])))], (41191 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41187 ^ [_1592876, _1592878, _1592880, _1592882]), _1592878)))], (41193 ^ _782652) ^ [] : [-(hAPP(_1592880, 41187 ^ [_1592876, _1592878, _1592880, _1592882]) = _1592882)]]], (41195 ^ _782652) ^ [_1593502, _1593504, _1593506] : [class_Divides_Osemiring__div(_1593502), -(_1593504 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1593502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1593502), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1593502), _1593504), _1593506)), _1593506)), c_Divides_Odiv__class_Omod(_1593502, _1593504, _1593506)))], (41201 ^ _782652) ^ [_1593635, _1593637, _1593639] : [class_Orderings_Olinorder(_1593635), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593635), _1593637)), -(hBOOL(hAPP(hAPP(c_member(_1593635), _1593639), _1593637))), -(c_Big__Operators_Olattice_OSup__fin(_1593635, c_Orderings_Oord__class_Omax(_1593635), hAPP(hAPP(c_Set_Oinsert(_1593635), _1593639), _1593637)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593635, _1593635, c_Orderings_Oord__class_Omax(_1593635)), _1593639), _1593637))], (41215 ^ _782652) ^ [_1593855, _1593857, _1593859] : [class_Orderings_Olinorder(_1593855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593855), _1593857)), -(hBOOL(hAPP(hAPP(c_member(_1593855), _1593859), _1593857))), -(c_Big__Operators_Olattice_OInf__fin(_1593855, c_Orderings_Oord__class_Omin(_1593855), hAPP(hAPP(c_Set_Oinsert(_1593855), _1593859), _1593857)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593855, _1593855, c_Orderings_Oord__class_Omin(_1593855)), _1593859), _1593857))], (41229 ^ _782652) ^ [_1594075, _1594077, _1594079, _1594081, _1594083, _1594085] : [c_Finite__Set_Ofolding(_1594075, _1594077, _1594079, _1594081), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594075), _1594083)), -(hAPP(hAPP(_1594081, _1594083), _1594085) = hAPP(hAPP(c_Finite__Set_Ofold(_1594075, _1594077, _1594079), _1594085), _1594083))], (41239 ^ _782652) ^ [_1594264, _1594266, _1594268, _1594270] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1594264, _1594266, _1594268), _1594270), c_Orderings_Obot__class_Obot(tc_fun(_1594264, tc_HOL_Obool))) = _1594270)], (41241 ^ _782652) ^ [_1594308, _1594310, _1594312, _1594314] : [-(hAPP(c_Finite__Set_Ofold__image(_1594308, _1594310, _1594312), _1594314) = c_Finite__Set_Ofold(_1594310, _1594308, hAPP(hAPP(c_COMBB(_1594308, tc_fun(_1594308, _1594308), _1594310), _1594312), _1594314)))], (41243 ^ _782652) ^ [_1594361, _1594363, _1594365, _1594367, _1594369] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1594361, _1594363, _1594365), _1594367), _1594369) = c_HOL_OThe(_1594363, c_Finite__Set_Ofold__graph(_1594361, _1594363, _1594365, _1594367, _1594369)))], (41245 ^ _782652) ^ [_1594411, _1594413, _1594415] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1594411), _1594413)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1594411, tc_HOL_Obool)), _1594413), _1594415) = hAPP(hAPP(c_Finite__Set_Ofold(_1594411, tc_fun(_1594411, tc_HOL_Obool), c_Set_Oinsert(_1594411)), _1594415), _1594413))], (41251 ^ _782652) ^ [_1594550, _1594552, _1594554, _1594556] : [class_Lattices_Osemilattice__sup(_1594550), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594550), _1594552)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594550, _1594550, c_Lattices_Osemilattice__sup__class_Osup(_1594550)), _1594554), hAPP(hAPP(c_Set_Oinsert(_1594550), _1594556), _1594552)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1594550), _1594556), hAPP(hAPP(c_Finite__Set_Ofold(_1594550, _1594550, c_Lattices_Osemilattice__sup__class_Osup(_1594550)), _1594554), _1594552)))], (41261 ^ _782652) ^ [_1594773, _1594775, _1594777, _1594779] : [class_Lattices_Osemilattice__inf(_1594773), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594773), _1594775)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594773, _1594773, c_Lattices_Osemilattice__inf__class_Oinf(_1594773)), _1594777), hAPP(hAPP(c_Set_Oinsert(_1594773), _1594779), _1594775)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1594773), _1594779), hAPP(hAPP(c_Finite__Set_Ofold(_1594773, _1594773, c_Lattices_Osemilattice__inf__class_Oinf(_1594773)), _1594777), _1594775)))], (41271 ^ _782652) ^ [_1594996, _1594998, _1595000, _1595002] : [class_Orderings_Olinorder(_1594996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594996), _1594998)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1594996, _1594996, c_Orderings_Oord__class_Omin(_1594996)), _1595000), hAPP(hAPP(c_Set_Oinsert(_1594996), _1595002), _1594998)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1594996), _1595002), hAPP(hAPP(c_Finite__Set_Ofold(_1594996, _1594996, c_Orderings_Oord__class_Omin(_1594996)), _1595000), _1594998)))], (41281 ^ _782652) ^ [_1595219, _1595221, _1595223, _1595225] : [class_Orderings_Olinorder(_1595219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595219), _1595221)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1595219, _1595219, c_Orderings_Oord__class_Omax(_1595219)), _1595223), hAPP(hAPP(c_Set_Oinsert(_1595219), _1595225), _1595221)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1595219), _1595225), hAPP(hAPP(c_Finite__Set_Ofold(_1595219, _1595219, c_Orderings_Oord__class_Omax(_1595219)), _1595223), _1595221)))], (41291 ^ _782652) ^ [_1595442, _1595444, _1595446, _1595448, _1595450, _1595452] : [c_Finite__Set_Ofun__left__comm__idem(_1595442, _1595444, _1595446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595442), _1595448)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1595442, _1595444, _1595446), _1595450), hAPP(hAPP(c_Set_Oinsert(_1595442), _1595452), _1595448)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595442, _1595444, _1595446), hAPP(hAPP(_1595446, _1595452), _1595450)), _1595448))], (41301 ^ _782652) ^ [_1595665, _1595667, _1595669, _1595671, _1595673, _1595675] : [c_Finite__Set_Ofun__left__comm__idem(_1595665, _1595667, _1595669), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595665), _1595671)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1595665, _1595667, _1595669), _1595673), hAPP(hAPP(c_Set_Oinsert(_1595665), _1595675), _1595671)) = hAPP(hAPP(_1595669, _1595675), hAPP(hAPP(c_Finite__Set_Ofold(_1595665, _1595667, _1595669), _1595673), _1595671)))], (41311 ^ _782652) ^ [_1595888, _1595890, _1595892, _1595894, _1595896] : [class_Complete__Lattice_Ocomplete__lattice(_1595888), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595890), _1595892)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1595888), _1595894), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1595890, _1595888), _1595892), _1595896)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595890, _1595888, hAPP(hAPP(c_COMBB(_1595888, tc_fun(_1595888, _1595888), _1595890), c_Lattices_Osemilattice__sup__class_Osup(_1595888)), _1595896)), _1595894), _1595892))], (41321 ^ _782652) ^ [_1596119, _1596121, _1596123, _1596125, _1596127] : [c_Finite__Set_Ofolding__one__idem(_1596119, _1596121, _1596123), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596119), _1596125)), -(hAPP(_1596123, hAPP(hAPP(c_Set_Oinsert(_1596119), _1596127), _1596125)) = hAPP(hAPP(c_Finite__Set_Ofold(_1596119, _1596119, _1596121), _1596127), _1596125))], (41331 ^ _782652) ^ [_1596312, _1596314, _1596316, _1596318] : [class_Lattices_Osemilattice__sup(_1596312), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596312), _1596314)), hBOOL(hAPP(hAPP(c_member(_1596312), _1596316), _1596314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596312), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1596312), _1596316), _1596318)), hAPP(hAPP(c_Finite__Set_Ofold(_1596312, _1596312, c_Lattices_Osemilattice__sup__class_Osup(_1596312)), _1596318), _1596314))))], (41345 ^ _782652) ^ [_1596579, _1596581, _1596583, _1596585] : [class_Lattices_Osemilattice__inf(_1596579), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596579), _1596581)), hBOOL(hAPP(hAPP(c_member(_1596579), _1596583), _1596581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596579), hAPP(hAPP(c_Finite__Set_Ofold(_1596579, _1596579, c_Lattices_Osemilattice__inf__class_Oinf(_1596579)), _1596585), _1596581)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1596579), _1596583), _1596585))))], (41359 ^ _782652) ^ [_1596846, _1596848, _1596850, _1596852] : [class_Orderings_Olinorder(_1596846), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596846), _1596848)), hBOOL(hAPP(hAPP(c_member(_1596846), _1596850), _1596848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1596846), hAPP(hAPP(c_Finite__Set_Ofold(_1596846, _1596846, c_Orderings_Oord__class_Omin(_1596846)), _1596852), _1596848)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1596846), _1596850), _1596852))))], (41373 ^ _782652) ^ [_1597113, _1597115, _1597117, _1597119] : [class_Orderings_Olinorder(_1597113), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597113), _1597115)), hBOOL(hAPP(hAPP(c_member(_1597113), _1597117), _1597115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1597113), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1597113), _1597117), _1597119)), hAPP(hAPP(c_Finite__Set_Ofold(_1597113, _1597113, c_Orderings_Oord__class_Omax(_1597113)), _1597119), _1597115))))], (41387 ^ _782652) ^ [_1597380, _1597382, _1597384] : [class_Lattices_Oab__semigroup__idem__mult(_1597380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597380), _1597382)), -(hAPP(c_Finite__Set_Ofold1(_1597380, c_Groups_Otimes__class_Otimes(_1597380)), hAPP(hAPP(c_Set_Oinsert(_1597380), _1597384), _1597382)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597380, _1597380, c_Groups_Otimes__class_Otimes(_1597380)), _1597384), _1597382))], (41397 ^ _782652) ^ [_1597575, _1597577, _1597579] : [class_Lattices_Olattice(_1597575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597575), _1597577)), -(c_Big__Operators_Olattice__class_OSup__fin(_1597575, hAPP(hAPP(c_Set_Oinsert(_1597575), _1597579), _1597577)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597575, _1597575, c_Lattices_Osemilattice__sup__class_Osup(_1597575)), _1597579), _1597577))], (41407 ^ _782652) ^ [_1597760, _1597762, _1597764] : [class_Lattices_Olattice(_1597760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597760), _1597762)), -(c_Big__Operators_Olattice__class_OInf__fin(_1597760, hAPP(hAPP(c_Set_Oinsert(_1597760), _1597764), _1597762)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597760, _1597760, c_Lattices_Osemilattice__inf__class_Oinf(_1597760)), _1597764), _1597762))], (41417 ^ _782652) ^ [_1597945, _1597947, _1597949] : [class_Orderings_Olinorder(_1597945), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597945), _1597947)), -(c_Big__Operators_Olinorder__class_OMin(_1597945, hAPP(hAPP(c_Set_Oinsert(_1597945), _1597949), _1597947)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597945, _1597945, c_Orderings_Oord__class_Omin(_1597945)), _1597949), _1597947))], (41427 ^ _782652) ^ [_1598130, _1598132, _1598134] : [class_Orderings_Olinorder(_1598130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598130), _1598132)), -(c_Big__Operators_Olinorder__class_OMax(_1598130, hAPP(hAPP(c_Set_Oinsert(_1598130), _1598134), _1598132)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598130, _1598130, c_Orderings_Oord__class_Omax(_1598130)), _1598134), _1598132))], (41437 ^ _782652) ^ [_1598315, _1598317, _1598319] : [class_Orderings_Olinorder(_1598315), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598315), _1598317)), -(c_Big__Operators_Olattice_OInf__fin(_1598315, c_Orderings_Oord__class_Omin(_1598315), hAPP(hAPP(c_Set_Oinsert(_1598315), _1598319), _1598317)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598315, _1598315, c_Orderings_Oord__class_Omin(_1598315)), _1598319), _1598317))], (41447 ^ _782652) ^ [_1598506, _1598508, _1598510] : [class_Orderings_Olinorder(_1598506), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598506), _1598508)), -(c_Big__Operators_Olattice_OSup__fin(_1598506, c_Orderings_Oord__class_Omax(_1598506), hAPP(hAPP(c_Set_Oinsert(_1598506), _1598510), _1598508)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598506, _1598506, c_Orderings_Oord__class_Omax(_1598506)), _1598510), _1598508))], (41457 ^ _782652) ^ [_1598697, _1598699, _1598701] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1598697), _1598699)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1598697, tc_HOL_Obool)), _1598701), _1598699) = hAPP(hAPP(c_Finite__Set_Ofold(_1598697, tc_fun(_1598697, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1598697, tc_HOL_Obool), tc_fun(tc_fun(_1598697, tc_HOL_Obool), tc_fun(_1598697, tc_HOL_Obool)), _1598697), hAPP(c_COMBC(tc_fun(_1598697, tc_HOL_Obool), tc_fun(_1598697, tc_HOL_Obool), tc_fun(_1598697, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1598697, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1598697, tc_fun(_1598697, tc_HOL_Obool), tc_fun(_1598697, tc_HOL_Obool)), c_Set_Oinsert(_1598697)), c_Orderings_Obot__class_Obot(tc_fun(_1598697, tc_HOL_Obool))))), _1598701), _1598699))], (41463 ^ _782652) ^ [_1598964, _1598966, _1598968, _1598970, _1598972] : [c_Finite__Set_Ofolding__one(_1598964, _1598966, _1598968), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598964), _1598970)), -(hBOOL(hAPP(hAPP(c_member(_1598964), _1598972), _1598970))), -(hAPP(_1598968, hAPP(hAPP(c_Set_Oinsert(_1598964), _1598972), _1598970)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598964, _1598964, _1598966), _1598972), _1598970))], (41477 ^ _782652) ^ [_1599186, _1599188, _1599190, _1599192] : [class_Complete__Lattice_Ocomplete__lattice(_1599186), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599188), _1599190)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1599188, _1599186), _1599190), _1599192) = hAPP(hAPP(c_Finite__Set_Ofold(_1599188, _1599186, hAPP(hAPP(c_COMBB(_1599186, tc_fun(_1599186, _1599186), _1599188), c_Lattices_Osemilattice__sup__class_Osup(_1599186)), _1599192)), c_Orderings_Obot__class_Obot(_1599186)), _1599190))], (41487 ^ _782652) ^ [_1599401, _1599403, _1599405] : [class_Groups_Oab__semigroup__mult(_1599401), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599401), _1599403)), -(hBOOL(hAPP(hAPP(c_member(_1599401), _1599405), _1599403))), -(hAPP(c_Finite__Set_Ofold1(_1599401, c_Groups_Otimes__class_Otimes(_1599401)), hAPP(hAPP(c_Set_Oinsert(_1599401), _1599405), _1599403)) = hAPP(hAPP(c_Finite__Set_Ofold(_1599401, _1599401, c_Groups_Otimes__class_Otimes(_1599401)), _1599405), _1599403))], (41501 ^ _782652) ^ [_1599625, _1599627, _1599629] : [class_Lattices_Olattice(_1599625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599625), _1599627)), -(hBOOL(hAPP(hAPP(c_member(_1599625), _1599629), _1599627))), -(c_Big__Operators_Olattice__class_OSup__fin(_1599625, hAPP(hAPP(c_Set_Oinsert(_1599625), _1599629), _1599627)) = hAPP(hAPP(c_Finite__Set_Ofold(_1599625, _1599625, c_Lattices_Osemilattice__sup__class_Osup(_1599625)), _1599629), _1599627))], (41515 ^ _782652) ^ [_1599839, _1599841, _1599843] : [class_Lattices_Olattice(_1599839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599839), _1599841)), -(hBOOL(hAPP(hAPP(c_member(_1599839), _1599843), _1599841))), -(c_Big__Operators_Olattice__class_OInf__fin(_1599839, hAPP(hAPP(c_Set_Oinsert(_1599839), _1599843), _1599841)) = hAPP(hAPP(c_Finite__Set_Ofold(_1599839, _1599839, c_Lattices_Osemilattice__inf__class_Oinf(_1599839)), _1599843), _1599841))], (41529 ^ _782652) ^ [_1600053, _1600055, _1600057] : [class_Orderings_Olinorder(_1600053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600053), _1600055)), -(hBOOL(hAPP(hAPP(c_member(_1600053), _1600057), _1600055))), -(c_Big__Operators_Olinorder__class_OMin(_1600053, hAPP(hAPP(c_Set_Oinsert(_1600053), _1600057), _1600055)) = hAPP(hAPP(c_Finite__Set_Ofold(_1600053, _1600053, c_Orderings_Oord__class_Omin(_1600053)), _1600057), _1600055))], (41543 ^ _782652) ^ [_1600267, _1600269, _1600271] : [class_Orderings_Olinorder(_1600267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600267), _1600269)), -(hBOOL(hAPP(hAPP(c_member(_1600267), _1600271), _1600269))), -(c_Big__Operators_Olinorder__class_OMax(_1600267, hAPP(hAPP(c_Set_Oinsert(_1600267), _1600271), _1600269)) = hAPP(hAPP(c_Finite__Set_Ofold(_1600267, _1600267, c_Orderings_Oord__class_Omax(_1600267)), _1600271), _1600269))], (41557 ^ _782652) ^ [_1600481, _1600483, _1600485, _1600487, _1600489, _1600491] : [c_Finite__Set_Ofun__left__comm(_1600481, _1600483, _1600485), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600481), _1600487)), hBOOL(hAPP(hAPP(c_member(_1600481), _1600489), _1600487)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1600481, _1600483, _1600485), _1600491), _1600487) = hAPP(hAPP(_1600485, _1600489), hAPP(hAPP(c_Finite__Set_Ofold(_1600481, _1600483, _1600485), _1600491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1600481, tc_HOL_Obool)), _1600487), hAPP(hAPP(c_Set_Oinsert(_1600481), _1600489), c_Orderings_Obot__class_Obot(tc_fun(_1600481, tc_HOL_Obool)))))))], (41571 ^ _782652) ^ [_1600810, _1600812, _1600814, _1600816, _1600818, _1600820] : [c_Finite__Set_Ofun__left__comm(_1600810, _1600812, _1600814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600810), _1600816)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1600810, _1600812, _1600814), _1600818), hAPP(hAPP(c_Set_Oinsert(_1600810), _1600820), _1600816)) = hAPP(hAPP(_1600814, _1600820), hAPP(hAPP(c_Finite__Set_Ofold(_1600810, _1600812, _1600814), _1600818), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1600810, tc_HOL_Obool)), _1600816), hAPP(hAPP(c_Set_Oinsert(_1600810), _1600820), c_Orderings_Obot__class_Obot(tc_fun(_1600810, tc_HOL_Obool)))))))], (41581 ^ _782652) ^ [_1601081, _1601083, _1601085, _1601087, _1601089] : [c_Finite__Set_Ofun__left__comm(_1601081, _1601083, _1601085), -(hAPP(c_Fun_Ocomp(_1601083, _1601083, _1601083, hAPP(_1601085, _1601087)), hAPP(_1601085, _1601089)) = hAPP(c_Fun_Ocomp(_1601083, _1601083, _1601083, hAPP(_1601085, _1601089)), hAPP(_1601085, _1601087)))], (41587 ^ _782652) ^ [_1601222] : [class_Groups_Oab__semigroup__mult(_1601222), -(c_Finite__Set_Ofun__left__comm(_1601222, _1601222, c_Groups_Otimes__class_Otimes(_1601222)))], (41593 ^ _782652) ^ [_1601301, _1601303, _1601305, _1601307, _1601309, _1601311] : [c_Finite__Set_Ofun__left__comm(_1601301, _1601303, _1601305), -(hAPP(hAPP(_1601305, _1601307), hAPP(hAPP(_1601305, _1601309), _1601311)) = hAPP(hAPP(_1601305, _1601309), hAPP(hAPP(_1601305, _1601307), _1601311)))], (41599 ^ _782652) ^ [_1601436, _1601438, _1601440, _1601442, _1601444] : [c_Finite__Set_Ofun__left__comm(_1601436, _1601438, _1601440), -(c_Finite__Set_Ofun__left__comm(_1601442, _1601438, hAPP(hAPP(c_COMBB(_1601436, tc_fun(_1601438, _1601438), _1601442), _1601440), _1601444)))], (41605 ^ _782652) ^ [_1601549, _1601551, _1601553, _1601555, _1601557, _1601559, _1601561] : [c_Finite__Set_Ofun__left__comm(_1601549, _1601551, _1601553), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1601549, _1601551, _1601553, _1601555, _1601557), _1601559)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1601549, _1601551, _1601553, _1601555, _1601557), _1601561)), -(_1601561 = _1601559)], (41619 ^ _782652) ^ [_1601794, _1601796, _1601798, _1601800, _1601802, _1601804] : [c_Finite__Set_Ofun__left__comm(_1601794, _1601796, _1601798), hBOOL(hAPP(c_Finite__Set_Ofinite(_1601794), _1601800)), -(hAPP(hAPP(_1601798, _1601802), hAPP(hAPP(c_Finite__Set_Ofold(_1601794, _1601796, _1601798), _1601804), _1601800)) = hAPP(hAPP(c_Finite__Set_Ofold(_1601794, _1601796, _1601798), hAPP(hAPP(_1601798, _1601802), _1601804)), _1601800))], (41629 ^ _782652) ^ [_1602013, _1602015, _1602017, _1602019, _1602021, _1602023] : [c_Finite__Set_Ofun__left__comm(_1602013, _1602015, _1602017), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1602013, _1602015, _1602017, _1602019, _1602021), _1602023)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1602013, _1602015, _1602017), _1602019), _1602021) = _1602023)], (41639 ^ _782652) ^ [_1602196, _1602198, _1602200, _1602202, _1602204] : [c_Finite__Set_Ofun__left__comm(_1602196, _1602198, _1602200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1602196), _1602202)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1602196, _1602198, _1602200, _1602204, _1602202), hAPP(hAPP(c_Finite__Set_Ofold(_1602196, _1602198, _1602200), _1602204), _1602202))))], (41649 ^ _782652) ^ [_1602383, _1602385, _1602387, _1602389, _1602391, _1602393] : [c_Finite__Set_Ofun__left__comm(_1602383, _1602385, _1602387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1602383), _1602389)), -(hBOOL(hAPP(hAPP(c_member(_1602383), _1602391), _1602389))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1602383, _1602385, _1602387), _1602393), hAPP(hAPP(c_Set_Oinsert(_1602383), _1602391), _1602389)) = hAPP(hAPP(c_Finite__Set_Ofold(_1602383, _1602385, _1602387), hAPP(hAPP(_1602387, _1602391), _1602393)), _1602389))], (41663 ^ _782652) ^ [_1602635, _1602637, _1602639, _1602641, _1602643, _1602645] : [c_Finite__Set_Ofun__left__comm(_1602635, _1602637, _1602639), hBOOL(hAPP(c_Finite__Set_Ofinite(_1602635), _1602641)), -(hBOOL(hAPP(hAPP(c_member(_1602635), _1602643), _1602641))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1602635, _1602637, _1602639), _1602645), hAPP(hAPP(c_Set_Oinsert(_1602635), _1602643), _1602641)) = hAPP(hAPP(_1602639, _1602643), hAPP(hAPP(c_Finite__Set_Ofold(_1602635, _1602637, _1602639), _1602645), _1602641)))], (41677 ^ _782652) ^ [_1602887, _1602889, _1602891, _1602893, _1602895, _1602897, _1602899] : [c_Finite__Set_Ofun__left__comm(_1602887, _1602889, _1602891), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1602887, _1602889, _1602891, _1602893, _1602895), _1602897)), hBOOL(hAPP(hAPP(c_member(_1602887), _1602899), _1602895)), 41689 ^ _782652 : [(41690 ^ _782652) ^ [] : [-(_1602897 = hAPP(hAPP(_1602891, _1602899), 41688 ^ [_1602887, _1602889, _1602891, _1602893, _1602895, _1602897, _1602899]))], (41692 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1602887, _1602889, _1602891, _1602893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1602887, tc_HOL_Obool)), _1602895), hAPP(hAPP(c_Set_Oinsert(_1602887), _1602899), c_Orderings_Obot__class_Obot(tc_fun(_1602887, tc_HOL_Obool))))), 41688 ^ [_1602887, _1602889, _1602891, _1602893, _1602895, _1602897, _1602899])))]]], (41694 ^ _782652) ^ [_1603271, _1603273, _1603275, _1603277] : [class_Complete__Lattice_Ocomplete__lattice(_1603271), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603273), _1603275)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603273, _1603271), _1603275), _1603277) = hAPP(hAPP(c_Finite__Set_Ofold(_1603273, _1603271, hAPP(hAPP(c_COMBB(_1603271, tc_fun(_1603271, _1603271), _1603273), c_Lattices_Osemilattice__inf__class_Oinf(_1603271)), _1603277)), c_Orderings_Otop__class_Otop(_1603271)), _1603275))], (41704 ^ _782652) ^ [_1603486, _1603488, _1603490, _1603492, _1603494, _1603496] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603486, tc_fun(_1603488, tc_HOL_Obool)), _1603490), _1603492), _1603494)), -(hBOOL(hAPP(hAPP(_1603492, _1603496), _1603494))), hBOOL(hAPP(hAPP(c_member(_1603486), _1603496), _1603490))], (41714 ^ _782652) ^ [_1603687, _1603689, _1603691, _1603693, _1603695, _1603697] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603687, tc_fun(_1603689, tc_HOL_Obool)), _1603691), _1603693), _1603695)), hBOOL(hAPP(hAPP(c_member(_1603687), _1603697), _1603691)), -(hBOOL(hAPP(hAPP(_1603693, _1603697), _1603695)))], (41724 ^ _782652) ^ [_1603884, _1603886, _1603888, _1603890, _1603892, _1603894] : [hBOOL(hAPP(hAPP(c_member(_1603884), _1603886), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603888, tc_fun(_1603884, tc_HOL_Obool)), _1603890), _1603892))), -(hBOOL(hAPP(hAPP(c_member(_1603884), _1603886), hAPP(_1603892, _1603894)))), hBOOL(hAPP(hAPP(c_member(_1603888), _1603894), _1603890))], (41734 ^ _782652) ^ [_1604105, _1604107, _1604109, _1604111, _1604113, _1604115] : [hBOOL(hAPP(hAPP(c_member(_1604105), _1604107), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604109, tc_fun(_1604105, tc_HOL_Obool)), _1604111), _1604113))), hBOOL(hAPP(hAPP(c_member(_1604109), _1604115), _1604111)), -(hBOOL(hAPP(hAPP(c_member(_1604105), _1604107), hAPP(_1604113, _1604115))))], (41744 ^ _782652) ^ [_1604322, _1604324, _1604326, _1604328, _1604330, _1604332, _1604334, _1604336] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604322, tc_fun(_1604324, tc_fun(_1604326, tc_HOL_Obool))), _1604328), _1604330), _1604332), _1604334)), hBOOL(hAPP(hAPP(c_member(_1604322), _1604336), _1604328)), -(hBOOL(hAPP(hAPP(hAPP(_1604330, _1604336), _1604332), _1604334)))], (41754 ^ _782652) ^ [_1604545, _1604547, _1604549, _1604551, _1604553, _1604555, _1604557, _1604559] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604545, tc_fun(_1604547, tc_fun(_1604549, tc_HOL_Obool))), _1604551), _1604553), _1604555), _1604557)), -(hBOOL(hAPP(hAPP(hAPP(_1604553, _1604559), _1604555), _1604557))), hBOOL(hAPP(hAPP(c_member(_1604545), _1604559), _1604551))], (41764 ^ _782652) ^ [_1604772, _1604774, _1604776, _1604778] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1604776), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604772, tc_fun(_1604776, tc_HOL_Obool)), _1604774), _1604778)))), 41765 ^ _782652 : [(41766 ^ _782652) ^ [_1604846] : [hBOOL(hAPP(hAPP(c_member(_1604772), _1604846), _1604774)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1604776), hAPP(_1604778, _1604846)))]]], (41774 ^ _782652) ^ [_1605000, _1605002, _1605004, _1605006, _1605008] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605000, tc_fun(_1605002, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605000, tc_HOL_Obool)), _1605004), _1605006)), _1605008) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1605002, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605000, tc_fun(_1605002, tc_HOL_Obool)), _1605004), _1605008)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605000, tc_fun(_1605002, tc_HOL_Obool)), _1605006), _1605008)))], (41776 ^ _782652) ^ [_1605089, _1605091, _1605093, _1605095, _1605097] : [class_Complete__Lattice_Ocomplete__lattice(_1605089), class_Orderings_Olinorder(_1605089), 41783 ^ _782652 : [(41784 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1605089), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605091, _1605089), _1605093), _1605095)), _1605097)), 41788 ^ _782652 : [(41789 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605091), 41787 ^ [_1605089, _1605091, _1605093, _1605095, _1605097]), _1605093)))], (41791 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1605089), hAPP(_1605095, 41787 ^ [_1605089, _1605091, _1605093, _1605095, _1605097])), _1605097)))]]], (41793 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1605089), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605091, _1605089), _1605093), _1605095)), _1605097))), 41794 ^ _782652 : [(41795 ^ _782652) ^ [_1605437] : [hBOOL(hAPP(hAPP(c_member(_1605091), _1605437), _1605093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1605089), hAPP(_1605095, _1605437)), _1605097))]]]]], (41803 ^ _782652) ^ [_1605607, _1605609, _1605611, _1605613, _1605615] : [class_Complete__Lattice_Ocomplete__lattice(_1605607), 41806 ^ _782652 : [(41817 ^ _782652) ^ [] : [41819 ^ _782652 : [(41820 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605611), 41818 ^ [_1605607, _1605609, _1605611, _1605613, _1605615]), _1605613)))], (41822 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1605607), _1605609), hAPP(_1605615, 41818 ^ [_1605607, _1605609, _1605611, _1605613, _1605615])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1605607), _1605609), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605611, _1605607), _1605613), _1605615))))], (41807 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1605607), _1605609), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605611, _1605607), _1605613), _1605615))), 41810 ^ _782652 : [(41811 ^ _782652) ^ [_1605788] : [hBOOL(hAPP(hAPP(c_member(_1605611), _1605788), _1605613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1605607), _1605609), hAPP(_1605615, _1605788))))]]]]], (41836 ^ _782652) ^ [_1606383, _1606385, _1606387, _1606389, _1606391] : [41838 ^ _782652 : [(41839 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606387), 41837 ^ [_1606383, _1606385, _1606387, _1606389, _1606391]), _1606389)))], (41841 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1606383, tc_HOL_Obool)), _1606385), hAPP(_1606391, 41837 ^ [_1606383, _1606385, _1606387, _1606389, _1606391])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1606383, tc_HOL_Obool)), _1606385), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606387, tc_fun(_1606383, tc_HOL_Obool)), _1606389), _1606391))))], (41826 ^ _782652) ^ [_1606125, _1606127, _1606129, _1606131, _1606133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1606125, tc_HOL_Obool)), _1606127), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606129, tc_fun(_1606125, tc_HOL_Obool)), _1606131), _1606133))), 41829 ^ _782652 : [(41830 ^ _782652) ^ [_1606258] : [hBOOL(hAPP(hAPP(c_member(_1606129), _1606258), _1606131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1606125, tc_HOL_Obool)), _1606127), hAPP(_1606133, _1606258))))]]], (41845 ^ _782652) ^ [_1606646, _1606648, _1606650, _1606652, _1606654] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606646, tc_fun(_1606648, tc_HOL_Obool)), _1606650), hAPP(hAPP(c_COMBB(tc_fun(_1606648, tc_HOL_Obool), tc_fun(_1606648, tc_HOL_Obool), _1606646), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606648, tc_HOL_Obool)), _1606652)), _1606654)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606648, tc_HOL_Obool)), _1606652), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606646, tc_fun(_1606648, tc_HOL_Obool)), _1606650), _1606654)))], (41847 ^ _782652) ^ [_1606736, _1606738, _1606740, _1606742, _1606744] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606736, tc_fun(_1606738, tc_HOL_Obool)), _1606740), hAPP(hAPP(c_COMBC(_1606736, tc_fun(_1606738, tc_HOL_Obool), tc_fun(_1606738, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1606738, tc_HOL_Obool), tc_fun(tc_fun(_1606738, tc_HOL_Obool), tc_fun(_1606738, tc_HOL_Obool)), _1606736), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606738, tc_HOL_Obool))), _1606742)), _1606744)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606738, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606736, tc_fun(_1606738, tc_HOL_Obool)), _1606740), _1606742)), _1606744))], (41849 ^ _782652) ^ [_1606845, _1606847, _1606849, _1606851, _1606853] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606845, tc_HOL_Obool)), _1606847), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606849, tc_fun(_1606845, tc_HOL_Obool)), _1606851), _1606853)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606849, tc_fun(_1606845, tc_HOL_Obool)), _1606851), hAPP(hAPP(c_COMBB(tc_fun(_1606845, tc_HOL_Obool), tc_fun(_1606845, tc_HOL_Obool), _1606849), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606845, tc_HOL_Obool)), _1606847)), _1606853)))], (41851 ^ _782652) ^ [_1606935, _1606937, _1606939, _1606941, _1606943] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606935, tc_HOL_Obool)), _1606937), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606939, tc_fun(_1606935, tc_HOL_Obool)), _1606941), _1606943)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606939, tc_fun(_1606935, tc_HOL_Obool)), _1606941), hAPP(hAPP(c_COMBB(tc_fun(_1606935, tc_HOL_Obool), tc_fun(_1606935, tc_HOL_Obool), _1606939), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1606935, tc_HOL_Obool)), _1606937)), _1606943)))], (41853 ^ _782652) ^ [_1607025, _1607027, _1607029, _1607031, _1607033] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607025, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607027, tc_fun(_1607025, tc_HOL_Obool)), _1607029), _1607031)), _1607033) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607027, tc_fun(_1607025, tc_HOL_Obool)), _1607029), hAPP(hAPP(c_COMBC(_1607027, tc_fun(_1607025, tc_HOL_Obool), tc_fun(_1607025, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1607025, tc_HOL_Obool), tc_fun(tc_fun(_1607025, tc_HOL_Obool), tc_fun(_1607025, tc_HOL_Obool)), _1607027), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607025, tc_HOL_Obool))), _1607031)), _1607033)))], (41855 ^ _782652) ^ [_1607134, _1607136, _1607138, _1607140, _1607142, _1607144, _1607146] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607134, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607136, tc_fun(_1607134, tc_HOL_Obool)), _1607138), _1607140)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607142, tc_fun(_1607134, tc_HOL_Obool)), _1607144), _1607146)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607136, tc_fun(_1607134, tc_HOL_Obool)), _1607138), hAPP(hAPP(c_COMBB(tc_fun(_1607142, tc_fun(_1607134, tc_HOL_Obool)), tc_fun(_1607134, tc_HOL_Obool), _1607136), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607142, tc_fun(_1607134, tc_HOL_Obool)), _1607144)), hAPP(hAPP(c_COMBC(_1607136, tc_fun(_1607142, tc_fun(_1607134, tc_HOL_Obool)), tc_fun(_1607142, tc_fun(_1607134, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1607134, tc_HOL_Obool), tc_fun(_1607134, tc_HOL_Obool)), tc_fun(tc_fun(_1607142, tc_fun(_1607134, tc_HOL_Obool)), tc_fun(_1607142, tc_fun(_1607134, tc_HOL_Obool))), _1607136), c_COMBB(tc_fun(_1607134, tc_HOL_Obool), tc_fun(_1607134, tc_HOL_Obool), _1607142)), hAPP(hAPP(c_COMBB(tc_fun(_1607134, tc_HOL_Obool), tc_fun(tc_fun(_1607134, tc_HOL_Obool), tc_fun(_1607134, tc_HOL_Obool)), _1607136), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1607134, tc_HOL_Obool))), _1607140))), _1607146))))], (41857 ^ _782652) ^ [_1607337, _1607339, _1607341, _1607343, _1607345] : [hBOOL(hAPP(hAPP(c_member(_1607337), _1607339), _1607341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607343, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607337, tc_fun(_1607343, tc_HOL_Obool)), _1607341), _1607345)), hAPP(_1607345, _1607339))))], (41863 ^ _782652) ^ [_1607484, _1607486, _1607488, _1607490, _1607492, _1607494] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607484, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1607486, _1607484, _1607488), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607490, tc_fun(_1607486, tc_HOL_Obool)), _1607492), _1607494))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607490, tc_fun(_1607484, tc_HOL_Obool)), _1607492), hAPP(hAPP(c_COMBB(tc_fun(_1607486, tc_HOL_Obool), tc_fun(_1607484, tc_HOL_Obool), _1607490), c_Relation_OImage(_1607486, _1607484, _1607488)), _1607494)))))], (41865 ^ _782652) ^ [_1607578, _1607580, _1607582, _1607584] : [-(hAPP(c_Set_OCollect(_1607578), hAPP(hAPP(c_COMBB(tc_fun(_1607580, tc_HOL_Obool), tc_HOL_Obool, _1607578), c_HOL_OAll(_1607580)), hAPP(hAPP(c_COMBB(tc_fun(_1607580, tc_HOL_Obool), tc_fun(_1607580, tc_HOL_Obool), _1607578), hAPP(c_COMBS(_1607580, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1607580), c_fimplies), hAPP(hAPP(c_COMBC(_1607580, tc_fun(_1607580, tc_HOL_Obool), tc_HOL_Obool), c_member(_1607580)), _1607582)))), _1607584))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607580, tc_fun(_1607578, tc_HOL_Obool)), _1607582), hAPP(hAPP(c_COMBB(tc_fun(_1607578, tc_HOL_Obool), tc_fun(_1607578, tc_HOL_Obool), _1607580), c_Set_OCollect(_1607578)), hAPP(c_COMBC(_1607578, _1607580, tc_HOL_Obool), _1607584))))], (41867 ^ _782652) ^ [_1607712, _1607714, _1607716, _1607718, _1607720, _1607722] : [hBOOL(hAPP(hAPP(c_member(_1607712), _1607714), _1607716)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607712, tc_fun(_1607718, tc_HOL_Obool)), _1607716), hAPP(hAPP(c_COMBB(tc_fun(_1607718, tc_HOL_Obool), tc_fun(_1607718, tc_HOL_Obool), _1607712), hAPP(c_Set_Oinsert(_1607718), _1607720)), _1607722)) = hAPP(hAPP(c_Set_Oinsert(_1607718), _1607720), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607712, tc_fun(_1607718, tc_HOL_Obool)), _1607716), _1607722)))], (41873 ^ _782652) ^ [_1607938, _1607940, _1607942, _1607944] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607938, tc_fun(_1607940, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1607938, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1607940, tc_HOL_Obool), tc_fun(_1607940, tc_HOL_Obool), _1607938), hAPP(c_COMBC(_1607940, tc_fun(_1607940, tc_HOL_Obool), tc_HOL_Obool), c_member(_1607940))), _1607942)), _1607944)), -(hBOOL(hAPP(hAPP(c_member(_1607940), _1607944), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607938, tc_fun(_1607940, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1607938, tc_HOL_Obool))), _1607942))))], (41879 ^ _782652) ^ [_1608157, _1608159, _1608161, _1608163] : [hBOOL(hAPP(hAPP(c_member(_1608159), _1608163), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608157, tc_fun(_1608159, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1608157, tc_HOL_Obool))), _1608161))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608157, tc_fun(_1608159, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1608157, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1608159, tc_HOL_Obool), tc_fun(_1608159, tc_HOL_Obool), _1608157), hAPP(c_COMBC(_1608159, tc_fun(_1608159, tc_HOL_Obool), tc_HOL_Obool), c_member(_1608159))), _1608161)), _1608163)))], (41885 ^ _782652) ^ [_1608382, _1608384, _1608386, _1608388, _1608390] : [hBOOL(hAPP(hAPP(c_member(_1608382), _1608384), _1608386)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1608388, tc_HOL_Obool)), hAPP(_1608390, _1608384)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608382, tc_fun(_1608388, tc_HOL_Obool)), _1608386), _1608390)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608382, tc_fun(_1608388, tc_HOL_Obool)), _1608386), _1608390))], (41891 ^ _782652) ^ [_1608555, _1608557, _1608559, _1608561] : [class_Complete__Lattice_Ocomplete__lattice(_1608555), -(_1608557 = c_Orderings_Obot__class_Obot(tc_fun(_1608559, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608559, _1608555), _1608557), hAPP(c_COMBK(_1608555, _1608559), _1608561)) = _1608561)], (41911 ^ _782652) ^ [_1608956, _1608958, _1608960, _1608962, _1608964] : [41913 ^ _782652 : [(41914 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608960), 41912 ^ [_1608956, _1608958, _1608960, _1608962, _1608964]), _1608962)))], (41916 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1608956), _1608958), hAPP(_1608964, 41912 ^ [_1608956, _1608958, _1608960, _1608962, _1608964])))]], -(hBOOL(hAPP(hAPP(c_member(_1608956), _1608958), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608960, tc_fun(_1608956, tc_HOL_Obool)), _1608962), _1608964))))], (41901 ^ _782652) ^ [_1608713, _1608715, _1608717, _1608719, _1608721] : [hBOOL(hAPP(hAPP(c_member(_1608713), _1608715), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608717, tc_fun(_1608713, tc_HOL_Obool)), _1608719), _1608721))), 41904 ^ _782652 : [(41905 ^ _782652) ^ [_1608837] : [hBOOL(hAPP(hAPP(c_member(_1608717), _1608837), _1608719)), -(hBOOL(hAPP(hAPP(c_member(_1608713), _1608715), hAPP(_1608721, _1608837))))]]], (41920 ^ _782652) ^ [_1609231, _1609233, _1609235, _1609237, _1609239, _1609241] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609231, tc_fun(_1609233, tc_fun(_1609235, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1609231, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1609233, _1609235), tc_HOL_Obool), tc_fun(_1609233, tc_fun(_1609235, tc_HOL_Obool)), _1609231), hAPP(c_COMBC(_1609233, tc_fun(tc_prod(_1609233, _1609235), tc_HOL_Obool), tc_fun(_1609235, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609235, tc_fun(tc_fun(tc_prod(_1609233, _1609235), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1609233, _1609235), tc_HOL_Obool), tc_fun(_1609235, tc_HOL_Obool)), _1609233), c_COMBC(_1609235, tc_fun(tc_prod(_1609233, _1609235), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609235, tc_prod(_1609233, _1609235)), tc_fun(_1609235, tc_fun(tc_fun(tc_prod(_1609233, _1609235), tc_HOL_Obool), tc_HOL_Obool)), _1609233), hAPP(c_COMBB(tc_prod(_1609233, _1609235), tc_fun(tc_fun(tc_prod(_1609233, _1609235), tc_HOL_Obool), tc_HOL_Obool), _1609235), c_member(tc_prod(_1609233, _1609235)))), c_Product__Type_OPair(_1609233, _1609235))))), _1609237)), _1609239), _1609241)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609233, _1609235)), hAPP(hAPP(c_Product__Type_OPair(_1609233, _1609235), _1609239), _1609241)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609231, tc_fun(tc_prod(_1609233, _1609235), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1609231, tc_HOL_Obool))), _1609237))))], (41926 ^ _782652) ^ [_1609714, _1609716, _1609718, _1609720, _1609722, _1609724] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609716, _1609718)), hAPP(hAPP(c_Product__Type_OPair(_1609716, _1609718), _1609722), _1609724)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609714, tc_fun(tc_prod(_1609716, _1609718), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1609714, tc_HOL_Obool))), _1609720))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609714, tc_fun(_1609716, tc_fun(_1609718, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1609714, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1609716, _1609718), tc_HOL_Obool), tc_fun(_1609716, tc_fun(_1609718, tc_HOL_Obool)), _1609714), hAPP(c_COMBC(_1609716, tc_fun(tc_prod(_1609716, _1609718), tc_HOL_Obool), tc_fun(_1609718, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609718, tc_fun(tc_fun(tc_prod(_1609716, _1609718), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1609716, _1609718), tc_HOL_Obool), tc_fun(_1609718, tc_HOL_Obool)), _1609716), c_COMBC(_1609718, tc_fun(tc_prod(_1609716, _1609718), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609718, tc_prod(_1609716, _1609718)), tc_fun(_1609718, tc_fun(tc_fun(tc_prod(_1609716, _1609718), tc_HOL_Obool), tc_HOL_Obool)), _1609716), hAPP(c_COMBB(tc_prod(_1609716, _1609718), tc_fun(tc_fun(tc_prod(_1609716, _1609718), tc_HOL_Obool), tc_HOL_Obool), _1609718), c_member(tc_prod(_1609716, _1609718)))), c_Product__Type_OPair(_1609716, _1609718))))), _1609720)), _1609722), _1609724)))], (41942 ^ _782652) ^ [_1610453, _1610455, _1610457, _1610459] : [41944 ^ _782652 : [(41945 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1610455), 41943 ^ [_1610453, _1610455, _1610457, _1610459]), _1610457)))], (41947 ^ _782652) ^ [] : [hAPP(_1610459, 41943 ^ [_1610453, _1610455, _1610457, _1610459]) = c_Orderings_Otop__class_Otop(tc_fun(_1610453, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1610453, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610455, tc_fun(_1610453, tc_HOL_Obool)), _1610457), _1610459))], (41932 ^ _782652) ^ [_1610224, _1610226, _1610228, _1610230] : [c_Orderings_Otop__class_Otop(tc_fun(_1610224, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610226, tc_fun(_1610224, tc_HOL_Obool)), _1610228), _1610230), 41935 ^ _782652 : [(41936 ^ _782652) ^ [_1610340] : [hBOOL(hAPP(hAPP(c_member(_1610226), _1610340), _1610228)), -(hAPP(_1610230, _1610340) = c_Orderings_Otop__class_Otop(tc_fun(_1610224, tc_HOL_Obool)))]]], (41961 ^ _782652) ^ [_1610933, _1610935, _1610937, _1610939] : [41963 ^ _782652 : [(41964 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1610933), 41962 ^ [_1610933, _1610935, _1610937, _1610939]), _1610937)))], (41966 ^ _782652) ^ [] : [hAPP(_1610939, 41962 ^ [_1610933, _1610935, _1610937, _1610939]) = c_Orderings_Otop__class_Otop(tc_fun(_1610935, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610933, tc_fun(_1610935, tc_HOL_Obool)), _1610937), _1610939) = c_Orderings_Otop__class_Otop(tc_fun(_1610935, tc_HOL_Obool)))], (41951 ^ _782652) ^ [_1610704, _1610706, _1610708, _1610710] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610704, tc_fun(_1610706, tc_HOL_Obool)), _1610708), _1610710) = c_Orderings_Otop__class_Otop(tc_fun(_1610706, tc_HOL_Obool)), 41954 ^ _782652 : [(41955 ^ _782652) ^ [_1610820] : [hBOOL(hAPP(hAPP(c_member(_1610704), _1610820), _1610708)), -(hAPP(_1610710, _1610820) = c_Orderings_Otop__class_Otop(tc_fun(_1610706, tc_HOL_Obool)))]]], (41970 ^ _782652) ^ [_1611163, _1611165, _1611167, _1611169, _1611171] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611163, tc_fun(_1611165, tc_HOL_Obool)), _1611167), hAPP(hAPP(c_COMBS(_1611163, tc_fun(_1611165, tc_HOL_Obool), tc_fun(_1611165, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1611165, tc_HOL_Obool), tc_fun(tc_fun(_1611165, tc_HOL_Obool), tc_fun(_1611165, tc_HOL_Obool)), _1611163), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1611165, tc_HOL_Obool))), _1611169)), _1611171)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1611165, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611163, tc_fun(_1611165, tc_HOL_Obool)), _1611167), _1611169)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611163, tc_fun(_1611165, tc_HOL_Obool)), _1611167), _1611171)))], (41972 ^ _782652) ^ [_1611284, _1611286, _1611288, _1611290] : [-(hAPP(c_Set_OPow(_1611284), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611286, tc_fun(_1611284, tc_HOL_Obool)), _1611288), _1611290)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611286, tc_fun(tc_fun(_1611284, tc_HOL_Obool), tc_HOL_Obool)), _1611288), hAPP(hAPP(c_COMBB(tc_fun(_1611284, tc_HOL_Obool), tc_fun(tc_fun(_1611284, tc_HOL_Obool), tc_HOL_Obool), _1611286), c_Set_OPow(_1611284)), _1611290)))], (41974 ^ _782652) ^ [_1611366, _1611368, _1611370, _1611372, _1611374, _1611376] : [class_Complete__Lattice_Ocomplete__lattice(_1611366), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611368, tc_fun(_1611370, _1611366)), _1611372), _1611374), _1611376) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611368, _1611366), _1611372), hAPP(hAPP(c_COMBC(_1611368, _1611370, _1611366), _1611374), _1611376)))], (41980 ^ _782652) ^ [_1611517, _1611519, _1611521, _1611523, _1611525, _1611527] : [class_Complete__Lattice_Ocomplete__lattice(_1611517), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611519, _1611517), _1611521), hAPP(hAPP(c_COMBB(tc_fun(_1611523, _1611517), _1611517, _1611519), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611523, _1611517), _1611525)), _1611527)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611523, _1611517), _1611525), hAPP(hAPP(c_COMBB(tc_fun(_1611519, _1611517), _1611517, _1611523), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611519, _1611517), _1611521)), hAPP(c_COMBC(_1611519, _1611523, _1611517), _1611527))))], (41986 ^ _782652) ^ [_1611726, _1611728, _1611730, _1611732, _1611734] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611726, tc_fun(_1611728, tc_HOL_Obool)), _1611730), hAPP(hAPP(c_COMBB(tc_fun(_1611728, tc_HOL_Obool), tc_fun(_1611728, tc_HOL_Obool), _1611726), hAPP(c_Set_Oinsert(_1611728), _1611732)), _1611734)) = hAPP(hAPP(c_Set_Oinsert(_1611728), _1611732), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611726, tc_fun(_1611728, tc_HOL_Obool)), _1611730), _1611734)))], (41988 ^ _782652) ^ [_1611810, _1611812, _1611814, _1611816, _1611818] : [-(hAPP(hAPP(c_Set_Oinsert(_1611810), _1611812), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611814, tc_fun(_1611810, tc_HOL_Obool)), _1611816), _1611818)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611814, tc_fun(_1611810, tc_HOL_Obool)), _1611816), hAPP(hAPP(c_COMBB(tc_fun(_1611810, tc_HOL_Obool), tc_fun(_1611810, tc_HOL_Obool), _1611814), hAPP(c_Set_Oinsert(_1611810), _1611812)), _1611818)))], (41990 ^ _782652) ^ [_1611894, _1611896, _1611898, _1611900, _1611902, _1611904] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611894, tc_fun(_1611896, tc_HOL_Obool)), _1611898), hAPP(hAPP(c_COMBB(_1611900, tc_fun(_1611896, tc_HOL_Obool), _1611894), _1611902), _1611904)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611900, tc_fun(_1611896, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1611894, _1611900, _1611904), _1611898)), _1611902))], (41992 ^ _782652) ^ [_1611971, _1611973, _1611975, _1611977, _1611979, _1611981] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611971, tc_fun(_1611973, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1611975, _1611971, _1611977), _1611979)), _1611981) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611975, tc_fun(_1611973, tc_HOL_Obool)), _1611979), hAPP(hAPP(c_COMBB(_1611971, tc_fun(_1611973, tc_HOL_Obool), _1611975), _1611981), _1611977)))], (41994 ^ _782652) ^ [_1612048, _1612050, _1612052, _1612054, _1612056, _1612058] : [-(hAPP(c_Set_Ovimage(_1612048, _1612050, _1612052), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612054, tc_fun(_1612050, tc_HOL_Obool)), _1612056), _1612058)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612054, tc_fun(_1612048, tc_HOL_Obool)), _1612056), hAPP(hAPP(c_COMBB(tc_fun(_1612050, tc_HOL_Obool), tc_fun(_1612048, tc_HOL_Obool), _1612054), c_Set_Ovimage(_1612048, _1612050, _1612052)), _1612058)))], (41996 ^ _782652) ^ [_1612132] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612132, tc_HOL_Obool) = c_Set_OBall(_1612132))], (41998 ^ _782652) ^ [_1612178, _1612180, _1612182, _1612184, _1612186] : [_1612178 = c_Orderings_Obot__class_Obot(tc_fun(_1612180, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612182, tc_HOL_Obool)), _1612184), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612180, tc_fun(_1612182, tc_HOL_Obool)), _1612178), _1612186)) = _1612184)], (42004 ^ _782652) ^ [_1612311, _1612313, _1612315, _1612317, _1612319] : [-(_1612311 = c_Orderings_Obot__class_Obot(tc_fun(_1612313, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612315, tc_HOL_Obool)), _1612317), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612313, tc_fun(_1612315, tc_HOL_Obool)), _1612311), _1612319)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612313, tc_fun(_1612315, tc_HOL_Obool)), _1612311), hAPP(hAPP(c_COMBB(tc_fun(_1612315, tc_HOL_Obool), tc_fun(_1612315, tc_HOL_Obool), _1612313), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612315, tc_HOL_Obool)), _1612317)), _1612319)))], (42010 ^ _782652) ^ [_1612437, _1612439, _1612441, _1612443, _1612445] : [_1612437 = c_Orderings_Obot__class_Obot(tc_fun(_1612439, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612441, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612439, tc_fun(_1612441, tc_HOL_Obool)), _1612437), _1612443)), _1612445) = _1612445)], (42016 ^ _782652) ^ [_1612570, _1612572, _1612574, _1612576, _1612578] : [-(_1612570 = c_Orderings_Obot__class_Obot(tc_fun(_1612572, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612574, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612572, tc_fun(_1612574, tc_HOL_Obool)), _1612570), _1612576)), _1612578) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612572, tc_fun(_1612574, tc_HOL_Obool)), _1612570), hAPP(hAPP(c_COMBC(_1612572, tc_fun(_1612574, tc_HOL_Obool), tc_fun(_1612574, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612574, tc_HOL_Obool), tc_fun(tc_fun(_1612574, tc_HOL_Obool), tc_fun(_1612574, tc_HOL_Obool)), _1612572), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612574, tc_HOL_Obool))), _1612576)), _1612578)))], (42022 ^ _782652) ^ [_1612697, _1612699, _1612701] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612697, tc_fun(_1612699, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1612697, tc_HOL_Obool))), _1612701) = c_Orderings_Otop__class_Otop(tc_fun(_1612699, tc_HOL_Obool)))], (42024 ^ _782652) ^ [_1612761, _1612763, _1612765, _1612767] : [_1612761 = c_Orderings_Obot__class_Obot(tc_fun(_1612763, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612763, tc_fun(_1612765, tc_HOL_Obool)), _1612761), hAPP(c_COMBK(tc_fun(_1612765, tc_HOL_Obool), _1612763), _1612767)) = c_Orderings_Otop__class_Otop(tc_fun(_1612765, tc_HOL_Obool)))], (42030 ^ _782652) ^ [_1612898, _1612900, _1612902, _1612904] : [-(_1612898 = c_Orderings_Obot__class_Obot(tc_fun(_1612900, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612900, tc_fun(_1612902, tc_HOL_Obool)), _1612898), hAPP(c_COMBK(tc_fun(_1612902, tc_HOL_Obool), _1612900), _1612904)) = _1612904)], (42036 ^ _782652) ^ [_1612966, _1612968, _1612970, _1612972, _1612974] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612966, tc_fun(_1612968, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1612966), _1612970), _1612972)), _1612974) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1612968, tc_HOL_Obool)), hAPP(_1612974, _1612970)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612966, tc_fun(_1612968, tc_HOL_Obool)), _1612972), _1612974)))], (42038 ^ _782652) ^ [_1613043, _1613045, _1613047, _1613049, _1613051] : [-(hAPP(c_Relation_Oconverse(_1613043, _1613045), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613047, tc_fun(tc_prod(_1613043, _1613045), tc_HOL_Obool)), _1613049), _1613051)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613047, tc_fun(tc_prod(_1613045, _1613043), tc_HOL_Obool)), _1613049), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1613043, _1613045), tc_HOL_Obool), tc_fun(tc_prod(_1613045, _1613043), tc_HOL_Obool), _1613047), c_Relation_Oconverse(_1613043, _1613045)), _1613051)))], (42040 ^ _782652) ^ [_1613135, _1613137, _1613139, _1613141, _1613143, _1613145] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613135, tc_fun(_1613137, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1613139, tc_fun(_1613135, tc_HOL_Obool)), _1613141), _1613143)), _1613145) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613139, tc_fun(_1613137, tc_HOL_Obool)), _1613141), hAPP(hAPP(c_COMBC(_1613139, tc_fun(_1613135, tc_fun(_1613137, tc_HOL_Obool)), tc_fun(_1613137, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1613135, tc_HOL_Obool), tc_fun(tc_fun(_1613135, tc_fun(_1613137, tc_HOL_Obool)), tc_fun(_1613137, tc_HOL_Obool)), _1613139), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613135, tc_fun(_1613137, tc_HOL_Obool))), _1613143)), _1613145)))], (42042 ^ _782652) ^ [_1613254, _1613256, _1613258, _1613260, _1613262, _1613264] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613254, tc_fun(_1613256, tc_HOL_Obool)), _1613258), hAPP(hAPP(c_COMBC(_1613254, tc_fun(_1613260, tc_fun(_1613256, tc_HOL_Obool)), tc_fun(_1613256, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1613260, tc_HOL_Obool), tc_fun(tc_fun(_1613260, tc_fun(_1613256, tc_HOL_Obool)), tc_fun(_1613256, tc_HOL_Obool)), _1613254), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613260, tc_fun(_1613256, tc_HOL_Obool))), _1613262)), _1613264)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613260, tc_fun(_1613256, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1613254, tc_fun(_1613260, tc_HOL_Obool)), _1613258), _1613262)), _1613264))], (42044 ^ _782652) ^ [_1613373, _1613375, _1613377, _1613379, _1613381] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1613373, tc_HOL_Obool)), _1613375), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613377, tc_fun(_1613373, tc_HOL_Obool)), _1613379), _1613381)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1613377, tc_fun(_1613373, tc_HOL_Obool)), _1613379), hAPP(hAPP(c_COMBB(tc_fun(_1613373, tc_HOL_Obool), tc_fun(_1613373, tc_HOL_Obool), _1613377), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1613373, tc_HOL_Obool)), _1613375)), _1613381)))], (42046 ^ _782652) ^ [_1613463, _1613465, _1613467, _1613469, _1613471] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1613463, tc_fun(_1613465, tc_HOL_Obool)), _1613467), hAPP(hAPP(c_COMBB(tc_fun(_1613465, tc_HOL_Obool), tc_fun(_1613465, tc_HOL_Obool), _1613463), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1613465, tc_HOL_Obool)), _1613469)), _1613471)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1613465, tc_HOL_Obool)), _1613469), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613463, tc_fun(_1613465, tc_HOL_Obool)), _1613467), _1613471)))], (42048 ^ _782652) ^ [_1613553, _1613555, _1613557, _1613559] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1613553, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1613555, tc_fun(_1613553, tc_HOL_Obool)), _1613557), _1613559)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613555, tc_fun(_1613553, tc_HOL_Obool)), _1613557), hAPP(hAPP(c_COMBB(tc_fun(_1613553, tc_HOL_Obool), tc_fun(_1613553, tc_HOL_Obool), _1613555), c_Groups_Ouminus__class_Ouminus(tc_fun(_1613553, tc_HOL_Obool))), _1613559)))], (42050 ^ _782652) ^ [_1613635, _1613637, _1613639, _1613641] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1613635, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613637, tc_fun(_1613635, tc_HOL_Obool)), _1613639), _1613641)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1613637, tc_fun(_1613635, tc_HOL_Obool)), _1613639), hAPP(hAPP(c_COMBB(tc_fun(_1613635, tc_HOL_Obool), tc_fun(_1613635, tc_HOL_Obool), _1613637), c_Groups_Ouminus__class_Ouminus(tc_fun(_1613635, tc_HOL_Obool))), _1613641)))], (42052 ^ _782652) ^ [_1613717, _1613719, _1613721, _1613723, _1613725] : [class_Complete__Lattice_Ocomplete__lattice(_1613717), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1613719, tc_HOL_Obool)), _1613721), _1613723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1613717), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613719, _1613717), _1613723), _1613725)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613719, _1613717), _1613721), _1613725))))], (42062 ^ _782652) ^ [_1613926, _1613928, _1613930, _1613932] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613926, tc_fun(_1613928, tc_HOL_Obool)), _1613930), _1613932) = hAPP(c_Set_OCollect(_1613928), hAPP(hAPP(c_COMBB(tc_fun(_1613926, tc_HOL_Obool), tc_HOL_Obool, _1613928), c_HOL_OAll(_1613926)), hAPP(hAPP(c_COMBB(tc_fun(_1613926, tc_HOL_Obool), tc_fun(_1613926, tc_HOL_Obool), _1613928), hAPP(c_COMBS(_1613926, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1613926), c_fimplies), hAPP(hAPP(c_COMBC(_1613926, tc_fun(_1613926, tc_HOL_Obool), tc_HOL_Obool), c_member(_1613926)), _1613930)))), hAPP(hAPP(c_COMBC(_1613928, tc_fun(_1613926, tc_fun(_1613928, tc_HOL_Obool)), tc_fun(_1613926, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1613928, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1613926, tc_fun(_1613928, tc_HOL_Obool)), tc_fun(_1613926, tc_HOL_Obool)), _1613928), c_COMBB(tc_fun(_1613928, tc_HOL_Obool), tc_HOL_Obool, _1613926)), c_member(_1613928))), _1613932)))))], (42064 ^ _782652) ^ [_1614109, _1614111, _1614113, _1614115, _1614117] : [_1614109 = c_Orderings_Obot__class_Obot(tc_fun(_1614111, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614111, tc_fun(_1614113, tc_HOL_Obool)), _1614109), hAPP(hAPP(c_COMBC(_1614111, tc_fun(_1614113, tc_HOL_Obool), tc_fun(_1614113, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614113, tc_HOL_Obool), tc_fun(tc_fun(_1614113, tc_HOL_Obool), tc_fun(_1614113, tc_HOL_Obool)), _1614111), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614113, tc_HOL_Obool))), _1614115)), _1614117)) = c_Orderings_Otop__class_Otop(tc_fun(_1614113, tc_HOL_Obool)))], (42070 ^ _782652) ^ [_1614316, _1614318, _1614320, _1614322, _1614324] : [-(_1614316 = c_Orderings_Obot__class_Obot(tc_fun(_1614318, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614318, tc_fun(_1614320, tc_HOL_Obool)), _1614316), hAPP(hAPP(c_COMBC(_1614318, tc_fun(_1614320, tc_HOL_Obool), tc_fun(_1614320, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614320, tc_HOL_Obool), tc_fun(tc_fun(_1614320, tc_HOL_Obool), tc_fun(_1614320, tc_HOL_Obool)), _1614318), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614320, tc_HOL_Obool))), _1614322)), _1614324)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614320, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614318, tc_fun(_1614320, tc_HOL_Obool)), _1614316), _1614322)), _1614324))], (42076 ^ _782652) ^ [_1614461, _1614463, _1614465, _1614467, _1614469] : [_1614461 = c_Orderings_Obot__class_Obot(tc_fun(_1614463, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614463, tc_fun(_1614465, tc_HOL_Obool)), _1614461), hAPP(hAPP(c_COMBB(tc_fun(_1614465, tc_HOL_Obool), tc_fun(_1614465, tc_HOL_Obool), _1614463), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614465, tc_HOL_Obool)), _1614467)), _1614469)) = c_Orderings_Otop__class_Otop(tc_fun(_1614465, tc_HOL_Obool)))], (42082 ^ _782652) ^ [_1614630, _1614632, _1614634, _1614636, _1614638] : [-(_1614630 = c_Orderings_Obot__class_Obot(tc_fun(_1614632, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614632, tc_fun(_1614634, tc_HOL_Obool)), _1614630), hAPP(hAPP(c_COMBB(tc_fun(_1614634, tc_HOL_Obool), tc_fun(_1614634, tc_HOL_Obool), _1614632), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614634, tc_HOL_Obool)), _1614636)), _1614638)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1614634, tc_HOL_Obool)), _1614636), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614632, tc_fun(_1614634, tc_HOL_Obool)), _1614630), _1614638)))], (42088 ^ _782652) ^ [_1614738, _1614740, _1614742] : [-(hAPP(c_Set_OCollect(_1614738), hAPP(hAPP(c_COMBB(tc_fun(_1614740, tc_HOL_Obool), tc_HOL_Obool, _1614738), c_HOL_OAll(_1614740)), _1614742)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614740, tc_fun(_1614738, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1614740, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1614738, tc_HOL_Obool), tc_fun(_1614738, tc_HOL_Obool), _1614740), c_Set_OCollect(_1614738)), hAPP(c_COMBC(_1614738, _1614740, tc_HOL_Obool), _1614742))))], (42090 ^ _782652) ^ [_1614845, _1614847, _1614849, _1614851, _1614853] : [_1614845 = c_Orderings_Obot__class_Obot(tc_fun(_1614847, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1614849, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614847, tc_fun(_1614849, tc_HOL_Obool)), _1614845), _1614851)), _1614853) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1614849, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1614849, tc_HOL_Obool))), _1614853))], (42096 ^ _782652) ^ [_1615010, _1615012, _1615014, _1615016, _1615018] : [-(_1615010 = c_Orderings_Obot__class_Obot(tc_fun(_1615012, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615014, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615012, tc_fun(_1615014, tc_HOL_Obool)), _1615010), _1615016)), _1615018) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615012, tc_fun(_1615014, tc_HOL_Obool)), _1615010), hAPP(hAPP(c_COMBC(_1615012, tc_fun(_1615014, tc_HOL_Obool), tc_fun(_1615014, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615014, tc_HOL_Obool), tc_fun(tc_fun(_1615014, tc_HOL_Obool), tc_fun(_1615014, tc_HOL_Obool)), _1615012), c_Groups_Ominus__class_Ominus(tc_fun(_1615014, tc_HOL_Obool))), _1615016)), _1615018)))], (42102 ^ _782652) ^ [_1615155, _1615157, _1615159, _1615161, _1615163] : [_1615155 = c_Orderings_Obot__class_Obot(tc_fun(_1615157, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615157, tc_fun(_1615159, tc_HOL_Obool)), _1615155), hAPP(hAPP(c_COMBC(_1615157, tc_fun(_1615159, tc_HOL_Obool), tc_fun(_1615159, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615159, tc_HOL_Obool), tc_fun(tc_fun(_1615159, tc_HOL_Obool), tc_fun(_1615159, tc_HOL_Obool)), _1615157), c_Groups_Ominus__class_Ominus(tc_fun(_1615159, tc_HOL_Obool))), _1615161)), _1615163)) = c_Orderings_Otop__class_Otop(tc_fun(_1615159, tc_HOL_Obool)))], (42108 ^ _782652) ^ [_1615362, _1615364, _1615366, _1615368, _1615370] : [-(_1615362 = c_Orderings_Obot__class_Obot(tc_fun(_1615364, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615364, tc_fun(_1615366, tc_HOL_Obool)), _1615362), hAPP(hAPP(c_COMBC(_1615364, tc_fun(_1615366, tc_HOL_Obool), tc_fun(_1615366, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615366, tc_HOL_Obool), tc_fun(tc_fun(_1615366, tc_HOL_Obool), tc_fun(_1615366, tc_HOL_Obool)), _1615364), c_Groups_Ominus__class_Ominus(tc_fun(_1615366, tc_HOL_Obool))), _1615368)), _1615370)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615366, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615364, tc_fun(_1615366, tc_HOL_Obool)), _1615362), _1615368)), _1615370))], (42114 ^ _782652) ^ [_1615507, _1615509, _1615511, _1615513, _1615515] : [_1615507 = c_Orderings_Obot__class_Obot(tc_fun(_1615509, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615511, tc_HOL_Obool)), _1615513), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615509, tc_fun(_1615511, tc_HOL_Obool)), _1615507), _1615515)) = _1615513)], (42120 ^ _782652) ^ [_1615640, _1615642, _1615644, _1615646, _1615648] : [-(_1615640 = c_Orderings_Obot__class_Obot(tc_fun(_1615642, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615644, tc_HOL_Obool)), _1615646), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615642, tc_fun(_1615644, tc_HOL_Obool)), _1615640), _1615648)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615642, tc_fun(_1615644, tc_HOL_Obool)), _1615640), hAPP(hAPP(c_COMBB(tc_fun(_1615644, tc_HOL_Obool), tc_fun(_1615644, tc_HOL_Obool), _1615642), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615644, tc_HOL_Obool)), _1615646)), _1615648)))], (42126 ^ _782652) ^ [_1615748, _1615750, _1615752, _1615754, _1615756] : [class_Complete__Lattice_Ocomplete__lattice(_1615748), hBOOL(hAPP(hAPP(c_member(_1615750), _1615752), _1615754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615748), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615750, _1615748), _1615754), _1615756)), hAPP(_1615756, _1615752))))], (42136 ^ _782652) ^ [] : [-(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)))], (42138 ^ _782652) ^ [_1615975, _1615977, _1615979, _1615981, _1615983] : [_1615975 = c_Orderings_Obot__class_Obot(tc_fun(_1615977, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615977, tc_fun(_1615979, tc_HOL_Obool)), _1615975), hAPP(hAPP(c_COMBB(tc_fun(_1615979, tc_HOL_Obool), tc_fun(_1615979, tc_HOL_Obool), _1615977), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615979, tc_HOL_Obool)), _1615981)), _1615983)) = c_Orderings_Otop__class_Otop(tc_fun(_1615979, tc_HOL_Obool)))], (42144 ^ _782652) ^ [_1616144, _1616146, _1616148, _1616150, _1616152] : [-(_1616144 = c_Orderings_Obot__class_Obot(tc_fun(_1616146, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616146, tc_fun(_1616148, tc_HOL_Obool)), _1616144), hAPP(hAPP(c_COMBB(tc_fun(_1616148, tc_HOL_Obool), tc_fun(_1616148, tc_HOL_Obool), _1616146), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616148, tc_HOL_Obool)), _1616150)), _1616152)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1616148, tc_HOL_Obool)), _1616150), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1616146, tc_fun(_1616148, tc_HOL_Obool)), _1616144), _1616152)))], (42150 ^ _782652) ^ [_1616252, _1616254, _1616256, _1616258, _1616260, _1616262] : [c_Relation_Osingle__valued(_1616252, _1616254, hAPP(c_Relation_Oconverse(_1616254, _1616252), _1616256)), -(_1616258 = c_Orderings_Obot__class_Obot(tc_fun(_1616260, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1616254, _1616252, _1616256), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616260, tc_fun(_1616254, tc_HOL_Obool)), _1616258), _1616262)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616260, tc_fun(_1616252, tc_HOL_Obool)), _1616258), hAPP(hAPP(c_COMBB(tc_fun(_1616254, tc_HOL_Obool), tc_fun(_1616252, tc_HOL_Obool), _1616260), c_Relation_OImage(_1616254, _1616252, _1616256)), _1616262)))], (42160 ^ _782652) ^ [_1616478, _1616480, _1616482, _1616484, _1616486] : [class_Complete__Lattice_Ocomplete__lattice(_1616478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616480), _1616482)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1616478), _1616484), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1616480, _1616478), _1616482), _1616486)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616480, _1616478, hAPP(hAPP(c_COMBB(_1616478, tc_fun(_1616478, _1616478), _1616480), c_Lattices_Osemilattice__inf__class_Oinf(_1616478)), _1616486)), _1616484), _1616482))], (42170 ^ _782652) ^ [_1616709, _1616711] : [class_Complete__Lattice_Ocomplete__lattice(_1616709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616709), _1616711)), -(c_Complete__Lattice_OInf__class_OInf(_1616709, _1616711) = hAPP(hAPP(c_Finite__Set_Ofold(_1616709, _1616709, c_Lattices_Osemilattice__inf__class_Oinf(_1616709)), c_Orderings_Otop__class_Otop(_1616709)), _1616711))], (42180 ^ _782652) ^ [_1616878, _1616880] : [class_Complete__Lattice_Ocomplete__lattice(_1616878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616878), _1616880)), -(c_Complete__Lattice_OSup__class_OSup(_1616878, _1616880) = hAPP(hAPP(c_Finite__Set_Ofold(_1616878, _1616878, c_Lattices_Osemilattice__sup__class_Osup(_1616878)), c_Orderings_Obot__class_Obot(_1616878)), _1616880))], (42190 ^ _782652) ^ [_1617047, _1617049] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1617047), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617047, tc_HOL_Obool), _1617049)))), 42191 ^ _782652 : [(42192 ^ _782652) ^ [_1617111] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1617047, tc_HOL_Obool)), _1617111), _1617049)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617047), _1617111))]]], (42200 ^ _782652) ^ [_1617255, _1617257, _1617259, _1617261] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1617255, tc_HOL_Obool)), _1617257), _1617259)), hBOOL(hAPP(hAPP(c_member(_1617255), _1617261), _1617257)), -(hBOOL(hAPP(hAPP(c_member(_1617255), _1617261), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617255, tc_HOL_Obool), _1617259))))], (42210 ^ _782652) ^ [_1617452, _1617454, _1617456, _1617458] : [hBOOL(hAPP(hAPP(c_member(_1617452), _1617454), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617452, tc_HOL_Obool), _1617456))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1617452, tc_HOL_Obool)), _1617458), _1617456)), -(hBOOL(hAPP(hAPP(c_member(_1617452), _1617454), _1617458)))], (42220 ^ _782652) ^ [_1617649, _1617651, _1617653, _1617655] : [hBOOL(hAPP(hAPP(c_member(_1617649), _1617651), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617649, tc_HOL_Obool), _1617653))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1617649, tc_HOL_Obool)), _1617655), _1617653)), -(hBOOL(hAPP(hAPP(c_member(_1617649), _1617651), _1617655)))], (42230 ^ _782652) ^ [_1617846, _1617848, _1617850] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1617846, tc_HOL_Obool)), _1617848), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1617846, tc_HOL_Obool), _1617850)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1617846, tc_HOL_Obool), tc_fun(_1617846, tc_HOL_Obool)), _1617850), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1617846, tc_HOL_Obool)), _1617848)))], (42242 ^ _782652) ^ [_1618190, _1618192, _1618194, _1618196, _1618198, _1618200, _1618202] : [42244 ^ _782652 : [(42245 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618190), 42243 ^ [_1618190, _1618192, _1618194, _1618196, _1618198, _1618200, _1618202]), _1618196)))], (42247 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1618198, 42243 ^ [_1618190, _1618192, _1618194, _1618196, _1618198, _1618200, _1618202]), _1618200), _1618202))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618190, tc_fun(_1618192, tc_fun(_1618194, tc_HOL_Obool))), _1618196), _1618198), _1618200), _1618202)))], (42232 ^ _782652) ^ [_1617943, _1617945, _1617947, _1617949, _1617951, _1617953, _1617955] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1617943, tc_fun(_1617945, tc_fun(_1617947, tc_HOL_Obool))), _1617949), _1617951), _1617953), _1617955)), 42235 ^ _782652 : [(42236 ^ _782652) ^ [_1618071] : [hBOOL(hAPP(hAPP(c_member(_1617943), _1618071), _1617949)), -(hBOOL(hAPP(hAPP(hAPP(_1617951, _1618071), _1617953), _1617955)))]]], (42261 ^ _782652) ^ [_1618692, _1618694, _1618696, _1618698, _1618700] : [42263 ^ _782652 : [(42264 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618692), 42262 ^ [_1618692, _1618694, _1618696, _1618698, _1618700]), _1618696)))], (42266 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1618698, 42262 ^ [_1618692, _1618694, _1618696, _1618698, _1618700]), _1618700))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618692, tc_fun(_1618694, tc_HOL_Obool)), _1618696), _1618698), _1618700)))], (42251 ^ _782652) ^ [_1618474, _1618476, _1618478, _1618480, _1618482] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618474, tc_fun(_1618476, tc_HOL_Obool)), _1618478), _1618480), _1618482)), 42254 ^ _782652 : [(42255 ^ _782652) ^ [_1618583] : [hBOOL(hAPP(hAPP(c_member(_1618474), _1618583), _1618478)), -(hBOOL(hAPP(hAPP(_1618480, _1618583), _1618482)))]]], (42270 ^ _782652) ^ [_1618915, _1618917, _1618919, _1618921] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618915, tc_fun(_1618917, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618915, tc_HOL_Obool), _1618919)), _1618921) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1618915, tc_HOL_Obool), tc_fun(_1618917, tc_HOL_Obool)), _1618919), hAPP(hAPP(c_COMBC(tc_fun(_1618915, tc_HOL_Obool), tc_fun(_1618915, tc_fun(_1618917, tc_HOL_Obool)), tc_fun(_1618917, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1618915, tc_fun(_1618917, tc_HOL_Obool))), _1618921)))], (42272 ^ _782652) ^ [_1619005, _1619007, _1619009, _1619011] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1619005, tc_HOL_Obool), tc_fun(_1619007, tc_HOL_Obool)), _1619009), hAPP(hAPP(c_COMBC(tc_fun(_1619005, tc_HOL_Obool), tc_fun(_1619005, tc_fun(_1619007, tc_HOL_Obool)), tc_fun(_1619007, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619005, tc_fun(_1619007, tc_HOL_Obool))), _1619011)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619005, tc_fun(_1619007, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619005, tc_HOL_Obool), _1619009)), _1619011))], (42274 ^ _782652) ^ [_1619095, _1619097, _1619099, _1619101] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619095, tc_HOL_Obool), hAPP(c_Set_Oimage(_1619097, tc_fun(_1619095, tc_HOL_Obool), _1619099), _1619101)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619097, tc_fun(_1619095, tc_HOL_Obool)), _1619101), _1619099))], (42276 ^ _782652) ^ [_1619152, _1619154, _1619156, _1619158] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1619152, tc_fun(_1619154, tc_HOL_Obool)), _1619156), _1619158) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619154, tc_HOL_Obool), hAPP(c_Set_Oimage(_1619152, tc_fun(_1619154, tc_HOL_Obool), _1619158), _1619156)))], (42278 ^ _782652) ^ [_1619209] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619209, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1619209, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1619209, tc_HOL_Obool)))], (42280 ^ _782652) ^ [_1619251, _1619253, _1619255] : [-(hAPP(c_Relation_ODomain(_1619251, _1619253), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1619251, _1619253), tc_HOL_Obool), _1619255)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1619251, _1619253), tc_HOL_Obool), tc_fun(_1619251, tc_HOL_Obool)), _1619255), c_Relation_ODomain(_1619251, _1619253)))], (42282 ^ _782652) ^ [_1619314, _1619316, _1619318] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619314, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619314, tc_HOL_Obool), _1619316)), _1619318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1619314, tc_HOL_Obool), tc_fun(_1619314, tc_HOL_Obool)), _1619316), hAPP(hAPP(c_COMBC(tc_fun(_1619314, tc_HOL_Obool), tc_fun(_1619314, tc_HOL_Obool), tc_fun(_1619314, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619314, tc_HOL_Obool))), _1619318)))], (42284 ^ _782652) ^ [_1619397, _1619399, _1619401] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619397, tc_HOL_Obool)), _1619399), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619397, tc_HOL_Obool), _1619401)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1619397, tc_HOL_Obool), tc_fun(_1619397, tc_HOL_Obool)), _1619401), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619397, tc_HOL_Obool)), _1619399)))], (42286 ^ _782652) ^ [_1619464, _1619466, _1619468, _1619470] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1619464, tc_fun(_1619466, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619464, tc_HOL_Obool), _1619468)), _1619470) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1619464, tc_HOL_Obool), tc_fun(_1619466, tc_HOL_Obool)), _1619468), hAPP(hAPP(c_COMBC(tc_fun(_1619464, tc_HOL_Obool), tc_fun(_1619464, tc_fun(_1619466, tc_HOL_Obool)), tc_fun(_1619466, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1619464, tc_fun(_1619466, tc_HOL_Obool))), _1619470)))], (42288 ^ _782652) ^ [_1619554, _1619556, _1619558, _1619560] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1619554, tc_HOL_Obool), tc_fun(_1619556, tc_HOL_Obool)), _1619558), hAPP(hAPP(c_COMBC(tc_fun(_1619554, tc_HOL_Obool), tc_fun(_1619554, tc_fun(_1619556, tc_HOL_Obool)), tc_fun(_1619556, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1619554, tc_fun(_1619556, tc_HOL_Obool))), _1619560)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1619554, tc_fun(_1619556, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619554, tc_HOL_Obool), _1619558)), _1619560))], (42290 ^ _782652) ^ [_1619644, _1619646, _1619648] : [-(hAPP(c_Relation_ORange(_1619644, _1619646), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1619644, _1619646), tc_HOL_Obool), _1619648)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1619644, _1619646), tc_HOL_Obool), tc_fun(_1619646, tc_HOL_Obool)), _1619648), c_Relation_ORange(_1619644, _1619646)))], (42292 ^ _782652) ^ [_1619707, _1619709, _1619711, _1619713] : [-(hAPP(c_Set_Oimage(_1619707, _1619709, _1619711), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619707, tc_HOL_Obool), _1619713)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1619707, tc_HOL_Obool), tc_fun(_1619709, tc_HOL_Obool)), _1619713), c_Set_Oimage(_1619707, _1619709, _1619711)))], (42294 ^ _782652) ^ [_1619768, _1619770, _1619772, _1619774] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1619768, _1619770), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619768, tc_HOL_Obool), _1619772)), _1619774) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1619768, tc_HOL_Obool), tc_fun(tc_prod(_1619768, _1619770), tc_HOL_Obool)), _1619772), hAPP(hAPP(c_COMBC(tc_fun(_1619768, tc_HOL_Obool), tc_fun(_1619768, tc_fun(_1619770, tc_HOL_Obool)), tc_fun(tc_prod(_1619768, _1619770), tc_HOL_Obool)), c_Product__Type_OSigma(_1619768, _1619770)), _1619774)))], (42296 ^ _782652) ^ [_1619858, _1619860, _1619862, _1619864] : [-(hAPP(c_Set_Ovimage(_1619858, _1619860, _1619862), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619860, tc_HOL_Obool), _1619864)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1619860, tc_HOL_Obool), tc_fun(_1619858, tc_HOL_Obool)), _1619864), c_Set_Ovimage(_1619858, _1619860, _1619862)))], (42298 ^ _782652) ^ [_1619919, _1619921, _1619923] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1619919, tc_HOL_Obool)), _1619921), _1619923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619919, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619919, tc_HOL_Obool), _1619923)), _1619921)))], (42304 ^ _782652) ^ [_1620050, _1620052] : [-(hAPP(c_Relation_OField(_1620050), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1620050, _1620050), tc_HOL_Obool), _1620052)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620050, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1620050, _1620050), tc_HOL_Obool), tc_fun(_1620050, tc_HOL_Obool), c_Relation_OField(_1620050)), _1620052)))], (42316 ^ _782652) ^ [_1620399, _1620401, _1620403] : [42318 ^ _782652 : [(42319 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1620399, tc_HOL_Obool)), 42317 ^ [_1620399, _1620401, _1620403]), _1620401)))], (42321 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620399, tc_HOL_Obool)), 42317 ^ [_1620399, _1620401, _1620403]), _1620403) = c_Orderings_Obot__class_Obot(tc_fun(_1620399, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620399, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620399, tc_HOL_Obool), _1620401)), _1620403) = c_Orderings_Obot__class_Obot(tc_fun(_1620399, tc_HOL_Obool)))], (42306 ^ _782652) ^ [_1620131, _1620133, _1620135] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620131, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620131, tc_HOL_Obool), _1620133)), _1620135) = c_Orderings_Obot__class_Obot(tc_fun(_1620131, tc_HOL_Obool)), 42309 ^ _782652 : [(42310 ^ _782652) ^ [_1620266] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1620131, tc_HOL_Obool)), _1620266), _1620133)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620131, tc_HOL_Obool)), _1620266), _1620135) = c_Orderings_Obot__class_Obot(tc_fun(_1620131, tc_HOL_Obool)))]]], (42325 ^ _782652) ^ [_1620662, _1620664] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620662, tc_HOL_Obool), hAPP(c_Set_OPow(_1620662), _1620664)) = _1620664)], (42327 ^ _782652) ^ [_1620698, _1620700, _1620702] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1620698, tc_HOL_Obool)), _1620700), _1620702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1620698, tc_HOL_Obool)), _1620700), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620698, tc_HOL_Obool), _1620702))))], (42333 ^ _782652) ^ [_1620829, _1620831, _1620833] : [class_Complete__Lattice_Ocomplete__lattice(_1620829), class_Orderings_Olinorder(_1620829), 42340 ^ _782652 : [(42341 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1620829), _1620831), c_Complete__Lattice_OSup__class_OSup(_1620829, _1620833))), 42345 ^ _782652 : [(42346 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620829), 42344 ^ [_1620829, _1620831, _1620833]), _1620833)))], (42348 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1620829), _1620831), 42344 ^ [_1620829, _1620831, _1620833])))]]], (42350 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1620829), _1620831), c_Complete__Lattice_OSup__class_OSup(_1620829, _1620833)))), 42351 ^ _782652 : [(42352 ^ _782652) ^ [_1621135] : [hBOOL(hAPP(hAPP(c_member(_1620829), _1621135), _1620833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1620829), _1620831), _1621135))]]]]], (42360 ^ _782652) ^ [_1621289, _1621291, _1621293] : [class_Complete__Lattice_Ocomplete__lattice(_1621289), class_Orderings_Olinorder(_1621289), 42367 ^ _782652 : [(42368 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1621289), c_Complete__Lattice_OInf__class_OInf(_1621289, _1621291)), _1621293)), 42372 ^ _782652 : [(42373 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621289), 42371 ^ [_1621289, _1621291, _1621293]), _1621291)))], (42375 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1621289), 42371 ^ [_1621289, _1621291, _1621293]), _1621293)))]]], (42377 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1621289), c_Complete__Lattice_OInf__class_OInf(_1621289, _1621291)), _1621293))), 42378 ^ _782652 : [(42379 ^ _782652) ^ [_1621595] : [hBOOL(hAPP(hAPP(c_member(_1621289), _1621595), _1621291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1621289), _1621595), _1621293))]]]]], (42387 ^ _782652) ^ [_1621749, _1621751, _1621753] : [class_Complete__Lattice_Ocomplete__lattice(_1621749), 42390 ^ _782652 : [(42401 ^ _782652) ^ [] : [42403 ^ _782652 : [(42404 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621749), 42402 ^ [_1621749, _1621751, _1621753]), _1621753)))], (42406 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621749), _1621751), 42402 ^ [_1621749, _1621751, _1621753]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621749), _1621751), c_Complete__Lattice_OInf__class_OInf(_1621749, _1621753))))], (42391 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621749), _1621751), c_Complete__Lattice_OInf__class_OInf(_1621749, _1621753))), 42394 ^ _782652 : [(42395 ^ _782652) ^ [_1621907] : [hBOOL(hAPP(hAPP(c_member(_1621749), _1621907), _1621753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621749), _1621751), _1621907)))]]]]], (42410 ^ _782652) ^ [_1622183, _1622185, _1622187] : [class_Complete__Lattice_Ocomplete__lattice(_1622183), 42413 ^ _782652 : [(42424 ^ _782652) ^ [] : [42426 ^ _782652 : [(42427 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622183), 42425 ^ [_1622183, _1622185, _1622187]), _1622185)))], (42429 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1622183), 42425 ^ [_1622183, _1622185, _1622187]), _1622187))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1622183), c_Complete__Lattice_OSup__class_OSup(_1622183, _1622185)), _1622187)))], (42414 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1622183), c_Complete__Lattice_OSup__class_OSup(_1622183, _1622185)), _1622187)), 42417 ^ _782652 : [(42418 ^ _782652) ^ [_1622341] : [hBOOL(hAPP(hAPP(c_member(_1622183), _1622341), _1622185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1622183), _1622341), _1622187)))]]]]], (42433 ^ _782652) ^ [_1622617, _1622619] : [class_Complete__Lattice_Ocomplete__lattice(_1622617), -(c_Complete__Lattice_OSup__class_OSup(_1622617, _1622619) = c_Complete__Lattice_OInf__class_OInf(_1622617, hAPP(c_Set_OCollect(_1622617), hAPP(hAPP(c_COMBB(tc_fun(_1622617, tc_HOL_Obool), tc_HOL_Obool, _1622617), c_HOL_OAll(_1622617)), hAPP(hAPP(c_COMBB(tc_fun(_1622617, tc_HOL_Obool), tc_fun(_1622617, tc_HOL_Obool), _1622617), hAPP(c_COMBS(_1622617, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1622617), c_fimplies), hAPP(hAPP(c_COMBC(_1622617, tc_fun(_1622617, tc_HOL_Obool), tc_HOL_Obool), c_member(_1622617)), _1622619)))), hAPP(c_COMBC(_1622617, _1622617, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1622617)))))))], (42439 ^ _782652) ^ [_1622858, _1622860] : [class_Complete__Lattice_Ocomplete__lattice(_1622858), -(c_Complete__Lattice_OInf__class_OInf(_1622858, _1622860) = c_Complete__Lattice_OSup__class_OSup(_1622858, hAPP(c_Set_OCollect(_1622858), hAPP(hAPP(c_COMBB(tc_fun(_1622858, tc_HOL_Obool), tc_HOL_Obool, _1622858), c_HOL_OAll(_1622858)), hAPP(hAPP(c_COMBB(tc_fun(_1622858, tc_HOL_Obool), tc_fun(_1622858, tc_HOL_Obool), _1622858), hAPP(c_COMBS(_1622858, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1622858), c_fimplies), hAPP(hAPP(c_COMBC(_1622858, tc_fun(_1622858, tc_HOL_Obool), tc_HOL_Obool), c_member(_1622858)), _1622860)))), c_Orderings_Oord__class_Oless__eq(_1622858))))))], (42445 ^ _782652) ^ [_1623085, _1623087, _1623089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1623085, tc_HOL_Obool), tc_HOL_Obool)), _1623087), _1623089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1623085, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623085, tc_HOL_Obool), _1623087)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623085, tc_HOL_Obool), _1623089))))], (42451 ^ _782652) ^ [_1623234, _1623236, _1623238] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623234, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1623234, tc_HOL_Obool)), _1623236), _1623238)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623234, tc_HOL_Obool)), _1623236), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623234, tc_HOL_Obool), _1623238)))], (42453 ^ _782652) ^ [_1623295, _1623297, _1623299] : [c_Equiv__Relations_Oequiv(_1623295, _1623297, _1623299), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623295, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1623295), _1623297), _1623299)) = _1623297)], (42459 ^ _782652) ^ [_1623404, _1623406] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1623404), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623404, tc_HOL_Obool), _1623406))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1623404, tc_HOL_Obool)), _1623406)))], (42465 ^ _782652) ^ [_1623515, _1623517] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1623515, tc_HOL_Obool), tc_HOL_Obool)), _1623517), hAPP(c_Set_OPow(_1623515), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623515, tc_HOL_Obool), _1623517)))))], (42467 ^ _782652) ^ [_1623564, _1623566, _1623568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1623564, tc_HOL_Obool), tc_HOL_Obool)), _1623566), _1623568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1623564, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1623564, tc_HOL_Obool), _1623568)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1623564, tc_HOL_Obool), _1623566))))], (42473 ^ _782652) ^ [_1623713] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1623713, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1623713, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1623713, tc_HOL_Obool)))], (42475 ^ _782652) ^ [_1623755, _1623757] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1623755, tc_HOL_Obool), _1623757) = hAPP(c_Set_OCollect(_1623755), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1623755, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1623755), c_HOL_OAll(tc_fun(_1623755, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1623755, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1623755, tc_HOL_Obool), tc_HOL_Obool), _1623755), hAPP(c_COMBS(tc_fun(_1623755, 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(_1623755, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1623755, tc_HOL_Obool), tc_fun(tc_fun(_1623755, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1623755, tc_HOL_Obool))), _1623757)))), c_member(_1623755)))))], (42477 ^ _782652) ^ [_1623883] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623883, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1623883, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1623883, tc_HOL_Obool)))], (42479 ^ _782652) ^ [_1623925, _1623927, _1623929] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623925, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1623925, tc_HOL_Obool), tc_HOL_Obool)), _1623927), _1623929)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623925, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623925, tc_HOL_Obool), _1623927)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623925, tc_HOL_Obool), _1623929)))], (42481 ^ _782652) ^ [_1623995, _1623997, _1623999] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1623995, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1623995, tc_HOL_Obool)), _1623997), _1623999)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1623995, tc_HOL_Obool)), _1623997), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1623995, tc_HOL_Obool), _1623999)))], (42483 ^ _782652) ^ [_1624056, _1624058, _1624060, _1624062] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1624056, tc_fun(_1624058, tc_HOL_Obool)), _1624060), _1624062) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624058, tc_HOL_Obool), hAPP(c_Set_Oimage(_1624056, tc_fun(_1624058, tc_HOL_Obool), _1624062), _1624060)))], (42485 ^ _782652) ^ [_1624113, _1624115, _1624117, _1624119] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624113, tc_HOL_Obool), hAPP(c_Set_Oimage(_1624115, tc_fun(_1624113, tc_HOL_Obool), _1624117), _1624119)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1624115, tc_fun(_1624113, tc_HOL_Obool)), _1624119), _1624117))], (42487 ^ _782652) ^ [_1624170, _1624172, _1624174] : [class_Complete__Lattice_Ocomplete__lattice(_1624170), hBOOL(hAPP(hAPP(c_member(_1624170), _1624172), _1624174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624170), _1624172), c_Complete__Lattice_OSup__class_OSup(_1624170, _1624174))))], (42497 ^ _782652) ^ [_1624335] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1624335, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1624335, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1624335, tc_HOL_Obool)))], (42499 ^ _782652) ^ [_1624377, _1624379, _1624381] : [class_Complete__Lattice_Ocomplete__lattice(_1624377), hBOOL(hAPP(hAPP(c_member(_1624377), _1624379), _1624381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624377), c_Complete__Lattice_OInf__class_OInf(_1624377, _1624381)), _1624379)))], (42509 ^ _782652) ^ [_1624542] : [class_Complete__Lattice_Ocomplete__lattice(_1624542), -(c_Complete__Lattice_OSup__class_OSup(_1624542, c_Orderings_Obot__class_Obot(tc_fun(_1624542, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1624542))], (42515 ^ _782652) ^ [_1624635, _1624637, _1624639] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1624635, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1624635, tc_HOL_Obool), tc_HOL_Obool)), _1624637), _1624639)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624635, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1624635, tc_HOL_Obool), _1624637)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1624635, tc_HOL_Obool), _1624639)))], (42517 ^ _782652) ^ [_1624705, _1624707] : [class_Complete__Lattice_Ocomplete__lattice(_1624705), -(c_Complete__Lattice_OSup__class_OSup(_1624705, hAPP(hAPP(c_Set_Oinsert(_1624705), _1624707), c_Orderings_Obot__class_Obot(tc_fun(_1624705, tc_HOL_Obool)))) = _1624707)], (42523 ^ _782652) ^ [_1624812, _1624814, _1624816] : [class_Complete__Lattice_Ocomplete__lattice(_1624812), -(c_Complete__Lattice_OSup__class_OSup(_1624812, hAPP(hAPP(c_Set_Oinsert(_1624812), _1624814), _1624816)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1624812), _1624814), c_Complete__Lattice_OSup__class_OSup(_1624812, _1624816)))], (42529 ^ _782652) ^ [_1624933, _1624935, _1624937, _1624939, _1624941] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1624933, tc_fun(_1624935, tc_HOL_Obool)), _1624937), hAPP(hAPP(c_COMBS(_1624933, tc_fun(_1624935, tc_HOL_Obool), tc_fun(_1624935, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1624935, tc_HOL_Obool), tc_fun(tc_fun(_1624935, tc_HOL_Obool), tc_fun(_1624935, tc_HOL_Obool)), _1624933), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624935, tc_HOL_Obool))), _1624939)), _1624941)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624935, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1624935, tc_HOL_Obool), hAPP(c_Set_Oimage(_1624933, tc_fun(_1624935, tc_HOL_Obool), _1624939), _1624937))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1624935, tc_HOL_Obool), hAPP(c_Set_Oimage(_1624933, tc_fun(_1624935, tc_HOL_Obool), _1624941), _1624937))))], (42531 ^ _782652) ^ [_1625062, _1625064] : [class_Complete__Lattice_Ocomplete__lattice(_1625062), -(c_Complete__Lattice_OInf__class_OInf(_1625062, hAPP(hAPP(c_Set_Oinsert(_1625062), _1625064), c_Orderings_Obot__class_Obot(tc_fun(_1625062, tc_HOL_Obool)))) = _1625064)], (42537 ^ _782652) ^ [_1625169] : [class_Complete__Lattice_Ocomplete__lattice(_1625169), -(c_Complete__Lattice_OSup__class_OSup(_1625169, c_Orderings_Otop__class_Otop(tc_fun(_1625169, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1625169))], (42543 ^ _782652) ^ [_1625262] : [class_Complete__Lattice_Ocomplete__lattice(_1625262), -(c_Complete__Lattice_OInf__class_OInf(_1625262, c_Orderings_Obot__class_Obot(tc_fun(_1625262, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1625262))], (42549 ^ _782652) ^ [_1625355] : [class_Complete__Lattice_Ocomplete__lattice(_1625355), -(c_Complete__Lattice_OInf__class_OInf(_1625355, c_Orderings_Otop__class_Otop(tc_fun(_1625355, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1625355))], (42555 ^ _782652) ^ [_1625448, _1625450, _1625452] : [class_Complete__Lattice_Ocomplete__lattice(_1625448), -(c_Complete__Lattice_OInf__class_OInf(_1625448, hAPP(hAPP(c_Set_Oinsert(_1625448), _1625450), _1625452)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1625448), _1625450), c_Complete__Lattice_OInf__class_OInf(_1625448, _1625452)))], (42561 ^ _782652) ^ [_1625569, _1625571, _1625573] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1625569, tc_HOL_Obool)), _1625571), _1625573) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625569, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1625569, tc_HOL_Obool)), _1625571), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1625569, tc_HOL_Obool)), _1625573), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1625569, tc_HOL_Obool), tc_HOL_Obool))))))], (42563 ^ _782652) ^ [_1625643, _1625645, _1625647, _1625649, _1625651] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1625643, tc_fun(_1625645, tc_HOL_Obool)), _1625647), hAPP(hAPP(c_COMBS(_1625643, tc_fun(_1625645, tc_HOL_Obool), tc_fun(_1625645, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1625645, tc_HOL_Obool), tc_fun(tc_fun(_1625645, tc_HOL_Obool), tc_fun(_1625645, tc_HOL_Obool)), _1625643), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1625645, tc_HOL_Obool))), _1625649)), _1625651)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1625645, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625645, tc_HOL_Obool), hAPP(c_Set_Oimage(_1625643, tc_fun(_1625645, tc_HOL_Obool), _1625649), _1625647))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625645, tc_HOL_Obool), hAPP(c_Set_Oimage(_1625643, tc_fun(_1625645, tc_HOL_Obool), _1625651), _1625647))))], (42565 ^ _782652) ^ [_1625772, _1625774, _1625776] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1625772, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625772, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1625772, tc_HOL_Obool), tc_HOL_Obool)), _1625774), _1625776))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1625772, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625772, tc_HOL_Obool), _1625774)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1625772, tc_HOL_Obool), _1625776)))))], (42567 ^ _782652) ^ [_1625852, _1625854, _1625856] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1625852, tc_HOL_Obool)), _1625854), _1625856) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1625852, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1625852, tc_HOL_Obool)), _1625854), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1625852, tc_HOL_Obool)), _1625856), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1625852, tc_HOL_Obool), tc_HOL_Obool))))))], (42569 ^ _782652) ^ [_1625926, _1625928, _1625930] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1625926, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1625926, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1625926, tc_HOL_Obool), _1625928)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1625926, tc_HOL_Obool), _1625930))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1625926, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1625926, tc_HOL_Obool), tc_HOL_Obool)), _1625928), _1625930)))))], (42571 ^ _782652) ^ [_1626006, _1626008, _1626010] : [class_Complete__Lattice_Ocomplete__lattice(_1626006), -(c_Complete__Lattice_OSup__class_OSup(_1626006, hAPP(hAPP(c_Set_Oinsert(_1626006), _1626008), hAPP(hAPP(c_Set_Oinsert(_1626006), _1626010), c_Orderings_Obot__class_Obot(tc_fun(_1626006, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1626006), _1626008), _1626010))], (42577 ^ _782652) ^ [_1626147, _1626149, _1626151] : [class_Complete__Lattice_Ocomplete__lattice(_1626147), -(c_Complete__Lattice_OInf__class_OInf(_1626147, hAPP(hAPP(c_Set_Oinsert(_1626147), _1626149), hAPP(hAPP(c_Set_Oinsert(_1626147), _1626151), c_Orderings_Obot__class_Obot(tc_fun(_1626147, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1626147), _1626149), _1626151))], (42583 ^ _782652) ^ [_1626288, _1626290, _1626292] : [class_Complete__Lattice_Ocomplete__lattice(_1626288), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626288), _1626290)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1626288), _1626292), c_Complete__Lattice_OSup__class_OSup(_1626288, _1626290)) = hAPP(hAPP(c_Finite__Set_Ofold(_1626288, _1626288, c_Lattices_Osemilattice__sup__class_Osup(_1626288)), _1626292), _1626290))], (42593 ^ _782652) ^ [_1626473, _1626475] : [class_Complete__Lattice_Ocomplete__lattice(_1626473), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626473), _1626475)), -(_1626475 = c_Orderings_Obot__class_Obot(tc_fun(_1626473, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1626473, _1626475) = c_Complete__Lattice_OSup__class_OSup(_1626473, _1626475))], (42607 ^ _782652) ^ [_1626645, _1626647, _1626649] : [class_Complete__Lattice_Ocomplete__lattice(_1626645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626645), _1626647)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1626645), _1626649), c_Complete__Lattice_OInf__class_OInf(_1626645, _1626647)) = hAPP(hAPP(c_Finite__Set_Ofold(_1626645, _1626645, c_Lattices_Osemilattice__inf__class_Oinf(_1626645)), _1626649), _1626647))], (42617 ^ _782652) ^ [_1626830, _1626832] : [class_Complete__Lattice_Ocomplete__lattice(_1626830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626830), _1626832)), -(_1626832 = c_Orderings_Obot__class_Obot(tc_fun(_1626830, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1626830, _1626832) = c_Complete__Lattice_OInf__class_OInf(_1626830, _1626832))], (42631 ^ _782652) ^ [_1627002, _1627004, _1627006, _1627008, _1627010, _1627012, _1627014, _1627016] : [c_Fun_Oinj__on(_1627002, _1627004, _1627006, _1627008), 42637 ^ _782652 : [(42638 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627010), 42636 ^ [_1627002, _1627004, _1627006, _1627008, _1627010, _1627012, _1627014, _1627016]), _1627012)))], (42640 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1627002, tc_HOL_Obool)), hAPP(_1627014, 42636 ^ [_1627002, _1627004, _1627006, _1627008, _1627010, _1627012, _1627014, _1627016])), _1627008))]], hBOOL(hAPP(hAPP(c_member(_1627010), _1627016), _1627012)), -(hAPP(c_Set_Oimage(_1627002, _1627004, _1627006), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627010, tc_fun(_1627002, tc_HOL_Obool)), _1627012), _1627014)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1627010, tc_fun(_1627004, tc_HOL_Obool)), _1627012), hAPP(hAPP(c_COMBB(tc_fun(_1627002, tc_HOL_Obool), tc_fun(_1627004, tc_HOL_Obool), _1627010), c_Set_Oimage(_1627002, _1627004, _1627006)), _1627014)))], (42648 ^ _782652) ^ [_1627491, _1627493, _1627495] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1627491, tc_HOL_Obool)), _1627493)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627491), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1627491, tc_HOL_Obool), _1627493))), 42658 ^ _782652 : [(42659 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1627491, tc_HOL_Obool)), 42657 ^ [_1627491, _1627493, _1627495]), _1627493)))], (42661 ^ _782652) ^ [] : [hAPP(c_Finite__Set_Ocard(_1627491), 42657 ^ [_1627491, _1627493, _1627495]) = _1627495]], 42665 ^ _782652 : [(42666 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1627491, tc_HOL_Obool)), 42664 ^ [_1627491, _1627493, _1627495]), _1627493)))], (42669 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1627491, tc_HOL_Obool)), 42667 ^ [_1627491, _1627493, _1627495]), _1627493)))], (42671 ^ _782652) ^ [] : [42664 ^ [_1627491, _1627493, _1627495] = 42667 ^ [_1627491, _1627493, _1627495]], (42673 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1627491, tc_HOL_Obool)), 42664 ^ [_1627491, _1627493, _1627495]), 42667 ^ [_1627491, _1627493, _1627495]) = c_Orderings_Obot__class_Obot(tc_fun(_1627491, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1627495), hAPP(c_Finite__Set_Ocard(tc_fun(_1627491, tc_HOL_Obool)), _1627493)) = hAPP(c_Finite__Set_Ocard(_1627491), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1627491, tc_HOL_Obool), _1627493)))], (42677 ^ _782652) ^ [_1628273, _1628275] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1628273, tc_HOL_Obool), _1628275) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1628273, tc_HOL_Obool), tc_fun(_1628273, tc_HOL_Obool)), _1628275), c_COMBI(tc_fun(_1628273, tc_HOL_Obool))))], (42679 ^ _782652) ^ [_1628324, _1628326] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1628324, tc_HOL_Obool), _1628326) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1628324, tc_HOL_Obool), tc_fun(_1628324, tc_HOL_Obool)), _1628326), c_COMBI(tc_fun(_1628324, tc_HOL_Obool))))], (42681 ^ _782652) ^ [_1628375, _1628377] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1628375, tc_HOL_Obool)), _1628377)), 42687 ^ _782652 : [(42688 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628375, tc_HOL_Obool)), 42686 ^ [_1628375, _1628377]), _1628377)))], (42690 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1628375), 42686 ^ [_1628375, _1628377]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1628375), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1628375, tc_HOL_Obool), _1628377))))], (42694 ^ _782652) ^ [_1628633, _1628635, _1628637] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628633, tc_HOL_Obool)), _1628635), _1628637))), 42700 ^ _782652 : [(42701 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628633, tc_HOL_Obool)), 42699 ^ [_1628633, _1628635, _1628637]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1628633, tc_HOL_Obool)), _1628635), _1628637))))], (42704 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1628633, tc_HOL_Obool)), 42702 ^ [_1628633, _1628635, _1628637]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1628633, tc_HOL_Obool)), _1628635), _1628637))))], (42706 ^ _782652) ^ [] : [42699 ^ [_1628633, _1628635, _1628637] = 42702 ^ [_1628633, _1628635, _1628637]], (42708 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628633, tc_HOL_Obool)), 42699 ^ [_1628633, _1628635, _1628637]), 42702 ^ [_1628633, _1628635, _1628637]) = c_Orderings_Obot__class_Obot(tc_fun(_1628633, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1628633, tc_HOL_Obool)), _1628635), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1628633, tc_HOL_Obool), _1628637)) = c_Orderings_Obot__class_Obot(tc_fun(_1628633, tc_HOL_Obool)))], (42712 ^ _782652) ^ [_1629226, _1629228, _1629230, _1629232] : [-(_1629226 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1629228, tc_HOL_Obool), tc_HOL_Obool))), 42718 ^ _782652 : [(42719 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1629228, tc_HOL_Obool)), 42717 ^ [_1629226, _1629228, _1629230, _1629232]), _1629226)))], (42721 ^ _782652) ^ [] : [c_Fun_Oinj__on(_1629228, _1629230, _1629232, 42717 ^ [_1629226, _1629228, _1629230, _1629232])]], -(c_Fun_Oinj__on(_1629228, _1629230, _1629232, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1629228, tc_HOL_Obool), _1629226)))], (42725 ^ _782652) ^ [_1629487, _1629489, _1629491] : [42727 ^ _782652 : [(42728 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1629487, tc_HOL_Obool)), 42726 ^ [_1629487, _1629489, _1629491]), _1629489)))], (42730 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1629487, tc_HOL_Obool)), 42726 ^ [_1629487, _1629489, _1629491]), _1629491))]], -(_1629489 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1629487, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1629487, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1629487, tc_HOL_Obool), _1629489)), _1629491)))], (42738 ^ _782652) ^ [_1629748, _1629750, _1629752, _1629754, _1629756, _1629758] : [-(_1629748 = c_Orderings_Obot__class_Obot(tc_fun(_1629750, tc_HOL_Obool))), 42744 ^ _782652 : [(42745 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1629750), 42743 ^ [_1629748, _1629750, _1629752, _1629754, _1629756, _1629758]), _1629748)))], (42747 ^ _782652) ^ [] : [c_Fun_Oinj__on(_1629752, _1629754, _1629756, hAPP(_1629758, 42743 ^ [_1629748, _1629750, _1629752, _1629754, _1629756, _1629758]))]], -(c_Fun_Oinj__on(_1629752, _1629754, _1629756, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1629750, tc_fun(_1629752, tc_HOL_Obool)), _1629748), _1629758)))], (42751 ^ _782652) ^ [_1630040, _1630042, _1630044, _1630046, _1630048, _1630050, _1630052] : [c_Finite__Set_Ofun__left__comm(_1630040, _1630042, _1630044), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1630040, _1630042, _1630044, _1630046, hAPP(hAPP(c_Set_Oinsert(_1630040), _1630048), _1630050)), _1630052)), -(hBOOL(hAPP(hAPP(c_member(_1630040), _1630048), _1630050))), 42763 ^ _782652 : [(42764 ^ _782652) ^ [] : [-(_1630052 = hAPP(hAPP(_1630044, _1630048), 42762 ^ [_1630040, _1630042, _1630044, _1630046, _1630048, _1630050, _1630052]))], (42766 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1630040, _1630042, _1630044, _1630046, _1630050), 42762 ^ [_1630040, _1630042, _1630044, _1630046, _1630048, _1630050, _1630052])))]]], (42768 ^ _782652) ^ [_1630366, _1630368, _1630370, _1630372] : [class_Orderings_Olinorder(_1630366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630366), _1630368)), 42778 ^ _782652 : [(42779 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630366), 42777 ^ [_1630366, _1630368, _1630370, _1630372]), _1630368)))], (42781 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630366), 42777 ^ [_1630366, _1630368, _1630370, _1630372]), _1630370))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630366), hAPP(hAPP(c_Finite__Set_Ofold(_1630366, _1630366, c_Orderings_Oord__class_Omax(_1630366)), _1630372), _1630368)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1630366), _1630370), _1630372))))], (42785 ^ _782652) ^ [_1630730, _1630732, _1630734, _1630736] : [class_Orderings_Olinorder(_1630730), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630730), _1630732)), 42795 ^ _782652 : [(42796 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630730), 42794 ^ [_1630730, _1630732, _1630734, _1630736]), _1630732)))], (42798 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630730), _1630734), 42794 ^ [_1630730, _1630732, _1630734, _1630736]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1630730), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1630730), _1630734), _1630736)), hAPP(hAPP(c_Finite__Set_Ofold(_1630730, _1630730, c_Orderings_Oord__class_Omin(_1630730)), _1630736), _1630732))))], (42802 ^ _782652) ^ [_1631094, _1631096, _1631098] : [42804 ^ _782652 : [(42805 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1631094, tc_HOL_Obool)), 42803 ^ [_1631094, _1631096, _1631098]), _1631096)))], (42807 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1631094), _1631098), 42803 ^ [_1631094, _1631096, _1631098]))]], -(hBOOL(hAPP(hAPP(c_member(_1631094), _1631098), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1631094, tc_HOL_Obool), _1631096))))], (42811 ^ _782652) ^ [_1631310, _1631312, _1631314, _1631316] : [class_Lattices_Osemilattice__inf(_1631310), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631310), _1631312)), 42821 ^ _782652 : [(42822 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1631310), 42820 ^ [_1631310, _1631312, _1631314, _1631316]), _1631312)))], (42824 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1631310), _1631314), 42820 ^ [_1631310, _1631312, _1631314, _1631316]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1631310), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1631310), _1631314), _1631316)), hAPP(hAPP(c_Finite__Set_Ofold(_1631310, _1631310, c_Lattices_Osemilattice__inf__class_Oinf(_1631310)), _1631316), _1631312))))], (42828 ^ _782652) ^ [_1631674, _1631676, _1631678, _1631680] : [class_Lattices_Osemilattice__sup(_1631674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1631674), _1631676)), 42838 ^ _782652 : [(42839 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1631674), 42837 ^ [_1631674, _1631676, _1631678, _1631680]), _1631676)))], (42841 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1631674), 42837 ^ [_1631674, _1631676, _1631678, _1631680]), _1631678))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1631674), hAPP(hAPP(c_Finite__Set_Ofold(_1631674, _1631674, c_Lattices_Osemilattice__sup__class_Osup(_1631674)), _1631680), _1631676)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1631674), _1631678), _1631680))))], (42862 ^ _782652) ^ [_1632572, _1632574] : [-(c_Wellfounded_Owf(_1632572, _1632574)), 42865 ^ _782652 : [(42866 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1632572), 42864 ^ [_1632572, _1632574]), 42863 ^ [_1632572, _1632574])))], (42868 ^ _782652) ^ [_1632792] : [hBOOL(hAPP(hAPP(c_member(_1632572), _1632792), 42863 ^ [_1632572, _1632574])), 42872 ^ _782652 : [(42873 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632572, _1632572)), hAPP(hAPP(c_Product__Type_OPair(_1632572, _1632572), 42871 ^ [_1632572, _1632574, _1632792]), _1632792)), _1632574)))], (42875 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1632572), 42871 ^ [_1632572, _1632574, _1632792]), 42863 ^ [_1632572, _1632574])))]]]]], (42845 ^ _782652) ^ [_1632053, _1632055] : [c_Wellfounded_Owf(_1632053, _1632055), 42848 ^ _782652 : [(42849 ^ _782652) ^ [_1632185] : [42850 ^ _782652 : [(42851 ^ _782652) ^ [_1632290] : [hBOOL(hAPP(hAPP(c_member(_1632053), _1632290), _1632185))]], 42853 ^ _782652 : [(42854 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1632053), 42852 ^ [_1632053, _1632055, _1632185]), _1632185)))], (42856 ^ _782652) ^ [_1632412] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632053, _1632053)), hAPP(hAPP(c_Product__Type_OPair(_1632053, _1632053), _1632412), 42852 ^ [_1632053, _1632055, _1632185])), _1632055)), hBOOL(hAPP(hAPP(c_member(_1632053), _1632412), _1632185))]]]]], (42879 ^ _782652) ^ [_1633048, _1633050] : [-(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)))), _1633048)) = 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)))), _1633050))), 42881 ^ _782652 : [(42882 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 42880 ^ [_1633048, _1633050])))], (42884 ^ _782652) ^ [] : [42885 ^ _782652 : [(42886 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1633048, 42880 ^ [_1633048, _1633050])))], (42888 ^ _782652) ^ [] : [hBOOL(hAPP(_1633050, 42880 ^ [_1633048, _1633050]))]], 42889 ^ _782652 : [(42890 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1633050, 42880 ^ [_1633048, _1633050])))], (42892 ^ _782652) ^ [] : [hBOOL(hAPP(_1633048, 42880 ^ [_1633048, _1633050]))]]]]], (42896 ^ _782652) ^ [_1633369, _1633371, _1633373] : [hBOOL(hAPP(hAPP(c_member(_1633369), _1633371), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1633369, tc_HOL_Obool), _1633373))), 42900 ^ _782652 : [(42901 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633369), _1633371), 42899 ^ [_1633369, _1633371, _1633373])))], (42903 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1633369, tc_HOL_Obool)), 42899 ^ [_1633369, _1633371, _1633373]), _1633373)))]]], (42905 ^ _782652) ^ [_1633561, _1633563, _1633565, _1633567, _1633569, _1633571] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633561, _1633563)), _1633565), hAPP(hAPP(c_Relation_Orel__comp(_1633561, _1633567, _1633563), _1633569), _1633571))), 42911 ^ _782652 : [(42912 ^ _782652) ^ [] : [-(_1633565 = hAPP(hAPP(c_Product__Type_OPair(_1633561, _1633563), 42908 ^ [_1633561, _1633563, _1633565, _1633567, _1633569, _1633571]), 42910 ^ [_1633561, _1633563, _1633565, _1633567, _1633569, _1633571]))], (42914 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633561, _1633567)), hAPP(hAPP(c_Product__Type_OPair(_1633561, _1633567), 42908 ^ [_1633561, _1633563, _1633565, _1633567, _1633569, _1633571]), 42909 ^ [_1633561, _1633563, _1633565, _1633567, _1633569, _1633571])), _1633569)))], (42916 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633567, _1633563)), hAPP(hAPP(c_Product__Type_OPair(_1633567, _1633563), 42909 ^ [_1633561, _1633563, _1633565, _1633567, _1633569, _1633571]), 42910 ^ [_1633561, _1633563, _1633565, _1633567, _1633569, _1633571])), _1633571)))]]], (42918 ^ _782652) ^ [_1633939, _1633941, _1633943, _1633945] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633939, _1633941)), _1633943), hAPP(c_Relation_Oconverse(_1633941, _1633939), _1633945))), 42923 ^ _782652 : [(42924 ^ _782652) ^ [] : [-(_1633943 = hAPP(hAPP(c_Product__Type_OPair(_1633939, _1633941), 42922 ^ [_1633939, _1633941, _1633943, _1633945]), 42921 ^ [_1633939, _1633941, _1633943, _1633945]))], (42926 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633941, _1633939)), hAPP(hAPP(c_Product__Type_OPair(_1633941, _1633939), 42921 ^ [_1633939, _1633941, _1633943, _1633945]), 42922 ^ [_1633939, _1633941, _1633943, _1633945])), _1633945)))]]], (42928 ^ _782652) ^ [_1634192, _1634194, _1634196] : [-(c_Nitpick_Oplus__frac(_1634192, _1634194, _1634196) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1634192), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1634192), _1634194), hAPP(c_Nitpick_Odenom(_1634192), _1634196))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1634192), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1634192), tc_Int_Oint), c_Nitpick_Ofrac(_1634192)), 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(_1634192), _1634194))), 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(_1634192), _1634194))))), 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(_1634192), _1634196))), 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(_1634192), _1634196)))))), c_COMBI(tc_Int_Oint))))], (42930 ^ _782652) ^ [_1634319, _1634321, _1634323, _1634325, _1634327, _1634329] : [-(hBOOL(hAPP(hAPP(c_member(_1634319), _1634321), c_Map_Odom(_1634319, _1634323, _1634325)))), -(c_Map_Omap__add(_1634319, _1634323, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1634319, tc_Option_Ooption(_1634323)), _1634327), _1634321), hAPP(c_Option_Ooption_OSome(_1634323), _1634329)), _1634325) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1634319, tc_Option_Ooption(_1634323)), c_Map_Omap__add(_1634319, _1634323, _1634327, _1634325)), _1634321), hAPP(c_Option_Ooption_OSome(_1634323), _1634329)))], (42936 ^ _782652) ^ [_1634418, _1634420, _1634422, _1634424, _1634426] : [-(hBOOL(hAPP(hAPP(c_member(_1634418), _1634420), c_Map_Odom(_1634418, _1634422, _1634424)))), -(hAPP(c_Map_Omap__add(_1634418, _1634422, _1634424, _1634426), _1634420) = hAPP(_1634426, _1634420))], (42942 ^ _782652) ^ [_1634478, _1634480, _1634482, _1634484, _1634486] : [-(hBOOL(hAPP(hAPP(c_member(_1634478), _1634480), c_Map_Odom(_1634478, _1634482, _1634484)))), -(hAPP(c_Map_Omap__add(_1634478, _1634482, _1634486, _1634484), _1634480) = hAPP(_1634486, _1634480))], (42948 ^ _782652) ^ [_1634542, _1634544, _1634546, _1634548, _1634550] : [hBOOL(hAPP(hAPP(c_member(_1634542), _1634544), c_Map_Odom(_1634542, _1634546, _1634548))), -(hAPP(c_Map_Omap__add(_1634542, _1634546, _1634550, _1634548), _1634544) = hAPP(_1634548, _1634544))], (42954 ^ _782652) ^ [_1634669, _1634671, _1634673] : [-(c_Map_Omap__add(_1634669, _1634671, _1634673, hAPP(c_COMBK(tc_Option_Ooption(_1634671), _1634669), c_Option_Ooption_ONone(_1634671))) = _1634673)], (42956 ^ _782652) ^ [_1634711, _1634713, _1634715] : [-(c_Map_Omap__add(_1634711, _1634713, hAPP(c_COMBK(tc_Option_Ooption(_1634713), _1634711), c_Option_Ooption_ONone(_1634713)), _1634715) = _1634715)], (42958 ^ _782652) ^ [_1634753, _1634755, _1634757, _1634759, _1634761] : [-(hAPP(c_Map_Omap__add(_1634753, _1634755, _1634757, _1634759), _1634761) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1634755), _1634755, hAPP(_1634757, _1634761), c_Option_Ooption_OSome(_1634755)), hAPP(_1634759, _1634761)))], (42960 ^ _782652) ^ [_1634810, _1634812, _1634814, _1634816, _1634818] : [-(c_Map_Omap__add(_1634810, _1634812, _1634814, c_Map_Omap__add(_1634810, _1634812, _1634816, _1634818)) = c_Map_Omap__add(_1634810, _1634812, c_Map_Omap__add(_1634810, _1634812, _1634814, _1634816), _1634818))], (42962 ^ _782652) ^ [_1634861, _1634863, _1634865, _1634867, _1634869, _1634871] : [hAPP(_1634861, _1634863) = hAPP(c_Option_Ooption_OSome(_1634865), _1634867), -(hAPP(c_Map_Omap__add(_1634869, _1634865, _1634871, _1634861), _1634863) = hAPP(c_Option_Ooption_OSome(_1634865), _1634867))], (42968 ^ _782652) ^ [_1635012, _1635014, _1635016, _1635018, _1635020] : [hAPP(c_Map_Omap__add(_1635012, _1635014, _1635016, _1635018), _1635020) = c_Option_Ooption_ONone(_1635014), 42971 ^ _782652 : [(42972 ^ _782652) ^ [] : [-(hAPP(_1635018, _1635020) = c_Option_Ooption_ONone(_1635014))], (42974 ^ _782652) ^ [] : [-(hAPP(_1635016, _1635020) = c_Option_Ooption_ONone(_1635014))]]], (42976 ^ _782652) ^ [_1635157, _1635159, _1635161, _1635163, _1635165] : [-(hAPP(c_Map_Omap__add(_1635157, _1635159, _1635161, _1635163), _1635165) = c_Option_Ooption_ONone(_1635159)), hAPP(_1635163, _1635165) = c_Option_Ooption_ONone(_1635159), hAPP(_1635161, _1635165) = c_Option_Ooption_ONone(_1635159)], (42986 ^ _782652) ^ [_1635340, _1635342, _1635344, _1635346, _1635348, _1635350] : [hAPP(c_Map_Omap__add(_1635340, _1635342, _1635344, _1635346), _1635348) = hAPP(c_Option_Ooption_OSome(_1635342), _1635350), -(hAPP(_1635346, _1635348) = hAPP(c_Option_Ooption_OSome(_1635342), _1635350)), 42993 ^ _782652 : [(42994 ^ _782652) ^ [] : [-(hAPP(_1635346, _1635348) = c_Option_Ooption_ONone(_1635342))], (42996 ^ _782652) ^ [] : [-(hAPP(_1635344, _1635348) = hAPP(c_Option_Ooption_OSome(_1635342), _1635350))]]], (42998 ^ _782652) ^ [_1635576, _1635578, _1635580, _1635582, _1635584, _1635586] : [hAPP(c_Map_Omap__add(_1635576, _1635578, _1635580, _1635582), _1635584) = hAPP(c_Option_Ooption_OSome(_1635578), _1635586), -(hAPP(_1635582, _1635584) = hAPP(c_Option_Ooption_OSome(_1635578), _1635586)), 43005 ^ _782652 : [(43006 ^ _782652) ^ [] : [-(hAPP(_1635582, _1635584) = c_Option_Ooption_ONone(_1635578))], (43008 ^ _782652) ^ [] : [-(hAPP(_1635580, _1635584) = hAPP(c_Option_Ooption_OSome(_1635578), _1635586))]]], (43010 ^ _782652) ^ [_1635781, _1635783, _1635785, _1635787, _1635789, _1635791] : [-(hAPP(c_Map_Omap__add(_1635781, _1635783, _1635785, _1635787), _1635789) = hAPP(c_Option_Ooption_OSome(_1635783), _1635791)), 43011 ^ _782652 : [(43012 ^ _782652) ^ [] : [hAPP(_1635787, _1635789) = hAPP(c_Option_Ooption_OSome(_1635783), _1635791)], (43014 ^ _782652) ^ [] : [hAPP(_1635787, _1635789) = c_Option_Ooption_ONone(_1635783), hAPP(_1635785, _1635789) = hAPP(c_Option_Ooption_OSome(_1635783), _1635791)]]], (43022 ^ _782652) ^ [_1636032, _1636034, _1636036, _1636038] : [-(c_Map_Odom(_1636032, _1636034, c_Map_Omap__add(_1636032, _1636034, _1636036, _1636038)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1636032, tc_HOL_Obool)), c_Map_Odom(_1636032, _1636034, _1636038)), c_Map_Odom(_1636032, _1636034, _1636036)))], (43024 ^ _782652) ^ [_1636089, _1636091, _1636093, _1636095, _1636097, _1636099] : [-(c_Map_Omap__add(_1636089, _1636091, _1636093, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1636089, tc_Option_Ooption(_1636091)), _1636095), _1636097), hAPP(c_Option_Ooption_OSome(_1636091), _1636099))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1636089, tc_Option_Ooption(_1636091)), c_Map_Omap__add(_1636089, _1636091, _1636093, _1636095)), _1636097), hAPP(c_Option_Ooption_OSome(_1636091), _1636099)))], (43026 ^ _782652) ^ [_1636191, _1636193, _1636195, _1636197] : [c_Fun_Oinj__on(_1636191, tc_Option_Ooption(_1636193), c_Map_Omap__add(_1636191, _1636193, _1636195, _1636197), c_Map_Odom(_1636191, _1636193, _1636197)), -(c_Fun_Oinj__on(_1636191, tc_Option_Ooption(_1636193), _1636197, c_Map_Odom(_1636191, _1636193, _1636197)))], (43032 ^ _782652) ^ [_1636310, _1636312, _1636314, _1636316] : [c_Fun_Oinj__on(_1636310, tc_Option_Ooption(_1636312), _1636316, c_Map_Odom(_1636310, _1636312, _1636316)), -(c_Fun_Oinj__on(_1636310, tc_Option_Ooption(_1636312), c_Map_Omap__add(_1636310, _1636312, _1636314, _1636316), c_Map_Odom(_1636310, _1636312, _1636316)))], (43038 ^ _782652) ^ [_1636435, _1636437, _1636439, _1636441] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1636435, tc_HOL_Obool)), c_Map_Odom(_1636435, _1636437, _1636439)), c_Map_Odom(_1636435, _1636437, _1636441)) = c_Orderings_Obot__class_Obot(tc_fun(_1636435, tc_HOL_Obool)), -(c_Map_Omap__add(_1636435, _1636437, _1636439, _1636441) = c_Map_Omap__add(_1636435, _1636437, _1636441, _1636439))], (43044 ^ _782652) ^ [_1636584, _1636586, _1636588] : [-(c_Nitpick_Otimes__frac(_1636584, _1636586, _1636588) = hAPP(hAPP(c_Nitpick_Ofrac(_1636584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1636584), _1636586)), hAPP(c_Nitpick_Onum(_1636584), _1636588))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1636584), _1636586)), hAPP(c_Nitpick_Odenom(_1636584), _1636588))))], (43046 ^ _782652) ^ [_1636655, _1636657, _1636659] : [-(c_Nitpick_Oof__frac(_1636657, _1636655, _1636659) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1636655), hAPP(c_Int_Oring__1__class_Oof__int(_1636655), hAPP(c_Nitpick_Onum(_1636657), _1636659))), hAPP(c_Int_Oring__1__class_Oof__int(_1636655), hAPP(c_Nitpick_Odenom(_1636657), _1636659)))), class_Rings_Oinverse(_1636655), class_Rings_Oring__1(_1636655)], (43056 ^ _782652) ^ [_1636848, _1636850] : [-(c_Nitpick_Oinverse__frac(_1636848, _1636850) = hAPP(hAPP(c_Nitpick_Ofrac(_1636848), hAPP(c_Nitpick_Odenom(_1636848), _1636850)), hAPP(c_Nitpick_Onum(_1636848), _1636850)))], (43058 ^ _782652) ^ [_1636894, _1636896] : [-(c_Nitpick_Ouminus__frac(_1636894, _1636896) = c_Nitpick_OAbs__Frac(_1636894, 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(_1636894), _1636896))), hAPP(c_Nitpick_Odenom(_1636894), _1636896))))], (43060 ^ _782652) ^ [_1636962, _1636964, _1636966] : [c_Nitpick_Oless__frac(_1636962, _1636964, _1636966), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1636962), c_Nitpick_Oplus__frac(_1636962, _1636964, c_Nitpick_Ouminus__frac(_1636962, _1636966)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43066 ^ _782652) ^ [_1637073, _1637075, _1637077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1637073), c_Nitpick_Oplus__frac(_1637073, _1637075, c_Nitpick_Ouminus__frac(_1637073, _1637077)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1637073, _1637075, _1637077))], (43072 ^ _782652) ^ [_1637208, _1637210, _1637212] : [c_Nitpick_Oless__eq__frac(_1637208, _1637210, _1637212), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1637208), c_Nitpick_Oplus__frac(_1637208, _1637210, c_Nitpick_Ouminus__frac(_1637208, _1637212)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43078 ^ _782652) ^ [_1637319, _1637321, _1637323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1637319), c_Nitpick_Oplus__frac(_1637319, _1637321, c_Nitpick_Ouminus__frac(_1637319, _1637323)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1637319, _1637321, _1637323))], (43084 ^ _782652) ^ [_1637436] : [-(c_Nitpick_Odenom(_1637436) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1637436, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1637436)))], (43086 ^ _782652) ^ [_1637471] : [-(c_Nitpick_Onum(_1637471) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1637471, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1637471)))], (43088 ^ _782652) ^ [_1637506, _1637508, _1637510] : [-(c_Smallcheck_Oorelse(_1637506, _1637508, _1637510) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1637506), _1637506, _1637510, c_Option_Ooption_OSome(_1637506)), _1637508))], (43090 ^ _782652) ^ [_1637549, _1637551, _1637553, _1637555, _1637557, _1637559] : [-(c_Map_Omap__comp(_1637549, _1637551, _1637553, _1637555, _1637557, _1637559) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1637551), _1637549, c_Option_Ooption_ONone(_1637551), _1637555), hAPP(_1637557, _1637559)))], (43092 ^ _782652) ^ [_1637604, _1637606, _1637608, _1637610, _1637612, _1637614, _1637616] : [hAPP(_1637604, _1637606) = hAPP(c_Option_Ooption_OSome(_1637608), _1637610), -(c_Map_Omap__comp(_1637608, _1637612, _1637614, _1637616, _1637604, _1637606) = hAPP(_1637616, _1637610))], (43098 ^ _782652) ^ [_1637757, _1637759, _1637761, _1637763, _1637765, _1637767, _1637769] : [c_Map_Omap__comp(_1637757, _1637759, _1637761, _1637763, _1637765, _1637767) = hAPP(c_Option_Ooption_OSome(_1637759), _1637769), 43102 ^ _782652 : [(43103 ^ _782652) ^ [] : [-(hAPP(_1637765, _1637767) = hAPP(c_Option_Ooption_OSome(_1637757), 43101 ^ [_1637757, _1637759, _1637761, _1637763, _1637765, _1637767, _1637769]))], (43105 ^ _782652) ^ [] : [-(hAPP(_1637763, 43101 ^ [_1637757, _1637759, _1637761, _1637763, _1637765, _1637767, _1637769]) = hAPP(c_Option_Ooption_OSome(_1637759), _1637769))]]], (43107 ^ _782652) ^ [_1637961, _1637963, _1637965, _1637967, _1637969, _1637971, _1637973] : [-(c_Map_Omap__comp(_1637961, _1637963, _1637965, _1637967, _1637969, _1637971) = hAPP(c_Option_Ooption_OSome(_1637963), _1637973)), 43108 ^ _782652 : [(43109 ^ _782652) ^ [_1638039] : [hAPP(_1637969, _1637971) = hAPP(c_Option_Ooption_OSome(_1637961), _1638039), hAPP(_1637967, _1638039) = hAPP(c_Option_Ooption_OSome(_1637963), _1637973)]]], (43117 ^ _782652) ^ [_1638201, _1638203, _1638205, _1638207, _1638209, _1638211] : [hAPP(_1638201, _1638203) = c_Option_Ooption_ONone(_1638205), -(c_Map_Omap__comp(_1638205, _1638207, _1638209, _1638211, _1638201, _1638203) = c_Option_Ooption_ONone(_1638207))], (43123 ^ _782652) ^ [_1638314, _1638316, _1638318, _1638320, _1638322] : [-(c_Map_Omap__comp(_1638314, _1638316, _1638318, _1638320, hAPP(c_COMBK(tc_Option_Ooption(_1638314), _1638318), c_Option_Ooption_ONone(_1638314)), _1638322) = c_Option_Ooption_ONone(_1638316))], (43125 ^ _782652) ^ [_1638364, _1638366, _1638368, _1638370, _1638372] : [-(c_Map_Omap__comp(_1638364, _1638366, _1638368, hAPP(c_COMBK(tc_Option_Ooption(_1638366), _1638364), c_Option_Ooption_ONone(_1638366)), _1638370, _1638372) = c_Option_Ooption_ONone(_1638366))], (43127 ^ _782652) ^ [_1638441, _1638443, _1638445, _1638447, _1638449, _1638451] : [c_Map_Omap__comp(_1638441, _1638443, _1638445, _1638447, _1638449, _1638451) = c_Option_Ooption_ONone(_1638443), -(hAPP(_1638449, _1638451) = c_Option_Ooption_ONone(_1638441)), 43135 ^ _782652 : [(43136 ^ _782652) ^ [] : [-(hAPP(_1638449, _1638451) = hAPP(c_Option_Ooption_OSome(_1638441), 43134 ^ [_1638441, _1638443, _1638445, _1638447, _1638449, _1638451]))], (43138 ^ _782652) ^ [] : [-(hAPP(_1638447, 43134 ^ [_1638441, _1638443, _1638445, _1638447, _1638449, _1638451]) = c_Option_Ooption_ONone(_1638443))]]], (43140 ^ _782652) ^ [_1638667, _1638669, _1638671, _1638673, _1638675, _1638677] : [-(c_Map_Omap__comp(_1638667, _1638669, _1638671, _1638673, _1638675, _1638677) = c_Option_Ooption_ONone(_1638669)), 43141 ^ _782652 : [(43142 ^ _782652) ^ [] : [hAPP(_1638675, _1638677) = c_Option_Ooption_ONone(_1638667)], (43144 ^ _782652) ^ [_1638779] : [hAPP(_1638675, _1638677) = hAPP(c_Option_Ooption_OSome(_1638667), _1638779), hAPP(_1638673, _1638779) = c_Option_Ooption_ONone(_1638669)]]], (43152 ^ _782652) ^ [_1638932, _1638934] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1638932, _1638934) = c_Smallcheck_Ofull__small_H(_1638932, hAPP(c_Code__Numeral_Oint__of, _1638934), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1638934))))], (43154 ^ _782652) ^ [_1638986, _1638988, _1638990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1638986), _1638988)), -(c_Smallcheck_Osmall_H(_1638990, _1638986, _1638988) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (43160 ^ _782652) ^ [_1639077, _1639079, _1639081] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1639077), _1639079))), -(c_Smallcheck_Osmall_H(_1639081, _1639077, _1639079) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1639081, _1639077, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1639079), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1639081, _1639079)))], (43166 ^ _782652) ^ [_1639147, _1639149, _1639151] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1639147), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1639149), _1639151)))), 43169 ^ _782652 : [(43170 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1639149), _1639151)), -(c_Smallcheck_Osmall_H(_1639147, _1639149, _1639151) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (43176 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1639149), _1639151))), -(c_Smallcheck_Osmall_H(_1639147, _1639149, _1639151) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1639147, _1639149, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1639151), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1639147, _1639151)))]]], (43182 ^ _782652) ^ [_1639433, _1639435] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1639433), _1639435) = c_Smallcheck_Osmall_H(_1639433, hAPP(c_Code__Numeral_Oint__of, _1639435), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1639435))))], (43184 ^ _782652) ^ [_1639477, _1639479, _1639481, _1639483] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1639479, _1639477)), _1639481), _1639483) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1639479), hAPP(hAPP(c_COMBC(_1639479, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1639477, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1639479), c_Smallcheck_Osmall__class_Osmall(_1639477)), hAPP(hAPP(c_COMBB(tc_fun(_1639477, tc_prod(_1639479, _1639477)), tc_fun(_1639477, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1639479), hAPP(c_COMBB(tc_prod(_1639479, _1639477), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1639477), _1639481)), c_Product__Type_OPair(_1639479, _1639477)))), _1639483)), _1639483)), class_Smallcheck_Osmall(_1639477), class_Smallcheck_Osmall(_1639479)], (43194 ^ _782652) ^ [_1639762, _1639764, _1639766, _1639768] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1639762), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1639764), _1639766)))), -(hBOOL(hAPP(hAPP(hAPP(_1639768, _1639762), _1639764), _1639766))), 43202 ^ _782652 : [(43203 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 43199 ^ [_1639762, _1639764, _1639766, _1639768]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 43200 ^ [_1639762, _1639764, _1639766, _1639768]), 43201 ^ [_1639762, _1639764, _1639766, _1639768])))))], (43215 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1639768, 43199 ^ [_1639762, _1639764, _1639766, _1639768]), 43200 ^ [_1639762, _1639764, _1639766, _1639768]), 43201 ^ [_1639762, _1639764, _1639766, _1639768]))], (43205 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 43200 ^ [_1639762, _1639764, _1639766, _1639768]), 43201 ^ [_1639762, _1639764, _1639766, _1639768]))), hAPP(43199 ^ [_1639762, _1639764, _1639766, _1639768], 43201 ^ [_1639762, _1639764, _1639766, _1639768]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1639768, 43199 ^ [_1639762, _1639764, _1639766, _1639768]), 43200 ^ [_1639762, _1639764, _1639766, _1639768]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43201 ^ [_1639762, _1639764, _1639766, _1639768]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (43219 ^ _782652) ^ [_1640501, _1640503, _1640505] : [-(hAPP(c_Option_Omap(_1640501, _1640503), _1640505) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1640503), _1640501, c_Option_Ooption_ONone(_1640503), hAPP(hAPP(c_COMBB(_1640503, tc_Option_Ooption(_1640503), _1640501), c_Option_Ooption_OSome(_1640503)), _1640505)))], (43221 ^ _782652) ^ [_1640557, _1640559, _1640561, _1640563, _1640565] : [-(c_Map_Odom(_1640557, _1640559, hAPP(hAPP(c_COMBS(_1640557, tc_Option_Ooption(_1640561), tc_Option_Ooption(_1640559)), hAPP(hAPP(c_COMBB(tc_fun(_1640561, _1640559), tc_fun(tc_Option_Ooption(_1640561), tc_Option_Ooption(_1640559)), _1640557), c_Option_Omap(_1640561, _1640559)), _1640563)), _1640565)) = c_Map_Odom(_1640557, _1640561, _1640565))], (43223 ^ _782652) ^ [_1640633] : [-(hAPP(c_Option_Omap(_1640633, _1640633), c_COMBI(_1640633)) = c_Fun_Oid(tc_Option_Ooption(_1640633)))], (43225 ^ _782652) ^ [_1640668] : [-(hAPP(c_Option_Omap(_1640668, _1640668), c_Fun_Oid(_1640668)) = c_Fun_Oid(tc_Option_Ooption(_1640668)))], (43227 ^ _782652) ^ [_1640703, _1640705, _1640707, _1640709, _1640711] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1640703), tc_Option_Ooption(_1640705), tc_Option_Ooption(_1640707), hAPP(c_Option_Omap(_1640703, _1640705), _1640709)), hAPP(c_Option_Omap(_1640707, _1640703), _1640711)) = hAPP(c_Option_Omap(_1640707, _1640705), hAPP(c_Fun_Ocomp(_1640703, _1640705, _1640707, _1640709), _1640711)))], (43229 ^ _782652) ^ [_1640774, _1640776, _1640778, _1640780, _1640782, _1640784] : [-(hAPP(hAPP(c_Option_Omap(_1640774, _1640776), _1640778), hAPP(hAPP(c_Option_Omap(_1640780, _1640774), _1640782), _1640784)) = hAPP(hAPP(c_Option_Omap(_1640780, _1640776), hAPP(c_Fun_Ocomp(_1640774, _1640776, _1640780, _1640778), _1640782)), _1640784))], (43231 ^ _782652) ^ [_1640842, _1640844, _1640846, _1640848, _1640850, _1640852] : [-(hAPP(hAPP(c_Option_Omap(_1640842, _1640844), _1640846), hAPP(hAPP(c_Option_Omap(_1640848, _1640842), _1640850), _1640852)) = hAPP(hAPP(c_Option_Omap(_1640848, _1640844), hAPP(c_Fun_Ocomp(_1640842, _1640844, _1640848, _1640846), _1640850)), _1640852))], (43233 ^ _782652) ^ [_1640910, _1640912, _1640914, _1640916, _1640918] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1640910), tc_Option_Ooption(_1640912), _1640914, hAPP(c_Option_Omap(_1640910, _1640912), _1640916)), hAPP(c_COMBK(tc_Option_Ooption(_1640910), _1640914), c_Option_Ooption_ONone(_1640910))), _1640918) = c_Option_Ooption_ONone(_1640912))], (43235 ^ _782652) ^ [_1640998, _1641000, _1641002, _1641004, _1641006] : [hAPP(hAPP(c_Option_Omap(_1640998, _1641000), _1641002), _1641004) = hAPP(c_Option_Ooption_OSome(_1641000), _1641006), 43239 ^ _782652 : [(43240 ^ _782652) ^ [] : [-(_1641004 = hAPP(c_Option_Ooption_OSome(_1640998), 43238 ^ [_1640998, _1641000, _1641002, _1641004, _1641006]))], (43242 ^ _782652) ^ [] : [-(hAPP(_1641002, 43238 ^ [_1640998, _1641000, _1641002, _1641004, _1641006]) = _1641006)]]], (43244 ^ _782652) ^ [_1641178, _1641180, _1641182, _1641184, _1641186] : [-(hAPP(hAPP(c_Option_Omap(_1641178, _1641180), _1641182), _1641184) = hAPP(c_Option_Ooption_OSome(_1641180), _1641186)), 43245 ^ _782652 : [(43246 ^ _782652) ^ [_1641246] : [_1641184 = hAPP(c_Option_Ooption_OSome(_1641178), _1641246), hAPP(_1641182, _1641246) = _1641186]]], (43254 ^ _782652) ^ [_1641390, _1641392, _1641394, _1641396] : [-(hAPP(hAPP(c_Option_Omap(_1641390, _1641392), _1641394), hAPP(c_Option_Ooption_OSome(_1641390), _1641396)) = hAPP(c_Option_Ooption_OSome(_1641392), hAPP(_1641394, _1641396)))], (43256 ^ _782652) ^ [_1641462, _1641464, _1641466, _1641468] : [hAPP(hAPP(c_Option_Omap(_1641462, _1641464), _1641466), _1641468) = c_Option_Ooption_ONone(_1641464), -(_1641468 = c_Option_Ooption_ONone(_1641462))], (43262 ^ _782652) ^ [_1641565, _1641567, _1641569, _1641571] : [_1641571 = c_Option_Ooption_ONone(_1641565), -(hAPP(hAPP(c_Option_Omap(_1641565, _1641567), _1641569), _1641571) = c_Option_Ooption_ONone(_1641567))], (43268 ^ _782652) ^ [_1641674, _1641676, _1641678] : [-(hAPP(hAPP(c_Option_Omap(_1641674, _1641676), _1641678), c_Option_Ooption_ONone(_1641674)) = c_Option_Ooption_ONone(_1641676))], (43270 ^ _782652) ^ [_1641714, _1641716, _1641718, _1641720, _1641722, _1641724, _1641726] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1641714), tc_Option_Ooption(_1641716), _1641718, hAPP(c_Option_Omap(_1641714, _1641716), _1641720)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1641718, tc_Option_Ooption(_1641714)), _1641722), _1641724), hAPP(c_Option_Ooption_OSome(_1641714), _1641726))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1641718, tc_Option_Ooption(_1641716)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1641714), tc_Option_Ooption(_1641716), _1641718, hAPP(c_Option_Omap(_1641714, _1641716), _1641720)), _1641722)), _1641724), hAPP(c_Option_Ooption_OSome(_1641716), hAPP(_1641720, _1641726))))], (43272 ^ _782652) ^ [_1641826, _1641828, _1641830, _1641832] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1641826)), hAPP(c_Set_Oimage(_1641828, tc_Option_Ooption(_1641826), _1641830), c_Orderings_Otop__class_Otop(tc_fun(_1641828, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1641826)), hAPP(c_Set_Oimage(_1641828, tc_Option_Ooption(_1641826), c_Map_Omap__add(_1641828, _1641826, _1641830, hAPP(c_Map_Omap__of(_1641828, _1641826), _1641832))), c_Orderings_Otop__class_Otop(tc_fun(_1641828, tc_HOL_Obool))))))], (43278 ^ _782652) ^ [_1642009, _1642011, _1642013, _1642015] : [class_Rings_Olinordered__semidom(_1642009), 43284 ^ _782652 : [(43285 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1642011), 43283 ^ [_1642009, _1642011, _1642013, _1642015]), _1642013)))], (43287 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1642009), c_Groups_Ozero__class_Ozero(_1642009)), hAPP(_1642015, 43283 ^ [_1642009, _1642011, _1642013, _1642015])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1642009), c_Groups_Ozero__class_Ozero(_1642009)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1642011, _1642009), _1642015), _1642013))))], (43291 ^ _782652) ^ [_1642305, _1642307, _1642309] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1642305), c_Map_Odom(_1642305, _1642307, hAPP(c_Map_Omap__of(_1642305, _1642307), _1642309)))))], (43293 ^ _782652) ^ [_1642346, _1642348, _1642350] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1642346)), hAPP(c_Set_Oimage(_1642348, tc_Option_Ooption(_1642346), hAPP(c_Map_Omap__of(_1642348, _1642346), _1642350)), c_Orderings_Otop__class_Otop(tc_fun(_1642348, tc_HOL_Obool))))))], (43295 ^ _782652) ^ [_1642399, _1642401, _1642403, _1642405] : [-(c_Map_Omap__add(_1642399, _1642401, _1642403, hAPP(c_Map_Omap__of(_1642399, _1642401), _1642405)) = c_List_Ofoldr(tc_prod(_1642399, _1642401), tc_fun(_1642399, tc_Option_Ooption(_1642401)), hAPP(c_Product__Type_Oprod_Oprod__case(_1642399, _1642401, tc_fun(tc_fun(_1642399, tc_Option_Ooption(_1642401)), tc_fun(_1642399, tc_Option_Ooption(_1642401)))), hAPP(hAPP(c_COMBC(_1642399, tc_fun(_1642401, tc_Option_Ooption(_1642401)), tc_fun(_1642401, tc_fun(tc_fun(_1642399, tc_Option_Ooption(_1642401)), tc_fun(_1642399, tc_Option_Ooption(_1642401))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1642401), tc_fun(tc_fun(_1642399, tc_Option_Ooption(_1642401)), tc_fun(_1642399, tc_Option_Ooption(_1642401)))), tc_fun(tc_fun(_1642401, tc_Option_Ooption(_1642401)), tc_fun(_1642401, tc_fun(tc_fun(_1642399, tc_Option_Ooption(_1642401)), tc_fun(_1642399, tc_Option_Ooption(_1642401))))), _1642399), c_COMBB(tc_Option_Ooption(_1642401), tc_fun(tc_fun(_1642399, tc_Option_Ooption(_1642401)), tc_fun(_1642399, tc_Option_Ooption(_1642401))), _1642401)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1642399, tc_Option_Ooption(_1642401)), tc_fun(tc_Option_Ooption(_1642401), tc_fun(_1642399, tc_Option_Ooption(_1642401)))), tc_fun(tc_Option_Ooption(_1642401), tc_fun(tc_fun(_1642399, tc_Option_Ooption(_1642401)), tc_fun(_1642399, tc_Option_Ooption(_1642401)))), _1642399), c_COMBC(tc_fun(_1642399, tc_Option_Ooption(_1642401)), tc_Option_Ooption(_1642401), tc_fun(_1642399, tc_Option_Ooption(_1642401)))), hAPP(c_COMBC(tc_fun(_1642399, tc_Option_Ooption(_1642401)), _1642399, tc_fun(tc_Option_Ooption(_1642401), tc_fun(_1642399, tc_Option_Ooption(_1642401)))), c_Fun_Ofun__upd(_1642399, tc_Option_Ooption(_1642401)))))), c_Option_Ooption_OSome(_1642401))), _1642405, _1642403))], (43297 ^ _782652) ^ [_1642666, _1642668, _1642670, _1642672, _1642674, _1642676, _1642678] : [c_Fun_Oinj__on(_1642666, _1642668, _1642670, c_Orderings_Otop__class_Otop(tc_fun(_1642666, tc_HOL_Obool))), hAPP(hAPP(c_Map_Omap__of(_1642666, _1642672), _1642674), _1642676) = hAPP(c_Option_Ooption_OSome(_1642672), _1642678), -(hAPP(hAPP(c_Map_Omap__of(_1642668, _1642672), hAPP(hAPP(c_List_Omap(tc_prod(_1642666, _1642672), tc_prod(_1642668, _1642672)), hAPP(c_Product__Type_Oprod_Oprod__case(_1642666, _1642672, tc_prod(_1642668, _1642672)), hAPP(hAPP(c_COMBB(_1642668, tc_fun(_1642672, tc_prod(_1642668, _1642672)), _1642666), c_Product__Type_OPair(_1642668, _1642672)), _1642670))), _1642674)), hAPP(_1642670, _1642676)) = hAPP(c_Option_Ooption_OSome(_1642672), _1642678))], (43307 ^ _782652) ^ [_1642979, _1642981, _1642983] : [c_Fun_Oinj__on(_1642979, _1642981, _1642983, c_Orderings_Otop__class_Otop(tc_fun(_1642979, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1642979), tc_List_Olist(_1642981), hAPP(c_List_Omap(_1642979, _1642981), _1642983), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1642979), tc_HOL_Obool))))], (43313 ^ _782652) ^ [_1643110, _1643112, _1643114, _1643116, _1643118, _1643120] : [-(hAPP(hAPP(c_List_Omap(_1643110, _1643112), _1643114), hAPP(hAPP(c_List_Omap(_1643116, _1643110), _1643118), _1643120)) = hAPP(hAPP(c_List_Omap(_1643116, _1643112), hAPP(c_Fun_Ocomp(_1643110, _1643112, _1643116, _1643114), _1643118)), _1643120))], (43315 ^ _782652) ^ [_1643178, _1643180, _1643182, _1643184, _1643186, _1643188] : [-(hAPP(hAPP(c_List_Omap(_1643178, _1643180), _1643182), hAPP(hAPP(c_List_Omap(_1643184, _1643178), _1643186), _1643188)) = hAPP(hAPP(c_List_Omap(_1643184, _1643180), hAPP(c_Fun_Ocomp(_1643178, _1643180, _1643184, _1643182), _1643186)), _1643188))], (43317 ^ _782652) ^ [_1643246, _1643248, _1643250, _1643252, _1643254] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1643246), tc_List_Olist(_1643248), tc_List_Olist(_1643250), hAPP(c_List_Omap(_1643246, _1643248), _1643252)), hAPP(c_List_Omap(_1643250, _1643246), _1643254)) = hAPP(c_List_Omap(_1643250, _1643248), hAPP(c_Fun_Ocomp(_1643246, _1643248, _1643250, _1643252), _1643254)))], (43319 ^ _782652) ^ [_1643317, _1643319, _1643321, _1643323, _1643325] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1643317), tc_List_Olist(_1643319), tc_List_Olist(_1643321), hAPP(c_List_Omap(_1643317, _1643319), _1643323)), hAPP(c_List_Omap(_1643321, _1643317), _1643325)) = hAPP(c_List_Omap(_1643321, _1643319), hAPP(c_Fun_Ocomp(_1643317, _1643319, _1643321, _1643323), _1643325)))], (43321 ^ _782652) ^ [_1643388, _1643390, _1643392, _1643394, _1643396, _1643398, _1643400] : [-(c_List_Ofoldr(_1643388, _1643390, _1643392, hAPP(hAPP(c_List_Omap(_1643394, _1643388), _1643396), _1643398), _1643400) = c_List_Ofoldr(_1643394, _1643390, hAPP(c_Fun_Ocomp(_1643388, tc_fun(_1643390, _1643390), _1643394, _1643392), _1643396), _1643398, _1643400))], (43323 ^ _782652) ^ [_1643455] : [-(hAPP(c_List_Omap(_1643455, _1643455), c_COMBI(_1643455)) = c_Fun_Oid(tc_List_Olist(_1643455)))], (43325 ^ _782652) ^ [_1643490] : [-(hAPP(c_List_Omap(_1643490, _1643490), c_Fun_Oid(_1643490)) = c_Fun_Oid(tc_List_Olist(_1643490)))], (43327 ^ _782652) ^ [_1643525, _1643527, _1643529, _1643531, _1643533] : [hAPP(hAPP(c_List_Omap(_1643525, _1643527), _1643529), _1643531) = hAPP(hAPP(c_List_Omap(_1643525, _1643527), _1643529), _1643533), c_Fun_Oinj__on(_1643525, _1643527, _1643529, c_Orderings_Otop__class_Otop(tc_fun(_1643525, tc_HOL_Obool))), -(_1643531 = _1643533)], (43337 ^ _782652) ^ [_1643716, _1643718, _1643720] : [c_Fun_Oinj__on(tc_List_Olist(_1643716), tc_List_Olist(_1643718), hAPP(c_List_Omap(_1643716, _1643718), _1643720), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1643716), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1643716, _1643718, _1643720, c_Orderings_Otop__class_Otop(tc_fun(_1643716, tc_HOL_Obool))))], (43343 ^ _782652) ^ [_1643847, _1643849, _1643851, _1643853, _1643855] : [c_Fun_Oinj__on(_1643847, _1643849, _1643851, c_Orderings_Otop__class_Otop(tc_fun(_1643847, tc_HOL_Obool))), 43346 ^ _782652 : [(43347 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Omap(_1643847, _1643849), _1643851), _1643853) = hAPP(hAPP(c_List_Omap(_1643847, _1643849), _1643851), _1643855), -(_1643853 = _1643855)], (43353 ^ _782652) ^ [] : [_1643853 = _1643855, -(hAPP(hAPP(c_List_Omap(_1643847, _1643849), _1643851), _1643853) = hAPP(hAPP(c_List_Omap(_1643847, _1643849), _1643851), _1643855))]]], (43359 ^ _782652) ^ [_1644158, _1644160, _1644162] : [c_Fun_Oinj__on(tc_List_Olist(_1644158), tc_List_Olist(_1644160), hAPP(c_List_Omap(_1644158, _1644160), _1644162), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1644158), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1644158, _1644160, _1644162, c_Orderings_Otop__class_Otop(tc_fun(_1644158, tc_HOL_Obool))))], (43365 ^ _782652) ^ [_1644285, _1644287, _1644289] : [c_Fun_Oinj__on(_1644285, _1644287, _1644289, c_Orderings_Otop__class_Otop(tc_fun(_1644285, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1644285), tc_List_Olist(_1644287), hAPP(c_List_Omap(_1644285, _1644287), _1644289), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1644285), tc_HOL_Obool))))], (43371 ^ _782652) ^ [_1644418, _1644420] : [-(hAPP(hAPP(c_List_Omap(_1644418, _1644418), c_COMBI(_1644418)), _1644420) = _1644420)], (43373 ^ _782652) ^ [_1644454, _1644456, _1644458, _1644460, _1644462] : [-(hAPP(c_Map_Omap__of(_1644454, _1644456), hAPP(hAPP(c_List_Omap(tc_prod(_1644454, _1644458), tc_prod(_1644454, _1644456)), hAPP(c_Product__Type_Oprod_Oprod__case(_1644454, _1644458, tc_prod(_1644454, _1644456)), hAPP(hAPP(c_COMBC(_1644454, tc_fun(_1644458, _1644456), tc_fun(_1644458, tc_prod(_1644454, _1644456))), hAPP(hAPP(c_COMBB(tc_fun(_1644456, tc_prod(_1644454, _1644456)), tc_fun(tc_fun(_1644458, _1644456), tc_fun(_1644458, tc_prod(_1644454, _1644456))), _1644454), c_COMBB(_1644456, tc_prod(_1644454, _1644456), _1644458)), c_Product__Type_OPair(_1644454, _1644456))), _1644460))), _1644462)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1644458), tc_Option_Ooption(_1644456), _1644454, hAPP(c_Option_Omap(_1644458, _1644456), _1644460)), hAPP(c_Map_Omap__of(_1644454, _1644458), _1644462)))], (43375 ^ _782652) ^ [_1644597, _1644599, _1644601, _1644603] : [-(hAPP(c_Map_Omap__of(_1644597, _1644599), hAPP(hAPP(c_List_Omap(_1644597, tc_prod(_1644597, _1644599)), hAPP(hAPP(c_COMBS(_1644597, _1644599, tc_prod(_1644597, _1644599)), c_Product__Type_OPair(_1644597, _1644599)), _1644601)), _1644603)) = c_Map_Orestrict__map(_1644597, _1644599, hAPP(c_Fun_Ocomp(_1644599, tc_Option_Ooption(_1644599), _1644597, c_Option_Ooption_OSome(_1644599)), _1644601), hAPP(c_List_Oset(_1644597), _1644603)))], (43377 ^ _782652) ^ [] : [-(c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))], (43379 ^ _782652) ^ [_1644700, _1644702] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1644700), hAPP(c_List_Oset(_1644700), _1644702))))], (43381 ^ _782652) ^ [_1644734, _1644736, _1644738, _1644740] : [-(hAPP(c_List_Oset(_1644734), hAPP(hAPP(c_List_Omap(_1644736, _1644734), _1644738), _1644740)) = hAPP(c_Set_Oimage(_1644736, _1644734, _1644738), hAPP(c_List_Oset(_1644736), _1644740)))], (43393 ^ _782652) ^ [_1645057, _1645059, _1645061, _1645063, _1645065] : [43395 ^ _782652 : [(43396 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1645057), 43394 ^ [_1645057, _1645059, _1645061, _1645063, _1645065]), hAPP(c_List_Oset(_1645057), _1645063))))], (43398 ^ _782652) ^ [] : [hAPP(_1645061, 43394 ^ [_1645057, _1645059, _1645061, _1645063, _1645065]) = hAPP(_1645065, 43394 ^ [_1645057, _1645059, _1645061, _1645063, _1645065])]], -(hAPP(hAPP(c_List_Omap(_1645057, _1645059), _1645061), _1645063) = hAPP(hAPP(c_List_Omap(_1645057, _1645059), _1645065), _1645063))], (43383 ^ _782652) ^ [_1644813, _1644815, _1644817, _1644819, _1644821] : [hAPP(hAPP(c_List_Omap(_1644813, _1644815), _1644817), _1644819) = hAPP(hAPP(c_List_Omap(_1644813, _1644815), _1644821), _1644819), 43386 ^ _782652 : [(43387 ^ _782652) ^ [_1644936] : [hBOOL(hAPP(hAPP(c_member(_1644813), _1644936), hAPP(c_List_Oset(_1644813), _1644819))), -(hAPP(_1644817, _1644936) = hAPP(_1644821, _1644936))]]], (43402 ^ _782652) ^ [_1645323] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1645323)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1645323), tc_HOL_Obool))))], (43414 ^ _782652) ^ [] : [43416 ^ _782652 : [(43417 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 43415 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))], (43419 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 43415 ^ []))]], -(c_Com_OWT__bodies)], (43404 ^ _782652) ^ [] : [c_Com_OWT__bodies, 43407 ^ _782652 : [(43408 ^ _782652) ^ [_1645405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1645405), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1645405)))]]], (43423 ^ _782652) ^ [_1645596, _1645598, _1645600, _1645602, _1645604] : [hAPP(hAPP(c_List_Omap(_1645596, _1645598), _1645600), _1645602) = hAPP(hAPP(c_List_Omap(_1645596, _1645598), _1645600), _1645604), c_Fun_Oinj__on(_1645596, _1645598, _1645600, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1645596, tc_HOL_Obool)), hAPP(c_List_Oset(_1645596), _1645602)), hAPP(c_List_Oset(_1645596), _1645604))), -(_1645602 = _1645604)], (43433 ^ _782652) ^ [_1645819, _1645821, _1645823, _1645825, _1645827] : [c_Fun_Oinj__on(_1645819, _1645821, _1645823, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1645819, tc_HOL_Obool)), hAPP(c_List_Oset(_1645819), _1645825)), hAPP(c_List_Oset(_1645819), _1645827))), 43436 ^ _782652 : [(43437 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Omap(_1645819, _1645821), _1645823), _1645825) = hAPP(hAPP(c_List_Omap(_1645819, _1645821), _1645823), _1645827), -(_1645825 = _1645827)], (43443 ^ _782652) ^ [] : [_1645825 = _1645827, -(hAPP(hAPP(c_List_Omap(_1645819, _1645821), _1645823), _1645825) = hAPP(hAPP(c_List_Omap(_1645819, _1645821), _1645823), _1645827))]]], (43449 ^ _782652) ^ [_1646140, _1646142, _1646144, _1646146, _1646148, _1646150] : [-(hBOOL(hAPP(hAPP(c_member(_1646140), _1646142), hAPP(c_List_Oset(_1646140), _1646144)))), -(hAPP(hAPP(c_List_Omap(_1646140, _1646146), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1646140, _1646146), _1646148), _1646142), _1646150)), _1646144) = hAPP(hAPP(c_List_Omap(_1646140, _1646146), _1646148), _1646144))], (43455 ^ _782652) ^ [_1646226, _1646228, _1646230, _1646232] : [c_Fun_Oinj__on(_1646226, _1646228, _1646230, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1646226, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1646226), tc_fun(_1646226, tc_HOL_Obool), c_List_Oset(_1646226)), _1646232))), -(c_Fun_Oinj__on(tc_List_Olist(_1646226), tc_List_Olist(_1646228), hAPP(c_List_Omap(_1646226, _1646228), _1646230), _1646232))], (43461 ^ _782652) ^ [_1646375, _1646377, _1646379, _1646381] : [hAPP(c_Map_Omap__of(_1646375, _1646377), _1646379) = hAPP(c_Map_Omap__of(_1646375, _1646377), _1646381), -(hAPP(c_Set_Oimage(tc_prod(_1646375, _1646377), _1646375, c_Product__Type_Ofst(_1646375, _1646377)), hAPP(c_List_Oset(tc_prod(_1646375, _1646377)), _1646379)) = hAPP(c_Set_Oimage(tc_prod(_1646375, _1646377), _1646375, c_Product__Type_Ofst(_1646375, _1646377)), hAPP(c_List_Oset(tc_prod(_1646375, _1646377)), _1646381)))], (43467 ^ _782652) ^ [_1646564, _1646566, _1646568, _1646570, _1646572] : [hAPP(hAPP(c_Map_Omap__of(_1646564, _1646566), _1646568), _1646570) = hAPP(c_Option_Ooption_OSome(_1646566), _1646572), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646564, _1646566)), hAPP(hAPP(c_Product__Type_OPair(_1646564, _1646566), _1646570), _1646572)), hAPP(c_List_Oset(tc_prod(_1646564, _1646566)), _1646568))))], (43473 ^ _782652) ^ [_1646729, _1646731, _1646733, _1646735, _1646737] : [hAPP(hAPP(c_Map_Omap__of(_1646729, _1646731), _1646733), _1646735) = hAPP(c_Option_Ooption_OSome(_1646731), _1646737), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646729, _1646731)), hAPP(hAPP(c_Product__Type_OPair(_1646729, _1646731), _1646735), _1646737)), hAPP(c_List_Oset(tc_prod(_1646729, _1646731)), _1646733))))], (43479 ^ _782652) ^ [_1646894, _1646896, _1646898] : [-(c_Map_Odom(_1646894, _1646896, hAPP(c_Map_Omap__of(_1646894, _1646896), _1646898)) = hAPP(c_Set_Oimage(tc_prod(_1646894, _1646896), _1646894, c_Product__Type_Ofst(_1646894, _1646896)), hAPP(c_List_Oset(tc_prod(_1646894, _1646896)), _1646898)))], (43481 ^ _782652) ^ [_1646973, _1646975, _1646977, _1646979] : [hAPP(hAPP(c_Map_Omap__of(_1646973, _1646975), _1646977), _1646979) = c_Option_Ooption_ONone(_1646975), hBOOL(hAPP(hAPP(c_member(_1646973), _1646979), hAPP(c_Set_Oimage(tc_prod(_1646973, _1646975), _1646973, c_Product__Type_Ofst(_1646973, _1646975)), hAPP(c_List_Oset(tc_prod(_1646973, _1646975)), _1646977))))], (43487 ^ _782652) ^ [_1647127, _1647129, _1647131, _1647133] : [-(hBOOL(hAPP(hAPP(c_member(_1647127), _1647133), hAPP(c_Set_Oimage(tc_prod(_1647127, _1647129), _1647127, c_Product__Type_Ofst(_1647127, _1647129)), hAPP(c_List_Oset(tc_prod(_1647127, _1647129)), _1647131))))), -(hAPP(hAPP(c_Map_Omap__of(_1647127, _1647129), _1647131), _1647133) = c_Option_Ooption_ONone(_1647129))], (43493 ^ _782652) ^ [_1647208, _1647210, _1647212, _1647214] : [hAPP(c_List_Oset(_1647208), _1647210) = c_Map_Odom(_1647208, _1647212, _1647214), -(hAPP(c_Map_Omap__of(_1647208, _1647212), hAPP(hAPP(c_List_Omap(_1647208, tc_prod(_1647208, _1647212)), hAPP(hAPP(c_COMBS(_1647208, _1647212, tc_prod(_1647208, _1647212)), c_Product__Type_OPair(_1647208, _1647212)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1647212), _1647212, _1647208), c_Option_Othe(_1647212)), _1647214))), _1647210)) = _1647214)], (43499 ^ _782652) ^ [_1647403, _1647405, _1647407] : [hBOOL(hAPP(c_List_Odistinct(_1647403), hAPP(hAPP(c_List_Omap(tc_prod(_1647403, _1647405), _1647403), c_Product__Type_Ofst(_1647403, _1647405)), _1647407))), -(c_Map_Oran(_1647403, _1647405, hAPP(c_Map_Omap__of(_1647403, _1647405), _1647407)) = hAPP(c_Set_Oimage(tc_prod(_1647403, _1647405), _1647405, c_Product__Type_Osnd(_1647403, _1647405)), hAPP(c_List_Oset(tc_prod(_1647403, _1647405)), _1647407)))], (43505 ^ _782652) ^ [_1647582, _1647584, _1647586] : [hBOOL(hAPP(c_List_Odistinct(_1647582), hAPP(hAPP(c_List_Omap(tc_prod(_1647582, _1647584), _1647582), c_Product__Type_Ofst(_1647582, _1647584)), _1647586))), -(hAPP(c_List_Oset(tc_prod(_1647582, _1647584)), _1647586) = hAPP(c_Set_OCollect(tc_prod(_1647582, _1647584)), hAPP(c_Product__Type_Oprod_Oprod__case(_1647582, _1647584, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1647582, tc_fun(_1647584, tc_Option_Ooption(_1647584)), tc_fun(_1647584, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1647584), tc_HOL_Obool), tc_fun(tc_fun(_1647584, tc_Option_Ooption(_1647584)), tc_fun(_1647584, tc_HOL_Obool)), _1647582), c_COMBB(tc_Option_Ooption(_1647584), tc_HOL_Obool, _1647584)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1647584), tc_fun(tc_Option_Ooption(_1647584), tc_HOL_Obool), _1647582), c_fequal), hAPP(c_Map_Omap__of(_1647582, _1647584), _1647586)))), c_Option_Ooption_OSome(_1647584)))))], (43511 ^ _782652) ^ [_1647916, _1647918, _1647920, _1647922] : [hBOOL(hAPP(c_List_Odistinct(_1647916), hAPP(hAPP(c_List_Omap(_1647918, _1647916), _1647920), _1647922))), 43514 ^ _782652 : [(43515 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1647918), _1647922)))], (43517 ^ _782652) ^ [] : [-(c_Fun_Oinj__on(_1647918, _1647916, _1647920, hAPP(c_List_Oset(_1647918), _1647922)))]]], (43519 ^ _782652) ^ [_1648067, _1648069, _1648071, _1648073] : [-(hBOOL(hAPP(c_List_Odistinct(_1648067), hAPP(hAPP(c_List_Omap(_1648069, _1648067), _1648071), _1648073)))), hBOOL(hAPP(c_List_Odistinct(_1648069), _1648073)), c_Fun_Oinj__on(_1648069, _1648067, _1648071, hAPP(c_List_Oset(_1648069), _1648073))], (43529 ^ _782652) ^ [_1648254, _1648256, _1648258, _1648260] : [hBOOL(hAPP(c_List_Odistinct(_1648254), hAPP(hAPP(c_List_Omap(tc_prod(_1648254, _1648256), _1648254), c_Product__Type_Ofst(_1648254, _1648256)), _1648258))), hBOOL(hAPP(c_List_Odistinct(_1648254), hAPP(hAPP(c_List_Omap(tc_prod(_1648254, _1648256), _1648254), c_Product__Type_Ofst(_1648254, _1648256)), _1648260))), 43536 ^ _782652 : [(43537 ^ _782652) ^ [] : [hAPP(c_Map_Omap__of(_1648254, _1648256), _1648258) = hAPP(c_Map_Omap__of(_1648254, _1648256), _1648260), -(hAPP(c_List_Oset(tc_prod(_1648254, _1648256)), _1648258) = hAPP(c_List_Oset(tc_prod(_1648254, _1648256)), _1648260))], (43543 ^ _782652) ^ [] : [hAPP(c_List_Oset(tc_prod(_1648254, _1648256)), _1648258) = hAPP(c_List_Oset(tc_prod(_1648254, _1648256)), _1648260), -(hAPP(c_Map_Omap__of(_1648254, _1648256), _1648258) = hAPP(c_Map_Omap__of(_1648254, _1648256), _1648260))]]], (43549 ^ _782652) ^ [_1648689, _1648691, _1648693, _1648695, _1648697] : [hBOOL(hAPP(c_List_Odistinct(_1648689), hAPP(hAPP(c_List_Omap(tc_prod(_1648689, _1648691), _1648689), c_Product__Type_Ofst(_1648689, _1648691)), _1648693))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1648689, _1648691)), hAPP(hAPP(c_Product__Type_OPair(_1648689, _1648691), _1648695), _1648697)), hAPP(c_List_Oset(tc_prod(_1648689, _1648691)), _1648693))), -(hAPP(hAPP(c_Map_Omap__of(_1648689, _1648691), _1648693), _1648695) = hAPP(c_Option_Ooption_OSome(_1648691), _1648697))], (43559 ^ _782652) ^ [_1648950, _1648952, _1648954, _1648956, _1648958] : [hBOOL(hAPP(c_List_Odistinct(_1648950), hAPP(hAPP(c_List_Omap(tc_prod(_1648950, _1648952), _1648950), c_Product__Type_Ofst(_1648950, _1648952)), _1648954))), 43562 ^ _782652 : [(43563 ^ _782652) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1648950, _1648952), _1648954), _1648956) = hAPP(c_Option_Ooption_OSome(_1648952), _1648958), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1648950, _1648952)), hAPP(hAPP(c_Product__Type_OPair(_1648950, _1648952), _1648956), _1648958)), hAPP(c_List_Oset(tc_prod(_1648950, _1648952)), _1648954))))], (43569 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1648950, _1648952)), hAPP(hAPP(c_Product__Type_OPair(_1648950, _1648952), _1648956), _1648958)), hAPP(c_List_Oset(tc_prod(_1648950, _1648952)), _1648954))), -(hAPP(hAPP(c_Map_Omap__of(_1648950, _1648952), _1648954), _1648956) = hAPP(c_Option_Ooption_OSome(_1648952), _1648958))]]], (43575 ^ _782652) ^ [_1649336, _1649338, _1649340, _1649342, _1649344] : [hBOOL(hAPP(c_List_Odistinct(_1649336), hAPP(hAPP(c_List_Omap(tc_prod(_1649336, _1649338), _1649336), c_Product__Type_Ofst(_1649336, _1649338)), _1649340))), 43578 ^ _782652 : [(43579 ^ _782652) ^ [] : [hAPP(c_Option_Ooption_OSome(_1649338), _1649342) = hAPP(hAPP(c_Map_Omap__of(_1649336, _1649338), _1649340), _1649344), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649336, _1649338)), hAPP(hAPP(c_Product__Type_OPair(_1649336, _1649338), _1649344), _1649342)), hAPP(c_List_Oset(tc_prod(_1649336, _1649338)), _1649340))))], (43585 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649336, _1649338)), hAPP(hAPP(c_Product__Type_OPair(_1649336, _1649338), _1649344), _1649342)), hAPP(c_List_Oset(tc_prod(_1649336, _1649338)), _1649340))), -(hAPP(c_Option_Ooption_OSome(_1649338), _1649342) = hAPP(hAPP(c_Map_Omap__of(_1649336, _1649338), _1649340), _1649344))]]], (43591 ^ _782652) ^ [_1649722, _1649724] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1649722, _1649724) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1649722), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1649724), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43593 ^ _782652) ^ [_1649769, _1649771, _1649773, _1649775, _1649777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649769, _1649771)), hAPP(hAPP(c_Product__Type_OPair(_1649769, _1649771), _1649773), _1649775)), hAPP(c_List_Oset(tc_prod(_1649769, _1649771)), _1649777))), -(hAPP(hAPP(c_Map_Omap__of(_1649769, _1649771), _1649777), _1649773) = hAPP(c_Option_Ooption_OSome(_1649771), 43596 ^ [_1649769, _1649771, _1649773, _1649775, _1649777]))], (43600 ^ _782652) ^ [_1649952, _1649954] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1649952, _1649954) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1649952, _1649954)))], (43602 ^ _782652) ^ [_1649987, _1649989] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1649987, _1649989)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1649987, _1649989))], (43604 ^ _782652) ^ [_1650022, _1650024] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1650022, _1650024))))], (43606 ^ _782652) ^ [_1650052, _1650054] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1650052), _1650054) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1650052, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1650054), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43608 ^ _782652) ^ [_1650095, _1650097] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1650095, _1650097) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1650095), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1650097)))], (43610 ^ _782652) ^ [_1650148] : [c_List_Onat__list(_1650148), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1650148)))], (43616 ^ _782652) ^ [_1650221] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1650221)), -(c_List_Onat__list(_1650221))], (43622 ^ _782652) ^ [_1650300, _1650302, _1650304] : [hBOOL(hAPP(c_List_Odistinct(_1650300), _1650302)), -(hAPP(c_List_Oset(_1650300), c_List_Oremove1(_1650300, _1650304, _1650302)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650300, tc_HOL_Obool)), hAPP(c_List_Oset(_1650300), _1650302)), hAPP(hAPP(c_Set_Oinsert(_1650300), _1650304), c_Orderings_Obot__class_Obot(tc_fun(_1650300, tc_HOL_Obool)))))], (43628 ^ _782652) ^ [_1650463, _1650465, _1650467, _1650469] : [-(c_List_Oremove1(_1650463, _1650465, c_List_Oremove1(_1650463, _1650467, _1650469)) = c_List_Oremove1(_1650463, _1650467, c_List_Oremove1(_1650463, _1650465, _1650469)))], (43630 ^ _782652) ^ [_1650508, _1650510, _1650512] : [hBOOL(hAPP(c_List_Odistinct(_1650508), _1650510)), -(hBOOL(hAPP(c_List_Odistinct(_1650508), c_List_Oremove1(_1650508, _1650512, _1650510))))], (43636 ^ _782652) ^ [_1650610, _1650612, _1650614, _1650616] : [-(_1650610 = _1650612), 43639 ^ _782652 : [(43640 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1650614), _1650610), hAPP(c_List_Oset(_1650614), c_List_Oremove1(_1650614, _1650612, _1650616)))), -(hBOOL(hAPP(hAPP(c_member(_1650614), _1650610), hAPP(c_List_Oset(_1650614), _1650616))))], (43646 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1650614), _1650610), hAPP(c_List_Oset(_1650614), _1650616))), -(hBOOL(hAPP(hAPP(c_member(_1650614), _1650610), hAPP(c_List_Oset(_1650614), c_List_Oremove1(_1650614, _1650612, _1650616)))))]]], (43652 ^ _782652) ^ [_1650910, _1650912, _1650914, _1650916] : [-(hBOOL(hAPP(hAPP(c_member(_1650910), _1650912), hAPP(c_List_Oset(_1650910), _1650914)))), hBOOL(hAPP(hAPP(c_member(_1650910), _1650912), hAPP(c_List_Oset(_1650910), c_List_Oremove1(_1650910, _1650916, _1650914))))], (43658 ^ _782652) ^ [_1651030, _1651032, _1651034] : [-(hBOOL(hAPP(hAPP(c_member(_1651030), _1651032), hAPP(c_List_Oset(_1651030), _1651034)))), -(c_List_Oremove1(_1651030, _1651032, _1651034) = _1651034)], (43664 ^ _782652) ^ [_1651084, _1651086, _1651088] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1651084, tc_HOL_Obool)), hAPP(c_List_Oset(_1651084), c_List_Oremove1(_1651084, _1651086, _1651088))), hAPP(c_List_Oset(_1651084), _1651088))))], (43666 ^ _782652) ^ [_1651135, _1651137, _1651139] : [class_Orderings_Olinorder(_1651135), hBOOL(hAPP(c_Finite__Set_Ofinite(_1651135), _1651137)), -(c_List_Olinorder__class_Osorted__list__of__set(_1651135, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1651135, tc_HOL_Obool)), _1651137), hAPP(hAPP(c_Set_Oinsert(_1651135), _1651139), c_Orderings_Obot__class_Obot(tc_fun(_1651135, tc_HOL_Obool))))) = c_List_Oremove1(_1651135, _1651139, c_List_Olinorder__class_Osorted__list__of__set(_1651135, _1651137)))], (43676 ^ _782652) ^ [_1651360, _1651362, _1651364, _1651366, _1651368] : [hBOOL(hAPP(hAPP(c_member(_1651360), _1651362), hAPP(c_List_Oset(_1651360), _1651364))), -(hAPP(hAPP(c_Map_Omap__of(_1651360, _1651366), hAPP(hAPP(c_List_Ozip(_1651360, _1651366), _1651364), hAPP(hAPP(c_List_Omap(_1651360, _1651366), _1651368), _1651364))), _1651362) = hAPP(c_Option_Ooption_OSome(_1651366), hAPP(_1651368, _1651362)))], (43682 ^ _782652) ^ [_1651531, _1651533, _1651535, _1651537, _1651539] : [-(hBOOL(hAPP(hAPP(c_member(_1651531), _1651533), hAPP(c_List_Oset(_1651531), _1651535)))), -(hAPP(hAPP(c_Map_Omap__of(_1651531, _1651537), hAPP(hAPP(c_List_Ozip(_1651531, _1651537), _1651535), hAPP(hAPP(c_List_Omap(_1651531, _1651537), _1651539), _1651535))), _1651533) = c_Option_Ooption_ONone(_1651537))], (43688 ^ _782652) ^ [_1651616, _1651618, _1651620, _1651622] : [hBOOL(hAPP(c_List_Odistinct(_1651616), _1651618)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1651616, _1651620)), hAPP(hAPP(c_List_Ozip(_1651616, _1651620), _1651618), _1651622))))], (43694 ^ _782652) ^ [_1651737, _1651739, _1651741, _1651743] : [hBOOL(hAPP(c_List_Odistinct(_1651737), _1651739)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1651741, _1651737)), hAPP(hAPP(c_List_Ozip(_1651741, _1651737), _1651743), _1651739))))], (43700 ^ _782652) ^ [_1651858, _1651860] : [-(hAPP(hAPP(c_List_Ozip(_1651858, _1651858), _1651860), _1651860) = hAPP(hAPP(c_List_Omap(_1651858, tc_prod(_1651858, _1651858)), hAPP(hAPP(c_COMBS(_1651858, _1651858, tc_prod(_1651858, _1651858)), c_Product__Type_OPair(_1651858, _1651858)), c_COMBI(_1651858))), _1651860))], (43702 ^ _782652) ^ [_1651922, _1651924, _1651926] : [-(hAPP(hAPP(c_List_Ozip(_1651922, _1651924), hAPP(hAPP(c_List_Omap(tc_prod(_1651922, _1651924), _1651922), c_Product__Type_Ofst(_1651922, _1651924)), _1651926)), hAPP(hAPP(c_List_Omap(tc_prod(_1651922, _1651924), _1651924), c_Product__Type_Osnd(_1651922, _1651924)), _1651926)) = _1651926)], (43704 ^ _782652) ^ [_1651988, _1651990, _1651992, _1651994, _1651996, _1651998, _1652000, _1652002] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1651988, _1651990), _1651992), _1651994), hAPP(hAPP(c_List_Ozip(_1651988, _1651990), hAPP(hAPP(c_List_Omap(_1651996, _1651988), _1651998), _1652000)), _1652002)) = hAPP(hAPP(c_List_Omap(tc_prod(_1651996, _1651990), _1651992), hAPP(c_Product__Type_Oprod_Oprod__case(_1651996, _1651990, _1651992), hAPP(hAPP(c_COMBB(tc_fun(_1651990, tc_prod(_1651988, _1651990)), tc_fun(_1651990, _1651992), _1651996), hAPP(c_COMBB(tc_prod(_1651988, _1651990), _1651992, _1651990), _1651994)), hAPP(hAPP(c_COMBB(_1651988, tc_fun(_1651990, tc_prod(_1651988, _1651990)), _1651996), c_Product__Type_OPair(_1651988, _1651990)), _1651998)))), hAPP(hAPP(c_List_Ozip(_1651996, _1651990), _1652000), _1652002)))], (43706 ^ _782652) ^ [_1652131, _1652133, _1652135, _1652137, _1652139, _1652141, _1652143, _1652145] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1652131, _1652133), _1652135), _1652137), hAPP(hAPP(c_List_Ozip(_1652131, _1652133), _1652139), hAPP(hAPP(c_List_Omap(_1652141, _1652133), _1652143), _1652145))) = hAPP(hAPP(c_List_Omap(tc_prod(_1652131, _1652141), _1652135), hAPP(c_Product__Type_Oprod_Oprod__case(_1652131, _1652141, _1652135), hAPP(hAPP(c_COMBB(tc_fun(_1652141, tc_prod(_1652131, _1652133)), tc_fun(_1652141, _1652135), _1652131), hAPP(c_COMBB(tc_prod(_1652131, _1652133), _1652135, _1652141), _1652137)), hAPP(hAPP(c_COMBC(_1652131, tc_fun(_1652141, _1652133), tc_fun(_1652141, tc_prod(_1652131, _1652133))), hAPP(hAPP(c_COMBB(tc_fun(_1652133, tc_prod(_1652131, _1652133)), tc_fun(tc_fun(_1652141, _1652133), tc_fun(_1652141, tc_prod(_1652131, _1652133))), _1652131), c_COMBB(_1652133, tc_prod(_1652131, _1652133), _1652141)), c_Product__Type_OPair(_1652131, _1652133))), _1652143)))), hAPP(hAPP(c_List_Ozip(_1652131, _1652141), _1652139), _1652145)))], (43708 ^ _782652) ^ [_1652333, _1652335, _1652337, _1652339] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652333, _1652333)), hAPP(hAPP(c_Product__Type_OPair(_1652333, _1652333), _1652335), _1652337)), hAPP(c_List_Oset(tc_prod(_1652333, _1652333)), hAPP(hAPP(c_List_Ozip(_1652333, _1652333), _1652339), _1652339)))), 43711 ^ _782652 : [(43712 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652333), _1652335), hAPP(c_List_Oset(_1652333), _1652339))))], (43714 ^ _782652) ^ [] : [-(_1652335 = _1652337)]]], (43716 ^ _782652) ^ [_1652532, _1652534, _1652536, _1652538] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652532, _1652532)), hAPP(hAPP(c_Product__Type_OPair(_1652532, _1652532), _1652534), _1652536)), hAPP(c_List_Oset(tc_prod(_1652532, _1652532)), hAPP(hAPP(c_List_Ozip(_1652532, _1652532), _1652538), _1652538))))), hBOOL(hAPP(hAPP(c_member(_1652532), _1652534), hAPP(c_List_Oset(_1652532), _1652538))), _1652534 = _1652536], (43726 ^ _782652) ^ [_1652767, _1652769, _1652771, _1652773, _1652775, _1652777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652767, _1652769)), hAPP(hAPP(c_Product__Type_OPair(_1652767, _1652769), _1652771), _1652773)), hAPP(c_List_Oset(tc_prod(_1652767, _1652769)), hAPP(hAPP(c_List_Ozip(_1652767, _1652769), _1652775), _1652777)))), -(hBOOL(hAPP(hAPP(c_member(_1652767), _1652771), hAPP(c_List_Oset(_1652767), _1652775))))], (43732 ^ _782652) ^ [_1652948, _1652950, _1652952, _1652954, _1652956, _1652958] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652948, _1652950)), hAPP(hAPP(c_Product__Type_OPair(_1652948, _1652950), _1652952), _1652954)), hAPP(c_List_Oset(tc_prod(_1652948, _1652950)), hAPP(hAPP(c_List_Ozip(_1652948, _1652950), _1652956), _1652958)))), -(hBOOL(hAPP(hAPP(c_member(_1652950), _1652954), hAPP(c_List_Oset(_1652950), _1652958))))], (43738 ^ _782652) ^ [_1653129, _1653131, _1653133, _1653135, _1653137, _1653139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653129, _1653131)), hAPP(hAPP(c_Product__Type_OPair(_1653129, _1653131), _1653133), _1653135)), hAPP(c_List_Oset(tc_prod(_1653129, _1653131)), hAPP(hAPP(c_List_Ozip(_1653129, _1653131), _1653137), _1653139)))), 43741 ^ _782652 : [(43742 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653129), _1653133), hAPP(c_List_Oset(_1653129), _1653137))))], (43744 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653131), _1653135), hAPP(c_List_Oset(_1653131), _1653139))))]]], (43746 ^ _782652) ^ [_1653364, _1653366, _1653368, _1653370, _1653372, _1653374, _1653376, _1653378] : [-(hAPP(hAPP(c_List_Ozip(_1653364, _1653366), hAPP(hAPP(c_List_Omap(_1653368, _1653364), _1653370), _1653372)), hAPP(hAPP(c_List_Omap(_1653374, _1653366), _1653376), _1653378)) = hAPP(hAPP(c_List_Omap(tc_prod(_1653368, _1653374), tc_prod(_1653364, _1653366)), hAPP(c_Product__Type_Oprod_Oprod__case(_1653368, _1653374, tc_prod(_1653364, _1653366)), hAPP(hAPP(c_COMBC(_1653368, tc_fun(_1653374, _1653366), tc_fun(_1653374, tc_prod(_1653364, _1653366))), hAPP(hAPP(c_COMBB(tc_fun(_1653366, tc_prod(_1653364, _1653366)), tc_fun(tc_fun(_1653374, _1653366), tc_fun(_1653374, tc_prod(_1653364, _1653366))), _1653368), c_COMBB(_1653366, tc_prod(_1653364, _1653366), _1653374)), hAPP(hAPP(c_COMBB(_1653364, tc_fun(_1653366, tc_prod(_1653364, _1653366)), _1653368), c_Product__Type_OPair(_1653364, _1653366)), _1653370))), _1653376))), hAPP(hAPP(c_List_Ozip(_1653368, _1653374), _1653372), _1653378)))], (43748 ^ _782652) ^ [_1653535, _1653537, _1653539, _1653541, _1653543, _1653545] : [-(hAPP(hAPP(c_List_Ozip(_1653535, _1653537), hAPP(hAPP(c_List_Omap(_1653539, _1653535), _1653541), _1653543)), _1653545) = hAPP(hAPP(c_List_Omap(tc_prod(_1653539, _1653537), tc_prod(_1653535, _1653537)), hAPP(c_Product__Type_Oprod_Oprod__case(_1653539, _1653537, tc_prod(_1653535, _1653537)), hAPP(hAPP(c_COMBB(_1653535, tc_fun(_1653537, tc_prod(_1653535, _1653537)), _1653539), c_Product__Type_OPair(_1653535, _1653537)), _1653541))), hAPP(hAPP(c_List_Ozip(_1653539, _1653537), _1653543), _1653545)))], (43750 ^ _782652) ^ [_1653639, _1653641, _1653643, _1653645, _1653647, _1653649] : [-(hAPP(hAPP(c_List_Ozip(_1653639, _1653641), _1653643), hAPP(hAPP(c_List_Omap(_1653645, _1653641), _1653647), _1653649)) = hAPP(hAPP(c_List_Omap(tc_prod(_1653639, _1653645), tc_prod(_1653639, _1653641)), hAPP(c_Product__Type_Oprod_Oprod__case(_1653639, _1653645, tc_prod(_1653639, _1653641)), hAPP(hAPP(c_COMBC(_1653639, tc_fun(_1653645, _1653641), tc_fun(_1653645, tc_prod(_1653639, _1653641))), hAPP(hAPP(c_COMBB(tc_fun(_1653641, tc_prod(_1653639, _1653641)), tc_fun(tc_fun(_1653645, _1653641), tc_fun(_1653645, tc_prod(_1653639, _1653641))), _1653639), c_COMBB(_1653641, tc_prod(_1653639, _1653641), _1653645)), c_Product__Type_OPair(_1653639, _1653641))), _1653647))), hAPP(hAPP(c_List_Ozip(_1653639, _1653645), _1653643), _1653649)))], (43752 ^ _782652) ^ [_1653781, _1653783, _1653785] : [class_Orderings_Olinorder(_1653781), hBOOL(hAPP(c_Finite__Set_Ofinite(_1653781), _1653783)), -(c_List_Olinorder__class_Osorted__list__of__set(_1653781, hAPP(hAPP(c_Set_Oinsert(_1653781), _1653785), _1653783)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1653781, _1653781, c_COMBI(_1653781)), _1653785), c_List_Olinorder__class_Osorted__list__of__set(_1653781, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1653781, tc_HOL_Obool)), _1653783), hAPP(hAPP(c_Set_Oinsert(_1653781), _1653785), c_Orderings_Obot__class_Obot(tc_fun(_1653781, tc_HOL_Obool)))))))], (43762 ^ _782652) ^ [_1654020, _1654022, _1654024, _1654026, _1654028, _1654030, _1654032, _1654034] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654020)), _1654022) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654024)), _1654026), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654020)), _1654028) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654024)), _1654026), -(hBOOL(hAPP(hAPP(c_member(_1654024), _1654030), hAPP(c_List_Oset(_1654024), _1654026)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1654024, tc_Option_Ooption(_1654020)), hAPP(c_Map_Omap__of(_1654024, _1654020), hAPP(hAPP(c_List_Ozip(_1654024, _1654020), _1654026), _1654022))), _1654030), hAPP(c_Option_Ooption_OSome(_1654020), _1654032)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1654024, tc_Option_Ooption(_1654020)), hAPP(c_Map_Omap__of(_1654024, _1654020), hAPP(hAPP(c_List_Ozip(_1654024, _1654020), _1654026), _1654028))), _1654030), hAPP(c_Option_Ooption_OSome(_1654020), _1654034)), -(hAPP(c_Map_Omap__of(_1654024, _1654020), hAPP(hAPP(c_List_Ozip(_1654024, _1654020), _1654026), _1654022)) = hAPP(c_Map_Omap__of(_1654024, _1654020), hAPP(hAPP(c_List_Ozip(_1654024, _1654020), _1654026), _1654028)))], (43780 ^ _782652) ^ [_1654580, _1654582, _1654584, _1654586] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1654580, _1654582))), hAPP(hAPP(c_List_Ozip(_1654580, _1654582), _1654584), _1654586)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654580)), _1654584)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654582)), _1654586)))], (43782 ^ _782652) ^ [_1654648, _1654650, _1654652, _1654654, _1654656] : [class_Orderings_Olinorder(_1654648), -(hAPP(c_List_Oset(_1654650), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1654650, _1654648, _1654652), _1654654), _1654656)) = hAPP(hAPP(c_Set_Oinsert(_1654650), _1654654), hAPP(c_List_Oset(_1654650), _1654656)))], (43788 ^ _782652) ^ [_1654785, _1654787, _1654789, _1654791, _1654793] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654785), tc_List_Olist(_1654785))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654785), tc_List_Olist(_1654785)), _1654787), _1654789)), hAPP(c_List_Olexn(_1654785, _1654791), _1654793))), 43791 ^ _782652 : [(43792 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654785)), _1654787) = _1654793)], (43794 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654785)), _1654789) = _1654793)]]], (43796 ^ _782652) ^ [_1654988, _1654990, _1654992, _1654994, _1654996, _1654998] : [class_Orderings_Olinorder(_1654988), -(hAPP(_1654990, _1654992) = hAPP(_1654990, _1654994)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1654996, _1654988, _1654990), _1654994), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1654996, _1654988, _1654990), _1654992), _1654998)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1654996, _1654988, _1654990), _1654992), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1654996, _1654988, _1654990), _1654994), _1654998)))], (43806 ^ _782652) ^ [_1655178, _1655180, _1655182, _1655184] : [class_Orderings_Olinorder(_1655178), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1655178, _1655178, c_COMBI(_1655178)), _1655180), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1655178, _1655178, c_COMBI(_1655178)), _1655182), _1655184)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1655178, _1655178, c_COMBI(_1655178)), _1655182), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1655178, _1655178, c_COMBI(_1655178)), _1655180), _1655184)))], (43812 ^ _782652) ^ [_1655352, _1655354, _1655356] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655352)), _1655354) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655352)), _1655356)), _1655354 = _1655356], (43818 ^ _782652) ^ [_1655444, _1655446, _1655448, _1655450, _1655452] : [class_Orderings_Olinorder(_1655444), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655446)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1655446, _1655444, _1655448), _1655450), _1655452)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655446)), _1655452)))], (43824 ^ _782652) ^ [_1655579] : [class_Orderings_Olinorder(_1655579), -(c_Finite__Set_Ofun__left__comm(_1655579, tc_List_Olist(_1655579), c_List_Olinorder__class_Oinsort__key(_1655579, _1655579, c_COMBI(_1655579))))], (43830 ^ _782652) ^ [_1655670, _1655672, _1655674, _1655676] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655670)), hAPP(hAPP(c_List_Omap(_1655672, _1655670), _1655674), _1655676)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655672)), _1655676))], (43832 ^ _782652) ^ [_1655722, _1655724, _1655726, _1655728, _1655730, _1655732, _1655734] : [hAPP(hAPP(c_List_Omap(_1655722, _1655724), _1655726), _1655728) = hAPP(hAPP(c_List_Omap(_1655730, _1655724), _1655732), _1655734), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655722)), _1655728) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655730)), _1655734))], (43838 ^ _782652) ^ [_1655873, _1655875, _1655877] : [class_Orderings_Olinorder(_1655873), -(c_List_Oremove1(_1655873, _1655875, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1655873, _1655873, c_COMBI(_1655873)), _1655875), _1655877)) = _1655877)], (43844 ^ _782652) ^ [_1655982, _1655984] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1655982), hAPP(c_List_Oset(_1655982), _1655984))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655982)), _1655984))))], (43846 ^ _782652) ^ [_1656029, _1656031] : [hAPP(c_Finite__Set_Ocard(_1656029), hAPP(c_List_Oset(_1656029), _1656031)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656029)), _1656031), -(hBOOL(hAPP(c_List_Odistinct(_1656029), _1656031)))], (43852 ^ _782652) ^ [_1656148, _1656150] : [hBOOL(hAPP(c_List_Odistinct(_1656148), _1656150)), -(hAPP(c_Finite__Set_Ocard(_1656148), hAPP(c_List_Oset(_1656148), _1656150)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656148)), _1656150))], (43858 ^ _782652) ^ [_1656267, _1656269, _1656271, _1656273, _1656275] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656267)), _1656269) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656271)), _1656273), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656267)), _1656275) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656271)), _1656273), hBOOL(hAPP(c_List_Odistinct(_1656271), _1656273)), hAPP(c_Map_Omap__of(_1656271, _1656267), hAPP(hAPP(c_List_Ozip(_1656271, _1656267), _1656273), _1656269)) = hAPP(c_Map_Omap__of(_1656271, _1656267), hAPP(hAPP(c_List_Ozip(_1656271, _1656267), _1656273), _1656275)), -(_1656269 = _1656275)], (43876 ^ _782652) ^ [_1656648, _1656650, _1656652, _1656654] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656648)), _1656650) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656652)), _1656654), -(hAPP(hAPP(c_List_Omap(tc_prod(_1656648, _1656652), _1656648), c_Product__Type_Ofst(_1656648, _1656652)), hAPP(hAPP(c_List_Ozip(_1656648, _1656652), _1656650), _1656654)) = _1656650)], (43882 ^ _782652) ^ [_1656805, _1656807, _1656809, _1656811] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656805)), _1656807) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656809)), _1656811), -(hAPP(hAPP(c_List_Omap(tc_prod(_1656805, _1656809), _1656809), c_Product__Type_Osnd(_1656805, _1656809)), hAPP(hAPP(c_List_Ozip(_1656805, _1656809), _1656807), _1656811)) = _1656811)], (43888 ^ _782652) ^ [_1656962, _1656964, _1656966, _1656968, _1656970] : [class_Orderings_Olinorder(_1656962), 43891 ^ _782652 : [(43892 ^ _782652) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1656964), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1656964, _1656962, _1656966), _1656968), _1656970))), 43895 ^ _782652 : [(43896 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1656964), _1656968), hAPP(c_List_Oset(_1656964), _1656970)))], (43898 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1656964), _1656970)))]]], (43900 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1656964), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1656964, _1656962, _1656966), _1656968), _1656970)))), -(hBOOL(hAPP(hAPP(c_member(_1656964), _1656968), hAPP(c_List_Oset(_1656964), _1656970)))), hBOOL(hAPP(c_List_Odistinct(_1656964), _1656970))]]], (43910 ^ _782652) ^ [_1657364, _1657366, _1657368] : [hBOOL(hAPP(hAPP(c_member(_1657364), _1657366), hAPP(c_List_Oset(_1657364), _1657368))), -(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(_1657364)), _1657368))))], (43916 ^ _782652) ^ [_1657485, _1657487, _1657489, _1657491, _1657493] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657485)), _1657487) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657489)), _1657491), 43919 ^ _782652 : [(43920 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Ozip(_1657485, _1657489), _1657487), _1657491) = _1657493, 43923 ^ _782652 : [(43924 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1657485, _1657489), _1657485), c_Product__Type_Ofst(_1657485, _1657489)), _1657493) = _1657487)], (43926 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1657485, _1657489), _1657489), c_Product__Type_Osnd(_1657485, _1657489)), _1657493) = _1657491)]]], (43928 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1657485, _1657489), _1657487), _1657491) = _1657493), hAPP(hAPP(c_List_Omap(tc_prod(_1657485, _1657489), _1657485), c_Product__Type_Ofst(_1657485, _1657489)), _1657493) = _1657487, hAPP(hAPP(c_List_Omap(tc_prod(_1657485, _1657489), _1657489), c_Product__Type_Osnd(_1657485, _1657489)), _1657493) = _1657491]]], (43938 ^ _782652) ^ [_1657933, _1657935] : [-(c_List_Olenlex(_1657933, _1657935) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1657933), tc_List_Olist(_1657933), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1657933), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1657933), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), tc_List_Olist(_1657933)), c_COMBS(tc_List_Olist(_1657933), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool), tc_fun(tc_List_Olist(_1657933), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1657933)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1657933)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1657933), tc_fun(tc_List_Olist(_1657933), tc_Nat_Onat), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1657933), tc_Nat_Onat), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), tc_List_Olist(_1657933)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1657933))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1657933)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1657933))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1657933)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1657933), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1657933), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), tc_List_Olist(_1657933)), c_COMBS(tc_List_Olist(_1657933), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool), tc_fun(tc_List_Olist(_1657933), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1657933)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1657933)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1657933), tc_fun(tc_List_Olist(_1657933), tc_Nat_Onat), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1657933), tc_Nat_Onat), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), tc_List_Olist(_1657933)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1657933))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1657933)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1657933))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1657933)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1657933), tc_fun(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1657933), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1657933), tc_HOL_Obool)), tc_List_Olist(_1657933)), c_COMBC(tc_List_Olist(_1657933), tc_fun(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1657933), tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933))), tc_fun(tc_List_Olist(_1657933), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1657933)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1657933)), c_member(tc_prod(tc_List_Olist(_1657933), tc_List_Olist(_1657933))))), c_Product__Type_OPair(tc_List_Olist(_1657933), tc_List_Olist(_1657933))))), c_List_Olex(_1657933, _1657935)))))))], (43940 ^ _782652) ^ [_1658489, _1658491] : [-(c_List_Olenlex(_1658489, _1658491) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1658489)), tc_List_Olist(_1658489)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1658489), c_Wellfounded_Oless__than, c_List_Olex(_1658489, _1658491))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1658489), tc_List_Olist(_1658489), tc_prod(tc_Nat_Onat, tc_List_Olist(_1658489))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1658489), tc_prod(tc_Nat_Onat, tc_List_Olist(_1658489))), tc_List_Olist(_1658489)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1658489))), c_Nat_Osize__class_Osize(tc_List_Olist(_1658489)))), c_COMBI(tc_List_Olist(_1658489)))))], (43942 ^ _782652) ^ [_1658597, _1658599, _1658601] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1658597), _1658599)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1658597)), hAPP(c_Set_OCollect(tc_List_Olist(_1658597)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1658597), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1658597)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1658597), tc_fun(_1658597, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1658597, tc_HOL_Obool), tc_fun(tc_fun(_1658597, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1658597)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1658597, tc_HOL_Obool))), c_List_Oset(_1658597))), _1658599))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1658597), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1658597)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1658597)))), _1658601))))))], (43948 ^ _782652) ^ [_1658918, _1658920, _1658922] : [_1658918 = _1658920, 43951 ^ _782652 : [(43952 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658922)), _1658918) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658922)), _1658920))], (43954 ^ _782652) ^ [_1659074] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1658922, _1658922)), _1659074), hAPP(c_List_Oset(tc_prod(_1658922, _1658922)), hAPP(hAPP(c_List_Ozip(_1658922, _1658922), _1658918), _1658920)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1658922, _1658922, tc_HOL_Obool), c_fequal), _1659074)))]]], (43960 ^ _782652) ^ [_1659229, _1659231, _1659233] : [-(_1659229 = _1659231), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659233)), _1659229) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659233)), _1659231), 43966 ^ _782652 : [(43967 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1659233, _1659233)), 43965 ^ [_1659229, _1659231, _1659233]), hAPP(c_List_Oset(tc_prod(_1659233, _1659233)), hAPP(hAPP(c_List_Ozip(_1659233, _1659233), _1659229), _1659231)))))], (43969 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1659233, _1659233, tc_HOL_Obool), c_fequal), 43965 ^ [_1659229, _1659231, _1659233]))]]], (43973 ^ _782652) ^ [_1659543, _1659545, _1659547, _1659549, _1659551] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659543)), _1659545) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659547)), _1659549), 43976 ^ _782652 : [(43977 ^ _782652) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1659543, _1659547), hAPP(hAPP(c_List_Ozip(_1659543, _1659547), _1659545), _1659549)), _1659551) = c_Option_Ooption_ONone(_1659547), hBOOL(hAPP(hAPP(c_member(_1659543), _1659551), hAPP(c_List_Oset(_1659543), _1659545)))], (43983 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1659543), _1659551), hAPP(c_List_Oset(_1659543), _1659545)))), -(hAPP(hAPP(c_Map_Omap__of(_1659543, _1659547), hAPP(hAPP(c_List_Ozip(_1659543, _1659547), _1659545), _1659549)), _1659551) = c_Option_Ooption_ONone(_1659547))]]], (43989 ^ _782652) ^ [_1659848, _1659850, _1659852, _1659854, _1659856] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659848)), _1659850) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659852)), _1659854), 43992 ^ _782652 : [(43993 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1659848), _1659856), hAPP(c_List_Oset(_1659848), _1659850))), -(hAPP(hAPP(c_Map_Omap__of(_1659848, _1659852), hAPP(hAPP(c_List_Ozip(_1659848, _1659852), _1659850), _1659854)), _1659856) = hAPP(c_Option_Ooption_OSome(_1659852), 43996 ^ [_1659848, _1659850, _1659852, _1659854, _1659856]))], (44000 ^ _782652) ^ [] : [44001 ^ _782652 : [(44002 ^ _782652) ^ [_1660140] : [hAPP(hAPP(c_Map_Omap__of(_1659848, _1659852), hAPP(hAPP(c_List_Ozip(_1659848, _1659852), _1659850), _1659854)), _1659856) = hAPP(c_Option_Ooption_OSome(_1659852), _1660140)]], -(hBOOL(hAPP(hAPP(c_member(_1659848), _1659856), hAPP(c_List_Oset(_1659848), _1659850))))]]], (44006 ^ _782652) ^ [_1660244, _1660246, _1660248] : [hBOOL(hAPP(hAPP(c_member(_1660244), _1660246), hAPP(c_List_Oset(_1660244), _1660248))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660244)), c_List_Oremove1(_1660244, _1660246, _1660248)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660244)), _1660248)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44012 ^ _782652) ^ [_1660389, _1660391, _1660393] : [-(hBOOL(hAPP(hAPP(c_member(_1660389), _1660391), hAPP(c_List_Oset(_1660389), _1660393)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660389)), c_List_Oremove1(_1660389, _1660391, _1660393)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660389)), _1660393))], (44018 ^ _782652) ^ [_1660459, _1660461, _1660463, _1660465] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660459)), _1660461) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660463)), _1660465), hBOOL(hAPP(c_List_Odistinct(_1660459), _1660461)), -(c_Map_Odom(_1660459, _1660463, hAPP(c_Map_Omap__of(_1660459, _1660463), hAPP(hAPP(c_List_Ozip(_1660459, _1660463), _1660461), _1660465))) = hAPP(c_List_Oset(_1660459), _1660461))], (44028 ^ _782652) ^ [_1660680, _1660682, _1660684] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1660680), _1660682)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1660680)), hAPP(c_Set_OCollect(tc_List_Olist(_1660680)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1660680), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1660680)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1660680), tc_fun(_1660680, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1660680, tc_HOL_Obool), tc_fun(tc_fun(_1660680, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1660680)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1660680, tc_HOL_Obool))), c_List_Oset(_1660680))), _1660682))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1660680), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1660680)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1660680)))), _1660684))))))], (44034 ^ _782652) ^ [_1660992, _1660994] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1660992), _1660994)), -(c_Nitpick_Ocard_H(_1660992, _1660994) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660992)), c_Hilbert__Choice_OEps(tc_List_Olist(_1660992), hAPP(hAPP(c_COMBS(tc_List_Olist(_1660992), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1660992)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1660992), tc_fun(_1660992, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1660992, tc_HOL_Obool), tc_fun(tc_fun(_1660992, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1660992)), c_fequal), c_List_Oset(_1660992))), _1660994))), c_List_Odistinct(_1660992)))))], (44040 ^ _782652) ^ [_1661229, _1661231] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1661229), _1661231))), -(c_Nitpick_Ocard_H(_1661229, _1661231) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44046 ^ _782652) ^ [_1661295, _1661297, _1661299, _1661301] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661295), tc_List_Olist(_1661295))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661295), tc_List_Olist(_1661295)), _1661297), _1661299)), c_List_Olistrel(_1661295, _1661301))), 44049 ^ _782652 : [(44050 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661295)), _1661297) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661295)), _1661299))], (44052 ^ _782652) ^ [_1661631] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1661295, _1661295)), _1661631), hAPP(c_List_Oset(tc_prod(_1661295, _1661295)), hAPP(hAPP(c_List_Ozip(_1661295, _1661295), _1661297), _1661299)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1661295, _1661295, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1661295, tc_fun(tc_prod(_1661295, _1661295), tc_HOL_Obool), tc_fun(_1661295, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1661295, tc_fun(tc_fun(tc_prod(_1661295, _1661295), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1661295, _1661295), tc_HOL_Obool), tc_fun(_1661295, tc_HOL_Obool)), _1661295), c_COMBC(_1661295, tc_fun(tc_prod(_1661295, _1661295), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1661295, tc_prod(_1661295, _1661295)), tc_fun(_1661295, tc_fun(tc_fun(tc_prod(_1661295, _1661295), tc_HOL_Obool), tc_HOL_Obool)), _1661295), hAPP(c_COMBB(tc_prod(_1661295, _1661295), tc_fun(tc_fun(tc_prod(_1661295, _1661295), tc_HOL_Obool), tc_HOL_Obool), _1661295), c_member(tc_prod(_1661295, _1661295)))), c_Product__Type_OPair(_1661295, _1661295)))), _1661301)), _1661631)))]]], (44058 ^ _782652) ^ [_1662024, _1662026, _1662028, _1662030] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662024), tc_List_Olist(_1662024))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662024), tc_List_Olist(_1662024)), _1662026), _1662028)), c_List_Olistrel(_1662024, _1662030)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662024)), _1662026) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662024)), _1662028), 44064 ^ _782652 : [(44065 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1662024, _1662024)), 44063 ^ [_1662024, _1662026, _1662028, _1662030]), hAPP(c_List_Oset(tc_prod(_1662024, _1662024)), hAPP(hAPP(c_List_Ozip(_1662024, _1662024), _1662026), _1662028)))))], (44067 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1662024, _1662024, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1662024, tc_fun(tc_prod(_1662024, _1662024), tc_HOL_Obool), tc_fun(_1662024, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1662024, tc_fun(tc_fun(tc_prod(_1662024, _1662024), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1662024, _1662024), tc_HOL_Obool), tc_fun(_1662024, tc_HOL_Obool)), _1662024), c_COMBC(_1662024, tc_fun(tc_prod(_1662024, _1662024), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1662024, tc_prod(_1662024, _1662024)), tc_fun(_1662024, tc_fun(tc_fun(tc_prod(_1662024, _1662024), tc_HOL_Obool), tc_HOL_Obool)), _1662024), hAPP(c_COMBB(tc_prod(_1662024, _1662024), tc_fun(tc_fun(tc_prod(_1662024, _1662024), tc_HOL_Obool), tc_HOL_Obool), _1662024), c_member(tc_prod(_1662024, _1662024)))), c_Product__Type_OPair(_1662024, _1662024)))), _1662030)), 44063 ^ [_1662024, _1662026, _1662028, _1662030]))]]], (44071 ^ _782652) ^ [_1662762, _1662764, _1662766] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662762), tc_List_Olist(_1662762))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662762), tc_List_Olist(_1662762)), _1662764), _1662764)), c_List_Olistrel(_1662762, c_Transitive__Closure_Ortrancl(_1662762, _1662766)))))], (44073 ^ _782652) ^ [_1662822, _1662824, _1662826, _1662828] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662822), tc_List_Olist(_1662822))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662822), tc_List_Olist(_1662822)), _1662824), _1662826)), c_List_Olistrel(_1662822, _1662828))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662822)), _1662824) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662822)), _1662826))], (44079 ^ _782652) ^ [_1662991, _1662993, _1662995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1662991, _1662991), tc_HOL_Obool)), _1662993), _1662995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1662991), tc_List_Olist(_1662991)), tc_HOL_Obool)), c_List_Olistrel(_1662991, _1662993)), c_List_Olistrel(_1662991, _1662995))))], (44085 ^ _782652) ^ [_1663142, _1663144, _1663146, _1663148, _1663150] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663142), tc_List_Olist(_1663142))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663142), tc_List_Olist(_1663142)), _1663144), _1663146)), c_List_Olistrel(_1663142, c_Transitive__Closure_Ortrancl(_1663142, _1663148)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663142), tc_List_Olist(_1663142))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663142), tc_List_Olist(_1663142)), _1663146), _1663150)), c_List_Olistrel(_1663142, c_Transitive__Closure_Ortrancl(_1663142, _1663148)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663142), tc_List_Olist(_1663142))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663142), tc_List_Olist(_1663142)), _1663144), _1663150)), c_List_Olistrel(_1663142, c_Transitive__Closure_Ortrancl(_1663142, _1663148)))))], (44095 ^ _782652) ^ [_1663502, _1663504, _1663506, _1663508] : [c_List_Olistrelp(_1663502, hAPP(hAPP(c_COMBC(_1663502, tc_fun(tc_prod(_1663502, _1663502), tc_HOL_Obool), tc_fun(_1663502, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1663502, tc_fun(tc_fun(tc_prod(_1663502, _1663502), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1663502, _1663502), tc_HOL_Obool), tc_fun(_1663502, tc_HOL_Obool)), _1663502), c_COMBC(_1663502, tc_fun(tc_prod(_1663502, _1663502), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1663502, tc_prod(_1663502, _1663502)), tc_fun(_1663502, tc_fun(tc_fun(tc_prod(_1663502, _1663502), tc_HOL_Obool), tc_HOL_Obool)), _1663502), hAPP(c_COMBB(tc_prod(_1663502, _1663502), tc_fun(tc_fun(tc_prod(_1663502, _1663502), tc_HOL_Obool), tc_HOL_Obool), _1663502), c_member(tc_prod(_1663502, _1663502)))), c_Product__Type_OPair(_1663502, _1663502)))), _1663504), _1663506, _1663508), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663502), tc_List_Olist(_1663502))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663502), tc_List_Olist(_1663502)), _1663506), _1663508)), c_List_Olistrel(_1663502, _1663504))))], (44101 ^ _782652) ^ [_1663879, _1663881, _1663883, _1663885] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663879), tc_List_Olist(_1663879))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663879), tc_List_Olist(_1663879)), _1663883), _1663885)), c_List_Olistrel(_1663879, _1663881))), -(c_List_Olistrelp(_1663879, hAPP(hAPP(c_COMBC(_1663879, tc_fun(tc_prod(_1663879, _1663879), tc_HOL_Obool), tc_fun(_1663879, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1663879, tc_fun(tc_fun(tc_prod(_1663879, _1663879), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1663879, _1663879), tc_HOL_Obool), tc_fun(_1663879, tc_HOL_Obool)), _1663879), c_COMBC(_1663879, tc_fun(tc_prod(_1663879, _1663879), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1663879, tc_prod(_1663879, _1663879)), tc_fun(_1663879, tc_fun(tc_fun(tc_prod(_1663879, _1663879), tc_HOL_Obool), tc_HOL_Obool)), _1663879), hAPP(c_COMBB(tc_prod(_1663879, _1663879), tc_fun(tc_fun(tc_prod(_1663879, _1663879), tc_HOL_Obool), tc_HOL_Obool), _1663879), c_member(tc_prod(_1663879, _1663879)))), c_Product__Type_OPair(_1663879, _1663879)))), _1663881), _1663883, _1663885))], (44107 ^ _782652) ^ [_1664262, _1664264, _1664266] : [-(hAPP(c_List_Olexn(_1664262, _1664264), hAPP(c_Nat_OSuc, _1664266)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1664262), tc_List_Olist(_1664262)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1664262, tc_List_Olist(_1664262)), tc_prod(_1664262, tc_List_Olist(_1664262))), tc_prod(tc_List_Olist(_1664262), tc_List_Olist(_1664262)), c_Product__Type_Omap__pair(tc_prod(_1664262, tc_List_Olist(_1664262)), tc_List_Olist(_1664262), tc_prod(_1664262, tc_List_Olist(_1664262)), tc_List_Olist(_1664262), hAPP(c_Product__Type_Oprod_Oprod__case(_1664262, tc_List_Olist(_1664262), tc_List_Olist(_1664262)), c_List_Olist_OCons(_1664262)), hAPP(c_Product__Type_Oprod_Oprod__case(_1664262, tc_List_Olist(_1664262), tc_List_Olist(_1664262)), c_List_Olist_OCons(_1664262)))), c_Wellfounded_Olex__prod(_1664262, tc_List_Olist(_1664262), _1664264, hAPP(c_List_Olexn(_1664262, _1664264), _1664266)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1664262), tc_List_Olist(_1664262))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1664262), tc_List_Olist(_1664262), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1664262), tc_fun(tc_List_Olist(_1664262), tc_HOL_Obool), tc_fun(tc_List_Olist(_1664262), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1664262), tc_HOL_Obool), tc_fun(tc_List_Olist(_1664262), tc_HOL_Obool)), tc_List_Olist(_1664262)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1664262))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1664262)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1664262), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1664262)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1664262)))), hAPP(c_Nat_OSuc, _1664266))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1664262), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1664262)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1664262)))), hAPP(c_Nat_OSuc, _1664266)))))))], (44109 ^ _782652) ^ [_1664553, _1664555, _1664557, _1664559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664553)), _1664555)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664553)), _1664557))), _1664555 = hAPP(hAPP(c_List_Olist_OCons(_1664553), _1664559), _1664557)], (44115 ^ _782652) ^ [_1664689, _1664691, _1664693, _1664695] : [hBOOL(hAPP(hAPP(c_member(_1664689), _1664691), hAPP(c_List_Oset(_1664689), hAPP(hAPP(c_List_Olist_OCons(_1664689), _1664693), _1664695)))), -(_1664691 = _1664693), -(hBOOL(hAPP(hAPP(c_member(_1664689), _1664691), hAPP(c_List_Oset(_1664689), _1664695))))], (44125 ^ _782652) ^ [_1664847, _1664849, _1664851, _1664853, _1664855, _1664857] : [-(hAPP(hAPP(c_List_Ozip(_1664847, _1664849), hAPP(hAPP(c_List_Olist_OCons(_1664847), _1664851), _1664853)), hAPP(hAPP(c_List_Olist_OCons(_1664849), _1664855), _1664857)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1664847, _1664849)), hAPP(hAPP(c_Product__Type_OPair(_1664847, _1664849), _1664851), _1664855)), hAPP(hAPP(c_List_Ozip(_1664847, _1664849), _1664853), _1664857)))], (44127 ^ _782652) ^ [_1664934, _1664936, _1664938] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1664934, tc_HOL_Obool)), hAPP(c_List_Oset(_1664934), _1664936)), hAPP(c_List_Oset(_1664934), hAPP(hAPP(c_List_Olist_OCons(_1664934), _1664938), _1664936)))))], (44129 ^ _782652) ^ [_1664989, _1664991, _1664993] : [-(hAPP(c_List_Oset(_1664989), hAPP(hAPP(c_List_Olist_OCons(_1664989), _1664991), _1664993)) = hAPP(hAPP(c_Set_Oinsert(_1664989), _1664991), hAPP(c_List_Oset(_1664989), _1664993)))], (44131 ^ _782652) ^ [_1665042, _1665044, _1665046, _1665048, _1665050, _1665052] : [-(c_List_Ofoldr(_1665042, _1665044, _1665046, hAPP(hAPP(c_List_Olist_OCons(_1665042), _1665048), _1665050), _1665052) = hAPP(hAPP(_1665046, _1665048), c_List_Ofoldr(_1665042, _1665044, _1665046, _1665050, _1665052)))], (44133 ^ _782652) ^ [_1665101, _1665103, _1665105, _1665107, _1665109, _1665111] : [hBOOL(hAPP(hAPP(_1665101, _1665103), _1665105)), c_List_Olistrelp(_1665107, _1665101, _1665109, _1665111), -(c_List_Olistrelp(_1665107, _1665101, hAPP(hAPP(c_List_Olist_OCons(_1665107), _1665103), _1665109), hAPP(hAPP(c_List_Olist_OCons(_1665107), _1665105), _1665111)))], (44143 ^ _782652) ^ [_1665323, _1665325, _1665327, _1665329, _1665331, _1665333] : [c_List_Olistrelp(_1665323, _1665325, hAPP(hAPP(c_List_Olist_OCons(_1665323), _1665327), _1665329), hAPP(hAPP(c_List_Olist_OCons(_1665323), _1665331), _1665333)), 44146 ^ _782652 : [(44147 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1665325, _1665327), _1665331)))], (44149 ^ _782652) ^ [] : [-(c_List_Olistrelp(_1665323, _1665325, _1665329, _1665333))]]], (44151 ^ _782652) ^ [_1665480, _1665482, _1665484, _1665486, _1665488, _1665490] : [-(c_List_Olistrelp(_1665480, _1665482, hAPP(hAPP(c_List_Olist_OCons(_1665480), _1665484), _1665486), hAPP(hAPP(c_List_Olist_OCons(_1665480), _1665488), _1665490))), hBOOL(hAPP(hAPP(_1665482, _1665484), _1665488)), c_List_Olistrelp(_1665480, _1665482, _1665486, _1665490)], (44161 ^ _782652) ^ [_1665701, _1665703, _1665705, _1665707, _1665709] : [hAPP(hAPP(c_List_Olist_OCons(_1665701), _1665703), _1665705) = hAPP(hAPP(c_List_Olist_OCons(_1665701), _1665707), _1665709), 44164 ^ _782652 : [(44165 ^ _782652) ^ [] : [-(_1665703 = _1665707)], (44167 ^ _782652) ^ [] : [-(_1665705 = _1665709)]]], (44169 ^ _782652) ^ [_1665838, _1665840, _1665842, _1665844, _1665846] : [-(hAPP(hAPP(c_List_Olist_OCons(_1665838), _1665840), _1665842) = hAPP(hAPP(c_List_Olist_OCons(_1665838), _1665844), _1665846)), _1665840 = _1665844, _1665842 = _1665846], (44179 ^ _782652) ^ [_1666028, _1666030, _1666032] : [hAPP(hAPP(c_List_Olist_OCons(_1666028), _1666030), _1666032) = _1666032], (44181 ^ _782652) ^ [_1666078, _1666080, _1666082] : [_1666078 = hAPP(hAPP(c_List_Olist_OCons(_1666080), _1666082), _1666078)], (44183 ^ _782652) ^ [_1666113, _1666115, _1666117, _1666119, _1666121] : [-(hAPP(hAPP(c_List_Omap(_1666113, _1666115), _1666117), hAPP(hAPP(c_List_Olist_OCons(_1666113), _1666119), _1666121)) = hAPP(hAPP(c_List_Olist_OCons(_1666115), hAPP(_1666117, _1666119)), hAPP(hAPP(c_List_Omap(_1666113, _1666115), _1666117), _1666121)))], (44185 ^ _782652) ^ [_1666196, _1666198, _1666200, _1666202] : [_1666196 = _1666198, -(c_List_Oremove1(_1666200, _1666196, hAPP(hAPP(c_List_Olist_OCons(_1666200), _1666198), _1666202)) = _1666202)], (44191 ^ _782652) ^ [_1666295, _1666297, _1666299, _1666301] : [-(_1666295 = _1666297), -(c_List_Oremove1(_1666299, _1666295, hAPP(hAPP(c_List_Olist_OCons(_1666299), _1666297), _1666301)) = hAPP(hAPP(c_List_Olist_OCons(_1666299), _1666297), c_List_Oremove1(_1666299, _1666295, _1666301)))], (44197 ^ _782652) ^ [_1666361, _1666363, _1666365, _1666367, _1666369, _1666371] : [class_Orderings_Olinorder(_1666361), 44200 ^ _782652 : [(44201 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666361), hAPP(_1666363, _1666365)), hAPP(_1666363, _1666367))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1666369, _1666361, _1666363), _1666365), hAPP(hAPP(c_List_Olist_OCons(_1666369), _1666367), _1666371)) = hAPP(hAPP(c_List_Olist_OCons(_1666369), _1666365), hAPP(hAPP(c_List_Olist_OCons(_1666369), _1666367), _1666371)))], (44207 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666361), hAPP(_1666363, _1666365)), hAPP(_1666363, _1666367)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1666369, _1666361, _1666363), _1666365), hAPP(hAPP(c_List_Olist_OCons(_1666369), _1666367), _1666371)) = hAPP(hAPP(c_List_Olist_OCons(_1666369), _1666367), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1666369, _1666361, _1666363), _1666365), _1666371)))]]], (44213 ^ _782652) ^ [_1666761, _1666763, _1666765] : [hBOOL(hAPP(c_List_Odistinct(_1666761), hAPP(hAPP(c_List_Olist_OCons(_1666761), _1666763), _1666765))), 44216 ^ _782652 : [(44217 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1666761), _1666763), hAPP(c_List_Oset(_1666761), _1666765)))], (44219 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1666761), _1666765)))]]], (44221 ^ _782652) ^ [_1666928, _1666930, _1666932] : [-(hBOOL(hAPP(c_List_Odistinct(_1666928), hAPP(hAPP(c_List_Olist_OCons(_1666928), _1666930), _1666932)))), -(hBOOL(hAPP(hAPP(c_member(_1666928), _1666930), hAPP(c_List_Oset(_1666928), _1666932)))), hBOOL(hAPP(c_List_Odistinct(_1666928), _1666932))], (44231 ^ _782652) ^ [_1667143, _1667145, _1667147, _1667149, _1667151, _1667153] : [_1667143 = _1667145, -(hAPP(hAPP(c_Map_Omap__of(_1667147, _1667149), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1667147, _1667149)), hAPP(hAPP(c_Product__Type_OPair(_1667147, _1667149), _1667143), _1667151)), _1667153)), _1667145) = hAPP(c_Option_Ooption_OSome(_1667149), _1667151))], (44237 ^ _782652) ^ [_1667290, _1667292, _1667294, _1667296, _1667298, _1667300] : [-(_1667290 = _1667292), -(hAPP(hAPP(c_Map_Omap__of(_1667294, _1667296), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1667294, _1667296)), hAPP(hAPP(c_Product__Type_OPair(_1667294, _1667296), _1667290), _1667298)), _1667300)), _1667292) = hAPP(hAPP(c_Map_Omap__of(_1667294, _1667296), _1667300), _1667292))], (44243 ^ _782652) ^ [_1667374, _1667376, _1667378] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667374)), hAPP(hAPP(c_List_Olist_OCons(_1667374), _1667376), _1667378)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667374)), _1667378)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44245 ^ _782652) ^ [_1667429, _1667431, _1667433, _1667435, _1667437, _1667439] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1667429, _1667429)), hAPP(hAPP(c_Product__Type_OPair(_1667429, _1667429), _1667431), _1667433)), _1667435)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667429), tc_List_Olist(_1667429))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667429), tc_List_Olist(_1667429)), _1667437), _1667439)), c_List_Olistrel(_1667429, _1667435))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667429), tc_List_Olist(_1667429))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667429), tc_List_Olist(_1667429)), hAPP(hAPP(c_List_Olist_OCons(_1667429), _1667431), _1667437)), hAPP(hAPP(c_List_Olist_OCons(_1667429), _1667433), _1667439))), c_List_Olistrel(_1667429, _1667435))))], (44255 ^ _782652) ^ [_1667764, _1667766, _1667768, _1667770] : [-(hAPP(c_Map_Omap__of(_1667764, _1667766), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1667764, _1667766)), _1667768), _1667770)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1667764, tc_Option_Ooption(_1667766)), hAPP(c_Map_Omap__of(_1667764, _1667766), _1667770)), hAPP(c_Product__Type_Ofst(_1667764, _1667766), _1667768)), hAPP(c_Option_Ooption_OSome(_1667766), hAPP(c_Product__Type_Osnd(_1667764, _1667766), _1667768))))], (44257 ^ _782652) ^ [_1667874, _1667876, _1667878, _1667880, _1667882, _1667884] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667874), tc_List_Olist(_1667874))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667874), tc_List_Olist(_1667874)), hAPP(hAPP(c_List_Olist_OCons(_1667874), _1667876), _1667878)), hAPP(hAPP(c_List_Olist_OCons(_1667874), _1667880), _1667882))), c_List_Olex(_1667874, _1667884))), 44262 ^ _782652 : [(44263 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1667874, _1667874)), hAPP(hAPP(c_Product__Type_OPair(_1667874, _1667874), _1667876), _1667880)), _1667884)))], (44265 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667874)), _1667878) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667874)), _1667882))]], 44266 ^ _782652 : [(44267 ^ _782652) ^ [] : [-(_1667876 = _1667880)], (44269 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667874), tc_List_Olist(_1667874))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667874), tc_List_Olist(_1667874)), _1667878), _1667882)), c_List_Olex(_1667874, _1667884))))]]], (44271 ^ _782652) ^ [_1668272, _1668274, _1668276, _1668278, _1668280, _1668282] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668272), tc_List_Olist(_1668272))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668272), tc_List_Olist(_1668272)), hAPP(hAPP(c_List_Olist_OCons(_1668272), _1668274), _1668276)), hAPP(hAPP(c_List_Olist_OCons(_1668272), _1668278), _1668280))), c_List_Olex(_1668272, _1668282)))), 44272 ^ _782652 : [(44273 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1668272, _1668272)), hAPP(hAPP(c_Product__Type_OPair(_1668272, _1668272), _1668274), _1668278)), _1668282)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668272)), _1668276) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668272)), _1668280)], (44279 ^ _782652) ^ [] : [_1668274 = _1668278, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668272), tc_List_Olist(_1668272))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668272), tc_List_Olist(_1668272)), _1668276), _1668280)), c_List_Olex(_1668272, _1668282)))]]], (44287 ^ _782652) ^ [_1668728, _1668730, _1668732, _1668734] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1668728), tc_List_Olist(_1668728), c_List_Olistrel(_1668728, _1668730)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1668728)), hAPP(hAPP(c_List_Olist_OCons(_1668728), _1668732), _1668734)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1668728), tc_HOL_Obool)))) = c_List_Oset__Cons(_1668728, hAPP(c_Relation_OImage(_1668728, _1668728, _1668730), hAPP(hAPP(c_Set_Oinsert(_1668728), _1668732), c_Orderings_Obot__class_Obot(tc_fun(_1668728, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1668728), tc_List_Olist(_1668728), c_List_Olistrel(_1668728, _1668730)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1668728)), _1668734), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1668728), tc_HOL_Obool))))))], (44289 ^ _782652) ^ [_1668851, _1668853, _1668855] : [-(c_List_Oset__Cons(_1668851, _1668853, _1668855) = hAPP(c_Set_OCollect(tc_List_Olist(_1668851)), hAPP(hAPP(c_COMBB(tc_fun(_1668851, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1668851)), c_HOL_OEx(_1668851)), hAPP(hAPP(c_COMBB(tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), tc_fun(_1668851, tc_HOL_Obool), tc_List_Olist(_1668851)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_HOL_Obool, _1668851), c_HOL_OEx(tc_List_Olist(_1668851)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1668851), tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1668851, tc_fun(tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool))), tc_fun(tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool))), tc_List_Olist(_1668851)), c_COMBS(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1668851, tc_fun(tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool))), tc_List_Olist(_1668851)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1668851), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), _1668851), c_COMBS(tc_List_Olist(_1668851), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1668851)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_fun(tc_List_Olist(_1668851), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1668851), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1668851)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1668851), tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_List_Olist(_1668851))), tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1668851), tc_List_Olist(_1668851)), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), tc_fun(tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_List_Olist(_1668851))), tc_fun(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool))), tc_List_Olist(_1668851)), c_COMBB(tc_fun(tc_List_Olist(_1668851), tc_List_Olist(_1668851)), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), _1668851)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1668851), tc_List_Olist(_1668851)), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), tc_List_Olist(_1668851)), c_COMBB(tc_List_Olist(_1668851), tc_HOL_Obool, tc_List_Olist(_1668851))), c_fequal))), c_List_Olist_OCons(_1668851)))))), hAPP(hAPP(c_COMBC(_1668851, tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool)), _1668851), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1668851))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1668851), c_fconj), hAPP(hAPP(c_COMBC(_1668851, tc_fun(_1668851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1668851)), _1668853)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1668851), tc_fun(tc_List_Olist(_1668851), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1668851))), _1668855)))))))], (44291 ^ _782652) ^ [_1669386, _1669388, _1669390, _1669392, _1669394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669386), tc_List_Olist(_1669386))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669386), tc_List_Olist(_1669386)), _1669388), hAPP(hAPP(c_List_Olist_OCons(_1669386), _1669390), _1669392))), c_List_Olistrel(_1669386, _1669394))), 44296 ^ _782652 : [(44297 ^ _782652) ^ [] : [-(_1669388 = hAPP(hAPP(c_List_Olist_OCons(_1669386), 44294 ^ [_1669386, _1669388, _1669390, _1669392, _1669394]), 44295 ^ [_1669386, _1669388, _1669390, _1669392, _1669394]))], (44299 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1669386, _1669386)), hAPP(hAPP(c_Product__Type_OPair(_1669386, _1669386), 44294 ^ [_1669386, _1669388, _1669390, _1669392, _1669394]), _1669390)), _1669394)))], (44301 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669386), tc_List_Olist(_1669386))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669386), tc_List_Olist(_1669386)), 44295 ^ [_1669386, _1669388, _1669390, _1669392, _1669394]), _1669392)), c_List_Olistrel(_1669386, _1669394))))]]], (44303 ^ _782652) ^ [_1669775, _1669777, _1669779, _1669781, _1669783] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669775), tc_List_Olist(_1669775))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669775), tc_List_Olist(_1669775)), hAPP(hAPP(c_List_Olist_OCons(_1669775), _1669777), _1669779)), _1669781)), c_List_Olistrel(_1669775, _1669783))), 44308 ^ _782652 : [(44309 ^ _782652) ^ [] : [-(_1669781 = hAPP(hAPP(c_List_Olist_OCons(_1669775), 44306 ^ [_1669775, _1669777, _1669779, _1669781, _1669783]), 44307 ^ [_1669775, _1669777, _1669779, _1669781, _1669783]))], (44311 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1669775, _1669775)), hAPP(hAPP(c_Product__Type_OPair(_1669775, _1669775), _1669777), 44306 ^ [_1669775, _1669777, _1669779, _1669781, _1669783])), _1669783)))], (44313 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1669775), tc_List_Olist(_1669775))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1669775), tc_List_Olist(_1669775)), _1669779), 44307 ^ [_1669775, _1669777, _1669779, _1669781, _1669783])), c_List_Olistrel(_1669775, _1669783))))]]], (44315 ^ _782652) ^ [_1670164, _1670166, _1670168] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670164)), c_List_Osublist(_1670164, _1670166, _1670168)) = 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(_1670164)), _1670166)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1670168)))))], (44317 ^ _782652) ^ [_1670245, _1670247, _1670249, _1670251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1670245), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1670247), _1670249))), -(hAPP(c_Random_Opick(_1670247, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1670247)), _1670249), _1670251)), _1670245) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1670247), _1670249))], (44323 ^ _782652) ^ [_1670388, _1670390, _1670392, _1670394] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1670388), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1670390), _1670392)))), -(hAPP(c_Random_Opick(_1670390, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1670390)), _1670392), _1670394)), _1670388) = hAPP(c_Random_Opick(_1670390, _1670394), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1670388), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1670390), _1670392))))], (44329 ^ _782652) ^ [_1670476, _1670478, _1670480] : [hBOOL(hAPP(c_List_Odistinct(_1670476), _1670478)), -(hBOOL(hAPP(c_List_Odistinct(_1670476), c_List_Osublist(_1670476, _1670478, _1670480))))], (44335 ^ _782652) ^ [_1670579, _1670581, _1670583, _1670585] : [hBOOL(hAPP(hAPP(c_member(_1670579), _1670581), hAPP(c_List_Oset(_1670579), c_List_Osublist(_1670579, _1670583, _1670585)))), -(hBOOL(hAPP(hAPP(c_member(_1670579), _1670581), hAPP(c_List_Oset(_1670579), _1670583))))], (44341 ^ _782652) ^ [_1670715, _1670717, _1670719, _1670721] : [-(hBOOL(hAPP(hAPP(c_member(_1670715), _1670717), hAPP(c_List_Oset(_1670715), _1670719)))), hBOOL(hAPP(hAPP(c_member(_1670715), _1670717), hAPP(c_List_Oset(_1670715), c_List_Osublist(_1670715, _1670719, _1670721))))], (44347 ^ _782652) ^ [_1670839, _1670841, _1670843] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1670839, tc_HOL_Obool)), hAPP(c_List_Oset(_1670839), c_List_Osublist(_1670839, _1670841, _1670843))), hAPP(c_List_Oset(_1670839), _1670841))))], (44349 ^ _782652) ^ [_1670890, _1670892, _1670894] : [-(c_Random_Oselect__weight(_1670890, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1670890)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1670890), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1670892)), _1670894)) = c_Random_Oselect__weight(_1670890, _1670894))], (44351 ^ _782652) ^ [_1670943, _1670945, _1670947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1670943), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1670945), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1670945)), _1670947)))), -(hBOOL(hAPP(hAPP(c_member(_1670945), hAPP(c_Random_Opick(_1670945, _1670947), _1670943)), hAPP(c_List_Oset(_1670945), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1670945), _1670945), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1670945)), _1670947)))))], (44357 ^ _782652) ^ [_1671134, _1671136, _1671138] : [class_Groups_Omonoid__add(_1671134), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671134), hAPP(hAPP(c_List_Olist_OCons(_1671134), _1671136), _1671138)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1671134), _1671136), hAPP(c_List_Omonoid__add__class_Olistsum(_1671134), _1671138)))], (44363 ^ _782652) ^ [_1671263, _1671265, _1671267] : [class_Groups_Omonoid__add(_1671263), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671263), hAPP(hAPP(c_List_Omap(_1671265, _1671263), hAPP(c_COMBK(_1671263, _1671265), c_Groups_Ozero__class_Ozero(_1671263))), _1671267)) = c_Groups_Ozero__class_Ozero(_1671263))], (44369 ^ _782652) ^ [_1671388, _1671390, _1671392, _1671394, _1671396] : [class_Groups_Ocomm__monoid__add(_1671388), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671388), hAPP(hAPP(c_List_Omap(_1671390, _1671388), hAPP(hAPP(c_COMBS(_1671390, _1671388, _1671388), hAPP(hAPP(c_COMBB(_1671388, tc_fun(_1671388, _1671388), _1671390), c_Groups_Oplus__class_Oplus(_1671388)), _1671392)), _1671394)), _1671396)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1671388), hAPP(c_List_Omonoid__add__class_Olistsum(_1671388), hAPP(hAPP(c_List_Omap(_1671390, _1671388), _1671392), _1671396))), hAPP(c_List_Omonoid__add__class_Olistsum(_1671388), hAPP(hAPP(c_List_Omap(_1671390, _1671388), _1671394), _1671396))))], (44375 ^ _782652) ^ [_1671619, _1671621, _1671623, _1671625, _1671627] : [class_Rings_Osemiring__0(_1671619), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671619), hAPP(hAPP(c_List_Omap(_1671621, _1671619), hAPP(hAPP(c_COMBC(_1671621, _1671619, _1671619), hAPP(hAPP(c_COMBB(_1671619, tc_fun(_1671619, _1671619), _1671621), c_Groups_Otimes__class_Otimes(_1671619)), _1671623)), _1671625)), _1671627)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1671619), hAPP(c_List_Omonoid__add__class_Olistsum(_1671619), hAPP(hAPP(c_List_Omap(_1671621, _1671619), _1671623), _1671627))), _1671625))], (44381 ^ _782652) ^ [_1671822, _1671824, _1671826, _1671828, _1671830] : [class_Rings_Osemiring__0(_1671822), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671822), hAPP(hAPP(c_List_Omap(_1671824, _1671822), hAPP(hAPP(c_COMBB(_1671822, _1671822, _1671824), hAPP(c_Groups_Otimes__class_Otimes(_1671822), _1671826)), _1671828)), _1671830)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1671822), _1671826), hAPP(c_List_Omonoid__add__class_Olistsum(_1671822), hAPP(hAPP(c_List_Omap(_1671824, _1671822), _1671828), _1671830))))], (44387 ^ _782652) ^ [_1672005, _1672007, _1672009, _1672011, _1672013] : [class_Groups_Oab__group__add(_1672005), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672005), hAPP(hAPP(c_List_Omap(_1672007, _1672005), hAPP(hAPP(c_COMBS(_1672007, _1672005, _1672005), hAPP(hAPP(c_COMBB(_1672005, tc_fun(_1672005, _1672005), _1672007), c_Groups_Ominus__class_Ominus(_1672005)), _1672009)), _1672011)), _1672013)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1672005), hAPP(c_List_Omonoid__add__class_Olistsum(_1672005), hAPP(hAPP(c_List_Omap(_1672007, _1672005), _1672009), _1672013))), hAPP(c_List_Omonoid__add__class_Olistsum(_1672005), hAPP(hAPP(c_List_Omap(_1672007, _1672005), _1672011), _1672013))))], (44393 ^ _782652) ^ [_1672236, _1672238] : [class_Groups_Oordered__ab__group__add__abs(_1672236), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1672236), hAPP(c_Groups_Oabs__class_Oabs(_1672236), hAPP(c_List_Omonoid__add__class_Olistsum(_1672236), _1672238))), hAPP(c_List_Omonoid__add__class_Olistsum(_1672236), hAPP(hAPP(c_List_Omap(_1672236, _1672236), c_Groups_Oabs__class_Oabs(_1672236)), _1672238)))))], (44399 ^ _782652) ^ [_1672377, _1672379, _1672381, _1672383] : [class_Groups_Oab__group__add(_1672377), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1672377), hAPP(c_List_Omonoid__add__class_Olistsum(_1672377), hAPP(hAPP(c_List_Omap(_1672379, _1672377), _1672381), _1672383))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1672377), hAPP(hAPP(c_List_Omap(_1672379, _1672377), hAPP(c_Fun_Ocomp(_1672377, _1672377, _1672379, c_Groups_Ouminus__class_Ouminus(_1672377)), _1672381)), _1672383)))], (44405 ^ _782652) ^ [_1672542, _1672544] : [-(c_Random_Oselect__weight(_1672542, _1672544) = 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(_1672542, 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, _1672542), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1672542)), _1672544)))), hAPP(hAPP(c_COMBB(_1672542, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1672542, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1672542, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1672542, _1672544))))], (44407 ^ _782652) ^ [_1672626, _1672628] : [class_Groups_Ocomm__monoid__add(_1672626), hBOOL(hAPP(c_List_Odistinct(_1672626), _1672628)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672626), _1672628) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1672626, _1672626), c_COMBI(_1672626)), hAPP(c_List_Oset(_1672626), _1672628)))], (44417 ^ _782652) ^ [_1672803, _1672805, _1672807, _1672809] : [class_Groups_Ocomm__monoid__add(_1672803), hBOOL(hAPP(c_List_Odistinct(_1672805), _1672807)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672803), hAPP(hAPP(c_List_Omap(_1672805, _1672803), _1672809), _1672807)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1672805, _1672803), _1672809), hAPP(c_List_Oset(_1672805), _1672807)))], (44427 ^ _782652) ^ [_1673002, _1673004, _1673006, _1673008] : [class_Groups_Ocomm__monoid__add(_1673002), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1673002), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1673002), _1673004), c_List_Oupto(_1673006, _1673008))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1673002), _1673004), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1673006, _1673008))))], (44433 ^ _782652) ^ [_1673145, _1673147, _1673149, _1673151] : [class_Groups_Ocomm__monoid__add(_1673145), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1673145), _1673147), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1673149, _1673151))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1673145), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1673145), _1673147), c_List_Oupto(_1673149, _1673151))))], (44439 ^ _782652) ^ [_1673288, _1673290, _1673292, _1673294] : [class_Rings_Osemiring__1(_1673288), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1673288), hAPP(hAPP(c_List_Omap(_1673290, _1673288), hAPP(c_COMBK(_1673288, _1673290), _1673292)), _1673294)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1673288), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1673288), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673290)), _1673294))), _1673292))], (44445 ^ _782652) ^ [_1673447, _1673449, _1673451, _1673453, _1673455] : [class_Groups_Ocomm__monoid__add(_1673447), hBOOL(hAPP(hAPP(c_member(_1673449), _1673451), hAPP(c_List_Oset(_1673449), _1673453))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1673447), hAPP(hAPP(c_List_Omap(_1673449, _1673447), _1673455), _1673453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1673447), hAPP(_1673455, _1673451)), hAPP(c_List_Omonoid__add__class_Olistsum(_1673447), hAPP(hAPP(c_List_Omap(_1673449, _1673447), _1673455), c_List_Oremove1(_1673449, _1673451, _1673453)))))], (44455 ^ _782652) ^ [_1673696, _1673698, _1673700] : [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, _1673696), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1673696)), _1673698)))), -(hBOOL(hAPP(hAPP(c_member(_1673696), hAPP(c_Product__Type_Ofst(_1673696, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1673696, _1673698), _1673700))), hAPP(c_List_Oset(_1673696), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1673696), _1673696), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1673696)), _1673698)))))], (44461 ^ _782652) ^ [_1673893, _1673895, _1673897, _1673899] : [class_Groups_Ocomm__monoid__add(_1673893), 44464 ^ _782652 : [(44465 ^ _782652) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1673895), _1673897)), -(c_Nitpick_Osetsum_H(_1673895, _1673893, _1673899, _1673897) = hAPP(c_List_Omonoid__add__class_Olistsum(_1673893), hAPP(hAPP(c_List_Omap(_1673895, _1673893), _1673899), c_Hilbert__Choice_OEps(tc_List_Olist(_1673895), hAPP(hAPP(c_COMBS(tc_List_Olist(_1673895), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1673895)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1673895), tc_fun(_1673895, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1673895, tc_HOL_Obool), tc_fun(tc_fun(_1673895, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1673895)), c_fequal), c_List_Oset(_1673895))), _1673897))), c_List_Odistinct(_1673895))))))], (44471 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1673895), _1673897))), -(c_Nitpick_Osetsum_H(_1673895, _1673893, _1673899, _1673897) = c_Groups_Ozero__class_Ozero(_1673893))]]], (44477 ^ _782652) ^ [_1674281, _1674283, _1674285, _1674287, _1674289] : [class_Orderings_Olinorder(_1674281), -(hBOOL(hAPP(hAPP(c_member(_1674281), hAPP(_1674283, _1674285)), hAPP(c_Set_Oimage(_1674287, _1674281, _1674283), hAPP(c_List_Oset(_1674287), _1674289))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1674287, _1674281, _1674283, _1674285, _1674289) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1674287, _1674281, _1674283), _1674285), _1674289))], (44497 ^ _782652) ^ [_1674633] : [44499 ^ _782652 : [(44500 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44498 ^ [_1674633]), hAPP(c_List_Oset(tc_Nat_Onat), _1674633))))], (44502 ^ _782652) ^ [] : [44498 ^ [_1674633] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1674633) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44487 ^ _782652) ^ [_1674465] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1674465) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44490 ^ _782652 : [(44491 ^ _782652) ^ [_1674540] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1674540), hAPP(c_List_Oset(tc_Nat_Onat), _1674465))), -(_1674540 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44506 ^ _782652) ^ [_1674789, _1674791, _1674793, _1674795, _1674797] : [class_Orderings_Olinorder(_1674789), hBOOL(hAPP(c_List_Odistinct(_1674791), _1674793)), -(hBOOL(hAPP(c_List_Odistinct(_1674791), c_List_Olinorder__class_Oinsort__insert__key(_1674791, _1674789, _1674795, _1674797, _1674793))))], (44516 ^ _782652) ^ [_1674956, _1674958, _1674960] : [class_Orderings_Olinorder(_1674956), hBOOL(hAPP(hAPP(c_member(_1674956), _1674958), hAPP(c_List_Oset(_1674956), _1674960))), -(c_List_Olinorder__class_Oinsort__insert__key(_1674956, _1674956, c_COMBI(_1674956), _1674958, _1674960) = _1674960)], (44526 ^ _782652) ^ [_1675127, _1675129, _1675131] : [class_Orderings_Olinorder(_1675127), -(hAPP(c_List_Oset(_1675127), c_List_Olinorder__class_Oinsort__insert__key(_1675127, _1675127, c_COMBI(_1675127), _1675129, _1675131)) = hAPP(hAPP(c_Set_Oinsert(_1675127), _1675129), hAPP(c_List_Oset(_1675127), _1675131)))], (44532 ^ _782652) ^ [_1675256, _1675258, _1675260, _1675262, _1675264] : [class_Orderings_Olinorder(_1675256), hBOOL(hAPP(hAPP(c_member(_1675256), hAPP(_1675258, _1675260)), hAPP(c_Set_Oimage(_1675262, _1675256, _1675258), hAPP(c_List_Oset(_1675262), _1675264)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1675262, _1675256, _1675258, _1675260, _1675264) = _1675264)], (44542 ^ _782652) ^ [_1675451, _1675453, _1675455] : [class_Orderings_Olinorder(_1675451), -(hBOOL(hAPP(hAPP(c_member(_1675451), _1675453), hAPP(c_List_Oset(_1675451), _1675455)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1675451, _1675451, c_COMBI(_1675451), _1675453, _1675455) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1675451, _1675451, c_COMBI(_1675451)), _1675453), _1675455))], (44552 ^ _782652) ^ [_1675634, _1675636, _1675638, _1675640, _1675642, _1675644] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675634), tc_List_Olist(_1675634))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675634), tc_List_Olist(_1675634)), hAPP(hAPP(c_List_Olist_OCons(_1675634), _1675636), _1675638)), hAPP(hAPP(c_List_Olist_OCons(_1675634), _1675640), _1675642))), c_List_Olexord(_1675634, _1675644))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1675634, _1675634)), hAPP(hAPP(c_Product__Type_OPair(_1675634, _1675634), _1675636), _1675640)), _1675644))), 44559 ^ _782652 : [(44560 ^ _782652) ^ [] : [-(_1675636 = _1675640)], (44562 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675634), tc_List_Olist(_1675634))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675634), tc_List_Olist(_1675634)), _1675638), _1675642)), c_List_Olexord(_1675634, _1675644))))]]], (44564 ^ _782652) ^ [_1675961, _1675963, _1675965, _1675967, _1675969, _1675971] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675961), tc_List_Olist(_1675961))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675961), tc_List_Olist(_1675961)), hAPP(hAPP(c_List_Olist_OCons(_1675961), _1675963), _1675965)), hAPP(hAPP(c_List_Olist_OCons(_1675961), _1675967), _1675969))), c_List_Olexord(_1675961, _1675971)))), 44565 ^ _782652 : [(44566 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1675961, _1675961)), hAPP(hAPP(c_Product__Type_OPair(_1675961, _1675961), _1675963), _1675967)), _1675971))], (44568 ^ _782652) ^ [] : [_1675963 = _1675967, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1675961), tc_List_Olist(_1675961))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675961), tc_List_Olist(_1675961)), _1675965), _1675969)), c_List_Olexord(_1675961, _1675971)))]]], (44576 ^ _782652) ^ [_1676334, _1676336, _1676338, _1676340] : [-(hAPP(c_List_Oset(tc_prod(_1676334, _1676336)), hAPP(hAPP(c_List_Ozip(_1676334, _1676336), _1676338), _1676340)) = hAPP(c_Set_OCollect(tc_prod(_1676334, _1676336)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1676334, _1676336)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1676334, _1676336), 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(_1676334, _1676336)), 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(_1676334, _1676336)), 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(_1676334, _1676336), tc_fun(tc_Nat_Onat, tc_prod(_1676334, _1676336)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1676334, _1676336), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1676334, _1676336)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1676334, _1676336)), c_COMBB(tc_prod(_1676334, _1676336), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1676336, tc_prod(_1676334, _1676336)), hAPP(hAPP(c_COMBB(_1676334, tc_fun(_1676336, tc_prod(_1676334, _1676336)), tc_Nat_Onat), c_Product__Type_OPair(_1676334, _1676336)), hAPP(c_List_Onth(_1676334), _1676338))), hAPP(c_List_Onth(_1676336), _1676340)))))), 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(_1676334)), _1676338)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676336)), _1676340)))))))], (44578 ^ _782652) ^ [_1676559, _1676561, _1676563, _1676565, _1676567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1676559), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676561)), _1676563))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1676559), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676565)), _1676567))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1676561, _1676565)), hAPP(hAPP(c_List_Ozip(_1676561, _1676565), _1676563), _1676567)), _1676559) = hAPP(hAPP(c_Product__Type_OPair(_1676561, _1676565), hAPP(hAPP(c_List_Onth(_1676561), _1676563), _1676559)), hAPP(hAPP(c_List_Onth(_1676565), _1676567), _1676559)))], (44588 ^ _782652) ^ [_1676838, _1676840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1676838), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1676840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1676840), _1676838)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1676840))))], (44594 ^ _782652) ^ [_1676959, _1676961, _1676963] : [-(hAPP(hAPP(c_List_Onth(_1676959), hAPP(hAPP(c_List_Olist_OCons(_1676959), _1676961), _1676963)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1676961)], (44596 ^ _782652) ^ [_1677002, _1677004, _1677006, _1677008] : [-(hAPP(hAPP(c_List_Onth(_1677002), hAPP(hAPP(c_List_Olist_OCons(_1677002), _1677004), _1677006)), _1677008) = c_Nat_Onat_Onat__case(_1677002, _1677004, hAPP(c_List_Onth(_1677002), _1677006), _1677008))], (44598 ^ _782652) ^ [_1677057, _1677059, _1677061, _1677063] : [-(hAPP(hAPP(c_List_Onth(_1677057), hAPP(hAPP(c_List_Olist_OCons(_1677057), _1677059), _1677061)), hAPP(c_Nat_OSuc, _1677063)) = hAPP(hAPP(c_List_Onth(_1677057), _1677061), _1677063))], (44600 ^ _782652) ^ [_1677131, _1677133, _1677135] : [_1677131 = _1677133, 44603 ^ _782652 : [(44604 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677135)), _1677131) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677135)), _1677133))], (44606 ^ _782652) ^ [_1677279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1677279), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677135)), _1677131))), -(hAPP(hAPP(c_List_Onth(_1677135), _1677131), _1677279) = hAPP(hAPP(c_List_Onth(_1677135), _1677133), _1677279))]]], (44612 ^ _782652) ^ [_1677418, _1677420, _1677422] : [-(_1677418 = _1677420), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677422)), _1677418) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677422)), _1677420), 44618 ^ _782652 : [(44619 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44617 ^ [_1677418, _1677420, _1677422]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677422)), _1677418))))], (44621 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Onth(_1677422), _1677418), 44617 ^ [_1677418, _1677420, _1677422]) = hAPP(hAPP(c_List_Onth(_1677422), _1677420), 44617 ^ [_1677418, _1677420, _1677422])]]], (44625 ^ _782652) ^ [_1677751, _1677753, _1677755] : [44627 ^ _782652 : [(44628 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1677751), 44626 ^ [_1677751, _1677753, _1677755]), hAPP(c_List_Oset(_1677751), _1677753))))], (44630 ^ _782652) ^ [] : [hBOOL(hAPP(_1677755, 44626 ^ [_1677751, _1677753, _1677755]))]], 44631 ^ _782652 : [(44632 ^ _782652) ^ [_1677935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1677935), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677751)), _1677753))), -(hBOOL(hAPP(_1677755, hAPP(hAPP(c_List_Onth(_1677751), _1677753), _1677935))))]]], (44638 ^ _782652) ^ [_1678062, _1678064, _1678066] : [44640 ^ _782652 : [(44641 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44639 ^ [_1678062, _1678064, _1678066]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678062)), _1678064))))], (44643 ^ _782652) ^ [] : [hBOOL(hAPP(_1678066, hAPP(hAPP(c_List_Onth(_1678062), _1678064), 44639 ^ [_1678062, _1678064, _1678066])))]], 44644 ^ _782652 : [(44645 ^ _782652) ^ [_1678264] : [hBOOL(hAPP(hAPP(c_member(_1678062), _1678264), hAPP(c_List_Oset(_1678062), _1678064))), -(hBOOL(hAPP(_1678066, _1678264)))]]], (44651 ^ _782652) ^ [_1678381, _1678383, _1678385, _1678387, _1678389] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678381), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678383)), _1678385))), -(hAPP(hAPP(c_List_Onth(_1678387), hAPP(hAPP(c_List_Omap(_1678383, _1678387), _1678389), _1678385)), _1678381) = hAPP(_1678389, hAPP(hAPP(c_List_Onth(_1678383), _1678385), _1678381)))], (44657 ^ _782652) ^ [_1678544, _1678546, _1678548, _1678550] : [hBOOL(hAPP(c_List_Odistinct(_1678544), _1678546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678548), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678544)), _1678546))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678550), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678544)), _1678546))), 44668 ^ _782652 : [(44669 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Onth(_1678544), _1678546), _1678548) = hAPP(hAPP(c_List_Onth(_1678544), _1678546), _1678550), -(_1678548 = _1678550)], (44675 ^ _782652) ^ [] : [_1678548 = _1678550, -(hAPP(hAPP(c_List_Onth(_1678544), _1678546), _1678548) = hAPP(hAPP(c_List_Onth(_1678544), _1678546), _1678550))]]], (44699 ^ _782652) ^ [_1679454, _1679456] : [44701 ^ _782652 : [(44702 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44700 ^ [_1679454, _1679456]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679454)), _1679456))))], (44705 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44703 ^ [_1679454, _1679456]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679454)), _1679456))))], (44707 ^ _782652) ^ [] : [44700 ^ [_1679454, _1679456] = 44703 ^ [_1679454, _1679456]], (44709 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1679454), _1679456), 44700 ^ [_1679454, _1679456]) = hAPP(hAPP(c_List_Onth(_1679454), _1679456), 44703 ^ [_1679454, _1679456]))]], -(hBOOL(hAPP(c_List_Odistinct(_1679454), _1679456)))], (44681 ^ _782652) ^ [_1678994, _1678996] : [hBOOL(hAPP(c_List_Odistinct(_1678994), _1678996)), 44684 ^ _782652 : [(44685 ^ _782652) ^ [_1679126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679126), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678994)), _1678996))), 44688 ^ _782652 : [(44689 ^ _782652) ^ [_1679253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679253), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678994)), _1678996))), -(_1679126 = _1679253), hAPP(hAPP(c_List_Onth(_1678994), _1678996), _1679126) = hAPP(hAPP(c_List_Onth(_1678994), _1678996), _1679253)]]]]], (44713 ^ _782652) ^ [_1679904, _1679906, _1679908] : [hBOOL(hAPP(hAPP(c_member(_1679904), _1679906), hAPP(c_List_Oset(_1679904), _1679908))), 44717 ^ _782652 : [(44718 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44716 ^ [_1679904, _1679906, _1679908]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679904)), _1679908))))], (44720 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1679904), _1679908), 44716 ^ [_1679904, _1679906, _1679908]) = _1679906)]]], (44722 ^ _782652) ^ [_1680092, _1680094, _1680096] : [-(hBOOL(hAPP(hAPP(c_member(_1680092), _1680094), hAPP(c_List_Oset(_1680092), _1680096)))), 44723 ^ _782652 : [(44724 ^ _782652) ^ [_1680166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680166), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680092)), _1680096))), hAPP(hAPP(c_List_Onth(_1680092), _1680096), _1680166) = _1680094]]], (44732 ^ _782652) ^ [_1680328, _1680330, _1680332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680328), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680330)), _1680332))), -(hBOOL(hAPP(hAPP(c_member(_1680330), hAPP(hAPP(c_List_Onth(_1680330), _1680332), _1680328)), hAPP(c_List_Oset(_1680330), _1680332))))], (44738 ^ _782652) ^ [_1680486, _1680488, _1680490, _1680492] : [_1680486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1680488), hAPP(hAPP(c_List_Olist_OCons(_1680488), _1680490), _1680492)), _1680486) = _1680490)], (44744 ^ _782652) ^ [_1680593, _1680595, _1680597, _1680599] : [-(_1680593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1680595), hAPP(hAPP(c_List_Olist_OCons(_1680595), _1680597), _1680599)), _1680593) = hAPP(hAPP(c_List_Onth(_1680595), _1680599), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1680593), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44750 ^ _782652) ^ [_1680665, _1680667] : [-(hAPP(c_List_Oset(_1680665), _1680667) = hAPP(c_Set_OCollect(_1680665), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1680665), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1680665, 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)), _1680665), 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)), _1680665), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1680665, tc_fun(tc_Nat_Onat, _1680665), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1680665, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1680665), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1680665), c_COMBB(_1680665, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1680665), _1680667))))), 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(_1680665)), _1680667))))))], (44752 ^ _782652) ^ [_1680806, _1680808, _1680810, _1680812] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1680806) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1680808), hAPP(hAPP(c_List_Olist_OCons(_1680808), _1680810), _1680812)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1680806)) = _1680810)], (44758 ^ _782652) ^ [_1680925, _1680927, _1680929, _1680931] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1680925) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1680927), hAPP(hAPP(c_List_Olist_OCons(_1680927), _1680929), _1680931)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1680925)) = hAPP(hAPP(c_List_Onth(_1680927), _1680931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1680925)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44764 ^ _782652) ^ [_1681006, _1681008] : [class_Groups_Ocomm__monoid__add(_1681006), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1681006), _1681008) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1681006), hAPP(c_List_Onth(_1681006), _1681008)), 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(_1681006)), _1681008))))], (44770 ^ _782652) ^ [_1681139, _1681141, _1681143] : [-(hAPP(c_List_Oset(_1681139), c_List_Osublist(_1681139, _1681141, _1681143)) = hAPP(c_Set_OCollect(_1681139), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1681139), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1681139, 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)), _1681139), 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)), _1681139), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1681139, tc_fun(tc_Nat_Onat, _1681139), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1681139, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1681139), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1681139), c_COMBB(_1681139, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1681139), _1681141))))), 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(_1681139)), _1681141)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1681143))))))], (44772 ^ _782652) ^ [_1681304, _1681306, _1681308, _1681310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681304), tc_List_Olist(_1681304))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681304), tc_List_Olist(_1681304)), _1681306), _1681308)), c_List_Olex(_1681304, _1681310))), 44775 ^ _782652 : [(44776 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681304), tc_List_Olist(_1681304))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681304), tc_List_Olist(_1681304)), _1681306), _1681308)), c_List_Olexord(_1681304, _1681310))))], (44778 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681304)), _1681306) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681304)), _1681308))]]], (44780 ^ _782652) ^ [_1681555, _1681557, _1681559, _1681561] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681555), tc_List_Olist(_1681555))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681555), tc_List_Olist(_1681555)), _1681557), _1681559)), c_List_Olex(_1681555, _1681561)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681555), tc_List_Olist(_1681555))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681555), tc_List_Olist(_1681555)), _1681557), _1681559)), c_List_Olexord(_1681555, _1681561))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681555)), _1681557) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681555)), _1681559)], (44790 ^ _782652) ^ [_1681863, _1681865, _1681867, _1681869] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681863), tc_List_Olist(_1681863))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681863), tc_List_Olist(_1681863)), _1681865), _1681867)), c_List_Olistrel(_1681863, _1681869))), 44793 ^ _782652 : [(44794 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681863)), _1681865) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681863)), _1681867))], (44796 ^ _782652) ^ [_1682092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682092), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681863)), _1681865))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1681863, _1681863)), hAPP(hAPP(c_Product__Type_OPair(_1681863, _1681863), hAPP(hAPP(c_List_Onth(_1681863), _1681865), _1682092)), hAPP(hAPP(c_List_Onth(_1681863), _1681867), _1682092))), _1681869)))]]], (44802 ^ _782652) ^ [_1682271, _1682273, _1682275, _1682277] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682271), tc_List_Olist(_1682271))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682271), tc_List_Olist(_1682271)), _1682273), _1682275)), c_List_Olistrel(_1682271, _1682277)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682271)), _1682273) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682271)), _1682275), 44808 ^ _782652 : [(44809 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44807 ^ [_1682271, _1682273, _1682275, _1682277]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682271)), _1682273))))], (44811 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1682271, _1682271)), hAPP(hAPP(c_Product__Type_OPair(_1682271, _1682271), hAPP(hAPP(c_List_Onth(_1682271), _1682273), 44807 ^ [_1682271, _1682273, _1682275, _1682277])), hAPP(hAPP(c_List_Onth(_1682271), _1682275), 44807 ^ [_1682271, _1682273, _1682275, _1682277]))), _1682277))]]], (44815 ^ _782652) ^ [_1682736, _1682738, _1682740, _1682742] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682736), tc_List_Olist(_1682736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682736), tc_List_Olist(_1682736)), _1682738), _1682740)), c_List_Olexord(_1682736, _1682742))), 44820 ^ _782652 : [(44821 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682736)), _1682738)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682736)), _1682740))))], (44823 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1682736), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682736)), _1682738)), _1682740) = _1682738)]], 44825 ^ _782652 : [(44826 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44824 ^ [_1682736, _1682738, _1682740, _1682742]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682736)), _1682738)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682736)), _1682740)))))], (44828 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1682736), 44824 ^ [_1682736, _1682738, _1682740, _1682742]), _1682738) = hAPP(hAPP(c_List_Otake(_1682736), 44824 ^ [_1682736, _1682738, _1682740, _1682742]), _1682740))], (44830 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682736, _1682736)), hAPP(hAPP(c_Product__Type_OPair(_1682736, _1682736), hAPP(hAPP(c_List_Onth(_1682736), _1682738), 44824 ^ [_1682736, _1682738, _1682740, _1682742])), hAPP(hAPP(c_List_Onth(_1682736), _1682740), 44824 ^ [_1682736, _1682738, _1682740, _1682742]))), _1682742)))]]], (44832 ^ _782652) ^ [_1683276, _1683278, _1683280, _1683282] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1683276), tc_List_Olist(_1683276))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1683276), tc_List_Olist(_1683276)), _1683278), _1683280)), c_List_Olexord(_1683276, _1683282)))), 44833 ^ _782652 : [(44834 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683276)), _1683278)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683276)), _1683280))), hAPP(hAPP(c_List_Otake(_1683276), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683276)), _1683278)), _1683280) = _1683278], (44840 ^ _782652) ^ [_1683583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683583), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683276)), _1683278)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683276)), _1683280)))), hAPP(hAPP(c_List_Otake(_1683276), _1683583), _1683278) = hAPP(hAPP(c_List_Otake(_1683276), _1683583), _1683280), hBOOL(hAPP(hAPP(c_member(tc_prod(_1683276, _1683276)), hAPP(hAPP(c_Product__Type_OPair(_1683276, _1683276), hAPP(hAPP(c_List_Onth(_1683276), _1683278), _1683583)), hAPP(hAPP(c_List_Onth(_1683276), _1683280), _1683583))), _1683282))]]], (44852 ^ _782652) ^ [_1683937, _1683939, _1683941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683937), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683939)), _1683941))), -(hAPP(c_Random_Opick(_1683939, hAPP(hAPP(c_List_Omap(_1683939, tc_prod(tc_Code__Numeral_Ocode__numeral, _1683939)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1683939), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1683941)), hAPP(c_Code__Numeral_Oof__nat, _1683937)) = hAPP(hAPP(c_List_Onth(_1683939), _1683941), _1683937))], (44858 ^ _782652) ^ [_1684110, _1684112, _1684114, _1684116] : [hBOOL(hAPP(hAPP(c_member(_1684110), _1684112), hAPP(c_List_Oset(_1684110), hAPP(hAPP(c_List_Otake(_1684110), _1684114), _1684116)))), -(hBOOL(hAPP(hAPP(c_member(_1684110), _1684112), hAPP(c_List_Oset(_1684110), _1684116))))], (44864 ^ _782652) ^ [_1684255, _1684257, _1684259, _1684261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684255), _1684257)), -(hAPP(hAPP(c_List_Onth(_1684259), hAPP(hAPP(c_List_Otake(_1684259), _1684257), _1684261)), _1684255) = hAPP(hAPP(c_List_Onth(_1684259), _1684261), _1684255))], (44870 ^ _782652) ^ [_1684394, _1684396, _1684398] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684394, tc_HOL_Obool)), hAPP(c_List_Oset(_1684394), hAPP(hAPP(c_List_Otake(_1684394), _1684396), _1684398))), hAPP(c_List_Oset(_1684394), _1684398))))], (44872 ^ _782652) ^ [_1684449, _1684451, _1684453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684449)), _1684451)), _1684453)), -(hAPP(hAPP(c_List_Otake(_1684449), _1684453), _1684451) = _1684451)], (44878 ^ _782652) ^ [_1684568, _1684570, _1684572] : [hBOOL(hAPP(c_List_Odistinct(_1684568), _1684570)), -(hBOOL(hAPP(c_List_Odistinct(_1684568), hAPP(hAPP(c_List_Otake(_1684568), _1684572), _1684570))))], (44884 ^ _782652) ^ [_1684694, _1684696] : [hAPP(c_Code__Numeral_Oof__nat, _1684694) = hAPP(c_Code__Numeral_Oof__nat, _1684696), -(_1684694 = _1684696)], (44890 ^ _782652) ^ [_1684779, _1684781] : [_1684779 = _1684781, -(hAPP(c_Code__Numeral_Oof__nat, _1684779) = hAPP(c_Code__Numeral_Oof__nat, _1684781))], (44896 ^ _782652) ^ [_1684870, _1684872] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1684870)), hAPP(c_Code__Numeral_Oof__nat, _1684872)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1684870), _1684872)))], (44898 ^ _782652) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (44900 ^ _782652) ^ [_1684934, _1684936, _1684938, _1684940] : [-(hAPP(hAPP(c_List_Otake(_1684934), _1684936), hAPP(hAPP(c_List_Otake(_1684934), _1684938), _1684940)) = hAPP(hAPP(c_List_Otake(_1684934), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1684936), _1684938)), _1684940))], (44902 ^ _782652) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44904 ^ _782652) ^ [_1685011, _1685013, _1685015, _1685017, _1685019] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1685011, _1685013)), _1685015), hAPP(hAPP(c_List_Ozip(_1685011, _1685013), _1685017), _1685019)) = hAPP(hAPP(c_List_Ozip(_1685011, _1685013), hAPP(hAPP(c_List_Otake(_1685011), _1685015), _1685017)), hAPP(hAPP(c_List_Otake(_1685013), _1685015), _1685019)))], (44906 ^ _782652) ^ [_1685087, _1685089, _1685091] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685087)), hAPP(hAPP(c_List_Otake(_1685087), _1685089), _1685091)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685087)), _1685091)), _1685089))], (44908 ^ _782652) ^ [_1685142, _1685144, _1685146, _1685148] : [-(hAPP(hAPP(c_List_Otake(_1685142), hAPP(c_Nat_OSuc, _1685144)), hAPP(hAPP(c_List_Olist_OCons(_1685142), _1685146), _1685148)) = hAPP(hAPP(c_List_Olist_OCons(_1685142), _1685146), hAPP(hAPP(c_List_Otake(_1685142), _1685144), _1685148)))], (44910 ^ _782652) ^ [_1685206, _1685208, _1685210] : [-(c_List_Osublist(_1685206, _1685208, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1685210)) = hAPP(hAPP(c_List_Otake(_1685206), _1685210), _1685208))], (44912 ^ _782652) ^ [_1685248, _1685250, _1685252, _1685254, _1685256] : [-(hAPP(hAPP(c_List_Otake(_1685248), _1685250), hAPP(hAPP(c_List_Omap(_1685252, _1685248), _1685254), _1685256)) = hAPP(hAPP(c_List_Omap(_1685252, _1685248), _1685254), hAPP(hAPP(c_List_Otake(_1685252), _1685250), _1685256)))], (44914 ^ _782652) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44916 ^ _782652) ^ [_1685346, _1685348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1685346)), hAPP(c_Code__Numeral_Oof__nat, _1685348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685346), _1685348)))], (44922 ^ _782652) ^ [_1685451, _1685453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685451), _1685453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1685451)), hAPP(c_Code__Numeral_Oof__nat, _1685453))))], (44928 ^ _782652) ^ [_1685562, _1685564] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1685562), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1685564), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 44935 ^ _782652 : [(44936 ^ _782652) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1685562) = hAPP(c_Code__Numeral_Oof__nat, _1685564), -(_1685562 = _1685564)], (44942 ^ _782652) ^ [] : [_1685562 = _1685564, -(hAPP(c_Code__Numeral_Oof__nat, _1685562) = hAPP(c_Code__Numeral_Oof__nat, _1685564))]]], (44948 ^ _782652) ^ [] : [-(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))], (44950 ^ _782652) ^ [_1685877, _1685879, _1685881, _1685883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1685877), _1685879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1685881, tc_HOL_Obool)), hAPP(c_List_Oset(_1685881), hAPP(hAPP(c_List_Otake(_1685881), _1685877), _1685883))), hAPP(c_List_Oset(_1685881), hAPP(hAPP(c_List_Otake(_1685881), _1685879), _1685883)))))], (44956 ^ _782652) ^ [_1686040, _1686042] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1686040)), hAPP(c_Code__Numeral_Oof__nat, _1686042)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686040), _1686042)))], (44958 ^ _782652) ^ [_1686101, _1686103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1686101)), hAPP(c_Code__Numeral_Oof__nat, _1686103))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1686101), _1686103)))], (44964 ^ _782652) ^ [_1686206, _1686208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1686206), _1686208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1686206)), hAPP(c_Code__Numeral_Oof__nat, _1686208))))], (44970 ^ _782652) ^ [_1686323] : [-(_1686323 = 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)), _1686323)))], (44976 ^ _782652) ^ [_1686355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1686355)), _1686355 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44982 ^ _782652) ^ [_1686437, _1686439, _1686441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1686439))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1686439), _1686437), _1686441)) = 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), _1686439)), _1686441)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1686439), _1686437)))], (44988 ^ _782652) ^ [_1686598, _1686600, _1686602, _1686604] : [hBOOL(hAPP(c_List_Odistinct(_1686598), _1686600)), -(hBOOL(hAPP(hAPP(c_member(_1686598), _1686602), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1686598, tc_HOL_Obool)), hAPP(c_List_Oset(_1686598), _1686600)), hAPP(hAPP(c_Set_Oinsert(_1686598), hAPP(hAPP(c_List_Onth(_1686598), _1686600), _1686604)), c_Orderings_Obot__class_Obot(tc_fun(_1686598, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1686598), hAPP(hAPP(c_List_Olist__update(_1686598, _1686600), _1686604), _1686602))))], (44998 ^ _782652) ^ [_1686812, _1686814, _1686816, _1686818, _1686820] : [-(_1686812 = _1686814), -(hAPP(hAPP(c_List_Onth(_1686816), hAPP(hAPP(c_List_Olist__update(_1686816, _1686818), _1686812), _1686820)), _1686814) = hAPP(hAPP(c_List_Onth(_1686816), _1686818), _1686814))], (45004 ^ _782652) ^ [_1686879, _1686881, _1686883] : [-(hAPP(hAPP(c_List_Olist__update(_1686879, _1686881), _1686883), hAPP(hAPP(c_List_Onth(_1686879), _1686881), _1686883)) = _1686881)], (45006 ^ _782652) ^ [_1686923, _1686925, _1686927, _1686929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686923)), _1686925)), _1686927)), -(hAPP(hAPP(c_List_Olist__update(_1686923, _1686925), _1686927), _1686929) = _1686925)], (45012 ^ _782652) ^ [_1687046, _1687048, _1687050, _1687052] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687046)), hAPP(hAPP(c_List_Olist__update(_1687046, _1687048), _1687050), _1687052)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687046)), _1687048))], (45014 ^ _782652) ^ [_1687098, _1687100, _1687102, _1687104, _1687106, _1687108] : [-(hAPP(hAPP(c_List_Omap(_1687098, _1687100), _1687102), hAPP(hAPP(c_List_Olist__update(_1687098, _1687104), _1687106), _1687108)) = hAPP(hAPP(c_List_Olist__update(_1687100, hAPP(hAPP(c_List_Omap(_1687098, _1687100), _1687102), _1687104)), _1687106), hAPP(_1687102, _1687108)))], (45016 ^ _782652) ^ [_1687170, _1687172, _1687174, _1687176, _1687178, _1687180, _1687182] : [-(hAPP(hAPP(c_List_Ozip(_1687170, _1687172), hAPP(hAPP(c_List_Olist__update(_1687170, _1687174), _1687176), _1687178)), hAPP(hAPP(c_List_Olist__update(_1687172, _1687180), _1687176), _1687182)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1687170, _1687172), hAPP(hAPP(c_List_Ozip(_1687170, _1687172), _1687174), _1687180)), _1687176), hAPP(hAPP(c_Product__Type_OPair(_1687170, _1687172), _1687178), _1687182)))], (45018 ^ _782652) ^ [_1687262, _1687264, _1687266, _1687268, _1687270, _1687272] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1687262, _1687264), hAPP(hAPP(c_List_Ozip(_1687262, _1687264), _1687266), _1687268)), _1687270), _1687272) = hAPP(hAPP(c_List_Ozip(_1687262, _1687264), hAPP(hAPP(c_List_Olist__update(_1687262, _1687266), _1687270), hAPP(c_Product__Type_Ofst(_1687262, _1687264), _1687272))), hAPP(hAPP(c_List_Olist__update(_1687264, _1687268), _1687270), hAPP(c_Product__Type_Osnd(_1687262, _1687264), _1687272))))], (45020 ^ _782652) ^ [_1687355, _1687357, _1687359, _1687361] : [-(hAPP(hAPP(c_List_Olist__update(_1687355, hAPP(hAPP(c_List_Olist_OCons(_1687355), _1687357), _1687359)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1687361) = hAPP(hAPP(c_List_Olist_OCons(_1687355), _1687361), _1687359))], (45022 ^ _782652) ^ [_1687409, _1687411, _1687413, _1687415, _1687417] : [-(hAPP(hAPP(c_List_Olist__update(_1687409, hAPP(hAPP(c_List_Olist_OCons(_1687409), _1687411), _1687413)), _1687415), _1687417) = c_Nat_Onat_Onat__case(tc_List_Olist(_1687409), hAPP(hAPP(c_List_Olist_OCons(_1687409), _1687417), _1687413), hAPP(hAPP(c_COMBB(tc_List_Olist(_1687409), tc_List_Olist(_1687409), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1687409), _1687411)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1687409, tc_List_Olist(_1687409)), c_List_Olist__update(_1687409, _1687413)), _1687417)), _1687415))], (45024 ^ _782652) ^ [_1687506, _1687508, _1687510, _1687512, _1687514] : [-(hAPP(hAPP(c_List_Olist__update(_1687506, hAPP(hAPP(c_List_Olist_OCons(_1687506), _1687508), _1687510)), hAPP(c_Nat_OSuc, _1687512)), _1687514) = hAPP(hAPP(c_List_Olist_OCons(_1687506), _1687508), hAPP(hAPP(c_List_Olist__update(_1687506, _1687510), _1687512), _1687514)))], (45026 ^ _782652) ^ [_1687570, _1687572, _1687574, _1687576, _1687578, _1687580] : [-(_1687570 = _1687572), -(hAPP(hAPP(c_List_Olist__update(_1687574, hAPP(hAPP(c_List_Olist__update(_1687574, _1687576), _1687570), _1687578)), _1687572), _1687580) = hAPP(hAPP(c_List_Olist__update(_1687574, hAPP(hAPP(c_List_Olist__update(_1687574, _1687576), _1687572), _1687580)), _1687570), _1687578))], (45032 ^ _782652) ^ [_1687650, _1687652, _1687654, _1687656, _1687658] : [-(hAPP(hAPP(c_List_Olist__update(_1687650, hAPP(hAPP(c_List_Olist__update(_1687650, _1687652), _1687654), _1687656)), _1687654), _1687658) = hAPP(hAPP(c_List_Olist__update(_1687650, _1687652), _1687654), _1687658))], (45034 ^ _782652) ^ [_1687708, _1687710, _1687712, _1687714, _1687716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1687708, tc_HOL_Obool)), hAPP(c_List_Oset(_1687708), _1687710)), _1687712)), hBOOL(hAPP(hAPP(c_member(_1687708), _1687714), _1687712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1687708, tc_HOL_Obool)), hAPP(c_List_Oset(_1687708), hAPP(hAPP(c_List_Olist__update(_1687708, _1687710), _1687716), _1687714))), _1687712)))], (45044 ^ _782652) ^ [_1687941, _1687943, _1687945, _1687947] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1687941, tc_HOL_Obool)), hAPP(c_List_Oset(_1687941), hAPP(hAPP(c_List_Olist__update(_1687941, _1687943), _1687945), _1687947))), hAPP(hAPP(c_Set_Oinsert(_1687941), _1687947), hAPP(c_List_Oset(_1687941), _1687943)))))], (45046 ^ _782652) ^ [_1688007, _1688009, _1688011, _1688013, _1688015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688007), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688009)), _1688011))), 45049 ^ _782652 : [(45050 ^ _782652) ^ [] : [_1688007 = _1688013, -(hAPP(hAPP(c_List_Onth(_1688009), hAPP(hAPP(c_List_Olist__update(_1688009, _1688011), _1688007), _1688015)), _1688013) = _1688015)], (45056 ^ _782652) ^ [] : [-(_1688007 = _1688013), -(hAPP(hAPP(c_List_Onth(_1688009), hAPP(hAPP(c_List_Olist__update(_1688009, _1688011), _1688007), _1688015)), _1688013) = hAPP(hAPP(c_List_Onth(_1688009), _1688011), _1688013))]]], (45062 ^ _782652) ^ [_1688303, _1688305, _1688307, _1688309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688303), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688305)), _1688307))), 45065 ^ _782652 : [(45066 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1688305, _1688307), _1688303), _1688309) = _1688307, -(hAPP(hAPP(c_List_Onth(_1688305), _1688307), _1688303) = _1688309)], (45072 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Onth(_1688305), _1688307), _1688303) = _1688309, -(hAPP(hAPP(c_List_Olist__update(_1688305, _1688307), _1688303), _1688309) = _1688307)]]], (45078 ^ _782652) ^ [_1688597, _1688599, _1688601, _1688603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688597), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688599)), _1688601))), -(hAPP(hAPP(c_List_Onth(_1688599), hAPP(hAPP(c_List_Olist__update(_1688599, _1688601), _1688597), _1688603)), _1688597) = _1688603)], (45084 ^ _782652) ^ [_1688736, _1688738, _1688740, _1688742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688736), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688738)), _1688740))), -(hBOOL(hAPP(hAPP(c_member(_1688738), _1688742), hAPP(c_List_Oset(_1688738), hAPP(hAPP(c_List_Olist__update(_1688738, _1688740), _1688736), _1688742)))))], (45090 ^ _782652) ^ [_1688907, _1688909, _1688911, _1688913, _1688915, _1688917, _1688919] : [hBOOL(hAPP(hAPP(c_member(_1688907), _1688909), hAPP(c_List_Oset(_1688907), hAPP(hAPP(c_List_Otake(_1688907), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688911)), _1688913)), _1688915)))), -(c_Map_Omap__upds(_1688907, _1688911, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1688907, tc_Option_Ooption(_1688911)), _1688917), _1688909), hAPP(c_Option_Ooption_OSome(_1688911), _1688919)), _1688915, _1688913) = c_Map_Omap__upds(_1688907, _1688911, _1688917, _1688915, _1688913))], (45096 ^ _782652) ^ [_1689104, _1689106, _1689108, _1689110, _1689112, _1689114, _1689116] : [-(hBOOL(hAPP(hAPP(c_member(_1689104), _1689106), hAPP(c_List_Oset(_1689104), hAPP(hAPP(c_List_Otake(_1689104), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689108)), _1689110)), _1689112))))), -(c_Map_Omap__upds(_1689104, _1689108, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1689104, tc_Option_Ooption(_1689108)), _1689114), _1689106), hAPP(c_Option_Ooption_OSome(_1689108), _1689116)), _1689112, _1689110) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1689104, tc_Option_Ooption(_1689108)), c_Map_Omap__upds(_1689104, _1689108, _1689114, _1689112, _1689110)), _1689106), hAPP(c_Option_Ooption_OSome(_1689108), _1689116)))], (45102 ^ _782652) ^ [_1689229, _1689231] : [-(c_Random_Oselect(_1689229, _1689231) = 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(_1689229, 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(_1689229)), _1689231)))), hAPP(hAPP(c_COMBB(_1689229, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1689229, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1689229, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1689229, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1689229), _1689231)), c_Code__Numeral_Onat__of))))], (45104 ^ _782652) ^ [_1689313, _1689315, _1689317, _1689319, _1689321, _1689323] : [-(hBOOL(hAPP(hAPP(c_member(_1689313), _1689315), hAPP(c_List_Oset(_1689313), _1689317)))), -(hAPP(c_Map_Omap__upds(_1689313, _1689319, _1689321, _1689317, _1689323), _1689315) = hAPP(_1689321, _1689315))], (45110 ^ _782652) ^ [_1689381, _1689383, _1689385, _1689387, _1689389, _1689391] : [-(c_Map_Omap__add(_1689381, _1689383, _1689385, c_Map_Omap__upds(_1689381, _1689383, _1689387, _1689389, _1689391)) = c_Map_Omap__upds(_1689381, _1689383, c_Map_Omap__add(_1689381, _1689383, _1689385, _1689387), _1689389, _1689391))], (45112 ^ _782652) ^ [_1689451, _1689453] : [hAPP(c_Code__Numeral_Onat__of, _1689451) = hAPP(c_Code__Numeral_Onat__of, _1689453), -(_1689451 = _1689453)], (45118 ^ _782652) ^ [_1689536, _1689538] : [_1689536 = _1689538, -(hAPP(c_Code__Numeral_Onat__of, _1689536) = hAPP(c_Code__Numeral_Onat__of, _1689538))], (45124 ^ _782652) ^ [_1689642, _1689644] : [hAPP(c_Code__Numeral_Onat__of, _1689642) = hAPP(c_Code__Numeral_Onat__of, _1689644), -(_1689642 = _1689644)], (45130 ^ _782652) ^ [_1689727, _1689729] : [_1689727 = _1689729, -(hAPP(c_Code__Numeral_Onat__of, _1689727) = hAPP(c_Code__Numeral_Onat__of, _1689729))], (45136 ^ _782652) ^ [_1689818] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1689818)) = _1689818)], (45138 ^ _782652) ^ [_1689847] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1689847)) = _1689847)], (45140 ^ _782652) ^ [_1689876] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1689876)) = _1689876)], (45142 ^ _782652) ^ [] : [-(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))))], (45144 ^ _782652) ^ [_1689938, _1689940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1689938), _1689940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1689938)), hAPP(c_Code__Numeral_Onat__of, _1689940))))], (45150 ^ _782652) ^ [_1690043, _1690045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690043)), hAPP(c_Code__Numeral_Onat__of, _1690045))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1690043), _1690045)))], (45156 ^ _782652) ^ [_1690154] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690154)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45158 ^ _782652) ^ [_1690185] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1690185)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1690185))], (45160 ^ _782652) ^ [] : [-(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))], (45162 ^ _782652) ^ [_1690250, _1690252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1690250), _1690252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690250)), hAPP(c_Code__Numeral_Onat__of, _1690252))))], (45168 ^ _782652) ^ [_1690355, _1690357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690355)), hAPP(c_Code__Numeral_Onat__of, _1690357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1690355), _1690357)))], (45174 ^ _782652) ^ [_1690466] : [-(hAPP(c_Code__Numeral_Onat__of, _1690466) = c_Code__Numeral_Onat__of__aux(_1690466, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45176 ^ _782652) ^ [_1690495, _1690497] : [-(c_Code__Numeral_Onat__of__aux(_1690495, _1690497) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690495)), _1690497))], (45178 ^ _782652) ^ [_1690532, _1690534, _1690536, _1690538, _1690540, _1690542, _1690544] : [-(c_Map_Omap__upds(_1690532, _1690534, _1690536, hAPP(hAPP(c_List_Olist_OCons(_1690532), _1690538), _1690540), hAPP(hAPP(c_List_Olist_OCons(_1690534), _1690542), _1690544)) = c_Map_Omap__upds(_1690532, _1690534, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1690532, tc_Option_Ooption(_1690534)), _1690536), _1690538), hAPP(c_Option_Ooption_OSome(_1690534), _1690542)), _1690540, _1690544))], (45180 ^ _782652) ^ [_1690614] : [-(c_Code__Numeral_OSuc__code__numeral(_1690614) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1690614))))], (45182 ^ _782652) ^ [_1690648, _1690650] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1690648), _1690650) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690648)), hAPP(c_Code__Numeral_Onat__of, _1690650))))], (45184 ^ _782652) ^ [_1690694] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1690694), 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, _1690694)) = _1690694)], (45190 ^ _782652) ^ [_1690791, _1690793] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1690791), _1690793) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690791)), hAPP(c_Code__Numeral_Onat__of, _1690793))))], (45192 ^ _782652) ^ [_1690837, _1690839] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1690837), _1690839) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690837)), hAPP(c_Code__Numeral_Onat__of, _1690839))))], (45194 ^ _782652) ^ [_1690883, _1690885] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1690883), _1690885) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1690883)), hAPP(c_Code__Numeral_Onat__of, _1690885))))], (45196 ^ _782652) ^ [_1690929, _1690931] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1690929, _1690931) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1690929), hAPP(c_Code__Numeral_Onat__of, _1690931))))], (45198 ^ _782652) ^ [_1690971, _1690973, _1690975, _1690977, _1690979, _1690981, _1690983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690971)), _1690973)), _1690975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690975), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690977)), _1690979))), -(c_Map_Omap__upds(_1690971, _1690977, _1690981, _1690973, hAPP(hAPP(c_List_Olist__update(_1690977, _1690979), _1690975), _1690983)) = c_Map_Omap__upds(_1690971, _1690977, _1690981, _1690973, _1690979))], (45208 ^ _782652) ^ [_1691206, _1691208, _1691210, _1691212, _1691214, _1691216, _1691218] : [-(hBOOL(hAPP(hAPP(c_member(_1691206), _1691208), hAPP(c_List_Oset(_1691206), _1691210)))), -(c_Map_Omap__upds(_1691206, _1691212, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1691206, tc_Option_Ooption(_1691212)), _1691214), _1691208), hAPP(c_Option_Ooption_OSome(_1691212), _1691216)), _1691210, _1691218) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1691206, tc_Option_Ooption(_1691212)), c_Map_Omap__upds(_1691206, _1691212, _1691214, _1691210, _1691218)), _1691208), hAPP(c_Option_Ooption_OSome(_1691212), _1691216)))], (45214 ^ _782652) ^ [_1691310] : [-(_1691310 = 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, _1691310)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1691310))))], (45220 ^ _782652) ^ [_1691361, _1691363, _1691365, _1691367, _1691369, _1691371] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691361)), _1691363) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691365)), _1691367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1691361, tc_HOL_Obool)), hAPP(c_List_Oset(_1691361), _1691363)), _1691369)), -(c_Map_Orestrict__map(_1691361, _1691365, c_Map_Omap__upds(_1691361, _1691365, _1691371, _1691363, _1691367), _1691369) = c_Map_Omap__upds(_1691361, _1691365, c_Map_Orestrict__map(_1691361, _1691365, _1691371, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1691361, tc_HOL_Obool)), _1691369), hAPP(c_List_Oset(_1691361), _1691363))), _1691363, _1691367))], (45230 ^ _782652) ^ [_1691640, _1691642, _1691644, _1691646, _1691648] : [-(c_Map_Odom(_1691640, _1691642, c_Map_Omap__upds(_1691640, _1691642, _1691644, _1691646, _1691648)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1691640, tc_HOL_Obool)), hAPP(c_List_Oset(_1691640), hAPP(hAPP(c_List_Otake(_1691640), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691642)), _1691648)), _1691646))), c_Map_Odom(_1691640, _1691642, _1691644)))], (45232 ^ _782652) ^ [_1691712, _1691714] : [-(_1691712 = c_List_Olist_ONil(_1691714)), -(c_Random_Oselect__weight(_1691714, hAPP(hAPP(c_List_Omap(_1691714, tc_prod(tc_Code__Numeral_Ocode__numeral, _1691714)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1691714), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1691712)) = c_Random_Oselect(_1691714, _1691712))], (45238 ^ _782652) ^ [_1691774, _1691776] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1691774)), hAPP(c_Code__Numeral_Oof__nat, _1691776)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1691774), _1691776)))], (45240 ^ _782652) ^ [_1691820, _1691822, _1691824] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691820), tc_List_Olist(_1691820))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691820), tc_List_Olist(_1691820)), _1691822), c_List_Olist_ONil(_1691820))), c_List_Olistrel(_1691820, _1691824))), -(_1691822 = c_List_Olist_ONil(_1691820))], (45246 ^ _782652) ^ [_1691967, _1691969, _1691971] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691967), tc_List_Olist(_1691967))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691967), tc_List_Olist(_1691967)), c_List_Olist_ONil(_1691967)), _1691969)), c_List_Olistrel(_1691967, _1691971))), -(_1691969 = c_List_Olist_ONil(_1691967))], (45252 ^ _782652) ^ [_1692114, _1692116, _1692118] : [-(hAPP(hAPP(c_List_Olist__update(_1692114, c_List_Olist_ONil(_1692114)), _1692116), _1692118) = c_List_Olist_ONil(_1692114))], (45254 ^ _782652) ^ [_1692154, _1692156, _1692158] : [-(hAPP(hAPP(c_List_Olist__update(_1692154, c_List_Olist_ONil(_1692154)), _1692156), _1692158) = c_List_Olist_ONil(_1692154))], (45256 ^ _782652) ^ [_1692215, _1692217, _1692219, _1692221] : [hAPP(hAPP(c_List_Olist__update(_1692215, _1692217), _1692219), _1692221) = c_List_Olist_ONil(_1692215), -(_1692217 = c_List_Olist_ONil(_1692215))], (45262 ^ _782652) ^ [_1692318, _1692320, _1692322, _1692324] : [_1692320 = c_List_Olist_ONil(_1692318), -(hAPP(hAPP(c_List_Olist__update(_1692318, _1692320), _1692322), _1692324) = c_List_Olist_ONil(_1692318))], (45268 ^ _782652) ^ [_1692427, _1692429, _1692431, _1692433] : [-(c_Map_Omap__upds(_1692427, _1692429, _1692431, c_List_Olist_ONil(_1692427), _1692433) = _1692431)], (45270 ^ _782652) ^ [_1692464, _1692466, _1692468, _1692470] : [-(c_Map_Omap__upds(_1692464, _1692466, _1692468, _1692470, c_List_Olist_ONil(_1692466)) = _1692468)], (45272 ^ _782652) ^ [_1692501] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692501)), c_List_Olist_ONil(_1692501)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45274 ^ _782652) ^ [_1692548, _1692550] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692548)), _1692550) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1692550 = c_List_Olist_ONil(_1692548))], (45280 ^ _782652) ^ [_1692639, _1692641] : [_1692641 = c_List_Olist_ONil(_1692639), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692639)), _1692641) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45286 ^ _782652) ^ [_1692757, _1692759, _1692761, _1692763] : [hAPP(hAPP(c_List_Omap(_1692757, _1692759), _1692761), _1692763) = c_List_Olist_ONil(_1692759), -(_1692763 = c_List_Olist_ONil(_1692757))], (45292 ^ _782652) ^ [_1692860, _1692862, _1692864, _1692866] : [_1692866 = c_List_Olist_ONil(_1692860), -(hAPP(hAPP(c_List_Omap(_1692860, _1692862), _1692864), _1692866) = c_List_Olist_ONil(_1692862))], (45298 ^ _782652) ^ [_1692969, _1692971, _1692973] : [-(hAPP(hAPP(c_List_Omap(_1692969, _1692971), _1692973), c_List_Olist_ONil(_1692969)) = c_List_Olist_ONil(_1692971))], (45300 ^ _782652) ^ [_1693030, _1693032, _1693034, _1693036] : [c_List_Olist_ONil(_1693030) = hAPP(hAPP(c_List_Omap(_1693032, _1693030), _1693034), _1693036), -(_1693036 = c_List_Olist_ONil(_1693032))], (45306 ^ _782652) ^ [_1693133, _1693135, _1693137, _1693139] : [_1693139 = c_List_Olist_ONil(_1693135), -(c_List_Olist_ONil(_1693133) = hAPP(hAPP(c_List_Omap(_1693135, _1693133), _1693137), _1693139))], (45312 ^ _782652) ^ [_1693242, _1693244, _1693246] : [-(hAPP(hAPP(c_Map_Omap__of(_1693242, _1693244), c_List_Olist_ONil(tc_prod(_1693242, _1693244))), _1693246) = c_Option_Ooption_ONone(_1693244))], (45314 ^ _782652) ^ [_1693285, _1693287] : [-(c_List_Osublist(_1693285, c_List_Olist_ONil(_1693285), _1693287) = c_List_Olist_ONil(_1693285))], (45316 ^ _782652) ^ [_1693318, _1693320] : [-(c_List_Osublist(_1693318, _1693320, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1693318))], (45318 ^ _782652) ^ [_1693349, _1693351, _1693353, _1693355] : [class_Orderings_Olinorder(_1693349), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693351, _1693349, _1693353), _1693355), c_List_Olist_ONil(_1693351)) = hAPP(hAPP(c_List_Olist_OCons(_1693351), _1693355), c_List_Olist_ONil(_1693351)))], (45324 ^ _782652) ^ [_1693487, _1693489, _1693491] : [c_List_Olist_ONil(_1693487) = hAPP(hAPP(c_List_Olist_OCons(_1693487), _1693489), _1693491)], (45326 ^ _782652) ^ [_1693539, _1693541, _1693543] : [hAPP(hAPP(c_List_Olist_OCons(_1693539), _1693541), _1693543) = c_List_Olist_ONil(_1693539)], (45328 ^ _782652) ^ [_1693576] : [class_Orderings_Olinorder(_1693576), -(c_List_Olinorder__class_Osorted__list__of__set(_1693576, c_Orderings_Obot__class_Obot(tc_fun(_1693576, tc_HOL_Obool))) = c_List_Olist_ONil(_1693576))], (45334 ^ _782652) ^ [_1693669, _1693671, _1693673] : [-(hAPP(hAPP(c_List_Ozip(_1693669, _1693671), c_List_Olist_ONil(_1693669)), _1693673) = c_List_Olist_ONil(tc_prod(_1693669, _1693671)))], (45336 ^ _782652) ^ [_1693712, _1693714, _1693716] : [-(hAPP(hAPP(c_List_Ozip(_1693712, _1693714), _1693716), c_List_Olist_ONil(_1693714)) = c_List_Olist_ONil(tc_prod(_1693712, _1693714)))], (45338 ^ _782652) ^ [_1693755, _1693757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1693755), _1693757)), -(c_List_Oupto(_1693757, _1693755) = c_List_Olist_ONil(tc_Int_Oint))], (45344 ^ _782652) ^ [_1693848, _1693850, _1693852, _1693854] : [-(c_List_Ofoldr(_1693848, _1693850, _1693852, c_List_Olist_ONil(_1693848), _1693854) = _1693854)], (45346 ^ _782652) ^ [_1693885, _1693887, _1693889] : [-(hAPP(hAPP(c_Map_Omap__of(_1693885, _1693887), c_List_Olist_ONil(tc_prod(_1693885, _1693887))), _1693889) = c_Option_Ooption_ONone(_1693887))], (45348 ^ _782652) ^ [_1693928, _1693930] : [-(c_List_Oremove1(_1693928, _1693930, c_List_Olist_ONil(_1693928)) = c_List_Olist_ONil(_1693928))], (45350 ^ _782652) ^ [_1693961] : [-(hBOOL(hAPP(c_List_Odistinct(_1693961), c_List_Olist_ONil(_1693961))))], (45352 ^ _782652) ^ [_1693990, _1693992, _1693994, _1693996, _1693998] : [class_Orderings_Olinorder(_1693990), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693992, _1693990, _1693994), _1693996), _1693998) = c_List_Olist_ONil(_1693992)], (45358 ^ _782652) ^ [_1694096, _1694098] : [-(c_List_Olistrelp(_1694096, _1694098, c_List_Olist_ONil(_1694096), c_List_Olist_ONil(_1694096)))], (45360 ^ _782652) ^ [_1694127, _1694129] : [-(c_List_Olistrelp(_1694127, _1694129, c_List_Olist_ONil(_1694127), c_List_Olist_ONil(_1694127)))], (45362 ^ _782652) ^ [_1694158] : [-(hAPP(c_List_Oset(_1694158), c_List_Olist_ONil(_1694158)) = c_Orderings_Obot__class_Obot(tc_fun(_1694158, tc_HOL_Obool)))], (45364 ^ _782652) ^ [_1694208, _1694210] : [c_Orderings_Obot__class_Obot(tc_fun(_1694208, tc_HOL_Obool)) = hAPP(c_List_Oset(_1694208), _1694210), -(_1694210 = c_List_Olist_ONil(_1694208))], (45370 ^ _782652) ^ [_1694305, _1694307] : [_1694307 = c_List_Olist_ONil(_1694305), -(c_Orderings_Obot__class_Obot(tc_fun(_1694305, tc_HOL_Obool)) = hAPP(c_List_Oset(_1694305), _1694307))], (45376 ^ _782652) ^ [_1694423, _1694425] : [hAPP(c_List_Oset(_1694423), _1694425) = c_Orderings_Obot__class_Obot(tc_fun(_1694423, tc_HOL_Obool)), -(_1694425 = c_List_Olist_ONil(_1694423))], (45382 ^ _782652) ^ [_1694520, _1694522] : [_1694522 = c_List_Olist_ONil(_1694520), -(hAPP(c_List_Oset(_1694520), _1694522) = c_Orderings_Obot__class_Obot(tc_fun(_1694520, tc_HOL_Obool)))], (45388 ^ _782652) ^ [_1694623] : [class_Groups_Omonoid__add(_1694623), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1694623), c_List_Olist_ONil(_1694623)) = c_Groups_Ozero__class_Ozero(_1694623))], (45394 ^ _782652) ^ [_1694714, _1694716] : [-(hAPP(hAPP(c_List_Otake(_1694714), _1694716), c_List_Olist_ONil(_1694714)) = c_List_Olist_ONil(_1694714))], (45406 ^ _782652) ^ [_1694881, _1694883, _1694885] : [45407 ^ _782652 : [(45408 ^ _782652) ^ [] : [_1694883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45410 ^ _782652) ^ [] : [_1694885 = c_List_Olist_ONil(_1694881)]], -(hAPP(hAPP(c_List_Otake(_1694881), _1694883), _1694885) = c_List_Olist_ONil(_1694881))], (45396 ^ _782652) ^ [_1694769, _1694771, _1694773] : [hAPP(hAPP(c_List_Otake(_1694769), _1694771), _1694773) = c_List_Olist_ONil(_1694769), -(_1694771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1694773 = c_List_Olist_ONil(_1694769))], (45414 ^ _782652) ^ [_1695024, _1695026] : [-(hAPP(hAPP(c_List_Otake(_1695024), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1695026) = c_List_Olist_ONil(_1695024))], (45416 ^ _782652) ^ [_1695074, _1695076] : [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(_1695074)), _1695076))), _1695076 = c_List_Olist_ONil(_1695074)], (45422 ^ _782652) ^ [_1695168, _1695170] : [-(_1695170 = c_List_Olist_ONil(_1695168)), -(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(_1695168)), _1695170))))], (45428 ^ _782652) ^ [_1695217, _1695219, _1695221] : [-(hAPP(hAPP(c_List_Otake(_1695217), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1695217), _1695219), _1695221)) = hAPP(hAPP(c_List_Olist_OCons(_1695217), _1695219), c_List_Olist_ONil(_1695217)))], (45430 ^ _782652) ^ [_1695270, _1695272] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695270), tc_List_Olist(_1695270))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695270), tc_List_Olist(_1695270)), c_List_Olist_ONil(_1695270)), c_List_Olist_ONil(_1695270))), c_List_Olistrel(_1695270, _1695272))))], (45432 ^ _782652) ^ [_1695344, _1695346, _1695348] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695344), tc_List_Olist(_1695344))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695344), tc_List_Olist(_1695344)), _1695346), c_List_Olist_ONil(_1695344))), c_List_Olexord(_1695344, _1695348)))], (45434 ^ _782652) ^ [_1695418, _1695420, _1695422] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695418), tc_List_Olist(_1695418))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695418), tc_List_Olist(_1695418)), c_List_Olist_ONil(_1695418)), _1695420)), c_List_Olex(_1695418, _1695422)))], (45436 ^ _782652) ^ [_1695492, _1695494, _1695496] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695492), tc_List_Olist(_1695492))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695492), tc_List_Olist(_1695492)), _1695494), c_List_Olist_ONil(_1695492))), c_List_Olex(_1695492, _1695496)))], (45438 ^ _782652) ^ [_1695551, _1695553, _1695555, _1695557] : [-(hAPP(hAPP(c_List_Otake(_1695551), _1695553), hAPP(hAPP(c_List_Olist_OCons(_1695551), _1695555), _1695557)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1695551), c_List_Olist_ONil(_1695551), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695551), tc_List_Olist(_1695551), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1695551), _1695555)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1695551), tc_List_Olist(_1695551)), c_List_Otake(_1695551)), _1695557)), _1695553))], (45440 ^ _782652) ^ [_1695649, _1695651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1695649), _1695651)), -(c_List_Oupto(_1695649, _1695651) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1695649), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1695649), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1695651)))], (45446 ^ _782652) ^ [_1695766, _1695768] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1695766), _1695768))), -(c_List_Oupto(_1695766, _1695768) = c_List_Olist_ONil(tc_Int_Oint))], (45452 ^ _782652) ^ [_1695824, _1695826, _1695828] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1695824)), -(c_List_Osublist(_1695826, hAPP(hAPP(c_List_Olist_OCons(_1695826), _1695828), c_List_Olist_ONil(_1695826)), _1695824) = hAPP(hAPP(c_List_Olist_OCons(_1695826), _1695828), c_List_Olist_ONil(_1695826)))], (45458 ^ _782652) ^ [_1695949, _1695951, _1695953] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1695949))), -(c_List_Osublist(_1695951, hAPP(hAPP(c_List_Olist_OCons(_1695951), _1695953), c_List_Olist_ONil(_1695951)), _1695949) = c_List_Olist_ONil(_1695951))], (45464 ^ _782652) ^ [_1696007, _1696009] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1696007), _1696009) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1696007), _1696009))], (45466 ^ _782652) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (45468 ^ _782652) ^ [_1696077, _1696079, _1696081, _1696083] : [_1696077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1696079), _1696077), hAPP(hAPP(c_List_Olist_OCons(_1696079), _1696081), _1696083)) = c_List_Olist_ONil(_1696079))], (45474 ^ _782652) ^ [_1696188, _1696190, _1696192, _1696194] : [-(_1696188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1696190), _1696188), hAPP(hAPP(c_List_Olist_OCons(_1696190), _1696192), _1696194)) = hAPP(hAPP(c_List_Olist_OCons(_1696190), _1696192), hAPP(hAPP(c_List_Otake(_1696190), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1696188), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1696194)))], (45480 ^ _782652) ^ [_1696277, _1696279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696277)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696279))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696277), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696279)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696277)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696277)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696279))))], (45486 ^ _782652) ^ [_1696436, _1696438] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696436)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696438)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696436), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1696438)) = c_List_Olist_ONil(tc_Int_Oint))], (45492 ^ _782652) ^ [_1696490, _1696492, _1696494] : [-(_1696490 = c_List_Olist_ONil(_1696492)), -(hBOOL(hAPP(hAPP(c_member(_1696492), hAPP(c_Product__Type_Ofst(_1696492, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1696492, _1696490), _1696494))), hAPP(c_List_Oset(_1696492), _1696490))))], (45498 ^ _782652) ^ [_1696554, _1696556] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1696554), tc_List_Olist(_1696554), c_List_Olistrel(_1696554, _1696556)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1696554)), c_List_Olist_ONil(_1696554)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1696554), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1696554)), c_List_Olist_ONil(_1696554)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1696554), tc_HOL_Obool))))], (45500 ^ _782652) ^ [_1696631, _1696633] : [-(c_List_Oset__Cons(_1696631, _1696633, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1696631)), c_List_Olist_ONil(_1696631)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1696631), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1696631, tc_List_Olist(_1696631), hAPP(hAPP(c_COMBC(_1696631, tc_List_Olist(_1696631), tc_List_Olist(_1696631)), c_List_Olist_OCons(_1696631)), c_List_Olist_ONil(_1696631))), _1696633))], (45502 ^ _782652) ^ [_1696721, _1696723, _1696725, _1696727] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1696721) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1696723), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1696721)), hAPP(hAPP(c_List_Olist_OCons(_1696723), _1696725), _1696727)) = c_List_Olist_ONil(_1696723))], (45508 ^ _782652) ^ [_1696844, _1696846, _1696848, _1696850] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1696844) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1696846), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1696844)), hAPP(hAPP(c_List_Olist_OCons(_1696846), _1696848), _1696850)) = hAPP(hAPP(c_List_Olist_OCons(_1696846), _1696848), hAPP(hAPP(c_List_Otake(_1696846), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1696844)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1696850)))], (45514 ^ _782652) ^ [_1696933, _1696935] : [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), _1696933), _1696935))), 45517 ^ _782652 : [(45518 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1696933), _1696935)), -(c_List_Oupto(_1696933, _1696935) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1696933), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1696933), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1696935)))], (45524 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1696933), _1696935))), -(c_List_Oupto(_1696933, _1696935) = c_List_Olist_ONil(tc_Int_Oint))]]], (45530 ^ _782652) ^ [_1697205, _1697207, _1697209, _1697211, _1697213] : [_1697205 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1697207, _1697209, _1697211), _1697205), _1697213) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1697209), _1697207), c_List_Olist_ONil(_1697209)), _1697213))], (45536 ^ _782652) ^ [_1697328, _1697330, _1697332, _1697334, _1697336] : [-(_1697328 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1697330, _1697332, _1697334), _1697328), _1697336) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1697332), _1697330), tc_prod(_1697332, _1697330), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1697332), _1697330), c_List_Olist_ONil(_1697332)), _1697336), hAPP(c_Product__Type_Oprod_Oprod__case(_1697332, _1697330, tc_prod(tc_List_Olist(_1697332), _1697330)), hAPP(hAPP(c_COMBC(_1697332, tc_fun(_1697330, tc_prod(tc_List_Olist(_1697332), _1697330)), tc_fun(_1697330, tc_prod(tc_List_Olist(_1697332), _1697330))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1697332), _1697330), tc_prod(tc_List_Olist(_1697332), _1697330)), tc_fun(tc_fun(_1697330, tc_prod(tc_List_Olist(_1697332), _1697330)), tc_fun(_1697330, tc_prod(tc_List_Olist(_1697332), _1697330))), _1697332), c_COMBB(tc_prod(tc_List_Olist(_1697332), _1697330), tc_prod(tc_List_Olist(_1697332), _1697330), _1697330)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1697332), tc_fun(_1697330, tc_prod(tc_List_Olist(_1697332), _1697330))), tc_fun(tc_prod(tc_List_Olist(_1697332), _1697330), tc_prod(tc_List_Olist(_1697332), _1697330)), _1697332), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1697332), _1697330, tc_prod(tc_List_Olist(_1697332), _1697330))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1697332), tc_List_Olist(_1697332)), tc_fun(tc_List_Olist(_1697332), tc_fun(_1697330, tc_prod(tc_List_Olist(_1697332), _1697330))), _1697332), hAPP(c_COMBB(tc_List_Olist(_1697332), tc_fun(_1697330, tc_prod(tc_List_Olist(_1697332), _1697330)), tc_List_Olist(_1697332)), c_Product__Type_OPair(tc_List_Olist(_1697332), _1697330))), c_List_Olist_OCons(_1697332))))), hAPP(c_Lazy__Sequence_Oanamorph(_1697330, _1697332, _1697334), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1697328), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1697334, _1697336)))], (45542 ^ _782652) ^ [_1697624] : [-(c_List_Olistset(_1697624, c_List_Olist_ONil(tc_fun(_1697624, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1697624)), c_List_Olist_ONil(_1697624)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1697624), tc_HOL_Obool))))], (45544 ^ _782652) ^ [_1697674, _1697676, _1697678, _1697680, _1697682] : [-(hAPP(hAPP(c_List_Ozip(_1697674, _1697676), _1697678), hAPP(hAPP(c_List_Olist_OCons(_1697676), _1697680), _1697682)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1697674, _1697676)), _1697674, c_List_Olist_ONil(tc_prod(_1697674, _1697676)), hAPP(hAPP(c_COMBC(_1697674, tc_fun(tc_List_Olist(_1697674), tc_List_Olist(tc_prod(_1697674, _1697676))), tc_fun(tc_List_Olist(_1697674), tc_List_Olist(tc_prod(_1697674, _1697676)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1697674, _1697676)), tc_List_Olist(tc_prod(_1697674, _1697676))), tc_fun(tc_fun(tc_List_Olist(_1697674), tc_List_Olist(tc_prod(_1697674, _1697676))), tc_fun(tc_List_Olist(_1697674), tc_List_Olist(tc_prod(_1697674, _1697676)))), _1697674), c_COMBB(tc_List_Olist(tc_prod(_1697674, _1697676)), tc_List_Olist(tc_prod(_1697674, _1697676)), tc_List_Olist(_1697674))), hAPP(hAPP(c_COMBB(tc_prod(_1697674, _1697676), tc_fun(tc_List_Olist(tc_prod(_1697674, _1697676)), tc_List_Olist(tc_prod(_1697674, _1697676))), _1697674), c_List_Olist_OCons(tc_prod(_1697674, _1697676))), hAPP(hAPP(c_COMBC(_1697674, _1697676, tc_prod(_1697674, _1697676)), c_Product__Type_OPair(_1697674, _1697676)), _1697680)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1697674), tc_List_Olist(_1697676), tc_List_Olist(tc_prod(_1697674, _1697676))), c_List_Ozip(_1697674, _1697676)), _1697682))), _1697678))], (45546 ^ _782652) ^ [_1697901, _1697903, _1697905, _1697907, _1697909, _1697911] : [-(hAPP(c_List_Olist_Olist__case(_1697901, _1697903, _1697905, _1697907), hAPP(hAPP(c_List_Olist_OCons(_1697903), _1697909), _1697911)) = hAPP(hAPP(_1697907, _1697909), _1697911))], (45548 ^ _782652) ^ [_1697956, _1697958, _1697960, _1697962] : [-(hAPP(c_List_Olist_Olist__case(_1697956, _1697958, _1697960, _1697962), c_List_Olist_ONil(_1697958)) = _1697960)], (45550 ^ _782652) ^ [_1697995, _1697997, _1697999] : [-(c_List_Olistset(_1697995, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1697995, tc_HOL_Obool)), _1697997), _1697999)) = c_List_Oset__Cons(_1697995, _1697997, c_List_Olistset(_1697995, _1697999)))], (45552 ^ _782652) ^ [_1698043, _1698045, _1698047, _1698049, _1698051] : [-(hAPP(hAPP(c_List_Ozip(_1698043, _1698045), hAPP(hAPP(c_List_Olist_OCons(_1698043), _1698047), _1698049)), _1698051) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1698043, _1698045)), _1698045, c_List_Olist_ONil(tc_prod(_1698043, _1698045)), hAPP(hAPP(c_COMBC(_1698045, tc_fun(tc_List_Olist(_1698045), tc_List_Olist(tc_prod(_1698043, _1698045))), tc_fun(tc_List_Olist(_1698045), tc_List_Olist(tc_prod(_1698043, _1698045)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1698043, _1698045)), tc_List_Olist(tc_prod(_1698043, _1698045))), tc_fun(tc_fun(tc_List_Olist(_1698045), tc_List_Olist(tc_prod(_1698043, _1698045))), tc_fun(tc_List_Olist(_1698045), tc_List_Olist(tc_prod(_1698043, _1698045)))), _1698045), c_COMBB(tc_List_Olist(tc_prod(_1698043, _1698045)), tc_List_Olist(tc_prod(_1698043, _1698045)), tc_List_Olist(_1698045))), hAPP(hAPP(c_COMBB(tc_prod(_1698043, _1698045), tc_fun(tc_List_Olist(tc_prod(_1698043, _1698045)), tc_List_Olist(tc_prod(_1698043, _1698045))), _1698045), c_List_Olist_OCons(tc_prod(_1698043, _1698045))), hAPP(c_Product__Type_OPair(_1698043, _1698045), _1698047)))), hAPP(c_List_Ozip(_1698043, _1698045), _1698049))), _1698051))], (45554 ^ _782652) ^ [_1698244, _1698246, _1698248] : [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), _1698244), _1698246))), -(hBOOL(hAPP(hAPP(_1698248, _1698244), _1698246))), 45561 ^ _782652 : [(45562 ^ _782652) ^ [] : [-(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), 45559 ^ [_1698244, _1698246, _1698248]), 45560 ^ [_1698244, _1698246, _1698248]))))], (45570 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1698248, 45559 ^ [_1698244, _1698246, _1698248]), 45560 ^ [_1698244, _1698246, _1698248]))], (45564 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 45559 ^ [_1698244, _1698246, _1698248]), 45560 ^ [_1698244, _1698246, _1698248])), -(hBOOL(hAPP(hAPP(_1698248, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 45559 ^ [_1698244, _1698246, _1698248]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 45560 ^ [_1698244, _1698246, _1698248])))]]], (45574 ^ _782652) ^ [_1698735, _1698737, _1698739, _1698741, _1698743, _1698745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698735)), _1698737)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698739)), _1698741))), -(c_Map_Omap__upds(_1698735, _1698739, _1698743, hAPP(hAPP(c_List_Oappend(_1698735), _1698737), hAPP(hAPP(c_List_Olist_OCons(_1698735), _1698745), c_List_Olist_ONil(_1698735))), _1698741) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1698735, tc_Option_Ooption(_1698739)), c_Map_Omap__upds(_1698735, _1698739, _1698743, _1698737, _1698741)), _1698745), hAPP(c_Option_Ooption_OSome(_1698739), hAPP(hAPP(c_List_Onth(_1698739), _1698741), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698735)), _1698737)))))], (45580 ^ _782652) ^ [_1699010, _1699012, _1699014, _1699016, _1699018] : [hAPP(hAPP(c_List_Oappend(_1699010), _1699012), _1699014) = hAPP(hAPP(c_List_Olist_OCons(_1699010), _1699016), _1699018), 45585 ^ _782652 : [(45586 ^ _782652) ^ [] : [-(_1699012 = c_List_Olist_ONil(_1699010))], (45588 ^ _782652) ^ [] : [-(_1699014 = hAPP(hAPP(c_List_Olist_OCons(_1699010), _1699016), _1699018))]], 45590 ^ _782652 : [(45591 ^ _782652) ^ [] : [-(_1699012 = hAPP(hAPP(c_List_Olist_OCons(_1699010), _1699016), 45589 ^ [_1699010, _1699012, _1699014, _1699016, _1699018]))], (45593 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1699010), 45589 ^ [_1699010, _1699012, _1699014, _1699016, _1699018]), _1699014) = _1699018)]]], (45595 ^ _782652) ^ [_1699303, _1699305, _1699307, _1699309, _1699311] : [-(hAPP(hAPP(c_List_Oappend(_1699303), _1699305), _1699307) = hAPP(hAPP(c_List_Olist_OCons(_1699303), _1699309), _1699311)), 45596 ^ _782652 : [(45597 ^ _782652) ^ [] : [_1699305 = c_List_Olist_ONil(_1699303), _1699307 = hAPP(hAPP(c_List_Olist_OCons(_1699303), _1699309), _1699311)], (45603 ^ _782652) ^ [_1699486] : [_1699305 = hAPP(hAPP(c_List_Olist_OCons(_1699303), _1699309), _1699486), hAPP(hAPP(c_List_Oappend(_1699303), _1699486), _1699307) = _1699311]]], (45611 ^ _782652) ^ [_1699674, _1699676, _1699678, _1699680, _1699682] : [hAPP(hAPP(c_List_Olist_OCons(_1699674), _1699676), _1699678) = hAPP(hAPP(c_List_Oappend(_1699674), _1699680), _1699682), 45616 ^ _782652 : [(45617 ^ _782652) ^ [] : [-(_1699680 = c_List_Olist_ONil(_1699674))], (45619 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1699674), _1699676), _1699678) = _1699682)]], 45621 ^ _782652 : [(45622 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1699674), _1699676), 45620 ^ [_1699674, _1699676, _1699678, _1699680, _1699682]) = _1699680)], (45624 ^ _782652) ^ [] : [-(_1699678 = hAPP(hAPP(c_List_Oappend(_1699674), 45620 ^ [_1699674, _1699676, _1699678, _1699680, _1699682]), _1699682))]]], (45626 ^ _782652) ^ [_1699967, _1699969, _1699971, _1699973, _1699975] : [-(hAPP(hAPP(c_List_Olist_OCons(_1699967), _1699969), _1699971) = hAPP(hAPP(c_List_Oappend(_1699967), _1699973), _1699975)), 45627 ^ _782652 : [(45628 ^ _782652) ^ [] : [_1699973 = c_List_Olist_ONil(_1699967), hAPP(hAPP(c_List_Olist_OCons(_1699967), _1699969), _1699971) = _1699975], (45634 ^ _782652) ^ [_1700150] : [hAPP(hAPP(c_List_Olist_OCons(_1699967), _1699969), _1700150) = _1699973, _1699971 = hAPP(hAPP(c_List_Oappend(_1699967), _1700150), _1699975)]]], (45642 ^ _782652) ^ [_1700338, _1700340, _1700342, _1700344, _1700346] : [hAPP(hAPP(c_List_Oappend(_1700338), _1700340), hAPP(hAPP(c_List_Olist_OCons(_1700338), _1700342), c_List_Olist_ONil(_1700338))) = hAPP(hAPP(c_List_Oappend(_1700338), _1700344), hAPP(hAPP(c_List_Olist_OCons(_1700338), _1700346), c_List_Olist_ONil(_1700338))), 45645 ^ _782652 : [(45646 ^ _782652) ^ [] : [-(_1700340 = _1700344)], (45648 ^ _782652) ^ [] : [-(_1700342 = _1700346)]]], (45650 ^ _782652) ^ [_1700515, _1700517, _1700519, _1700521, _1700523] : [-(hAPP(hAPP(c_List_Oappend(_1700515), _1700517), hAPP(hAPP(c_List_Olist_OCons(_1700515), _1700519), c_List_Olist_ONil(_1700515))) = hAPP(hAPP(c_List_Oappend(_1700515), _1700521), hAPP(hAPP(c_List_Olist_OCons(_1700515), _1700523), c_List_Olist_ONil(_1700515)))), _1700517 = _1700521, _1700519 = _1700523], (45660 ^ _782652) ^ [_1700730, _1700732, _1700734] : [_1700730 = _1700732, -(_1700730 = hAPP(hAPP(c_List_Oappend(_1700734), c_List_Olist_ONil(_1700734)), _1700732))], (45666 ^ _782652) ^ [_1700847, _1700849, _1700851] : [hAPP(hAPP(c_List_Oappend(_1700847), _1700849), _1700851) = _1700851, -(_1700849 = c_List_Olist_ONil(_1700847))], (45672 ^ _782652) ^ [_1700942, _1700944, _1700946] : [_1700944 = c_List_Olist_ONil(_1700942), -(hAPP(hAPP(c_List_Oappend(_1700942), _1700944), _1700946) = _1700946)], (45678 ^ _782652) ^ [_1701061, _1701063, _1701065] : [hAPP(hAPP(c_List_Oappend(_1701061), _1701063), _1701065) = _1701063, -(_1701065 = c_List_Olist_ONil(_1701061))], (45684 ^ _782652) ^ [_1701156, _1701158, _1701160] : [_1701160 = c_List_Olist_ONil(_1701156), -(hAPP(hAPP(c_List_Oappend(_1701156), _1701158), _1701160) = _1701158)], (45690 ^ _782652) ^ [_1701275, _1701277, _1701279] : [hAPP(hAPP(c_List_Oappend(_1701275), _1701277), _1701279) = c_List_Olist_ONil(_1701275), 45693 ^ _782652 : [(45694 ^ _782652) ^ [] : [-(_1701277 = c_List_Olist_ONil(_1701275))], (45696 ^ _782652) ^ [] : [-(_1701279 = c_List_Olist_ONil(_1701275))]]], (45698 ^ _782652) ^ [_1701404, _1701406, _1701408] : [-(hAPP(hAPP(c_List_Oappend(_1701404), _1701406), _1701408) = c_List_Olist_ONil(_1701404)), _1701406 = c_List_Olist_ONil(_1701404), _1701408 = c_List_Olist_ONil(_1701404)], (45708 ^ _782652) ^ [_1701585, _1701587, _1701589] : [_1701585 = hAPP(hAPP(c_List_Oappend(_1701587), _1701589), _1701585), -(_1701589 = c_List_Olist_ONil(_1701587))], (45714 ^ _782652) ^ [_1701680, _1701682, _1701684] : [_1701684 = c_List_Olist_ONil(_1701682), -(_1701680 = hAPP(hAPP(c_List_Oappend(_1701682), _1701684), _1701680))], (45720 ^ _782652) ^ [_1701799, _1701801, _1701803] : [_1701799 = hAPP(hAPP(c_List_Oappend(_1701801), _1701799), _1701803), -(_1701803 = c_List_Olist_ONil(_1701801))], (45726 ^ _782652) ^ [_1701894, _1701896, _1701898] : [_1701898 = c_List_Olist_ONil(_1701896), -(_1701894 = hAPP(hAPP(c_List_Oappend(_1701896), _1701894), _1701898))], (45732 ^ _782652) ^ [_1701995, _1701997] : [-(hAPP(hAPP(c_List_Oappend(_1701995), _1701997), c_List_Olist_ONil(_1701995)) = _1701997)], (45734 ^ _782652) ^ [_1702048, _1702050, _1702052] : [c_List_Olist_ONil(_1702048) = hAPP(hAPP(c_List_Oappend(_1702048), _1702050), _1702052), 45737 ^ _782652 : [(45738 ^ _782652) ^ [] : [-(_1702050 = c_List_Olist_ONil(_1702048))], (45740 ^ _782652) ^ [] : [-(_1702052 = c_List_Olist_ONil(_1702048))]]], (45742 ^ _782652) ^ [_1702177, _1702179, _1702181] : [-(c_List_Olist_ONil(_1702177) = hAPP(hAPP(c_List_Oappend(_1702177), _1702179), _1702181)), _1702179 = c_List_Olist_ONil(_1702177), _1702181 = c_List_Olist_ONil(_1702177)], (45752 ^ _782652) ^ [_1702340, _1702342] : [-(hAPP(hAPP(c_List_Oappend(_1702340), c_List_Olist_ONil(_1702340)), _1702342) = _1702342)], (45754 ^ _782652) ^ [_1702375, _1702377, _1702379] : [class_Groups_Omonoid__add(_1702375), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702375), hAPP(hAPP(c_List_Oappend(_1702375), _1702377), _1702379)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1702375), hAPP(c_List_Omonoid__add__class_Olistsum(_1702375), _1702377)), hAPP(c_List_Omonoid__add__class_Olistsum(_1702375), _1702379)))], (45760 ^ _782652) ^ [_1702514, _1702516, _1702518] : [-(hAPP(c_List_Oset(_1702514), hAPP(hAPP(c_List_Oappend(_1702514), _1702516), _1702518)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1702514, tc_HOL_Obool)), hAPP(c_List_Oset(_1702514), _1702516)), hAPP(c_List_Oset(_1702514), _1702518)))], (45762 ^ _782652) ^ [_1702575, _1702577, _1702579, _1702581] : [-(hAPP(hAPP(c_List_Oappend(_1702575), hAPP(hAPP(c_List_Oappend(_1702575), _1702577), _1702579)), _1702581) = hAPP(hAPP(c_List_Oappend(_1702575), _1702577), hAPP(hAPP(c_List_Oappend(_1702575), _1702579), _1702581)))], (45764 ^ _782652) ^ [_1702660, _1702662, _1702664, _1702666, _1702668] : [hAPP(hAPP(c_List_Oappend(_1702660), _1702662), _1702664) = hAPP(hAPP(c_List_Oappend(_1702660), _1702666), _1702668), 45770 ^ _782652 : [(45771 ^ _782652) ^ [] : [-(_1702662 = hAPP(hAPP(c_List_Oappend(_1702660), _1702666), 45767 ^ [_1702660, _1702662, _1702664, _1702666, _1702668]))], (45773 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1702660), 45767 ^ [_1702660, _1702662, _1702664, _1702666, _1702668]), _1702664) = _1702668)]], 45774 ^ _782652 : [(45775 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1702660), _1702662), 45767 ^ [_1702660, _1702662, _1702664, _1702666, _1702668]) = _1702666)], (45777 ^ _782652) ^ [] : [-(_1702664 = hAPP(hAPP(c_List_Oappend(_1702660), 45767 ^ [_1702660, _1702662, _1702664, _1702666, _1702668]), _1702668))]]], (45779 ^ _782652) ^ [_1702991, _1702993, _1702995, _1702997, _1702999] : [-(hAPP(hAPP(c_List_Oappend(_1702991), _1702993), _1702995) = hAPP(hAPP(c_List_Oappend(_1702991), _1702997), _1702999)), 45780 ^ _782652 : [(45781 ^ _782652) ^ [_1703103] : [_1702993 = hAPP(hAPP(c_List_Oappend(_1702991), _1702997), _1703103), hAPP(hAPP(c_List_Oappend(_1702991), _1703103), _1702995) = _1702999], (45787 ^ _782652) ^ [_1703215] : [hAPP(hAPP(c_List_Oappend(_1702991), _1702993), _1703215) = _1702997, _1702995 = hAPP(hAPP(c_List_Oappend(_1702991), _1703215), _1702999)]]], (45795 ^ _782652) ^ [_1703400, _1703402, _1703404, _1703406] : [hAPP(hAPP(c_List_Oappend(_1703400), _1703402), _1703404) = hAPP(hAPP(c_List_Oappend(_1703400), _1703402), _1703406), -(_1703404 = _1703406)], (45801 ^ _782652) ^ [_1703509, _1703511, _1703513, _1703515] : [_1703513 = _1703515, -(hAPP(hAPP(c_List_Oappend(_1703509), _1703511), _1703513) = hAPP(hAPP(c_List_Oappend(_1703509), _1703511), _1703515))], (45807 ^ _782652) ^ [_1703645, _1703647, _1703649, _1703651] : [hAPP(hAPP(c_List_Oappend(_1703645), _1703647), _1703649) = hAPP(hAPP(c_List_Oappend(_1703645), _1703651), _1703649), -(_1703647 = _1703651)], (45813 ^ _782652) ^ [_1703754, _1703756, _1703758, _1703760] : [_1703756 = _1703760, -(hAPP(hAPP(c_List_Oappend(_1703754), _1703756), _1703758) = hAPP(hAPP(c_List_Oappend(_1703754), _1703760), _1703758))], (45819 ^ _782652) ^ [_1703869, _1703871, _1703873, _1703875, _1703877, _1703879] : [hAPP(hAPP(c_List_Oappend(_1703869), _1703871), _1703873) = _1703875, _1703877 = hAPP(hAPP(c_List_Oappend(_1703869), _1703873), _1703879), -(hAPP(hAPP(c_List_Oappend(_1703869), _1703871), _1703877) = hAPP(hAPP(c_List_Oappend(_1703869), _1703875), _1703879))], (45829 ^ _782652) ^ [_1704078, _1704080, _1704082, _1704084] : [-(hAPP(c_Map_Omap__of(_1704078, _1704080), hAPP(hAPP(c_List_Oappend(tc_prod(_1704078, _1704080)), _1704082), _1704084)) = c_Map_Omap__add(_1704078, _1704080, hAPP(c_Map_Omap__of(_1704078, _1704080), _1704084), hAPP(c_Map_Omap__of(_1704078, _1704080), _1704082)))], (45831 ^ _782652) ^ [_1704141, _1704143, _1704145, _1704147, _1704149, _1704151] : [-(c_List_Ofoldr(_1704141, _1704143, _1704145, hAPP(hAPP(c_List_Oappend(_1704141), _1704147), _1704149), _1704151) = c_List_Ofoldr(_1704141, _1704143, _1704145, _1704147, c_List_Ofoldr(_1704141, _1704143, _1704145, _1704149, _1704151)))], (45833 ^ _782652) ^ [_1704200, _1704202, _1704204, _1704206, _1704208] : [-(hAPP(hAPP(c_List_Omap(_1704200, _1704202), _1704204), hAPP(hAPP(c_List_Oappend(_1704200), _1704206), _1704208)) = hAPP(hAPP(c_List_Oappend(_1704202), hAPP(hAPP(c_List_Omap(_1704200, _1704202), _1704204), _1704206)), hAPP(hAPP(c_List_Omap(_1704200, _1704202), _1704204), _1704208)))], (45835 ^ _782652) ^ [_1704274, _1704276, _1704278, _1704280, _1704282, _1704284] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704274)), _1704276) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704278)), _1704280), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704274)), _1704282) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704278)), _1704284), -(hAPP(hAPP(c_List_Ozip(_1704274, _1704278), hAPP(hAPP(c_List_Oappend(_1704274), _1704276), _1704282)), hAPP(hAPP(c_List_Oappend(_1704278), _1704280), _1704284)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1704274, _1704278)), hAPP(hAPP(c_List_Ozip(_1704274, _1704278), _1704276), _1704280)), hAPP(hAPP(c_List_Ozip(_1704274, _1704278), _1704282), _1704284)))], (45845 ^ _782652) ^ [_1704583, _1704585, _1704587] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704583)), hAPP(hAPP(c_List_Oappend(_1704583), _1704585), _1704587)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704583)), _1704585)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704583)), _1704587)))], (45847 ^ _782652) ^ [_1704645, _1704647, _1704649, _1704651, _1704653, _1704655] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704645)), _1704647) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704649)), _1704651), -(c_Map_Omap__upds(_1704645, _1704649, _1704653, _1704647, hAPP(hAPP(c_List_Oappend(_1704649), _1704651), _1704655)) = c_Map_Omap__upds(_1704645, _1704649, _1704653, _1704647, _1704651))], (45853 ^ _782652) ^ [_1704798, _1704800, _1704802, _1704804, _1704806, _1704808] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704798)), _1704800) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704802)), _1704804), -(c_Map_Omap__upds(_1704798, _1704802, _1704806, hAPP(hAPP(c_List_Oappend(_1704798), _1704800), _1704808), _1704804) = c_Map_Omap__upds(_1704798, _1704802, _1704806, _1704800, _1704804))], (45859 ^ _782652) ^ [_1704951, _1704953, _1704955, _1704957] : [-(hAPP(hAPP(c_List_Oappend(_1704951), hAPP(hAPP(c_List_Olist_OCons(_1704951), _1704953), _1704955)), _1704957) = hAPP(hAPP(c_List_Olist_OCons(_1704951), _1704953), hAPP(hAPP(c_List_Oappend(_1704951), _1704955), _1704957)))], (45861 ^ _782652) ^ [_1705012, _1705014, _1705016, _1705018, _1705020, _1705022] : [hAPP(hAPP(c_List_Olist_OCons(_1705012), _1705014), _1705016) = _1705018, _1705020 = hAPP(hAPP(c_List_Oappend(_1705012), _1705016), _1705022), -(hAPP(hAPP(c_List_Olist_OCons(_1705012), _1705014), _1705020) = hAPP(hAPP(c_List_Oappend(_1705012), _1705018), _1705022))], (45871 ^ _782652) ^ [_1705221, _1705223, _1705225, _1705227] : [-(hAPP(hAPP(c_List_Onth(_1705221), hAPP(hAPP(c_List_Oappend(_1705221), _1705223), hAPP(hAPP(c_List_Olist_OCons(_1705221), _1705225), _1705227))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705221)), _1705223)) = _1705225)], (45873 ^ _782652) ^ [_1705281, _1705283, _1705285, _1705287] : [-(hAPP(hAPP(c_List_Onth(_1705281), hAPP(hAPP(c_List_Oappend(_1705281), _1705283), _1705285)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705281)), _1705283)), _1705287)) = hAPP(hAPP(c_List_Onth(_1705281), _1705285), _1705287))], (45875 ^ _782652) ^ [_1705347, _1705349, _1705351, _1705353] : [-(hAPP(hAPP(c_List_Otake(_1705347), _1705349), hAPP(hAPP(c_List_Oappend(_1705347), _1705351), _1705353)) = hAPP(hAPP(c_List_Oappend(_1705347), hAPP(hAPP(c_List_Otake(_1705347), _1705349), _1705351)), hAPP(hAPP(c_List_Otake(_1705347), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1705349), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705347)), _1705351))), _1705353)))], (45877 ^ _782652) ^ [_1705429, _1705431, _1705433, _1705435, _1705437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705429), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705431)), _1705433))), -(hAPP(hAPP(c_List_Olist__update(_1705431, hAPP(hAPP(c_List_Oappend(_1705431), _1705433), _1705435)), _1705429), _1705437) = hAPP(hAPP(c_List_Oappend(_1705431), hAPP(hAPP(c_List_Olist__update(_1705431, _1705433), _1705429), _1705437)), _1705435))], (45883 ^ _782652) ^ [_1705604, _1705606, _1705608, _1705610, _1705612] : [-(hAPP(hAPP(c_List_Olist__update(_1705604, hAPP(hAPP(c_List_Oappend(_1705604), _1705606), hAPP(hAPP(c_List_Olist_OCons(_1705604), _1705608), _1705610))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705604)), _1705606)), _1705612) = hAPP(hAPP(c_List_Oappend(_1705604), _1705606), hAPP(hAPP(c_List_Olist_OCons(_1705604), _1705612), _1705610)))], (45885 ^ _782652) ^ [_1705698, _1705700, _1705702, _1705704] : [hBOOL(hAPP(hAPP(c_member(_1705698), _1705700), hAPP(c_List_Oset(_1705698), _1705702))), -(c_List_Oremove1(_1705698, _1705700, hAPP(hAPP(c_List_Oappend(_1705698), _1705702), _1705704)) = hAPP(hAPP(c_List_Oappend(_1705698), c_List_Oremove1(_1705698, _1705700, _1705702)), _1705704))], (45891 ^ _782652) ^ [_1705845, _1705847, _1705849, _1705851] : [-(hBOOL(hAPP(hAPP(c_member(_1705845), _1705847), hAPP(c_List_Oset(_1705845), _1705849)))), -(c_List_Oremove1(_1705845, _1705847, hAPP(hAPP(c_List_Oappend(_1705845), _1705849), _1705851)) = hAPP(hAPP(c_List_Oappend(_1705845), _1705849), c_List_Oremove1(_1705845, _1705847, _1705851)))], (45897 ^ _782652) ^ [_1705923, _1705925, _1705927, _1705929, _1705931] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705923), tc_List_Olist(_1705923))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705923), tc_List_Olist(_1705923)), _1705925), _1705927)), c_List_Olexord(_1705923, _1705929))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705923), tc_List_Olist(_1705923))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705923), tc_List_Olist(_1705923)), hAPP(hAPP(c_List_Oappend(_1705923), _1705931), _1705925)), hAPP(hAPP(c_List_Oappend(_1705923), _1705931), _1705927))), c_List_Olexord(_1705923, _1705929))))], (45903 ^ _782652) ^ [_1706176, _1706178, _1706180] : [hBOOL(hAPP(c_List_Odistinct(_1706176), hAPP(hAPP(c_List_Oappend(_1706176), _1706178), _1706180))), 45906 ^ _782652 : [(45907 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1706176), _1706178)))], (45909 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1706176), _1706180)))], (45911 ^ _782652) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1706176, tc_HOL_Obool)), hAPP(c_List_Oset(_1706176), _1706178)), hAPP(c_List_Oset(_1706176), _1706180)) = c_Orderings_Obot__class_Obot(tc_fun(_1706176, tc_HOL_Obool)))]]], (45913 ^ _782652) ^ [_1706393, _1706395, _1706397] : [-(hBOOL(hAPP(c_List_Odistinct(_1706393), hAPP(hAPP(c_List_Oappend(_1706393), _1706395), _1706397)))), hBOOL(hAPP(c_List_Odistinct(_1706393), _1706395)), hBOOL(hAPP(c_List_Odistinct(_1706393), _1706397)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1706393, tc_HOL_Obool)), hAPP(c_List_Oset(_1706393), _1706395)), hAPP(c_List_Oset(_1706393), _1706397)) = c_Orderings_Obot__class_Obot(tc_fun(_1706393, tc_HOL_Obool))], (45927 ^ _782652) ^ [_1706689, _1706691, _1706693, _1706695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706689), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706691)), _1706693))), -(hAPP(hAPP(c_List_Onth(_1706691), hAPP(hAPP(c_List_Oappend(_1706691), _1706693), _1706695)), _1706689) = hAPP(hAPP(c_List_Onth(_1706691), _1706693), _1706689))], (45933 ^ _782652) ^ [_1706836, _1706838, _1706840, _1706842] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706836), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706838)), _1706840)))), -(hAPP(hAPP(c_List_Onth(_1706838), hAPP(hAPP(c_List_Oappend(_1706838), _1706840), _1706842)), _1706836) = hAPP(hAPP(c_List_Onth(_1706838), _1706842), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1706836), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706838)), _1706840))))], (45939 ^ _782652) ^ [_1706945, _1706947, _1706949, _1706951, _1706953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706947)), _1706949))), -(hAPP(hAPP(c_List_Olist__update(_1706947, hAPP(hAPP(c_List_Oappend(_1706947), _1706949), _1706951)), _1706945), _1706953) = hAPP(hAPP(c_List_Oappend(_1706947), hAPP(hAPP(c_List_Olist__update(_1706947, _1706949), _1706945), _1706953)), _1706951))], (45945 ^ _782652) ^ [_1707114, _1707116, _1707118, _1707120, _1707122] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707114), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707116)), _1707118)))), -(hAPP(hAPP(c_List_Olist__update(_1707116, hAPP(hAPP(c_List_Oappend(_1707116), _1707118), _1707120)), _1707114), _1707122) = hAPP(hAPP(c_List_Oappend(_1707116), _1707118), hAPP(hAPP(c_List_Olist__update(_1707116, _1707120), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1707114), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707116)), _1707118))), _1707122)))], (45951 ^ _782652) ^ [_1707217, _1707219, _1707221, _1707223] : [-(c_List_Osublist(_1707217, hAPP(hAPP(c_List_Oappend(_1707217), _1707219), _1707221), _1707223) = hAPP(hAPP(c_List_Oappend(_1707217), c_List_Osublist(_1707217, _1707219, _1707223)), c_List_Osublist(_1707217, _1707221, 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(_1707217)), _1707219)))), _1707223)))))], (45953 ^ _782652) ^ [_1707296, _1707298, _1707300, _1707302, _1707304, _1707306, _1707308] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1707296, _1707296)), hAPP(hAPP(c_Product__Type_OPair(_1707296, _1707296), _1707298), _1707300)), _1707302)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707296), tc_List_Olist(_1707296))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707296), tc_List_Olist(_1707296)), hAPP(hAPP(c_List_Oappend(_1707296), _1707304), hAPP(hAPP(c_List_Olist_OCons(_1707296), _1707298), _1707306))), hAPP(hAPP(c_List_Oappend(_1707296), _1707304), hAPP(hAPP(c_List_Olist_OCons(_1707296), _1707300), _1707308)))), c_List_Olexord(_1707296, _1707302))))], (45959 ^ _782652) ^ [_1707545, _1707547, _1707549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707545), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707547)), _1707549))), -(hAPP(hAPP(c_List_Otake(_1707547), hAPP(c_Nat_OSuc, _1707545)), _1707549) = hAPP(hAPP(c_List_Oappend(_1707547), hAPP(hAPP(c_List_Otake(_1707547), _1707545), _1707549)), hAPP(hAPP(c_List_Olist_OCons(_1707547), hAPP(hAPP(c_List_Onth(_1707547), _1707549), _1707545)), c_List_Olist_ONil(_1707547))))], (45965 ^ _782652) ^ [_1707738, _1707740, _1707742, _1707744] : [-(c_List_Osublist(_1707738, hAPP(hAPP(c_List_Olist_OCons(_1707738), _1707740), _1707742), _1707744) = hAPP(hAPP(c_List_Oappend(_1707738), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1707738)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1707744)), hAPP(hAPP(c_List_Olist_OCons(_1707738), _1707740), c_List_Olist_ONil(_1707738))), c_List_Olist_ONil(_1707738))), c_List_Osublist(_1707738, _1707742, 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)), _1707744)))))], (45967 ^ _782652) ^ [_1707852, _1707854, _1707856, _1707858, _1707860, _1707862] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707852), tc_List_Olist(_1707852))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707852), tc_List_Olist(_1707852)), hAPP(hAPP(c_List_Oappend(_1707852), _1707854), hAPP(hAPP(c_List_Olist_OCons(_1707852), _1707856), c_List_Olist_ONil(_1707852)))), hAPP(hAPP(c_List_Oappend(_1707852), _1707858), hAPP(hAPP(c_List_Olist_OCons(_1707852), _1707860), c_List_Olist_ONil(_1707852))))), c_List_Olistrel1(_1707852, _1707862))), 45972 ^ _782652 : [(45973 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1707852), tc_List_Olist(_1707852))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1707852), tc_List_Olist(_1707852)), _1707854), _1707858)), c_List_Olistrel1(_1707852, _1707862))))], (45975 ^ _782652) ^ [] : [-(_1707856 = _1707860)]], 45976 ^ _782652 : [(45977 ^ _782652) ^ [] : [-(_1707854 = _1707858)], (45979 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1707852, _1707852)), hAPP(hAPP(c_Product__Type_OPair(_1707852, _1707852), _1707856), _1707860)), _1707862)))]]], (45981 ^ _782652) ^ [_1708262, _1708264, _1708266, _1708268, _1708270, _1708272] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708262), tc_List_Olist(_1708262))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708262), tc_List_Olist(_1708262)), hAPP(hAPP(c_List_Oappend(_1708262), _1708264), hAPP(hAPP(c_List_Olist_OCons(_1708262), _1708266), c_List_Olist_ONil(_1708262)))), hAPP(hAPP(c_List_Oappend(_1708262), _1708268), hAPP(hAPP(c_List_Olist_OCons(_1708262), _1708270), c_List_Olist_ONil(_1708262))))), c_List_Olistrel1(_1708262, _1708272)))), 45982 ^ _782652 : [(45983 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708262), tc_List_Olist(_1708262))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708262), tc_List_Olist(_1708262)), _1708264), _1708268)), c_List_Olistrel1(_1708262, _1708272))), _1708266 = _1708270], (45989 ^ _782652) ^ [] : [_1708264 = _1708268, hBOOL(hAPP(hAPP(c_member(tc_prod(_1708262, _1708262)), hAPP(hAPP(c_Product__Type_OPair(_1708262, _1708262), _1708266), _1708270)), _1708272))]]], (45997 ^ _782652) ^ [_1708730, _1708732, _1708734, _1708736, _1708738] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708730), tc_List_Olist(_1708730))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708730), tc_List_Olist(_1708730)), hAPP(hAPP(c_List_Oappend(_1708730), _1708732), _1708734)), hAPP(hAPP(c_List_Oappend(_1708730), _1708732), _1708736))), c_List_Olexord(_1708730, _1708738))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1708730, _1708730)), hAPP(hAPP(c_Product__Type_OPair(_1708730, _1708730), 46002 ^ [_1708730, _1708732, _1708734, _1708736, _1708738]), 46002 ^ [_1708730, _1708732, _1708734, _1708736, _1708738])), _1708738))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1708730), tc_List_Olist(_1708730))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708730), tc_List_Olist(_1708730)), _1708734), _1708736)), c_List_Olexord(_1708730, _1708738))))], (46008 ^ _782652) ^ [_1709049, _1709051, _1709053, _1709055] : [hBOOL(hAPP(hAPP(c_member(_1709049), _1709051), c_Wellfounded_Oacc(_1709049, _1709053))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709049)), _1709055), c_Wellfounded_Oacc(tc_List_Olist(_1709049), c_List_Olistrel1(_1709049, _1709053)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709049)), hAPP(hAPP(c_List_Olist_OCons(_1709049), _1709051), _1709055)), c_Wellfounded_Oacc(tc_List_Olist(_1709049), c_List_Olistrel1(_1709049, _1709053)))))], (46018 ^ _782652) ^ [_1709290, _1709292] : [-(c_List_Olistrel(_1709290, c_Transitive__Closure_Ortrancl(_1709290, _1709292)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1709290), c_List_Olistrel1(_1709290, _1709292)))], (46020 ^ _782652) ^ [_1709329, _1709331] : [-(c_List_Olistrel1(_1709329, hAPP(c_Relation_Oconverse(_1709329, _1709329), _1709331)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1709329), tc_List_Olist(_1709329)), c_List_Olistrel1(_1709329, _1709331)))], (46022 ^ _782652) ^ [_1709376, _1709378] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1709376), tc_List_Olist(_1709376)), tc_HOL_Obool)), c_List_Olistrel1(_1709376, c_Transitive__Closure_Ortrancl(_1709376, _1709378))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1709376), c_List_Olistrel1(_1709376, _1709378)))))], (46024 ^ _782652) ^ [_1709432, _1709434, _1709436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1709432, _1709432), tc_HOL_Obool)), _1709434), _1709436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1709432), tc_List_Olist(_1709432)), tc_HOL_Obool)), c_List_Olistrel1(_1709432, _1709434)), c_List_Olistrel1(_1709432, _1709436))))], (46030 ^ _782652) ^ [_1709583, _1709585] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1709583), tc_List_Olist(_1709583)), tc_HOL_Obool)), c_List_Olistrel(_1709583, _1709585)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1709583), c_List_Olistrel1(_1709583, _1709585)))))], (46032 ^ _782652) ^ [_1709636, _1709638, _1709640, _1709642, _1709644] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709636), tc_List_Olist(_1709636))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709636), tc_List_Olist(_1709636)), _1709638), _1709640)), c_List_Olistrel1(_1709636, _1709642))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709636), tc_List_Olist(_1709636))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709636), tc_List_Olist(_1709636)), hAPP(hAPP(c_List_Olist_OCons(_1709636), _1709644), _1709638)), hAPP(hAPP(c_List_Olist_OCons(_1709636), _1709644), _1709640))), c_List_Olistrel1(_1709636, _1709642))))], (46038 ^ _782652) ^ [_1709871, _1709873, _1709875, _1709877, _1709879] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709871), tc_List_Olist(_1709871))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709871), tc_List_Olist(_1709871)), _1709873), _1709875)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1709871), c_List_Olistrel1(_1709871, _1709877)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1709871), tc_List_Olist(_1709871))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1709871), tc_List_Olist(_1709871)), hAPP(hAPP(c_List_Olist_OCons(_1709871), _1709879), _1709873)), hAPP(hAPP(c_List_Olist_OCons(_1709871), _1709879), _1709875))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1709871), c_List_Olistrel1(_1709871, _1709877)))))], (46044 ^ _782652) ^ [_1710126, _1710128, _1710130, _1710132] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710126), tc_List_Olist(_1710126))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710126), tc_List_Olist(_1710126)), _1710128), _1710130)), c_List_Olistrel1(_1710126, _1710132))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710126)), _1710128) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710126)), _1710130))], (46050 ^ _782652) ^ [_1710295, _1710297, _1710299, _1710301] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710295), tc_List_Olist(_1710295))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710295), tc_List_Olist(_1710295)), _1710297), _1710299)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1710295), c_List_Olistrel1(_1710295, _1710301)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710295)), _1710297) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710295)), _1710299))], (46056 ^ _782652) ^ [_1710489, _1710491, _1710493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710489), tc_List_Olist(_1710489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710489), tc_List_Olist(_1710489)), _1710491), c_List_Olist_ONil(_1710489))), c_List_Olistrel1(_1710489, _1710493)))], (46058 ^ _782652) ^ [_1710563, _1710565, _1710567] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710563), tc_List_Olist(_1710563))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710563), tc_List_Olist(_1710563)), c_List_Olist_ONil(_1710563)), _1710565)), c_List_Olistrel1(_1710563, _1710567)))], (46060 ^ _782652) ^ [_1710622, _1710624, _1710626, _1710628, _1710630, _1710632] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710622), tc_List_Olist(_1710622))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710622), tc_List_Olist(_1710622)), hAPP(hAPP(c_List_Oappend(_1710622), _1710624), _1710630)), hAPP(hAPP(c_List_Oappend(_1710622), _1710626), _1710632))), c_List_Olistrel1(_1710622, _1710628)))), 46061 ^ _782652 : [(46062 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710622), tc_List_Olist(_1710622))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710622), tc_List_Olist(_1710622)), _1710624), _1710626)), c_List_Olistrel1(_1710622, _1710628))), _1710630 = _1710632], (46068 ^ _782652) ^ [] : [_1710624 = _1710626, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710622), tc_List_Olist(_1710622))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710622), tc_List_Olist(_1710622)), _1710630), _1710632)), c_List_Olistrel1(_1710622, _1710628)))]]], (46076 ^ _782652) ^ [_1711091, _1711093, _1711095, _1711097] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711091), tc_List_Olist(_1711091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711091), tc_List_Olist(_1711091)), _1711093), _1711095)), c_List_Olistrel1(_1711091, hAPP(c_Relation_Oconverse(_1711091, _1711091), _1711097)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711091), tc_List_Olist(_1711091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711091), tc_List_Olist(_1711091)), _1711093), _1711095)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1711091), tc_List_Olist(_1711091)), c_List_Olistrel1(_1711091, _1711097)))))], (46082 ^ _782652) ^ [_1711320, _1711322, _1711324, _1711326] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711320), tc_List_Olist(_1711320))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711320), tc_List_Olist(_1711320)), _1711322), _1711324)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1711320), tc_List_Olist(_1711320)), c_List_Olistrel1(_1711320, _1711326)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711320), tc_List_Olist(_1711320))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711320), tc_List_Olist(_1711320)), _1711322), _1711324)), c_List_Olistrel1(_1711320, hAPP(c_Relation_Oconverse(_1711320, _1711320), _1711326)))))], (46088 ^ _782652) ^ [_1711555, _1711557, _1711559, _1711561] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711555), tc_List_Olist(_1711555))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711555), tc_List_Olist(_1711555)), _1711557), _1711559)), c_List_Olistrel(_1711555, _1711561))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711555), tc_List_Olist(_1711555))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711555), tc_List_Olist(_1711555)), _1711557), _1711559)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1711555), c_List_Olistrel1(_1711555, _1711561)))))], (46094 ^ _782652) ^ [_1711766, _1711768, _1711770, _1711772] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711766), tc_List_Olist(_1711766))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711766), tc_List_Olist(_1711766)), _1711768), _1711770)), c_List_Olistrel1(_1711766, _1711772))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711766), tc_List_Olist(_1711766))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711766), tc_List_Olist(_1711766)), _1711768), _1711770)), c_List_Olistrel(_1711766, c_Transitive__Closure_Ortrancl(_1711766, _1711772)))))], (46100 ^ _782652) ^ [_1712000, _1712002, _1712004, _1712006, _1712008, _1712010] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712000), tc_List_Olist(_1712000))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712000), tc_List_Olist(_1712000)), hAPP(hAPP(c_List_Olist_OCons(_1712000), _1712002), _1712004)), hAPP(hAPP(c_List_Olist_OCons(_1712000), _1712006), _1712008))), c_List_Olistrel1(_1712000, _1712010))), 46105 ^ _782652 : [(46106 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1712000, _1712000)), hAPP(hAPP(c_Product__Type_OPair(_1712000, _1712000), _1712002), _1712006)), _1712010)))], (46108 ^ _782652) ^ [] : [-(_1712004 = _1712008)]], 46109 ^ _782652 : [(46110 ^ _782652) ^ [] : [-(_1712002 = _1712006)], (46112 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712000), tc_List_Olist(_1712000))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712000), tc_List_Olist(_1712000)), _1712004), _1712008)), c_List_Olistrel1(_1712000, _1712010))))]]], (46114 ^ _782652) ^ [_1712370, _1712372, _1712374, _1712376, _1712378, _1712380] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712370), tc_List_Olist(_1712370))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712370), tc_List_Olist(_1712370)), hAPP(hAPP(c_List_Olist_OCons(_1712370), _1712372), _1712374)), hAPP(hAPP(c_List_Olist_OCons(_1712370), _1712376), _1712378))), c_List_Olistrel1(_1712370, _1712380)))), 46115 ^ _782652 : [(46116 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1712370, _1712370)), hAPP(hAPP(c_Product__Type_OPair(_1712370, _1712370), _1712372), _1712376)), _1712380)), _1712374 = _1712378], (46122 ^ _782652) ^ [] : [_1712372 = _1712376, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712370), tc_List_Olist(_1712370))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712370), tc_List_Olist(_1712370)), _1712374), _1712378)), c_List_Olistrel1(_1712370, _1712380)))]]], (46130 ^ _782652) ^ [_1712798, _1712800, _1712802, _1712804, _1712806] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1712798, _1712798)), hAPP(hAPP(c_Product__Type_OPair(_1712798, _1712798), _1712800), _1712802)), _1712804)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712798), tc_List_Olist(_1712798))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712798), tc_List_Olist(_1712798)), hAPP(hAPP(c_List_Olist_OCons(_1712798), _1712800), _1712806)), hAPP(hAPP(c_List_Olist_OCons(_1712798), _1712802), _1712806))), c_List_Olistrel1(_1712798, _1712804))))], (46136 ^ _782652) ^ [_1713011, _1713013, _1713015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1713011, _1713011), tc_HOL_Obool)), _1713013), _1713015)), c_Relation_Orefl__on(_1713011, c_Orderings_Otop__class_Otop(tc_fun(_1713011, tc_HOL_Obool)), _1713015), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1713011), tc_List_Olist(_1713011)), tc_HOL_Obool)), c_List_Olistrel1(_1713011, _1713013)), c_List_Olistrel(_1713011, _1713015))))], (46146 ^ _782652) ^ [_1713228, _1713230, _1713232, _1713234, _1713236, _1713238, _1713240, _1713242] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713228, _1713228)), hAPP(hAPP(c_Product__Type_OPair(_1713228, _1713228), _1713230), _1713232)), _1713234)), _1713236 = hAPP(hAPP(c_List_Oappend(_1713228), _1713238), hAPP(hAPP(c_List_Olist_OCons(_1713228), _1713230), _1713240)), _1713242 = hAPP(hAPP(c_List_Oappend(_1713228), _1713238), hAPP(hAPP(c_List_Olist_OCons(_1713228), _1713232), _1713240)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713228), tc_List_Olist(_1713228))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713228), tc_List_Olist(_1713228)), _1713236), _1713242)), c_List_Olistrel1(_1713228, _1713234))))], (46160 ^ _782652) ^ [_1713607, _1713609, _1713611, _1713613, _1713615, _1713617] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713607, _1713607)), hAPP(hAPP(c_Product__Type_OPair(_1713607, _1713607), _1713609), _1713611)), c_Transitive__Closure_Ortrancl(_1713607, _1713613))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713607), tc_List_Olist(_1713607))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713607), tc_List_Olist(_1713607)), _1713615), _1713617)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1713607), c_List_Olistrel1(_1713607, _1713613)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713607), tc_List_Olist(_1713607))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713607), tc_List_Olist(_1713607)), hAPP(hAPP(c_List_Olist_OCons(_1713607), _1713609), _1713615)), hAPP(hAPP(c_List_Olist_OCons(_1713607), _1713611), _1713617))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1713607), c_List_Olistrel1(_1713607, _1713613)))))], (46170 ^ _782652) ^ [_1713989, _1713991, _1713993, _1713995] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713989), tc_List_Olist(_1713989))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713989), tc_List_Olist(_1713989)), _1713991), _1713993)), c_List_Olistrel1(_1713989, _1713995))), 46175 ^ _782652 : [(46176 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1713989, _1713989)), hAPP(hAPP(c_Product__Type_OPair(_1713989, _1713989), hAPP(hAPP(c_List_Onth(_1713989), _1713991), 46174 ^ [_1713989, _1713991, _1713993, _1713995])), 46173 ^ [_1713989, _1713991, _1713993, _1713995])), _1713995)))], (46178 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46174 ^ [_1713989, _1713991, _1713993, _1713995]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713989)), _1713991))))], (46180 ^ _782652) ^ [] : [-(_1713993 = hAPP(hAPP(c_List_Olist__update(_1713989, _1713991), 46174 ^ [_1713989, _1713991, _1713993, _1713995]), 46173 ^ [_1713989, _1713991, _1713993, _1713995]))]]], (46182 ^ _782652) ^ [_1714337, _1714339, _1714341, _1714343] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714337), tc_List_Olist(_1714337))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714337), tc_List_Olist(_1714337)), _1714339), _1714341)), c_List_Olistrel1(_1714337, _1714343)))), 46183 ^ _782652 : [(46184 ^ _782652) ^ [_1714470, _1714472] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1714337, _1714337)), hAPP(hAPP(c_Product__Type_OPair(_1714337, _1714337), hAPP(hAPP(c_List_Onth(_1714337), _1714339), _1714470)), _1714472)), _1714343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714470), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714337)), _1714339))), _1714341 = hAPP(hAPP(c_List_Olist__update(_1714337, _1714339), _1714470), _1714472)]]], (46196 ^ _782652) ^ [_1714770, _1714772, _1714774, _1714776] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714770), tc_List_Olist(_1714770))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714770), tc_List_Olist(_1714770)), _1714772), _1714774)), c_List_Olistrel1(_1714770, _1714776))), 46201 ^ _782652 : [(46202 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714770, _1714770)), hAPP(hAPP(c_Product__Type_OPair(_1714770, _1714770), 46199 ^ [_1714770, _1714772, _1714774, _1714776]), 46200 ^ [_1714770, _1714772, _1714774, _1714776])), _1714776)))], (46206 ^ _782652) ^ [] : [-(_1714772 = hAPP(hAPP(c_List_Oappend(_1714770), 46203 ^ [_1714770, _1714772, _1714774, _1714776]), hAPP(hAPP(c_List_Olist_OCons(_1714770), 46199 ^ [_1714770, _1714772, _1714774, _1714776]), 46204 ^ [_1714770, _1714772, _1714774, _1714776])))], (46208 ^ _782652) ^ [] : [-(_1714774 = hAPP(hAPP(c_List_Oappend(_1714770), 46203 ^ [_1714770, _1714772, _1714774, _1714776]), hAPP(hAPP(c_List_Olist_OCons(_1714770), 46200 ^ [_1714770, _1714772, _1714774, _1714776]), 46204 ^ [_1714770, _1714772, _1714774, _1714776])))]]], (46210 ^ _782652) ^ [_1715175, _1715177] : [-(hAPP(c_List_Orotate1(_1715175), _1715177) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1715175), _1715175, c_List_Olist_ONil(_1715175), hAPP(hAPP(c_COMBB(tc_List_Olist(_1715175), tc_fun(tc_List_Olist(_1715175), tc_List_Olist(_1715175)), _1715175), hAPP(c_COMBC(tc_List_Olist(_1715175), tc_List_Olist(_1715175), tc_List_Olist(_1715175)), c_List_Oappend(_1715175))), hAPP(hAPP(c_COMBC(_1715175, tc_List_Olist(_1715175), tc_List_Olist(_1715175)), c_List_Olist_OCons(_1715175)), c_List_Olist_ONil(_1715175)))), _1715177))], (46212 ^ _782652) ^ [_1715269, _1715271, _1715273, _1715275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715269), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715271)), _1715273))), -(hAPP(hAPP(c_List_Olist__update(_1715271, _1715273), _1715269), _1715275) = hAPP(hAPP(c_List_Oappend(_1715271), hAPP(hAPP(c_List_Otake(_1715271), _1715269), _1715273)), hAPP(hAPP(c_List_Olist_OCons(_1715271), _1715275), hAPP(hAPP(c_List_Odrop(_1715271), hAPP(c_Nat_OSuc, _1715269)), _1715273))))], (46218 ^ _782652) ^ [_1715462, _1715464, _1715466, _1715468, _1715470] : [hAPP(hAPP(c_List_Odrop(_1715462), _1715464), _1715466) = hAPP(hAPP(c_List_Olist_OCons(_1715462), _1715468), _1715470), -(hAPP(hAPP(c_List_Onth(_1715462), _1715466), _1715464) = _1715468)], (46224 ^ _782652) ^ [_1715593, _1715595, _1715597, _1715599] : [-(hAPP(hAPP(c_List_Odrop(_1715593), hAPP(c_Nat_OSuc, _1715595)), hAPP(hAPP(c_List_Olist_OCons(_1715593), _1715597), _1715599)) = hAPP(hAPP(c_List_Odrop(_1715593), _1715595), _1715599))], (46226 ^ _782652) ^ [_1715649, _1715651, _1715653] : [-(hAPP(hAPP(c_List_Odrop(_1715649), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1715649), _1715651), _1715653)) = _1715653)], (46228 ^ _782652) ^ [_1715692, _1715694, _1715696] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715692)), hAPP(hAPP(c_List_Odrop(_1715692), _1715694), _1715696)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715692)), _1715696)), _1715694))], (46230 ^ _782652) ^ [_1715747, _1715749] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715747)), hAPP(c_List_Orotate1(_1715747), _1715749)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715747)), _1715749))], (46232 ^ _782652) ^ [_1715791, _1715793, _1715795, _1715797, _1715799] : [-(hAPP(hAPP(c_List_Odrop(_1715791), _1715793), hAPP(hAPP(c_List_Omap(_1715795, _1715791), _1715797), _1715799)) = hAPP(hAPP(c_List_Omap(_1715795, _1715791), _1715797), hAPP(hAPP(c_List_Odrop(_1715795), _1715793), _1715799)))], (46234 ^ _782652) ^ [_1715856, _1715858, _1715860, _1715862, _1715864] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1715856, _1715858)), _1715860), hAPP(hAPP(c_List_Ozip(_1715856, _1715858), _1715862), _1715864)) = hAPP(hAPP(c_List_Ozip(_1715856, _1715858), hAPP(hAPP(c_List_Odrop(_1715856), _1715860), _1715862)), hAPP(hAPP(c_List_Odrop(_1715858), _1715860), _1715864)))], (46236 ^ _782652) ^ [_1715932, _1715934] : [-(hAPP(hAPP(c_List_Odrop(_1715932), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1715934) = _1715934)], (46238 ^ _782652) ^ [_1715965, _1715967, _1715969, _1715971] : [-(hAPP(hAPP(c_List_Odrop(_1715965), _1715967), hAPP(hAPP(c_List_Odrop(_1715965), _1715969), _1715971)) = hAPP(hAPP(c_List_Odrop(_1715965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1715967), _1715969)), _1715971))], (46240 ^ _782652) ^ [_1716039, _1716041] : [hBOOL(hAPP(c_List_Odistinct(_1716039), hAPP(c_List_Orotate1(_1716039), _1716041))), -(hBOOL(hAPP(c_List_Odistinct(_1716039), _1716041)))], (46246 ^ _782652) ^ [_1716138, _1716140] : [hBOOL(hAPP(c_List_Odistinct(_1716138), _1716140)), -(hBOOL(hAPP(c_List_Odistinct(_1716138), hAPP(c_List_Orotate1(_1716138), _1716140))))], (46252 ^ _782652) ^ [_1716243, _1716245, _1716247] : [hBOOL(hAPP(c_List_Odistinct(_1716243), _1716245)), -(hBOOL(hAPP(c_List_Odistinct(_1716243), hAPP(hAPP(c_List_Odrop(_1716243), _1716247), _1716245))))], (46258 ^ _782652) ^ [_1716354, _1716356, _1716358] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1716354, tc_HOL_Obool)), hAPP(c_List_Oset(_1716354), hAPP(hAPP(c_List_Odrop(_1716354), _1716356), _1716358))), hAPP(c_List_Oset(_1716354), _1716358))))], (46260 ^ _782652) ^ [_1716409, _1716411] : [-(hAPP(c_List_Oset(_1716409), hAPP(c_List_Orotate1(_1716409), _1716411)) = hAPP(c_List_Oset(_1716409), _1716411))], (46262 ^ _782652) ^ [_1716449, _1716451, _1716453, _1716455] : [hBOOL(hAPP(hAPP(c_member(_1716449), _1716451), hAPP(c_List_Oset(_1716449), hAPP(hAPP(c_List_Odrop(_1716449), _1716453), _1716455)))), -(hBOOL(hAPP(hAPP(c_member(_1716449), _1716451), hAPP(c_List_Oset(_1716449), _1716455))))], (46268 ^ _782652) ^ [_1716594, _1716596, _1716598, _1716600] : [-(hAPP(hAPP(c_List_Odrop(_1716594), _1716596), hAPP(hAPP(c_List_Otake(_1716594), _1716598), _1716600)) = hAPP(hAPP(c_List_Otake(_1716594), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1716598), _1716596)), hAPP(hAPP(c_List_Odrop(_1716594), _1716596), _1716600)))], (46270 ^ _782652) ^ [_1716661, _1716663, _1716665, _1716667] : [-(hAPP(hAPP(c_List_Otake(_1716661), _1716663), hAPP(hAPP(c_List_Odrop(_1716661), _1716665), _1716667)) = hAPP(hAPP(c_List_Odrop(_1716661), _1716665), hAPP(hAPP(c_List_Otake(_1716661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1716663), _1716665)), _1716667)))], (46272 ^ _782652) ^ [_1716728, _1716730] : [-(hAPP(hAPP(c_List_Odrop(_1716728), _1716730), c_List_Olist_ONil(_1716728)) = c_List_Olist_ONil(_1716728))], (46274 ^ _782652) ^ [_1716780, _1716782] : [hAPP(c_List_Orotate1(_1716780), _1716782) = c_List_Olist_ONil(_1716780), -(_1716782 = c_List_Olist_ONil(_1716780))], (46280 ^ _782652) ^ [_1716871, _1716873] : [_1716873 = c_List_Olist_ONil(_1716871), -(hAPP(c_List_Orotate1(_1716871), _1716873) = c_List_Olist_ONil(_1716871))], (46286 ^ _782652) ^ [_1716968, _1716970, _1716972] : [-(hAPP(hAPP(c_List_Oappend(_1716968), hAPP(hAPP(c_List_Otake(_1716968), _1716970), _1716972)), hAPP(hAPP(c_List_Odrop(_1716968), _1716970), _1716972)) = _1716972)], (46288 ^ _782652) ^ [_1717019, _1717021, _1717023, _1717025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1717019), _1717021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1717023, tc_HOL_Obool)), hAPP(c_List_Oset(_1717023), hAPP(hAPP(c_List_Odrop(_1717023), _1717021), _1717025))), hAPP(c_List_Oset(_1717023), hAPP(hAPP(c_List_Odrop(_1717023), _1717019), _1717025)))))], (46294 ^ _782652) ^ [_1717182, _1717184, _1717186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717182)), _1717184)), _1717186)), -(hAPP(hAPP(c_List_Odrop(_1717182), _1717186), _1717184) = c_List_Olist_ONil(_1717182))], (46300 ^ _782652) ^ [_1717323, _1717325, _1717327] : [hAPP(hAPP(c_List_Odrop(_1717323), _1717325), _1717327) = c_List_Olist_ONil(_1717323), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717323)), _1717327)), _1717325)))], (46306 ^ _782652) ^ [_1717442, _1717444, _1717446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717442)), _1717446)), _1717444)), -(hAPP(hAPP(c_List_Odrop(_1717442), _1717444), _1717446) = c_List_Olist_ONil(_1717442))], (46312 ^ _782652) ^ [_1717567, _1717569, _1717571, _1717573] : [-(hAPP(hAPP(c_List_Odrop(_1717567), _1717569), hAPP(hAPP(c_List_Oappend(_1717567), _1717571), _1717573)) = hAPP(hAPP(c_List_Oappend(_1717567), hAPP(hAPP(c_List_Odrop(_1717567), _1717569), _1717571)), hAPP(hAPP(c_List_Odrop(_1717567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1717569), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717567)), _1717571))), _1717573)))], (46314 ^ _782652) ^ [_1717670, _1717672, _1717674, _1717676] : [hAPP(hAPP(c_List_Oappend(_1717670), _1717672), _1717674) = _1717676, 46317 ^ _782652 : [(46318 ^ _782652) ^ [] : [-(_1717672 = hAPP(hAPP(c_List_Otake(_1717670), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717670)), _1717672)), _1717676))], (46320 ^ _782652) ^ [] : [-(_1717674 = hAPP(hAPP(c_List_Odrop(_1717670), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717670)), _1717672)), _1717676))]]], (46322 ^ _782652) ^ [_1717849, _1717851, _1717853, _1717855] : [-(hAPP(hAPP(c_List_Oappend(_1717849), _1717851), _1717853) = _1717855), _1717851 = hAPP(hAPP(c_List_Otake(_1717849), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717849)), _1717851)), _1717855), _1717853 = hAPP(hAPP(c_List_Odrop(_1717849), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717849)), _1717851)), _1717855)], (46332 ^ _782652) ^ [_1718064, _1718066, _1718068, _1718070] : [-(hAPP(hAPP(c_List_Odrop(_1718064), _1718066), hAPP(hAPP(c_List_Olist_OCons(_1718064), _1718068), _1718070)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1718064), hAPP(hAPP(c_List_Olist_OCons(_1718064), _1718068), _1718070), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1718064), tc_List_Olist(_1718064)), c_List_Odrop(_1718064)), _1718070), _1718066))], (46334 ^ _782652) ^ [_1718155, _1718157, _1718159, _1718161] : [_1718155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1718157), _1718155), hAPP(hAPP(c_List_Olist_OCons(_1718157), _1718159), _1718161)) = hAPP(hAPP(c_List_Olist_OCons(_1718157), _1718159), _1718161))], (46340 ^ _782652) ^ [_1718278, _1718280, _1718282, _1718284] : [-(_1718278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1718280), _1718278), hAPP(hAPP(c_List_Olist_OCons(_1718280), _1718282), _1718284)) = hAPP(hAPP(c_List_Odrop(_1718280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1718278), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1718284))], (46346 ^ _782652) ^ [_1718350, _1718352, _1718354, _1718356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1718350), _1718352)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718354)), _1718356))), -(hAPP(hAPP(c_List_Onth(_1718354), hAPP(hAPP(c_List_Odrop(_1718354), _1718350), _1718356)), _1718352) = hAPP(hAPP(c_List_Onth(_1718354), _1718356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1718350), _1718352)))], (46352 ^ _782652) ^ [_1718551, _1718553, _1718555, _1718557, _1718559] : [hAPP(hAPP(c_List_Oappend(_1718551), _1718553), _1718555) = hAPP(hAPP(c_List_Oappend(_1718551), _1718557), _1718559), 46355 ^ _782652 : [(46356 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718551)), _1718553)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718551)), _1718557))), 46359 ^ _782652 : [(46360 ^ _782652) ^ [] : [-(_1718553 = hAPP(hAPP(c_List_Otake(_1718551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718551)), _1718553)), _1718557))], (46362 ^ _782652) ^ [] : [-(_1718555 = hAPP(hAPP(c_List_Oappend(_1718551), hAPP(hAPP(c_List_Odrop(_1718551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718551)), _1718553)), _1718557)), _1718559))]]], (46364 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718551)), _1718553)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718551)), _1718557)))), 46367 ^ _782652 : [(46368 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1718551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718551)), _1718557)), _1718553) = _1718557)], (46370 ^ _782652) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1718551), hAPP(hAPP(c_List_Odrop(_1718551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718551)), _1718557)), _1718553)), _1718555) = _1718559)]]]]], (46372 ^ _782652) ^ [_1719064, _1719066, _1719068, _1719070, _1719072] : [-(hAPP(hAPP(c_List_Oappend(_1719064), _1719066), _1719068) = hAPP(hAPP(c_List_Oappend(_1719064), _1719070), _1719072)), 46375 ^ _782652 : [(46376 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719064)), _1719066)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719064)), _1719070))))], (46378 ^ _782652) ^ [] : [_1719066 = hAPP(hAPP(c_List_Otake(_1719064), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719064)), _1719066)), _1719070), _1719068 = hAPP(hAPP(c_List_Oappend(_1719064), hAPP(hAPP(c_List_Odrop(_1719064), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719064)), _1719066)), _1719070)), _1719072)]], 46383 ^ _782652 : [(46384 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719064)), _1719066)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719064)), _1719070)))], (46386 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Otake(_1719064), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719064)), _1719070)), _1719066) = _1719070, hAPP(hAPP(c_List_Oappend(_1719064), hAPP(hAPP(c_List_Odrop(_1719064), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719064)), _1719070)), _1719066)), _1719068) = _1719072]]], (46394 ^ _782652) ^ [_1719652, _1719654, _1719656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719652), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719654)), _1719656))), -(hAPP(hAPP(c_List_Olist_OCons(_1719654), hAPP(hAPP(c_List_Onth(_1719654), _1719656), _1719652)), hAPP(hAPP(c_List_Odrop(_1719654), hAPP(c_Nat_OSuc, _1719652)), _1719656)) = hAPP(hAPP(c_List_Odrop(_1719654), _1719652), _1719656))], (46400 ^ _782652) ^ [_1719823, _1719825, _1719827, _1719829] : [-(hAPP(c_List_Orotate1(_1719823), c_List_Olist_ONil(_1719823)) = c_List_Olist_ONil(_1719823))], (46402 ^ _782652) ^ [_1719858, _1719860, _1719862, _1719864] : [-(hAPP(c_List_Orotate1(_1719860), hAPP(hAPP(c_List_Olist_OCons(_1719860), _1719862), _1719864)) = hAPP(hAPP(c_List_Oappend(_1719860), _1719864), hAPP(hAPP(c_List_Olist_OCons(_1719860), _1719862), c_List_Olist_ONil(_1719860))))], (46404 ^ _782652) ^ [_1719935, _1719937, _1719939, _1719941] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719935) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1719937), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1719935)), hAPP(hAPP(c_List_Olist_OCons(_1719937), _1719939), _1719941)) = hAPP(hAPP(c_List_Olist_OCons(_1719937), _1719939), _1719941))], (46410 ^ _782652) ^ [_1720070, _1720072, _1720074, _1720076] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720070) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1720072), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720070)), hAPP(hAPP(c_List_Olist_OCons(_1720072), _1720074), _1720076)) = hAPP(hAPP(c_List_Odrop(_1720072), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720070)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1720076))], (46416 ^ _782652) ^ [_1720151, _1720153, _1720155, _1720157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720151), _1720153)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720155)), _1720157))), -(hAPP(hAPP(c_List_Otake(_1720155), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720151), _1720153)), _1720157) = hAPP(hAPP(c_List_Oappend(_1720155), hAPP(hAPP(c_List_Otake(_1720155), _1720151), _1720157)), hAPP(hAPP(c_List_Otake(_1720155), _1720153), hAPP(hAPP(c_List_Odrop(_1720155), _1720151), _1720157))))], (46422 ^ _782652) ^ [_1720360, _1720362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720360)), _1720362)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1720360), _1720362) = _1720362)], (46428 ^ _782652) ^ [_1720471, _1720473, _1720475, _1720477, _1720479] : [-(hAPP(hAPP(c_List_Ozip(_1720471, _1720473), _1720475), hAPP(hAPP(c_List_Oappend(_1720473), _1720477), _1720479)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1720471, _1720473)), hAPP(hAPP(c_List_Ozip(_1720471, _1720473), hAPP(hAPP(c_List_Otake(_1720471), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720473)), _1720477)), _1720475)), _1720477)), hAPP(hAPP(c_List_Ozip(_1720471, _1720473), hAPP(hAPP(c_List_Odrop(_1720471), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720473)), _1720477)), _1720475)), _1720479)))], (46430 ^ _782652) ^ [_1720578, _1720580, _1720582, _1720584, _1720586] : [-(hAPP(hAPP(c_List_Ozip(_1720578, _1720580), hAPP(hAPP(c_List_Oappend(_1720578), _1720582), _1720584)), _1720586) = hAPP(hAPP(c_List_Oappend(tc_prod(_1720578, _1720580)), hAPP(hAPP(c_List_Ozip(_1720578, _1720580), _1720582), hAPP(hAPP(c_List_Otake(_1720580), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720578)), _1720582)), _1720586))), hAPP(hAPP(c_List_Ozip(_1720578, _1720580), _1720584), hAPP(hAPP(c_List_Odrop(_1720580), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720578)), _1720582)), _1720586))))], (46432 ^ _782652) ^ [_1720685, _1720687, _1720689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1720685), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720687)), _1720689))), -(_1720689 = hAPP(hAPP(c_List_Oappend(_1720687), hAPP(hAPP(c_List_Otake(_1720687), _1720685), _1720689)), hAPP(hAPP(c_List_Olist_OCons(_1720687), hAPP(hAPP(c_List_Onth(_1720687), _1720689), _1720685)), hAPP(hAPP(c_List_Odrop(_1720687), hAPP(c_Nat_OSuc, _1720685)), _1720689))))], (46438 ^ _782652) ^ [_1720874, _1720876, _1720878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1720874), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720876)), _1720878))), -(hAPP(hAPP(c_List_Oappend(_1720876), hAPP(hAPP(c_List_Otake(_1720876), _1720874), _1720878)), hAPP(hAPP(c_List_Olist_OCons(_1720876), hAPP(c_List_Ohd(_1720876), hAPP(hAPP(c_List_Odrop(_1720876), _1720874), _1720878))), c_List_Olist_ONil(_1720876))) = hAPP(hAPP(c_List_Otake(_1720876), hAPP(c_Nat_OSuc, _1720874)), _1720878))], (46444 ^ _782652) ^ [_1721076, _1721078, _1721080] : [-(_1721076 = c_List_Olist_ONil(_1721078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721080), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721078)), _1721076))), -(hAPP(c_List_Ohd(_1721078), hAPP(hAPP(c_List_Odrop(_1721078), _1721080), _1721076)) = hAPP(hAPP(c_List_Onth(_1721078), _1721076), _1721080))], (46454 ^ _782652) ^ [_1721275, _1721277, _1721279] : [-(hAPP(c_List_Ohd(_1721275), hAPP(hAPP(c_List_Olist_OCons(_1721275), _1721277), _1721279)) = _1721277)], (46456 ^ _782652) ^ [_1721311, _1721313, _1721315, _1721317] : [-(_1721311 = c_List_Olist_ONil(_1721313)), -(hAPP(c_List_Ohd(_1721315), hAPP(hAPP(c_List_Omap(_1721313, _1721315), _1721317), _1721311)) = hAPP(_1721317, hAPP(c_List_Ohd(_1721313), _1721311)))], (46462 ^ _782652) ^ [_1721371, _1721373, _1721375] : [-(_1721371 = c_List_Olist_ONil(_1721373)), -(hAPP(c_List_Ohd(_1721373), hAPP(hAPP(c_List_Oappend(_1721373), _1721371), _1721375)) = hAPP(c_List_Ohd(_1721373), _1721371))], (46468 ^ _782652) ^ [_1721441, _1721443, _1721445] : [_1721441 = c_List_Olist_ONil(_1721443), -(hAPP(c_List_Ohd(_1721443), hAPP(hAPP(c_List_Oappend(_1721443), _1721441), _1721445)) = hAPP(c_List_Ohd(_1721443), _1721445))], (46474 ^ _782652) ^ [_1721554, _1721556, _1721558] : [-(_1721554 = c_List_Olist_ONil(_1721556)), -(hAPP(c_List_Ohd(_1721556), hAPP(hAPP(c_List_Oappend(_1721556), _1721554), _1721558)) = hAPP(c_List_Ohd(_1721556), _1721554))], (46480 ^ _782652) ^ [_1721610, _1721612] : [-(_1721610 = c_List_Olist_ONil(_1721612)), -(hBOOL(hAPP(hAPP(c_member(_1721612), hAPP(c_List_Ohd(_1721612), _1721610)), hAPP(c_List_Oset(_1721612), _1721610))))], (46486 ^ _782652) ^ [_1721661, _1721663] : [-(_1721661 = c_List_Olist_ONil(_1721663)), -(hAPP(c_List_Ohd(_1721663), _1721661) = hAPP(hAPP(c_List_Onth(_1721663), _1721661), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46492 ^ _782652) ^ [_1721708, _1721710] : [-(_1721708 = c_List_Olist_ONil(_1721710)), -(hAPP(c_List_Orotate1(_1721710), _1721708) = hAPP(hAPP(c_List_Oappend(_1721710), hAPP(c_List_Otl(_1721710), _1721708)), hAPP(hAPP(c_List_Olist_OCons(_1721710), hAPP(c_List_Ohd(_1721710), _1721708)), c_List_Olist_ONil(_1721710))))], (46498 ^ _782652) ^ [_1721775, _1721777, _1721779] : [-(_1721775 = c_List_Olist_ONil(_1721777)), -(hAPP(c_List_Ohd(_1721777), hAPP(c_List_Orotate(_1721777, _1721779), _1721775)) = hAPP(hAPP(c_List_Onth(_1721777), _1721775), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1721779, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721777)), _1721775))))], (46504 ^ _782652) ^ [_1721845, _1721847, _1721849] : [-(hAPP(hAPP(c_List_Odrop(_1721845), _1721847), hAPP(c_List_Otl(_1721845), _1721849)) = hAPP(c_List_Otl(_1721845), hAPP(hAPP(c_List_Odrop(_1721845), _1721847), _1721849)))], (46506 ^ _782652) ^ [_1721898, _1721900, _1721902] : [-(hAPP(c_List_Otl(_1721898), hAPP(hAPP(c_List_Odrop(_1721898), _1721900), _1721902)) = hAPP(hAPP(c_List_Odrop(_1721898), _1721900), hAPP(c_List_Otl(_1721898), _1721902)))], (46508 ^ _782652) ^ [_1721951, _1721953, _1721955] : [-(hAPP(hAPP(c_List_Odrop(_1721951), hAPP(c_Nat_OSuc, _1721953)), _1721955) = hAPP(hAPP(c_List_Odrop(_1721951), _1721953), hAPP(c_List_Otl(_1721951), _1721955)))], (46510 ^ _782652) ^ [_1722002, _1722004, _1722006] : [-(hAPP(c_List_Otl(_1722002), hAPP(hAPP(c_List_Olist_OCons(_1722002), _1722004), _1722006)) = _1722006)], (46512 ^ _782652) ^ [_1722042, _1722044, _1722046] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722042)), hAPP(c_List_Orotate(_1722042, _1722044), _1722046)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722042)), _1722046))], (46514 ^ _782652) ^ [_1722089, _1722091, _1722093, _1722095, _1722097] : [-(hAPP(c_List_Orotate(_1722089, _1722091), hAPP(hAPP(c_List_Omap(_1722093, _1722089), _1722095), _1722097)) = hAPP(hAPP(c_List_Omap(_1722093, _1722089), _1722095), hAPP(c_List_Orotate(_1722093, _1722091), _1722097)))], (46516 ^ _782652) ^ [_1722150, _1722152, _1722154, _1722156] : [-(hAPP(hAPP(c_List_Omap(_1722150, _1722152), _1722154), hAPP(c_List_Otl(_1722150), _1722156)) = hAPP(c_List_Otl(_1722152), hAPP(hAPP(c_List_Omap(_1722150, _1722152), _1722154), _1722156)))], (46518 ^ _782652) ^ [_1722207, _1722209, _1722211, _1722213] : [-(hAPP(c_List_Orotate(_1722207, _1722209), hAPP(c_List_Orotate(_1722207, _1722211), _1722213)) = hAPP(c_List_Orotate(_1722207, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1722209), _1722211)), _1722213))], (46520 ^ _782652) ^ [_1722278, _1722280, _1722282] : [hBOOL(hAPP(c_List_Odistinct(_1722278), hAPP(c_List_Orotate(_1722278, _1722280), _1722282))), -(hBOOL(hAPP(c_List_Odistinct(_1722278), _1722282)))], (46526 ^ _782652) ^ [_1722381, _1722383, _1722385] : [hBOOL(hAPP(c_List_Odistinct(_1722381), _1722385)), -(hBOOL(hAPP(c_List_Odistinct(_1722381), hAPP(c_List_Orotate(_1722381, _1722383), _1722385))))], (46532 ^ _782652) ^ [_1722490, _1722492] : [hBOOL(hAPP(c_List_Odistinct(_1722490), _1722492)), -(hBOOL(hAPP(c_List_Odistinct(_1722490), hAPP(c_List_Otl(_1722490), _1722492))))], (46538 ^ _782652) ^ [_1722593, _1722595, _1722597] : [-(hAPP(c_List_Oset(_1722593), hAPP(c_List_Orotate(_1722593, _1722595), _1722597)) = hAPP(c_List_Oset(_1722593), _1722597))], (46540 ^ _782652) ^ [_1722636] : [-(hAPP(c_List_Otl(_1722636), c_List_Olist_ONil(_1722636)) = c_List_Olist_ONil(_1722636))], (46542 ^ _782652) ^ [_1722686, _1722688, _1722690] : [hAPP(c_List_Orotate(_1722686, _1722688), _1722690) = c_List_Olist_ONil(_1722686), -(_1722690 = c_List_Olist_ONil(_1722686))], (46548 ^ _782652) ^ [_1722781, _1722783, _1722785] : [_1722785 = c_List_Olist_ONil(_1722781), -(hAPP(c_List_Orotate(_1722781, _1722783), _1722785) = c_List_Olist_ONil(_1722781))], (46554 ^ _782652) ^ [_1722882, _1722884, _1722886] : [-(hAPP(c_List_Orotate(_1722882, _1722884), _1722886) = hAPP(c_List_Orotate(_1722882, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1722884, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722882)), _1722886))), _1722886))], (46556 ^ _782652) ^ [_1722932, _1722934, _1722936] : [-(hAPP(hAPP(c_List_Otake(_1722932), _1722934), hAPP(c_List_Otl(_1722932), _1722936)) = hAPP(c_List_Otl(_1722932), hAPP(hAPP(c_List_Otake(_1722932), hAPP(c_Nat_OSuc, _1722934)), _1722936)))], (46558 ^ _782652) ^ [_1722984, _1722986, _1722988] : [-(_1722984 = c_List_Olist_ONil(_1722986)), -(hAPP(c_List_Otl(_1722986), hAPP(hAPP(c_List_Oappend(_1722986), _1722984), _1722988)) = hAPP(hAPP(c_List_Oappend(_1722986), hAPP(c_List_Otl(_1722986), _1722984)), _1722988))], (46564 ^ _782652) ^ [_1723050, _1723052] : [-(c_List_Orotate(_1723050, _1723052) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1723050), tc_List_Olist(_1723050)), _1723052), c_List_Orotate1(_1723050)))], (46566 ^ _782652) ^ [_1723093, _1723095, _1723097] : [-(hAPP(c_List_Orotate1(_1723093), hAPP(c_List_Orotate(_1723093, _1723095), _1723097)) = hAPP(c_List_Orotate(_1723093, _1723095), hAPP(c_List_Orotate1(_1723093), _1723097)))], (46568 ^ _782652) ^ [_1723142, _1723144, _1723146] : [-(hAPP(c_List_Orotate(_1723142, hAPP(c_Nat_OSuc, _1723144)), _1723146) = hAPP(c_List_Orotate1(_1723142), hAPP(c_List_Orotate(_1723142, _1723144), _1723146)))], (46570 ^ _782652) ^ [_1723189, _1723191, _1723193] : [-(hAPP(c_List_Otl(_1723189), hAPP(hAPP(c_List_Oappend(_1723189), _1723191), _1723193)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1723189), _1723189, hAPP(c_List_Otl(_1723189), _1723193), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1723189), tc_List_Olist(_1723189)), _1723189), hAPP(hAPP(c_COMBC(tc_List_Olist(_1723189), tc_List_Olist(_1723189), tc_List_Olist(_1723189)), c_List_Oappend(_1723189)), _1723193))), _1723191))], (46572 ^ _782652) ^ [_1723275] : [-(c_List_Orotate(_1723275, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1723275)))], (46574 ^ _782652) ^ [_1723305, _1723307, _1723309] : [-(c_List_Orotate(_1723305, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1723307), _1723309)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1723305), tc_List_Olist(_1723305), tc_List_Olist(_1723305), c_List_Orotate(_1723305, _1723307)), c_List_Orotate(_1723305, _1723309)))], (46576 ^ _782652) ^ [_1723361, _1723363, _1723365] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1723361, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723363)), _1723365)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1723363, _1723361), _1723365) = _1723365)], (46582 ^ _782652) ^ [_1723474, _1723476, _1723478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723474)), _1723476)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1723474, _1723478), _1723476) = _1723476)], (46588 ^ _782652) ^ [_1723589, _1723591] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723589)), hAPP(c_List_Otl(_1723589), _1723591)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723589)), _1723591)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46590 ^ _782652) ^ [_1723639, _1723641, _1723643] : [-(hAPP(c_List_Otl(_1723639), hAPP(hAPP(c_List_Otake(_1723639), _1723641), _1723643)) = hAPP(hAPP(c_List_Otake(_1723639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1723641), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1723639), _1723643)))], (46592 ^ _782652) ^ [_1723694, _1723696, _1723698] : [-(_1723694 = c_List_Olist_ONil(_1723696)), -(hAPP(hAPP(c_List_Otake(_1723696), hAPP(c_Nat_OSuc, _1723698)), _1723694) = hAPP(hAPP(c_List_Olist_OCons(_1723696), hAPP(c_List_Ohd(_1723696), _1723694)), hAPP(hAPP(c_List_Otake(_1723696), _1723698), hAPP(c_List_Otl(_1723696), _1723694))))], (46598 ^ _782652) ^ [_1723771, _1723773, _1723775] : [-(hAPP(c_List_Orotate(_1723771, _1723773), _1723775) = hAPP(hAPP(c_List_Oappend(_1723771), hAPP(hAPP(c_List_Odrop(_1723771), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1723773, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723771)), _1723775))), _1723775)), hAPP(hAPP(c_List_Otake(_1723771), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1723773, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723771)), _1723775))), _1723775)))], (46600 ^ _782652) ^ [_1723850, _1723852] : [class_Lattices_Oab__semigroup__idem__mult(_1723850), -(_1723852 = c_List_Olist_ONil(_1723850)), -(hAPP(c_Finite__Set_Ofold1(_1723850, c_Groups_Otimes__class_Otimes(_1723850)), hAPP(c_List_Oset(_1723850), _1723852)) = hAPP(c_List_Ofoldl(_1723850, _1723850, c_Groups_Otimes__class_Otimes(_1723850), hAPP(c_List_Ohd(_1723850), _1723852)), hAPP(c_List_Otl(_1723850), _1723852)))], (46610 ^ _782652) ^ [_1724010, _1724012, _1724014, _1724016] : [-(c_List_Olist_Olist__size(_1724010, _1724012, hAPP(hAPP(c_List_Olist_OCons(_1724010), _1724014), _1724016)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1724012, _1724014)), c_List_Olist_Olist__size(_1724010, _1724012, _1724016))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46612 ^ _782652) ^ [_1724070, _1724072, _1724074, _1724076, _1724078, _1724080] : [-(hAPP(c_List_Ofoldl(_1724070, _1724072, _1724074, _1724076), hAPP(hAPP(c_List_Oappend(_1724072), _1724078), _1724080)) = hAPP(c_List_Ofoldl(_1724070, _1724072, _1724074, hAPP(c_List_Ofoldl(_1724070, _1724072, _1724074, _1724076), _1724078)), _1724080))], (46614 ^ _782652) ^ [_1724135, _1724137, _1724139, _1724141] : [-(hAPP(c_List_Ofoldl(_1724135, _1724137, _1724139, _1724141), c_List_Olist_ONil(_1724137)) = _1724141)], (46616 ^ _782652) ^ [_1724174, _1724176, _1724178, _1724180, _1724182] : [-(c_List_Olist_Olist__size(_1724174, _1724176, hAPP(hAPP(c_List_Omap(_1724178, _1724174), _1724180), _1724182)) = c_List_Olist_Olist__size(_1724178, hAPP(c_Fun_Ocomp(_1724174, tc_Nat_Onat, _1724178, _1724176), _1724180), _1724182))], (46618 ^ _782652) ^ [_1724230, _1724232, _1724234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724230), _1724232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724230), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1724232), _1724234))))], (46624 ^ _782652) ^ [_1724345, _1724347, _1724349, _1724351] : [class_Groups_Osemigroup__add(_1724345), -(hAPP(c_List_Ofoldl(_1724345, _1724345, c_Groups_Oplus__class_Oplus(_1724345), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1724345), _1724347), _1724349)), _1724351) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1724345), _1724347), hAPP(c_List_Ofoldl(_1724345, _1724345, c_Groups_Oplus__class_Oplus(_1724345), _1724349), _1724351)))], (46630 ^ _782652) ^ [_1724496, _1724498, _1724500] : [class_Groups_Omonoid__add(_1724496), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1724496), _1724498), hAPP(c_List_Ofoldl(_1724496, _1724496, c_Groups_Oplus__class_Oplus(_1724496), c_Groups_Ozero__class_Ozero(_1724496)), _1724500)) = hAPP(c_List_Ofoldl(_1724496, _1724496, c_Groups_Oplus__class_Oplus(_1724496), _1724498), _1724500))], (46636 ^ _782652) ^ [_1724633, _1724635, _1724637] : [class_Groups_Oab__semigroup__add(_1724633), -(c_List_Ofoldr(_1724633, _1724633, c_Groups_Oplus__class_Oplus(_1724633), _1724635, _1724637) = hAPP(c_List_Ofoldl(_1724633, _1724633, c_Groups_Oplus__class_Oplus(_1724633), _1724637), _1724635))], (46642 ^ _782652) ^ [_1724746, _1724748, _1724750, _1724752, _1724754, _1724756, _1724758] : [-(hAPP(c_List_Ofoldl(_1724746, _1724748, _1724750, _1724752), hAPP(hAPP(c_List_Omap(_1724754, _1724748), _1724756), _1724758)) = hAPP(c_List_Ofoldl(_1724746, _1724754, hAPP(hAPP(c_COMBC(_1724746, tc_fun(_1724754, _1724748), tc_fun(_1724754, _1724746)), hAPP(hAPP(c_COMBB(tc_fun(_1724748, _1724746), tc_fun(tc_fun(_1724754, _1724748), tc_fun(_1724754, _1724746)), _1724746), c_COMBB(_1724748, _1724746, _1724754)), _1724750)), _1724756), _1724752), _1724758))], (46644 ^ _782652) ^ [_1724848, _1724850, _1724852, _1724854, _1724856, _1724858] : [-(hAPP(c_List_Ofoldl(_1724848, _1724850, _1724852, _1724854), hAPP(hAPP(c_List_Olist_OCons(_1724850), _1724856), _1724858)) = hAPP(c_List_Ofoldl(_1724848, _1724850, _1724852, hAPP(hAPP(_1724852, _1724854), _1724856)), _1724858))], (46646 ^ _782652) ^ [_1724911] : [class_Groups_Omonoid__add(_1724911), -(c_List_Omonoid__add__class_Olistsum(_1724911) = c_List_Ofoldl(_1724911, _1724911, c_Groups_Oplus__class_Oplus(_1724911), c_Groups_Ozero__class_Ozero(_1724911)))], (46652 ^ _782652) ^ [_1725006, _1725008, _1725010] : [class_Groups_Omonoid__add(_1725006), -(hAPP(c_List_Ofoldl(_1725006, _1725006, c_Groups_Oplus__class_Oplus(_1725006), _1725008), _1725010) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1725006), _1725008), c_List_Ofoldr(_1725006, _1725006, c_Groups_Oplus__class_Oplus(_1725006), _1725010, c_Groups_Ozero__class_Ozero(_1725006))))], (46658 ^ _782652) ^ [_1725139, _1725141] : [class_Groups_Omonoid__add(_1725139), -(hAPP(c_List_Ofoldl(_1725139, _1725139, c_Groups_Oplus__class_Oplus(_1725139), c_Groups_Ozero__class_Ozero(_1725139)), _1725141) = c_List_Ofoldr(_1725139, _1725139, c_Groups_Oplus__class_Oplus(_1725139), _1725141, c_Groups_Ozero__class_Ozero(_1725139)))], (46664 ^ _782652) ^ [_1725273, _1725275] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725273), _1725275) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46667 ^ _782652 : [(46668 ^ _782652) ^ [] : [-(_1725273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46670 ^ _782652) ^ [_1725387] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1725387), hAPP(c_List_Oset(tc_Nat_Onat), _1725275))), -(_1725387 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46676 ^ _782652) ^ [_1725484, _1725486] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725484), _1725486) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1725484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46682 ^ _782652 : [(46683 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 46681 ^ [_1725484, _1725486]), hAPP(c_List_Oset(tc_Nat_Onat), _1725486))))], (46685 ^ _782652) ^ [] : [46681 ^ [_1725484, _1725486] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (46689 ^ _782652) ^ [_1725710, _1725712] : [-(c_List_Olist_Olist__size(_1725710, _1725712, c_List_Olist_ONil(_1725710)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46691 ^ _782652) ^ [_1725741, _1725743, _1725745, _1725747, _1725749] : [c_Finite__Set_Ofun__left__comm__idem(_1725741, _1725743, _1725745), -(hAPP(hAPP(c_Finite__Set_Ofold(_1725741, _1725743, _1725745), _1725747), hAPP(c_List_Oset(_1725741), _1725749)) = hAPP(c_List_Ofoldl(_1725743, _1725741, hAPP(c_COMBC(_1725741, _1725743, _1725743), _1725745), _1725747), _1725749))], (46697 ^ _782652) ^ [_1725886, _1725888] : [class_Complete__Lattice_Ocomplete__lattice(_1725886), -(c_Complete__Lattice_OSup__class_OSup(_1725886, hAPP(c_List_Oset(_1725886), _1725888)) = hAPP(c_List_Ofoldl(_1725886, _1725886, c_Lattices_Osemilattice__sup__class_Osup(_1725886), c_Orderings_Obot__class_Obot(_1725886)), _1725888))], (46703 ^ _782652) ^ [_1726001, _1726003] : [class_Complete__Lattice_Ocomplete__lattice(_1726001), -(c_Complete__Lattice_OInf__class_OInf(_1726001, hAPP(c_List_Oset(_1726001), _1726003)) = hAPP(c_List_Ofoldl(_1726001, _1726001, c_Lattices_Osemilattice__inf__class_Oinf(_1726001), c_Orderings_Otop__class_Otop(_1726001)), _1726003))], (46709 ^ _782652) ^ [_1726116, _1726118, _1726120] : [class_Lattices_Olattice(_1726116), -(c_Big__Operators_Olattice__class_OSup__fin(_1726116, hAPP(c_List_Oset(_1726116), hAPP(hAPP(c_List_Olist_OCons(_1726116), _1726118), _1726120))) = hAPP(c_List_Ofoldl(_1726116, _1726116, c_Lattices_Osemilattice__sup__class_Osup(_1726116), _1726118), _1726120))], (46715 ^ _782652) ^ [_1726245, _1726247, _1726249] : [class_Lattices_Olattice(_1726245), -(c_Big__Operators_Olattice__class_OInf__fin(_1726245, hAPP(c_List_Oset(_1726245), hAPP(hAPP(c_List_Olist_OCons(_1726245), _1726247), _1726249))) = hAPP(c_List_Ofoldl(_1726245, _1726245, c_Lattices_Osemilattice__inf__class_Oinf(_1726245), _1726247), _1726249))], (46721 ^ _782652) ^ [_1726374, _1726376, _1726378] : [class_Orderings_Olinorder(_1726374), -(c_Big__Operators_Olinorder__class_OMin(_1726374, hAPP(c_List_Oset(_1726374), hAPP(hAPP(c_List_Olist_OCons(_1726374), _1726376), _1726378))) = hAPP(c_List_Ofoldl(_1726374, _1726374, c_Orderings_Oord__class_Omin(_1726374), _1726376), _1726378))], (46727 ^ _782652) ^ [_1726503, _1726505, _1726507] : [class_Orderings_Olinorder(_1726503), -(c_Big__Operators_Olinorder__class_OMax(_1726503, hAPP(c_List_Oset(_1726503), hAPP(hAPP(c_List_Olist_OCons(_1726503), _1726505), _1726507))) = hAPP(c_List_Ofoldl(_1726503, _1726503, c_Orderings_Oord__class_Omax(_1726503), _1726505), _1726507))], (46733 ^ _782652) ^ [_1726632, _1726634, _1726636] : [class_Orderings_Olinorder(_1726632), -(c_Big__Operators_Olattice_OInf__fin(_1726632, c_Orderings_Oord__class_Omin(_1726632), hAPP(c_List_Oset(_1726632), hAPP(hAPP(c_List_Olist_OCons(_1726632), _1726634), _1726636))) = hAPP(c_List_Ofoldl(_1726632, _1726632, c_Orderings_Oord__class_Omin(_1726632), _1726634), _1726636))], (46739 ^ _782652) ^ [_1726767, _1726769, _1726771] : [class_Orderings_Olinorder(_1726767), -(c_Big__Operators_Olattice_OSup__fin(_1726767, c_Orderings_Oord__class_Omax(_1726767), hAPP(c_List_Oset(_1726767), hAPP(hAPP(c_List_Olist_OCons(_1726767), _1726769), _1726771))) = hAPP(c_List_Ofoldl(_1726767, _1726767, c_Orderings_Oord__class_Omax(_1726767), _1726769), _1726771))], (46745 ^ _782652) ^ [_1726902, _1726904, _1726906, _1726908] : [class_Complete__Lattice_Ocomplete__lattice(_1726902), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1726904, _1726902), hAPP(c_List_Oset(_1726904), _1726906)), _1726908) = hAPP(c_List_Ofoldl(_1726902, _1726904, hAPP(c_COMBC(_1726904, _1726902, _1726902), hAPP(hAPP(c_COMBB(_1726902, tc_fun(_1726902, _1726902), _1726904), c_Lattices_Osemilattice__sup__class_Osup(_1726902)), _1726908)), c_Orderings_Obot__class_Obot(_1726902)), _1726906))], (46751 ^ _782652) ^ [_1727073, _1727075, _1727077, _1727079] : [class_Complete__Lattice_Ocomplete__lattice(_1727073), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1727075, _1727073), hAPP(c_List_Oset(_1727075), _1727077)), _1727079) = hAPP(c_List_Ofoldl(_1727073, _1727075, hAPP(c_COMBC(_1727075, _1727073, _1727073), hAPP(hAPP(c_COMBB(_1727073, tc_fun(_1727073, _1727073), _1727075), c_Lattices_Osemilattice__inf__class_Oinf(_1727073)), _1727079)), c_Orderings_Otop__class_Otop(_1727073)), _1727077))], (46757 ^ _782652) ^ [_1727244, _1727246, _1727248, _1727250, _1727252] : [hBOOL(hAPP(hAPP(c_member(_1727244), _1727246), hAPP(c_List_Oset(_1727244), _1727248))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727250), hAPP(_1727252, _1727246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727250), c_List_Olist_Olist__size(_1727244, _1727252, _1727248))))], (46767 ^ _782652) ^ [_1727443, _1727445, _1727447, _1727449, _1727451] : [hBOOL(hAPP(hAPP(c_member(_1727443), _1727445), hAPP(c_List_Oset(_1727443), _1727447))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1727449), hAPP(_1727451, _1727445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1727449), c_List_Olist_Olist__size(_1727443, _1727451, _1727447))))], (46777 ^ _782652) ^ [_1727642, _1727644, _1727646, _1727648, _1727650] : [-(c_Map_Omap__upds(_1727642, _1727644, _1727646, _1727648, _1727650) = hAPP(c_List_Ofoldl(tc_fun(_1727642, tc_Option_Ooption(_1727644)), tc_prod(_1727642, _1727644), hAPP(hAPP(c_COMBB(tc_fun(_1727642, tc_fun(_1727644, tc_fun(_1727642, tc_Option_Ooption(_1727644)))), tc_fun(tc_prod(_1727642, _1727644), tc_fun(_1727642, tc_Option_Ooption(_1727644))), tc_fun(_1727642, tc_Option_Ooption(_1727644))), c_Product__Type_Oprod_Oprod__case(_1727642, _1727644, tc_fun(_1727642, tc_Option_Ooption(_1727644)))), hAPP(hAPP(c_COMBC(tc_fun(_1727642, tc_Option_Ooption(_1727644)), tc_fun(_1727644, tc_Option_Ooption(_1727644)), tc_fun(_1727642, tc_fun(_1727644, tc_fun(_1727642, tc_Option_Ooption(_1727644))))), hAPP(hAPP(c_COMBB(tc_fun(_1727642, tc_fun(tc_fun(_1727644, tc_Option_Ooption(_1727644)), tc_fun(_1727644, tc_fun(_1727642, tc_Option_Ooption(_1727644))))), tc_fun(tc_fun(_1727644, tc_Option_Ooption(_1727644)), tc_fun(_1727642, tc_fun(_1727644, tc_fun(_1727642, tc_Option_Ooption(_1727644))))), tc_fun(_1727642, tc_Option_Ooption(_1727644))), c_COMBC(_1727642, tc_fun(_1727644, tc_Option_Ooption(_1727644)), tc_fun(_1727644, tc_fun(_1727642, tc_Option_Ooption(_1727644))))), hAPP(hAPP(c_COMBB(tc_fun(_1727642, tc_fun(tc_Option_Ooption(_1727644), tc_fun(_1727642, tc_Option_Ooption(_1727644)))), tc_fun(_1727642, tc_fun(tc_fun(_1727644, tc_Option_Ooption(_1727644)), tc_fun(_1727644, tc_fun(_1727642, tc_Option_Ooption(_1727644))))), tc_fun(_1727642, tc_Option_Ooption(_1727644))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1727644), tc_fun(_1727642, tc_Option_Ooption(_1727644))), tc_fun(tc_fun(_1727644, tc_Option_Ooption(_1727644)), tc_fun(_1727644, tc_fun(_1727642, tc_Option_Ooption(_1727644)))), _1727642), c_COMBB(tc_Option_Ooption(_1727644), tc_fun(_1727642, tc_Option_Ooption(_1727644)), _1727644))), c_Fun_Ofun__upd(_1727642, tc_Option_Ooption(_1727644))))), c_Option_Ooption_OSome(_1727644))), _1727646), hAPP(hAPP(c_List_Ozip(_1727642, _1727644), _1727648), _1727650)))], (46779 ^ _782652) ^ [_1727949, _1727951] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1727949), hAPP(c_List_Oset(tc_Nat_Onat), _1727951))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1727949), 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)), _1727951))))], (46785 ^ _782652) ^ [_1728058, _1728060, _1728062] : [-(c_List_Olist_Olist__size(_1728058, _1728060, _1728062) = 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(_1728058, tc_Nat_Onat), _1728060), _1728062))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728058)), _1728062)))], (46787 ^ _782652) ^ [_1728114, _1728116, _1728118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1728114, _1728114), tc_HOL_Obool)), _1728116), hAPP(hAPP(c_Product__Type_OSigma(_1728114, _1728114), _1728118), hAPP(c_COMBK(tc_fun(_1728114, tc_HOL_Obool), _1728114), _1728118)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1728114), tc_List_Olist(_1728114)), tc_HOL_Obool)), c_List_Olistrel(_1728114, _1728116)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1728114), tc_List_Olist(_1728114)), c_List_Olists(_1728114, _1728118)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1728114), tc_HOL_Obool), tc_List_Olist(_1728114)), c_List_Olists(_1728114, _1728118))))))], (46793 ^ _782652) ^ [_1728359, _1728361, _1728363] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728359)), _1728361), c_Wellfounded_Oacc(tc_List_Olist(_1728359), c_List_Olistrel1(_1728359, _1728363)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728359)), _1728361), c_List_Olists(_1728359, c_Wellfounded_Oacc(_1728359, _1728363)))))], (46799 ^ _782652) ^ [_1728502, _1728504] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728502)), c_List_Olist_ONil(_1728502)), c_List_Olists(_1728502, _1728504))))], (46801 ^ _782652) ^ [_1728541, _1728543, _1728545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1728541, tc_HOL_Obool)), _1728543), _1728545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1728541), tc_HOL_Obool)), c_List_Olists(_1728541, _1728543)), c_List_Olists(_1728541, _1728545))))], (46807 ^ _782652) ^ [_1728697, _1728699, _1728701, _1728703] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728697)), hAPP(hAPP(c_List_Oappend(_1728697), _1728699), _1728701)), c_List_Olists(_1728697, _1728703))), 46810 ^ _782652 : [(46811 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728697)), _1728699), c_List_Olists(_1728697, _1728703))))], (46813 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728697)), _1728701), c_List_Olists(_1728697, _1728703))))]]], (46815 ^ _782652) ^ [_1728888, _1728890, _1728892, _1728894] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728888)), hAPP(hAPP(c_List_Oappend(_1728888), _1728890), _1728892)), c_List_Olists(_1728888, _1728894)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728888)), _1728890), c_List_Olists(_1728888, _1728894))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728888)), _1728892), c_List_Olists(_1728888, _1728894)))], (46825 ^ _782652) ^ [_1729115] : [-(c_List_Olists(_1729115, c_Orderings_Otop__class_Otop(tc_fun(_1729115, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1729115), tc_HOL_Obool)))], (46827 ^ _782652) ^ [_1729153, _1729155, _1729157] : [c_Equiv__Relations_Oequiv(_1729153, _1729155, _1729157), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1729153), c_List_Olists(_1729153, _1729155), c_List_Olistrel(_1729153, _1729157)))], (46833 ^ _782652) ^ [_1729252, _1729254, _1729256] : [c_Relation_Orefl__on(_1729252, _1729254, _1729256), -(c_Relation_Orefl__on(tc_List_Olist(_1729252), c_List_Olists(_1729252, _1729254), c_List_Olistrel(_1729252, _1729256)))], (46839 ^ _782652) ^ [_1729372, _1729374, _1729376, _1729378] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729372)), hAPP(hAPP(c_List_Olist_OCons(_1729372), _1729374), _1729376)), c_List_Olists(_1729372, _1729378))), 46842 ^ _782652 : [(46843 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729372), _1729374), _1729378)))], (46845 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729372)), _1729376), c_List_Olists(_1729372, _1729378))))]]], (46847 ^ _782652) ^ [_1729553, _1729555, _1729557, _1729559] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729553)), hAPP(hAPP(c_List_Olist_OCons(_1729553), _1729555), _1729557)), c_List_Olists(_1729553, _1729559)))), hBOOL(hAPP(hAPP(c_member(_1729553), _1729555), _1729559)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729553)), _1729557), c_List_Olists(_1729553, _1729559)))], (46867 ^ _782652) ^ [_1730015, _1730017, _1730019] : [46869 ^ _782652 : [(46870 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730015), 46868 ^ [_1730015, _1730017, _1730019]), hAPP(c_List_Oset(_1730015), _1730017))))], (46872 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1730015), 46868 ^ [_1730015, _1730017, _1730019]), _1730019))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730015)), _1730017), c_List_Olists(_1730015, _1730019))))], (46857 ^ _782652) ^ [_1729788, _1729790, _1729792] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729788)), _1729790), c_List_Olists(_1729788, _1729792))), 46860 ^ _782652 : [(46861 ^ _782652) ^ [_1729896] : [hBOOL(hAPP(hAPP(c_member(_1729788), _1729896), hAPP(c_List_Oset(_1729788), _1729790))), -(hBOOL(hAPP(hAPP(c_member(_1729788), _1729896), _1729792)))]]], (46876 ^ _782652) ^ [_1730235, _1730237] : [-(c_List_Olists(_1730235, _1730237) = hAPP(c_Set_OCollect(tc_List_Olist(_1730235)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1730235), tc_fun(_1730235, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1730235, tc_HOL_Obool), tc_fun(tc_fun(_1730235, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1730235)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1730235, tc_HOL_Obool))), c_List_Oset(_1730235))), _1730237)))], (46878 ^ _782652) ^ [_1730313] : [-(c_List_Olists(_1730313, c_Orderings_Obot__class_Obot(tc_fun(_1730313, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1730313)), c_List_Olist_ONil(_1730313)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1730313), tc_HOL_Obool))))], (46880 ^ _782652) ^ [_1730363, _1730365, _1730367] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730363)), _1730365), c_List_Olists(_1730363, c_Wellfounded_Oacc(_1730363, _1730367)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730363)), _1730365), c_Wellfounded_Oacc(tc_List_Olist(_1730363), c_List_Olistrel1(_1730363, _1730367)))))], (46886 ^ _782652) ^ [_1730506, _1730508, _1730510, _1730512] : [46887 ^ _782652 : [(46888 ^ _782652) ^ [_1730603, _1730605] : [_1730506 = hAPP(hAPP(c_List_Olist_OCons(_1730508), _1730605), _1730603)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730508), tc_List_Olist(_1730508))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730508), tc_List_Olist(_1730508)), _1730510), hAPP(hAPP(c_List_Oappend(_1730508), _1730510), _1730506))), c_List_Olexord(_1730508, _1730512))))], (46892 ^ _782652) ^ [_1730720, _1730722, _1730724] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730720), tc_List_Olist(_1730720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730720), tc_List_Olist(_1730720)), c_List_Olist_ONil(_1730720)), _1730722)), c_List_Olexord(_1730720, _1730724))), -(_1730722 = hAPP(hAPP(c_List_Olist_OCons(_1730720), 46895 ^ [_1730720, _1730722, _1730724]), 46896 ^ [_1730720, _1730722, _1730724]))], (46900 ^ _782652) ^ [_1730903, _1730905, _1730907] : [46901 ^ _782652 : [(46902 ^ _782652) ^ [_1730992, _1730994] : [_1730905 = hAPP(hAPP(c_List_Olist_OCons(_1730903), _1730994), _1730992)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730903), tc_List_Olist(_1730903))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730903), tc_List_Olist(_1730903)), c_List_Olist_ONil(_1730903)), _1730905)), c_List_Olexord(_1730903, _1730907))))], (46906 ^ _782652) ^ [_1731086, _1731088, _1731090, _1731092] : [-(_1731086 = c_List_Olist_ONil(_1731088)), 46909 ^ _782652 : [(46910 ^ _782652) ^ [] : [_1731090 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731088)), _1731086)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1731088, hAPP(hAPP(c_List_Olist__update(_1731088, _1731086), _1731090), _1731092)) = _1731092)], (46916 ^ _782652) ^ [] : [-(_1731090 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731088)), _1731086)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1731088, hAPP(hAPP(c_List_Olist__update(_1731088, _1731086), _1731090), _1731092)) = c_List_Olast(_1731088, _1731086))]]], (46922 ^ _782652) ^ [_1731376, _1731378, _1731380, _1731382, _1731384] : [class_Groups_Omonoid__add(_1731376), class_Groups_Oordered__ab__semigroup__add(_1731376), 46932 ^ _782652 : [(46933 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1731378), 46931 ^ [_1731376, _1731378, _1731380, _1731382, _1731384]), hAPP(c_List_Oset(_1731378), _1731380))))], (46935 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1731376), hAPP(_1731382, 46931 ^ [_1731376, _1731378, _1731380, _1731382, _1731384])), hAPP(_1731384, 46931 ^ [_1731376, _1731378, _1731380, _1731382, _1731384])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1731376), hAPP(c_List_Omonoid__add__class_Olistsum(_1731376), hAPP(hAPP(c_List_Omap(_1731378, _1731376), _1731382), _1731380))), hAPP(c_List_Omonoid__add__class_Olistsum(_1731376), hAPP(hAPP(c_List_Omap(_1731378, _1731376), _1731384), _1731380)))))], (46939 ^ _782652) ^ [_1731812, _1731814, _1731816] : [_1731812 = c_List_Olist_ONil(_1731814), -(c_List_Olast(_1731814, hAPP(hAPP(c_List_Olist_OCons(_1731814), _1731816), _1731812)) = _1731816)], (46945 ^ _782652) ^ [_1731911, _1731913, _1731915] : [-(_1731911 = c_List_Olist_ONil(_1731913)), -(c_List_Olast(_1731913, hAPP(hAPP(c_List_Olist_OCons(_1731913), _1731915), _1731911)) = c_List_Olast(_1731913, _1731911))], (46951 ^ _782652) ^ [_1731963, _1731965, _1731967] : [-(_1731963 = c_List_Olist_ONil(_1731965)), -(c_List_Olast(_1731965, hAPP(hAPP(c_List_Olist_OCons(_1731965), _1731967), _1731963)) = c_List_Olast(_1731965, _1731963))], (46957 ^ _782652) ^ [_1732017, _1732019, _1732021] : [_1732017 = c_List_Olist_ONil(_1732019), -(c_List_Olast(_1732019, hAPP(hAPP(c_List_Olist_OCons(_1732019), _1732021), _1732017)) = _1732021)], (46963 ^ _782652) ^ [_1732134, _1732136, _1732138] : [_1732134 = c_List_Olist_ONil(_1732136), -(c_List_Olast(_1732136, hAPP(hAPP(c_List_Oappend(_1732136), _1732138), _1732134)) = c_List_Olast(_1732136, _1732138))], (46969 ^ _782652) ^ [_1732239, _1732241, _1732243] : [-(_1732239 = c_List_Olist_ONil(_1732241)), -(c_List_Olast(_1732241, hAPP(hAPP(c_List_Oappend(_1732241), _1732243), _1732239)) = c_List_Olast(_1732241, _1732239))], (46975 ^ _782652) ^ [_1732291, _1732293, _1732295] : [-(_1732291 = c_List_Olist_ONil(_1732293)), -(c_List_Olast(_1732293, hAPP(hAPP(c_List_Oappend(_1732293), _1732295), _1732291)) = c_List_Olast(_1732293, _1732291))], (46981 ^ _782652) ^ [_1732345, _1732347, _1732349] : [_1732345 = c_List_Olist_ONil(_1732347), -(c_List_Olast(_1732347, hAPP(hAPP(c_List_Oappend(_1732347), _1732349), _1732345)) = c_List_Olast(_1732347, _1732349))], (46987 ^ _782652) ^ [_1732452, _1732454, _1732456, _1732458] : [-(_1732452 = c_List_Olist_ONil(_1732454)), -(c_List_Olast(_1732456, hAPP(hAPP(c_List_Omap(_1732454, _1732456), _1732458), _1732452)) = hAPP(_1732458, c_List_Olast(_1732454, _1732452)))], (46993 ^ _782652) ^ [_1732508, _1732510] : [-(_1732508 = c_List_Olist_ONil(_1732510)), -(hBOOL(hAPP(hAPP(c_member(_1732510), c_List_Olast(_1732510, _1732508)), hAPP(c_List_Oset(_1732510), _1732508))))], (46999 ^ _782652) ^ [_1732561, _1732563, _1732565] : [-(c_List_Olast(_1732561, hAPP(hAPP(c_List_Oappend(_1732561), _1732563), hAPP(hAPP(c_List_Olist_OCons(_1732561), _1732565), c_List_Olist_ONil(_1732561)))) = _1732565)], (47001 ^ _782652) ^ [_1732609, _1732611, _1732613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732609), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732611)), _1732613))), -(c_List_Olast(_1732611, hAPP(hAPP(c_List_Odrop(_1732611), _1732609), _1732613)) = c_List_Olast(_1732611, _1732613))], (47007 ^ _782652) ^ [_1732736, _1732738] : [-(_1732736 = c_List_Olist_ONil(_1732738)), -(c_List_Olast(_1732738, _1732736) = hAPP(hAPP(c_List_Onth(_1732738), _1732736), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732738)), _1732736)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (47013 ^ _782652) ^ [_1732798, _1732800] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1732798), _1732800) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1732798, 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)))), _1732800))))], (47015 ^ _782652) ^ [_1732835, _1732837, _1732839] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1732835, _1732835)), hAPP(hAPP(c_Product__Type_OPair(_1732835, _1732835), 47016 ^ [_1732835, _1732837, _1732839]), 47016 ^ [_1732835, _1732837, _1732839])), _1732837))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1732835), tc_List_Olist(_1732835))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1732835), tc_List_Olist(_1732835)), _1732839), _1732839)), c_List_Olexord(_1732835, _1732837)))], (47022 ^ _782652) ^ [_1733010, _1733012, _1733014, _1733016] : [47025 ^ _782652 : [(47026 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1733010, _1733010)), hAPP(hAPP(c_Product__Type_OPair(_1733010, _1733010), 47023 ^ [_1733010, _1733012, _1733014, _1733016]), 47024 ^ [_1733010, _1733012, _1733014, _1733016])), _1733012))], (47028 ^ _782652) ^ [] : [47023 ^ [_1733010, _1733012, _1733014, _1733016] = 47024 ^ [_1733010, _1733012, _1733014, _1733016]], (47030 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1733010, _1733010)), hAPP(hAPP(c_Product__Type_OPair(_1733010, _1733010), 47024 ^ [_1733010, _1733012, _1733014, _1733016]), 47023 ^ [_1733010, _1733012, _1733014, _1733016])), _1733012))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733010), tc_List_Olist(_1733010))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733010), tc_List_Olist(_1733010)), _1733014), _1733016)), c_List_Olexord(_1733010, _1733012)))), -(_1733014 = _1733016), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733010), tc_List_Olist(_1733010))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733010), tc_List_Olist(_1733010)), _1733016), _1733014)), c_List_Olexord(_1733010, _1733012))))], (47042 ^ _782652) ^ [_1733575, _1733577, _1733579] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1733575)), _1733577), c_List_Olists(_1733575, _1733579))), -(_1733577 = c_List_Olist_ONil(_1733575)), 47051 ^ _782652 : [(47052 ^ _782652) ^ [] : [-(_1733577 = hAPP(hAPP(c_List_Olist_OCons(_1733575), 47049 ^ [_1733575, _1733577, _1733579]), 47050 ^ [_1733575, _1733577, _1733579]))], (47054 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733575), 47049 ^ [_1733575, _1733577, _1733579]), _1733579)))], (47056 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1733575)), 47050 ^ [_1733575, _1733577, _1733579]), c_List_Olists(_1733575, _1733579))))]]], (47058 ^ _782652) ^ [_1733858, _1733860, _1733862] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1733858)), _1733860), c_List_Olists(_1733858, _1733862)))), 47059 ^ _782652 : [(47060 ^ _782652) ^ [] : [_1733860 = c_List_Olist_ONil(_1733858)], (47062 ^ _782652) ^ [_1733986, _1733988] : [_1733860 = hAPP(hAPP(c_List_Olist_OCons(_1733858), _1733988), _1733986), hBOOL(hAPP(hAPP(c_member(_1733858), _1733988), _1733862)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1733858)), _1733986), c_List_Olists(_1733858, _1733862)))]]], (47074 ^ _782652) ^ [_1734224, _1734226, _1734228, _1734230] : [47076 ^ _782652 : [(47077 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734224), 47075 ^ [_1734224, _1734226, _1734228, _1734230]), hAPP(c_List_Oset(_1734224), _1734226))))], (47079 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1734228, 47075 ^ [_1734224, _1734226, _1734228, _1734230])), hAPP(_1734230, 47075 ^ [_1734224, _1734226, _1734228, _1734230])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1734224, _1734228, _1734226)), c_List_Olist_Olist__size(_1734224, _1734230, _1734226))))], (47083 ^ _782652) ^ [_1734474, _1734476, _1734478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1734474), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734476)), _1734478))), -(c_List_Obutlast(_1734476, hAPP(hAPP(c_List_Otake(_1734476), _1734474), _1734478)) = hAPP(hAPP(c_List_Otake(_1734476), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1734474), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1734478))], (47089 ^ _782652) ^ [_1734627, _1734629, _1734631, _1734633] : [-(hAPP(hAPP(c_List_Omap(_1734627, _1734629), _1734631), c_List_Obutlast(_1734627, _1734633)) = c_List_Obutlast(_1734629, hAPP(hAPP(c_List_Omap(_1734627, _1734629), _1734631), _1734633)))], (47091 ^ _782652) ^ [_1734692, _1734694, _1734696] : [_1734692 = c_List_Olist_ONil(_1734694), -(c_List_Obutlast(_1734694, hAPP(hAPP(c_List_Oappend(_1734694), _1734696), _1734692)) = c_List_Obutlast(_1734694, _1734696))], (47097 ^ _782652) ^ [_1734797, _1734799, _1734801] : [-(_1734797 = c_List_Olist_ONil(_1734799)), -(c_List_Obutlast(_1734799, hAPP(hAPP(c_List_Oappend(_1734799), _1734801), _1734797)) = hAPP(hAPP(c_List_Oappend(_1734799), _1734801), c_List_Obutlast(_1734799, _1734797)))], (47103 ^ _782652) ^ [_1734861] : [-(c_List_Obutlast(_1734861, c_List_Olist_ONil(_1734861)) = c_List_Olist_ONil(_1734861))], (47105 ^ _782652) ^ [_1734890, _1734892] : [-(_1734890 = c_List_Olist_ONil(_1734892)), hBOOL(hAPP(c_List_Odistinct(_1734892), _1734890)), -(hBOOL(hAPP(c_List_Odistinct(_1734892), c_List_Obutlast(_1734892, _1734890))))], (47115 ^ _782652) ^ [_1735041, _1735043, _1735045] : [hBOOL(hAPP(hAPP(c_member(_1735041), _1735043), hAPP(c_List_Oset(_1735041), c_List_Obutlast(_1735041, _1735045)))), -(hBOOL(hAPP(hAPP(c_member(_1735041), _1735043), hAPP(c_List_Oset(_1735041), _1735045))))], (47121 ^ _782652) ^ [_1735186, _1735188, _1735190] : [_1735186 = c_List_Olist_ONil(_1735188), -(c_List_Obutlast(_1735188, hAPP(hAPP(c_List_Olist_OCons(_1735188), _1735190), _1735186)) = c_List_Olist_ONil(_1735188))], (47127 ^ _782652) ^ [_1735289, _1735291, _1735293] : [-(_1735289 = c_List_Olist_ONil(_1735291)), -(c_List_Obutlast(_1735291, hAPP(hAPP(c_List_Olist_OCons(_1735291), _1735293), _1735289)) = hAPP(hAPP(c_List_Olist_OCons(_1735291), _1735293), c_List_Obutlast(_1735291, _1735289)))], (47133 ^ _782652) ^ [_1735353, _1735355, _1735357] : [-(c_List_Obutlast(_1735353, hAPP(hAPP(c_List_Odrop(_1735353), _1735355), _1735357)) = hAPP(hAPP(c_List_Odrop(_1735353), _1735355), c_List_Obutlast(_1735353, _1735357)))], (47135 ^ _782652) ^ [_1735402, _1735404, _1735406] : [-(hAPP(hAPP(c_List_Odrop(_1735402), _1735404), c_List_Obutlast(_1735402, _1735406)) = c_List_Obutlast(_1735402, hAPP(hAPP(c_List_Odrop(_1735402), _1735404), _1735406)))], (47137 ^ _782652) ^ [_1735451, _1735453, _1735455, _1735457] : [47138 ^ _782652 : [(47139 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1735451), _1735453), hAPP(c_List_Oset(_1735451), c_List_Obutlast(_1735451, _1735455))))], (47141 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1735451), _1735453), hAPP(c_List_Oset(_1735451), c_List_Obutlast(_1735451, _1735457))))]], -(hBOOL(hAPP(hAPP(c_member(_1735451), _1735453), hAPP(c_List_Oset(_1735451), c_List_Obutlast(_1735451, hAPP(hAPP(c_List_Oappend(_1735451), _1735455), _1735457))))))], (47145 ^ _782652) ^ [_1735676, _1735678, _1735680] : [-(c_List_Obutlast(_1735676, hAPP(hAPP(c_List_Oappend(_1735676), _1735678), hAPP(hAPP(c_List_Olist_OCons(_1735676), _1735680), c_List_Olist_ONil(_1735676)))) = _1735678)], (47147 ^ _782652) ^ [_1735724, _1735726, _1735728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735724), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735726)), _1735728))), -(hAPP(hAPP(c_List_Otake(_1735726), _1735724), c_List_Obutlast(_1735726, _1735728)) = hAPP(hAPP(c_List_Otake(_1735726), _1735724), _1735728))], (47153 ^ _782652) ^ [_1735865, _1735867] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735865)), c_List_Obutlast(_1735865, _1735867)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735865)), _1735867)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47155 ^ _782652) ^ [_1735913, _1735915] : [-(c_List_Obutlast(_1735913, _1735915) = hAPP(hAPP(c_List_Otake(_1735913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735913)), _1735915)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1735915))], (47157 ^ _782652) ^ [_1735977, _1735979, _1735981, _1735983] : [_1735977 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735979)), _1735981)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1735979, hAPP(hAPP(c_List_Olist__update(_1735979, _1735981), _1735977), _1735983)) = c_List_Obutlast(_1735979, _1735981))], (47163 ^ _782652) ^ [_1736108, _1736110, _1736112, _1736114] : [-(_1736108 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736110)), _1736112)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1736110, hAPP(hAPP(c_List_Olist__update(_1736110, _1736112), _1736108), _1736114)) = hAPP(hAPP(c_List_Olist__update(_1736110, c_List_Obutlast(_1736110, _1736112)), _1736108), _1736114))], (47169 ^ _782652) ^ [_1736208, _1736210, _1736212, _1736214] : [hAPP(hAPP(c_List_Oappend(_1736208), _1736210), hAPP(hAPP(c_List_Olist_OCons(_1736208), _1736212), c_List_Olist_ONil(_1736208))) = _1736214, 47172 ^ _782652 : [(47173 ^ _782652) ^ [] : [_1736214 = c_List_Olist_ONil(_1736208)], (47175 ^ _782652) ^ [] : [-(c_List_Obutlast(_1736208, _1736214) = _1736210)], (47177 ^ _782652) ^ [] : [-(c_List_Olast(_1736208, _1736214) = _1736212)]]], (47179 ^ _782652) ^ [_1736397, _1736399, _1736401, _1736403] : [-(hAPP(hAPP(c_List_Oappend(_1736397), _1736399), hAPP(hAPP(c_List_Olist_OCons(_1736397), _1736401), c_List_Olist_ONil(_1736397))) = _1736403), -(_1736403 = c_List_Olist_ONil(_1736397)), c_List_Obutlast(_1736397, _1736403) = _1736399, c_List_Olast(_1736397, _1736403) = _1736401], (47193 ^ _782652) ^ [_1736643, _1736645] : [-(_1736643 = c_List_Olist_ONil(_1736645)), -(hAPP(hAPP(c_List_Oappend(_1736645), c_List_Obutlast(_1736645, _1736643)), hAPP(hAPP(c_List_Olist_OCons(_1736645), c_List_Olast(_1736645, _1736643)), c_List_Olist_ONil(_1736645))) = _1736643)], (47199 ^ _782652) ^ [_1736705, _1736707, _1736709, _1736711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736705), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736707)), _1736709))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736705), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736707)), _1736711))), 47209 ^ _782652 : [(47210 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47208 ^ [_1736705, _1736707, _1736709, _1736711]), _1736705)))], (47212 ^ _782652) ^ [] : [hAPP(hAPP(c_List_Onth(_1736707), _1736709), 47208 ^ [_1736705, _1736707, _1736709, _1736711]) = hAPP(hAPP(c_List_Onth(_1736707), _1736711), 47208 ^ [_1736705, _1736707, _1736709, _1736711])]], -(hAPP(hAPP(c_List_Otake(_1736707), _1736705), _1736709) = hAPP(hAPP(c_List_Otake(_1736707), _1736705), _1736711))], (47216 ^ _782652) ^ [_1737122, _1737124, _1737126, _1737128] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737122)), _1737124))), c_List_Ofoldr(tc_List_Olist(_1737126), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1737126)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1737126))), _1737128, 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(_1737122)), _1737124)), c_List_Ofoldr(tc_List_Olist(_1737126), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1737126)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1737126), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1737126)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1737126)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1737126), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1737126)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1737126), tc_List_Olist(_1737126), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1737126)))), _1737128), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (47218 ^ _782652) ^ [_1737291, _1737293, _1737295] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1737291, tc_HOL_Obool)), hAPP(c_List_Oset(_1737291), hAPP(c_List_Ofilter(_1737291, _1737293), _1737295))), hAPP(c_List_Oset(_1737291), _1737295))))], (47220 ^ _782652) ^ [_1737344, _1737346, _1737348] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737344)), hAPP(c_List_Ofilter(_1737344, _1737346), _1737348))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737344)), _1737348))))], (47222 ^ _782652) ^ [_1737411, _1737413, _1737415, _1737417] : [hBOOL(hAPP(_1737411, _1737413)), -(hAPP(c_List_Ofilter(_1737415, _1737411), hAPP(hAPP(c_List_Olist_OCons(_1737415), _1737413), _1737417)) = hAPP(hAPP(c_List_Olist_OCons(_1737415), _1737413), hAPP(c_List_Ofilter(_1737415, _1737411), _1737417)))], (47228 ^ _782652) ^ [_1737546, _1737548, _1737550, _1737552] : [-(hBOOL(hAPP(_1737546, _1737548))), -(hAPP(c_List_Ofilter(_1737550, _1737546), hAPP(hAPP(c_List_Olist_OCons(_1737550), _1737548), _1737552)) = hAPP(c_List_Ofilter(_1737550, _1737546), _1737552))], (47234 ^ _782652) ^ [_1737610, _1737612, _1737614] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737610)), hAPP(c_List_Ofilter(_1737610, _1737612), _1737614))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737610)), hAPP(c_List_Ofilter(_1737610, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1737610), c_fNot), _1737612)), _1737614))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737610)), _1737614))], (47236 ^ _782652) ^ [_1737686, _1737688, _1737690, _1737692] : [-(hAPP(c_List_Ofilter(_1737686, _1737688), hAPP(c_List_Ofilter(_1737686, _1737690), _1737692)) = hAPP(c_List_Ofilter(_1737686, hAPP(hAPP(c_COMBS(_1737686, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1737686), c_fconj), _1737690)), _1737688)), _1737692))], (47238 ^ _782652) ^ [_1737753, _1737755, _1737757, _1737759] : [-(hAPP(c_List_Ofilter(_1737753, _1737755), c_List_Oremove1(_1737753, _1737757, _1737759)) = c_List_Oremove1(_1737753, _1737757, hAPP(c_List_Ofilter(_1737753, _1737755), _1737759)))], (47240 ^ _782652) ^ [_1737798, _1737800, _1737802, _1737804] : [-(hBOOL(hAPP(_1737798, _1737800))), -(c_List_Oremove1(_1737802, _1737800, hAPP(c_List_Ofilter(_1737802, _1737798), _1737804)) = hAPP(c_List_Ofilter(_1737802, _1737798), _1737804))], (47246 ^ _782652) ^ [_1737856, _1737858, _1737860] : [hBOOL(hAPP(c_List_Odistinct(_1737856), _1737858)), -(hBOOL(hAPP(c_List_Odistinct(_1737856), hAPP(c_List_Ofilter(_1737856, _1737860), _1737858))))], (47252 ^ _782652) ^ [_1737963, _1737965, _1737967, _1737969, _1737971, _1737973] : [class_Orderings_Olinorder(_1737963), -(hBOOL(hAPP(_1737965, _1737967))), -(hAPP(c_List_Ofilter(_1737969, _1737965), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1737969, _1737963, _1737971), _1737967), _1737973)) = hAPP(c_List_Ofilter(_1737969, _1737965), _1737973))], (47272 ^ _782652) ^ [_1738327, _1738329, _1738331] : [47274 ^ _782652 : [(47275 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738327), 47273 ^ [_1738327, _1738329, _1738331]), hAPP(c_List_Oset(_1738327), _1738331))))], (47277 ^ _782652) ^ [] : [hBOOL(hAPP(_1738329, 47273 ^ [_1738327, _1738329, _1738331]))]], -(hAPP(c_List_Ofilter(_1738327, _1738329), _1738331) = _1738331)], (47262 ^ _782652) ^ [_1738127, _1738129, _1738131] : [hAPP(c_List_Ofilter(_1738127, _1738129), _1738131) = _1738131, 47265 ^ _782652 : [(47266 ^ _782652) ^ [_1738218] : [hBOOL(hAPP(hAPP(c_member(_1738127), _1738218), hAPP(c_List_Oset(_1738127), _1738131))), -(hBOOL(hAPP(_1738129, _1738218)))]]], (47291 ^ _782652) ^ [_1738742, _1738744, _1738746] : [47293 ^ _782652 : [(47294 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738742), 47292 ^ [_1738742, _1738744, _1738746]), hAPP(c_List_Oset(_1738742), _1738746))))], (47296 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1738744, 47292 ^ [_1738742, _1738744, _1738746])))]], -(hAPP(c_List_Ofilter(_1738742, _1738744), _1738746) = c_List_Olist_ONil(_1738742))], (47281 ^ _782652) ^ [_1738537, _1738539, _1738541] : [hAPP(c_List_Ofilter(_1738537, _1738539), _1738541) = c_List_Olist_ONil(_1738537), 47284 ^ _782652 : [(47285 ^ _782652) ^ [_1738634] : [hBOOL(hAPP(hAPP(c_member(_1738537), _1738634), hAPP(c_List_Oset(_1738537), _1738541))), hBOOL(hAPP(_1738539, _1738634))]]], (47300 ^ _782652) ^ [_1738859, _1738861] : [-(hAPP(c_List_Ofilter(_1738859, _1738861), c_List_Olist_ONil(_1738859)) = c_List_Olist_ONil(_1738859))], (47302 ^ _782652) ^ [_1738894, _1738896, _1738898, _1738900] : [-(hAPP(c_List_Ofilter(_1738894, _1738896), hAPP(hAPP(c_List_Oappend(_1738894), _1738898), _1738900)) = hAPP(hAPP(c_List_Oappend(_1738894), hAPP(c_List_Ofilter(_1738894, _1738896), _1738898)), hAPP(c_List_Ofilter(_1738894, _1738896), _1738900)))], (47304 ^ _782652) ^ [_1738957, _1738959, _1738961, _1738963, _1738965] : [-(hAPP(c_List_Ofilter(_1738957, _1738959), hAPP(hAPP(c_List_Omap(_1738961, _1738957), _1738963), _1738965)) = hAPP(hAPP(c_List_Omap(_1738961, _1738957), _1738963), hAPP(c_List_Ofilter(_1738961, hAPP(c_Fun_Ocomp(_1738957, tc_HOL_Obool, _1738961, _1738959), _1738963)), _1738965)))], (47306 ^ _782652) ^ [_1739026, _1739028, _1739030] : [-(hAPP(c_List_Oset(_1739026), hAPP(c_List_Ofilter(_1739026, _1739028), _1739030)) = hAPP(c_Set_OCollect(_1739026), hAPP(hAPP(c_COMBS(_1739026, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1739026), c_fconj), hAPP(hAPP(c_COMBC(_1739026, tc_fun(_1739026, tc_HOL_Obool), tc_HOL_Obool), c_member(_1739026)), hAPP(c_List_Oset(_1739026), _1739030)))), _1739028)))], (47308 ^ _782652) ^ [_1739109, _1739111, _1739113, _1739115, _1739117] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739109)), hAPP(c_List_Ofilter(_1739109, _1739111), hAPP(hAPP(c_List_Omap(_1739113, _1739109), _1739115), _1739117))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739113)), hAPP(c_List_Ofilter(_1739113, hAPP(c_Fun_Ocomp(_1739109, tc_HOL_Obool, _1739113, _1739111), _1739115)), _1739117)))], (47310 ^ _782652) ^ [_1739183, _1739185, _1739187, _1739189] : [hBOOL(hAPP(hAPP(c_member(_1739183), _1739185), hAPP(c_List_Oset(_1739183), _1739187))), -(hBOOL(hAPP(_1739189, _1739185))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739183)), hAPP(c_List_Ofilter(_1739183, _1739189), _1739187))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739183)), _1739187))))], (47320 ^ _782652) ^ [_1739357, _1739359, _1739361] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1739357, tc_HOL_Obool)), hAPP(c_List_Oset(_1739357), _1739359)), hAPP(hAPP(c_Set_Oinsert(_1739357), _1739361), c_Orderings_Obot__class_Obot(tc_fun(_1739357, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1739357), hAPP(c_List_Ofilter(_1739357, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1739357), c_fNot), hAPP(hAPP(c_COMBC(_1739357, _1739357, tc_HOL_Obool), c_fequal), _1739361))), _1739359)))], (47322 ^ _782652) ^ [_1739444, _1739446, _1739448] : [hBOOL(hAPP(c_List_Odistinct(_1739444), _1739446)), -(hAPP(c_List_Ofilter(_1739444, hAPP(hAPP(c_COMBC(_1739444, tc_fun(_1739444, tc_HOL_Obool), tc_HOL_Obool), c_member(_1739444)), hAPP(c_List_Oset(_1739444), c_List_Osublist(_1739444, _1739446, _1739448)))), _1739446) = c_List_Osublist(_1739444, _1739446, _1739448))], (47328 ^ _782652) ^ [_1739599, _1739601, _1739603] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739599)), hAPP(c_List_Ofilter(_1739599, _1739601), _1739603)) = 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(_1739599)), _1739603)))), hAPP(hAPP(c_COMBB(_1739599, tc_HOL_Obool, tc_Nat_Onat), _1739601), hAPP(c_List_Onth(_1739599), _1739603))))))], (47330 ^ _782652) ^ [_1739679, _1739681, _1739683, _1739685] : [-(c_List_Omap__filter(_1739679, _1739681, _1739683, _1739685) = hAPP(hAPP(c_List_Omap(_1739679, _1739681), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1739681), _1739681, _1739679, c_Option_Othe(_1739681)), _1739683)), hAPP(c_List_Ofilter(_1739679, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1739679), c_fNot), hAPP(hAPP(c_COMBC(_1739679, tc_Option_Ooption(_1739681), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1739681), tc_fun(tc_Option_Ooption(_1739681), tc_HOL_Obool), _1739679), c_fequal), _1739683)), c_Option_Ooption_ONone(_1739681)))), _1739685)))], (47332 ^ _782652) ^ [_1739781, _1739783] : [-(c_List_Ofoldr(tc_List_Olist(_1739781), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1739781)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1739781))), c_List_Otranspose(_1739781, _1739783), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1739781))), hAPP(c_List_Ofilter(tc_List_Olist(_1739781), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1739781)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1739781), tc_List_Olist(_1739781), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1739781)))), _1739783)))], (47334 ^ _782652) ^ [_1739878, _1739880, _1739882, _1739884] : [-(c_List_Otranspose(_1739878, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1739880), tc_List_Olist(_1739878)), hAPP(c_List_Omap(_1739880, _1739878), _1739882)), _1739884)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1739880), tc_List_Olist(_1739878)), hAPP(c_List_Omap(_1739880, _1739878), _1739882)), c_List_Otranspose(_1739880, _1739884)))], (47336 ^ _782652) ^ [_1739951, _1739953, _1739955] : [-(c_List_Omap__filter(_1739951, _1739953, _1739955, c_List_Olist_ONil(_1739951)) = c_List_Olist_ONil(_1739953))], (47338 ^ _782652) ^ [_1739987] : [-(c_List_Otranspose(_1739987, c_List_Olist_ONil(tc_List_Olist(_1739987))) = c_List_Olist_ONil(tc_List_Olist(_1739987)))], (47350 ^ _782652) ^ [_1740246, _1740248] : [47352 ^ _782652 : [(47353 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1740246)), 47351 ^ [_1740246, _1740248]), hAPP(c_List_Oset(tc_List_Olist(_1740246)), _1740248))))], (47355 ^ _782652) ^ [] : [47351 ^ [_1740246, _1740248] = c_List_Olist_ONil(_1740246)]], -(c_List_Otranspose(_1740246, _1740248) = c_List_Olist_ONil(tc_List_Olist(_1740246)))], (47340 ^ _782652) ^ [_1740036, _1740038] : [c_List_Otranspose(_1740036, _1740038) = c_List_Olist_ONil(tc_List_Olist(_1740036)), 47343 ^ _782652 : [(47344 ^ _782652) ^ [_1740131] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1740036)), _1740131), hAPP(c_List_Oset(tc_List_Olist(_1740036)), _1740038))), -(_1740131 = c_List_Olist_ONil(_1740036))]]], (47359 ^ _782652) ^ [_1740441, _1740443] : [-(c_List_Otranspose(_1740441, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1740441)), c_List_Olist_ONil(_1740441)), _1740443)) = c_List_Otranspose(_1740441, _1740443))], (47361 ^ _782652) ^ [_1740484, _1740486, _1740488, _1740490, _1740492, _1740494] : [hAPP(hAPP(c_Map_Omap__of(_1740484, _1740486), _1740488), _1740490) = hAPP(c_Option_Ooption_OSome(_1740486), _1740492), hBOOL(hAPP(hAPP(_1740494, _1740490), _1740492)), -(hAPP(hAPP(c_Map_Omap__of(_1740484, _1740486), hAPP(c_List_Ofilter(tc_prod(_1740484, _1740486), hAPP(c_Product__Type_Oprod_Oprod__case(_1740484, _1740486, tc_HOL_Obool), _1740494)), _1740488)), _1740490) = hAPP(c_Option_Ooption_OSome(_1740486), _1740492))], (47371 ^ _782652) ^ [_1740727, _1740729, _1740731, _1740733, _1740735] : [-(c_List_Omap__filter(_1740727, _1740729, _1740731, hAPP(hAPP(c_List_Olist_OCons(_1740727), _1740733), _1740735)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1740729), _1740729, c_List_Omap__filter(_1740727, _1740729, _1740731, _1740735), hAPP(hAPP(c_COMBC(_1740729, tc_List_Olist(_1740729), tc_List_Olist(_1740729)), c_List_Olist_OCons(_1740729)), c_List_Omap__filter(_1740727, _1740729, _1740731, _1740735))), hAPP(_1740731, _1740733)))], (47373 ^ _782652) ^ [_1740810, _1740812, _1740814, _1740816] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1740810, tc_Nat_Onat), _1740810), c_Product__Type_Ofst(_1740810, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1740810, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1740810, tc_Nat_Onat)), _1740812), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1740810, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1740810, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1740810, tc_Nat_Onat), _1740814), _1740816))) = hAPP(hAPP(c_List_Omap(tc_prod(_1740810, tc_Nat_Onat), _1740810), c_Product__Type_Ofst(_1740810, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1740810, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1740810, tc_Nat_Onat)), _1740812), c_Product__Type_Osnd(_1740810, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1740810, tc_Nat_Onat), _1740814), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1740816)))))], (47375 ^ _782652) ^ [_1740953, _1740955] : [-(c_Random_Opick(_1740953, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1740953), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1740953, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1740953, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1740953)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1740955)) = c_Random_Opick(_1740953, _1740955))], (47377 ^ _782652) ^ [_1741016, _1741018] : [-(c_Random_Oselect__weight(_1741016, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1741016), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1741016, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1741016, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1741016)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1741018)) = c_Random_Oselect__weight(_1741016, _1741018))], (47379 ^ _782652) ^ [_1741079, _1741081, _1741083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741079), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1741081))), c_List_Otranspose(_1741081, _1741083)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1741081)), c_List_Otranspose(_1741081, _1741083)), _1741079) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1741081), _1741081), hAPP(hAPP(c_COMBC(tc_List_Olist(_1741081), tc_Nat_Onat, _1741081), c_List_Onth(_1741081)), _1741079)), hAPP(c_List_Ofilter(tc_List_Olist(_1741081), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1741081)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741079)), c_Nat_Osize__class_Osize(tc_List_Olist(_1741081)))), _1741083)))], (47385 ^ _782652) ^ [_1741322, _1741324] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1741322))), c_List_Otranspose(_1741322, _1741324)) = c_List_Ofoldr(tc_List_Olist(_1741322), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1741322)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1741322))), _1741324, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (47387 ^ _782652) ^ [_1741383, _1741385, _1741387, _1741389, _1741391] : [-(hAPP(hAPP(c_List_Omap(_1741383, _1741385), _1741387), hAPP(c_List_Ofilter(_1741383, _1741389), _1741391)) = c_List_Omap__filter(_1741383, _1741385, hAPP(hAPP(c_COMBC(_1741383, tc_Option_Ooption(_1741385), tc_Option_Ooption(_1741385)), hAPP(hAPP(c_COMBS(_1741383, tc_Option_Ooption(_1741385), tc_fun(tc_Option_Ooption(_1741385), tc_Option_Ooption(_1741385))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1741385), tc_fun(tc_Option_Ooption(_1741385), tc_Option_Ooption(_1741385))), _1741383), c_If(tc_Option_Ooption(_1741385))), _1741389)), hAPP(hAPP(c_COMBB(_1741385, tc_Option_Ooption(_1741385), _1741383), c_Option_Ooption_OSome(_1741385)), _1741387))), c_Option_Ooption_ONone(_1741385)), _1741391))], (47389 ^ _782652) ^ [_1741509, _1741511, _1741513, _1741515, _1741517] : [class_Orderings_Olinorder(_1741509), hBOOL(hAPP(hAPP(c_member(_1741511), _1741513), hAPP(c_List_Oset(_1741511), _1741515))), c_List_Olinorder__class_Osorted(_1741509, hAPP(hAPP(c_List_Omap(_1741511, _1741509), _1741517), _1741515)), hAPP(c_List_Ohd(_1741511), hAPP(c_List_Ofilter(_1741511, hAPP(hAPP(c_COMBB(_1741509, tc_HOL_Obool, _1741511), hAPP(c_fequal, hAPP(_1741517, _1741513))), _1741517)), _1741515)) = _1741513, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1741511, _1741509, _1741517), _1741513), c_List_Oremove1(_1741511, _1741513, _1741515)) = _1741515)], (47407 ^ _782652) ^ [_1741888, _1741890, _1741892] : [-(c_List_Osublist(_1741888, _1741890, _1741892) = hAPP(hAPP(c_List_Omap(tc_prod(_1741888, tc_Nat_Onat), _1741888), c_Product__Type_Ofst(_1741888, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1741888, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1741888, 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(_1741888, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1741888, tc_Nat_Onat))), _1741892)), hAPP(hAPP(c_List_Ozip(_1741888, tc_Nat_Onat), _1741890), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741888)), _1741890))))))], (47409 ^ _782652) ^ [_1741991] : [class_Orderings_Olinorder(_1741991), -(c_List_Olinorder__class_Osorted(_1741991, c_List_Olist_ONil(_1741991)))], (47415 ^ _782652) ^ [_1742068, _1742070] : [class_Orderings_Olinorder(_1742068), -(c_List_Olinorder__class_Osorted(_1742068, hAPP(hAPP(c_List_Olist_OCons(_1742068), _1742070), c_List_Olist_ONil(_1742068))))], (47421 ^ _782652) ^ [_1742163, _1742165, _1742167] : [class_Orderings_Olinorder(_1742163), -(c_List_Olinorder__class_Osorted(_1742163, hAPP(c_List_Ofilter(_1742163, hAPP(hAPP(c_COMBC(_1742163, _1742163, tc_HOL_Obool), c_fequal), hAPP(_1742165, _1742167))), _1742167)))], (47427 ^ _782652) ^ [_1742278, _1742280, _1742282, _1742284, _1742286] : [class_Orderings_Olinorder(_1742278), -(c_List_Olinorder__class_Osorted(_1742278, hAPP(hAPP(c_List_Omap(_1742280, _1742278), _1742282), hAPP(c_List_Ofilter(_1742280, hAPP(hAPP(c_COMBC(_1742280, _1742278, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1742278, tc_fun(_1742278, tc_HOL_Obool), _1742280), c_fequal), _1742282)), hAPP(_1742284, _1742286))), _1742286))))], (47433 ^ _782652) ^ [_1742441, _1742443, _1742445, _1742447, _1742449] : [class_Orderings_Olinorder(_1742441), c_List_Olinorder__class_Osorted(_1742441, hAPP(hAPP(c_List_Omap(_1742443, _1742441), _1742445), _1742447)), -(c_List_Olinorder__class_Osorted(_1742441, hAPP(hAPP(c_List_Omap(_1742443, _1742441), _1742445), hAPP(c_List_Ofilter(_1742443, _1742449), _1742447))))], (47443 ^ _782652) ^ [_1742628, _1742630] : [class_Orderings_Olinorder(_1742628), -(_1742630 = c_List_Olist_ONil(_1742628)), c_List_Olinorder__class_Osorted(_1742628, _1742630), -(c_List_Olinorder__class_Osorted(_1742628, c_List_Obutlast(_1742628, _1742630)))], (47457 ^ _782652) ^ [_1742820, _1742822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1742820), _1742822)), -(c_List_Oupt(_1742820, hAPP(c_Nat_OSuc, _1742822)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1742820, _1742822)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1742822), c_List_Olist_ONil(tc_Nat_Onat))))], (47463 ^ _782652) ^ [_1742958, _1742960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1742958), _1742960)), -(c_List_Oupt(_1742958, hAPP(c_Nat_OSuc, _1742960)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1742958, _1742960)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1742960), c_List_Olist_ONil(tc_Nat_Onat))))], (47469 ^ _782652) ^ [_1743081, _1743083] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743081), _1743083))), -(c_List_Oupt(_1743081, hAPP(c_Nat_OSuc, _1743083)) = c_List_Olist_ONil(tc_Nat_Onat))], (47475 ^ _782652) ^ [_1743130, _1743132, _1743134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743130), _1743132)), -(c_List_Oupt(_1743130, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743132), _1743134)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1743130, _1743132)), c_List_Oupt(_1743132, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743132), _1743134))))], (47481 ^ _782652) ^ [_1743273, _1743275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743273), _1743275)), -(c_List_Oupt(_1743275, _1743273) = c_List_Olist_ONil(tc_Nat_Onat))], (47497 ^ _782652) ^ [_1743483, _1743485] : [47498 ^ _782652 : [(47499 ^ _782652) ^ [] : [_1743485 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47501 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743485), _1743483))]], -(c_List_Oupt(_1743483, _1743485) = c_List_Olist_ONil(tc_Nat_Onat))], (47487 ^ _782652) ^ [_1743381, _1743383] : [c_List_Oupt(_1743381, _1743383) = c_List_Olist_ONil(tc_Nat_Onat), -(_1743383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743383), _1743381)))], (47505 ^ _782652) ^ [_1743616, _1743618, _1743620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743616), _1743618)), _1743620)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1743618), c_List_Oupt(_1743616, _1743620)) = c_List_Oupt(_1743616, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743616), _1743618)))], (47511 ^ _782652) ^ [_1743753, _1743755, _1743757, _1743759] : [class_Orderings_Olinorder(_1743753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743753), _1743755), _1743757)), c_List_Olinorder__class_Osorted(_1743753, hAPP(hAPP(c_List_Olist_OCons(_1743753), _1743757), _1743759)), -(c_List_Olinorder__class_Osorted(_1743753, hAPP(hAPP(c_List_Olist_OCons(_1743753), _1743755), hAPP(hAPP(c_List_Olist_OCons(_1743753), _1743757), _1743759))))], (47525 ^ _782652) ^ [_1744006, _1744008, _1744010, _1744012] : [class_Orderings_Olinorder(_1744006), 47528 ^ _782652 : [(47529 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1744006, hAPP(hAPP(c_List_Olist_OCons(_1744006), _1744008), hAPP(hAPP(c_List_Olist_OCons(_1744006), _1744010), _1744012))), 47532 ^ _782652 : [(47533 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1744006), _1744008), _1744010)))], (47535 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1744006, hAPP(hAPP(c_List_Olist_OCons(_1744006), _1744010), _1744012)))]]], (47537 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1744006, hAPP(hAPP(c_List_Olist_OCons(_1744006), _1744008), hAPP(hAPP(c_List_Olist_OCons(_1744006), _1744010), _1744012)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1744006), _1744008), _1744010)), c_List_Olinorder__class_Osorted(_1744006, hAPP(hAPP(c_List_Olist_OCons(_1744006), _1744010), _1744012))]]], (47547 ^ _782652) ^ [_1744392, _1744394, _1744396] : [class_Orderings_Olinorder(_1744392), c_List_Olinorder__class_Osorted(_1744392, _1744394), -(c_List_Olinorder__class_Osorted(_1744392, hAPP(hAPP(c_List_Odrop(_1744392), _1744396), _1744394)))], (47557 ^ _782652) ^ [_1744539, _1744541, _1744543] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1744539), c_List_Oupt(_1744541, _1744543)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1744541), _1744539), _1744543))], (47559 ^ _782652) ^ [_1744584, _1744586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744584), _1744586)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1744584, _1744586)) = _1744584)], (47565 ^ _782652) ^ [_1744692, _1744694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744692), _1744694)), -(c_List_Oupt(_1744692, _1744694) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1744692), c_List_Oupt(hAPP(c_Nat_OSuc, _1744692), _1744694)))], (47571 ^ _782652) ^ [_1744803, _1744805] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744803), _1744805))), -(c_List_Oupt(_1744803, _1744805) = c_List_Olist_ONil(tc_Nat_Onat))], (47577 ^ _782652) ^ [_1744849, _1744851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744849), _1744851)), -(c_List_Oupt(_1744849, _1744851) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1744849), c_List_Oupt(hAPP(c_Nat_OSuc, _1744849), _1744851)))], (47583 ^ _782652) ^ [_1744966, _1744968, _1744970] : [class_Orderings_Olinorder(_1744966), c_List_Olinorder__class_Osorted(_1744966, _1744968), -(c_List_Olinorder__class_Osorted(_1744966, c_List_Olinorder__class_Oinsort__insert__key(_1744966, _1744966, c_COMBI(_1744966), _1744970, _1744968)))], (47593 ^ _782652) ^ [_1745113, _1745115] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1745113), _1745115)) = c_List_Oupt(_1745113, _1745115))], (47595 ^ _782652) ^ [_1745150, _1745152] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1745150, _1745152)))], (47597 ^ _782652) ^ [_1745178, _1745180] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1745178, _1745180)))], (47599 ^ _782652) ^ [_1745206, _1745208, _1745210] : [class_Orderings_Olinorder(_1745206), c_List_Olinorder__class_Osorted(_1745206, _1745208), -(c_List_Olinorder__class_Osorted(_1745206, c_List_Oremove1(_1745206, _1745210, _1745208)))], (47609 ^ _782652) ^ [_1745345, _1745347] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1745345, _1745347))))], (47611 ^ _782652) ^ [_1745375, _1745377, _1745379] : [class_Orderings_Olinorder(_1745375), 47614 ^ _782652 : [(47615 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1745375, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1745375, _1745375, c_COMBI(_1745375)), _1745377), _1745379)), -(c_List_Olinorder__class_Osorted(_1745375, _1745379))], (47621 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1745375, _1745379), -(c_List_Olinorder__class_Osorted(_1745375, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1745375, _1745375, c_COMBI(_1745375)), _1745377), _1745379)))]]], (47627 ^ _782652) ^ [_1745622, _1745624, _1745626] : [class_Orderings_Olinorder(_1745622), c_List_Olinorder__class_Osorted(_1745622, _1745624), hBOOL(hAPP(c_List_Odistinct(_1745622), _1745624)), c_List_Olinorder__class_Osorted(_1745622, _1745626), hBOOL(hAPP(c_List_Odistinct(_1745622), _1745626)), hAPP(c_List_Oset(_1745622), _1745624) = hAPP(c_List_Oset(_1745622), _1745626), -(_1745624 = _1745626)], (47653 ^ _782652) ^ [_1746005, _1746007] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1746005), _1746007) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1746005, _1746007)))], (47655 ^ _782652) ^ [_1746042, _1746044] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1746042, _1746044)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1746042), _1746044))], (47657 ^ _782652) ^ [_1746079, _1746081, _1746083] : [class_Orderings_Olinorder(_1746079), c_List_Olinorder__class_Osorted(_1746079, _1746081), -(c_List_Olinorder__class_Osorted(_1746079, hAPP(hAPP(c_List_Otake(_1746079), _1746083), _1746081)))], (47667 ^ _782652) ^ [_1746226] : [-(c_List_Oupt(_1746226, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (47669 ^ _782652) ^ [_1746252] : [class_Orderings_Olinorder(_1746252), -(c_List_Olinorder__class_Osorted(_1746252, c_List_Olist_ONil(_1746252)))], (47675 ^ _782652) ^ [_1746329, _1746331] : [class_Orderings_Olinorder(_1746329), c_List_Olinorder__class_Osorted(_1746329, _1746331), -(c_List_Olinorder__class_Osorted(_1746329, hAPP(c_List_Otl(_1746329), _1746331)))], (47685 ^ _782652) ^ [_1746466, _1746468, _1746470, _1746472, _1746474] : [class_Orderings_Olinorder(_1746466), c_List_Olinorder__class_Osorted(_1746466, hAPP(hAPP(c_List_Omap(_1746468, _1746466), _1746470), _1746472)), -(c_List_Olinorder__class_Osorted(_1746466, hAPP(hAPP(c_List_Omap(_1746468, _1746466), _1746470), c_List_Olinorder__class_Oinsort__insert__key(_1746468, _1746466, _1746470, _1746474, _1746472))))], (47695 ^ _782652) ^ [_1746653, _1746655] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1746653, _1746655)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1746653), hAPP(c_Nat_OSuc, _1746655)))], (47697 ^ _782652) ^ [_1746693, _1746695, _1746697, _1746699, _1746701] : [class_Orderings_Olinorder(_1746693), c_List_Olinorder__class_Osorted(_1746693, hAPP(hAPP(c_List_Omap(_1746695, _1746693), _1746697), _1746699)), -(c_List_Olinorder__class_Osorted(_1746693, hAPP(hAPP(c_List_Omap(_1746695, _1746693), _1746697), c_List_Oremove1(_1746695, _1746701, _1746699))))], (47707 ^ _782652) ^ [_1746876, _1746878, _1746880, _1746882, _1746884] : [class_Orderings_Olinorder(_1746876), 47710 ^ _782652 : [(47711 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1746876, hAPP(hAPP(c_List_Omap(_1746878, _1746876), _1746880), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1746878, _1746876, _1746880), _1746882), _1746884))), -(c_List_Olinorder__class_Osorted(_1746876, hAPP(hAPP(c_List_Omap(_1746878, _1746876), _1746880), _1746884)))], (47717 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1746876, hAPP(hAPP(c_List_Omap(_1746878, _1746876), _1746880), _1746884)), -(c_List_Olinorder__class_Osorted(_1746876, hAPP(hAPP(c_List_Omap(_1746878, _1746876), _1746880), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1746878, _1746876, _1746880), _1746882), _1746884))))]]], (47723 ^ _782652) ^ [_1747183, _1747185] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1747183, _1747185)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1747185), _1747183))], (47725 ^ _782652) ^ [_1747220, _1747222, _1747224] : [class_Orderings_Olinorder(_1747220), 47728 ^ _782652 : [(47729 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1747220, hAPP(hAPP(c_List_Olist_OCons(_1747220), _1747222), _1747224)), 47732 ^ _782652 : [(47733 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747220, _1747224))], (47735 ^ _782652) ^ [_1747406] : [hBOOL(hAPP(hAPP(c_member(_1747220), _1747406), hAPP(c_List_Oset(_1747220), _1747224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747220), _1747222), _1747406)))]]], (47741 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747220, hAPP(hAPP(c_List_Olist_OCons(_1747220), _1747222), _1747224))), c_List_Olinorder__class_Osorted(_1747220, _1747224), 47747 ^ _782652 : [(47748 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747220), 47746 ^ [_1747220, _1747222, _1747224]), hAPP(c_List_Oset(_1747220), _1747224))))], (47750 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747220), _1747222), 47746 ^ [_1747220, _1747222, _1747224]))]]]]], (47754 ^ _782652) ^ [_1747745, _1747747, _1747749] : [class_Orderings_Olinorder(_1747745), 47757 ^ _782652 : [(47758 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1747745, hAPP(hAPP(c_List_Oappend(_1747745), _1747747), _1747749)), 47761 ^ _782652 : [(47762 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747745, _1747747))], (47764 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747745, _1747749))], (47766 ^ _782652) ^ [_1747981] : [hBOOL(hAPP(hAPP(c_member(_1747745), _1747981), hAPP(c_List_Oset(_1747745), _1747747))), 47769 ^ _782652 : [(47770 ^ _782652) ^ [_1748091] : [hBOOL(hAPP(hAPP(c_member(_1747745), _1748091), hAPP(c_List_Oset(_1747745), _1747749))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747745), _1747981), _1748091)))]]]]], (47776 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747745, hAPP(hAPP(c_List_Oappend(_1747745), _1747747), _1747749))), c_List_Olinorder__class_Osorted(_1747745, _1747747), c_List_Olinorder__class_Osorted(_1747745, _1747749), 47786 ^ _782652 : [(47787 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747745), 47785 ^ [_1747745, _1747747, _1747749]), hAPP(c_List_Oset(_1747745), _1747747))))], (47790 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747745), 47788 ^ [_1747745, _1747747, _1747749]), hAPP(c_List_Oset(_1747745), _1747749))))], (47792 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747745), 47785 ^ [_1747745, _1747747, _1747749]), 47788 ^ [_1747745, _1747747, _1747749]))]]]]], (47796 ^ _782652) ^ [_1748602, _1748604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748602)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748604))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748602), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748604)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748602)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748602)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748604))))], (47802 ^ _782652) ^ [_1748755, _1748757] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748755)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748757)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748755), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1748757)) = c_List_Olist_ONil(tc_Nat_Onat))], (47808 ^ _782652) ^ [_1748834, _1748836, _1748838, _1748840] : [c_List_Oupt(_1748834, _1748836) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1748838), _1748840), 47811 ^ _782652 : [(47812 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748834), _1748836)))], (47814 ^ _782652) ^ [] : [-(_1748834 = _1748838)], (47816 ^ _782652) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1748834), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1748836) = _1748840)]]], (47818 ^ _782652) ^ [_1749007, _1749009, _1749011, _1749013] : [-(c_List_Oupt(_1749007, _1749009) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1749011), _1749013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749007), _1749009)), _1749007 = _1749011, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1749007), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1749009) = _1749013], (47832 ^ _782652) ^ [_1749248, _1749250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749248), _1749250)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1749248, _1749250)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1749250), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47838 ^ _782652) ^ [_1749359, _1749361, _1749363, _1749365, _1749367, _1749369] : [class_Orderings_Olinorder(_1749359), c_List_Olinorder__class_Osorted(_1749359, hAPP(hAPP(c_List_Omap(_1749361, _1749359), _1749363), _1749365)), hBOOL(hAPP(_1749367, _1749369)), -(hAPP(c_List_Ofilter(_1749361, _1749367), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1749361, _1749359, _1749363), _1749369), _1749365)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1749361, _1749359, _1749363), _1749369), hAPP(c_List_Ofilter(_1749361, _1749367), _1749365)))], (47852 ^ _782652) ^ [_1749648, _1749650] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1749648), hAPP(c_List_Onth(_1749648), _1749650)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749648)), _1749650))) = _1749650)], (47854 ^ _782652) ^ [_1749697, _1749699] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1749697, _1749699) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1749697, hAPP(c_Nat_OSuc, _1749699))))], (47856 ^ _782652) ^ [_1749735] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1749735) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1749735)))], (47858 ^ _782652) ^ [_1749767, _1749769, _1749771, _1749773] : [class_Groups_Ocomm__monoid__add(_1749767), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1749767), _1749769), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1749771, _1749773))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1749767), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1749767), _1749769), c_List_Oupt(_1749771, _1749773))))], (47864 ^ _782652) ^ [_1749910, _1749912, _1749914, _1749916] : [class_Groups_Ocomm__monoid__add(_1749910), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1749910), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1749910), _1749912), c_List_Oupt(_1749914, _1749916))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1749910), _1749912), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1749914, _1749916))))], (47870 ^ _782652) ^ [_1750053, _1750055, _1750057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1750053), _1750055)), _1750057)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1750053, _1750057)), _1750055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1750053), _1750055))], (47876 ^ _782652) ^ [_1750184, _1750186] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1750184, _1750186) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1750184), hAPP(c_Nat_OSuc, _1750186))))], (47878 ^ _782652) ^ [_1750225, _1750227, _1750229] : [class_Orderings_Olinorder(_1750225), 47881 ^ _782652 : [(47882 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1750225, hAPP(hAPP(c_List_Olist_OCons(_1750225), _1750227), _1750229)), 47885 ^ _782652 : [(47892 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1750225, _1750229))], (47886 ^ _782652) ^ [_1750393] : [hBOOL(hAPP(hAPP(c_member(_1750225), _1750393), hAPP(c_List_Oset(_1750225), _1750229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750225), _1750227), _1750393)))]]], (47894 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1750225, hAPP(hAPP(c_List_Olist_OCons(_1750225), _1750227), _1750229))), 47898 ^ _782652 : [(47899 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750225), 47897 ^ [_1750225, _1750227, _1750229]), hAPP(c_List_Oset(_1750225), _1750229))))], (47901 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750225), _1750227), 47897 ^ [_1750225, _1750227, _1750229]))]], c_List_Olinorder__class_Osorted(_1750225, _1750229)]]], (47907 ^ _782652) ^ [_1750751, _1750753] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1750751, _1750753) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1750751), _1750753)))], (47909 ^ _782652) ^ [_1750789, _1750791, _1750793, _1750795, _1750797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1750789), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750791), _1750793))), -(hAPP(hAPP(c_List_Onth(_1750795), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1750795), _1750797), c_List_Oupt(_1750793, _1750791))), _1750789) = hAPP(_1750797, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1750793), _1750789)))], (47915 ^ _782652) ^ [_1750952, _1750954] : [class_Orderings_Olinorder(_1750952), hBOOL(hAPP(c_Finite__Set_Ofinite(_1750952), _1750954)), 47922 ^ _782652 : [(47923 ^ _782652) ^ [] : [-(hAPP(c_List_Oset(_1750952), c_List_Olinorder__class_Osorted__list__of__set(_1750952, _1750954)) = _1750954)], (47925 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1750952, c_List_Olinorder__class_Osorted__list__of__set(_1750952, _1750954)))], (47927 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1750952), c_List_Olinorder__class_Osorted__list__of__set(_1750952, _1750954))))]]], (47929 ^ _782652) ^ [_1751173] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1751173) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1751173))))], (47931 ^ _782652) ^ [_1751208, _1751210, _1751212] : [class_Orderings_Olinorder(_1751208), hBOOL(hAPP(hAPP(c_member(_1751208), _1751210), hAPP(c_List_Oset(_1751208), _1751212))), c_List_Olinorder__class_Osorted(_1751208, _1751212), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1751208, _1751208, c_COMBI(_1751208)), _1751210), c_List_Oremove1(_1751208, _1751210, _1751212)) = _1751212)], (47945 ^ _782652) ^ [_1751449, _1751451, _1751453, _1751455] : [class_Orderings_Olinorder(_1751449), c_List_Olinorder__class_Osorted(_1751449, _1751451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1751453), _1751455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751455), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751449)), _1751451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1751449), hAPP(hAPP(c_List_Onth(_1751449), _1751451), _1751453)), hAPP(hAPP(c_List_Onth(_1751449), _1751451), _1751455))))], (47963 ^ _782652) ^ [_1751776, _1751778] : [class_Orderings_Olinorder(_1751776), 47966 ^ _782652 : [(47981 ^ _782652) ^ [] : [47983 ^ _782652 : [(47984 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47982 ^ [_1751776, _1751778]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751776)), _1751778))))], (47987 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47985 ^ [_1751776, _1751778]), 47982 ^ [_1751776, _1751778])))], (47989 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1751776), hAPP(hAPP(c_List_Onth(_1751776), _1751778), 47985 ^ [_1751776, _1751778])), hAPP(hAPP(c_List_Onth(_1751776), _1751778), 47982 ^ [_1751776, _1751778])))]], -(c_List_Olinorder__class_Osorted(_1751776, _1751778))], (47967 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1751776, _1751778), 47970 ^ _782652 : [(47971 ^ _782652) ^ [_1751947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751947), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751776)), _1751778))), 47974 ^ _782652 : [(47975 ^ _782652) ^ [_1752064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1752064), _1751947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1751776), hAPP(hAPP(c_List_Onth(_1751776), _1751778), _1752064)), hAPP(hAPP(c_List_Onth(_1751776), _1751778), _1751947))))]]]]]]], (47993 ^ _782652) ^ [_1752500, _1752502, _1752504, _1752506, _1752508] : [class_Orderings_Olinorder(_1752500), c_Fun_Oinj__on(_1752502, _1752500, _1752504, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1752502, tc_HOL_Obool)), hAPP(c_List_Oset(_1752502), _1752506)), hAPP(c_List_Oset(_1752502), _1752508))), c_List_Olinorder__class_Osorted(_1752500, hAPP(hAPP(c_List_Omap(_1752502, _1752500), _1752504), _1752506)), hBOOL(hAPP(c_List_Odistinct(_1752500), hAPP(hAPP(c_List_Omap(_1752502, _1752500), _1752504), _1752506))), c_List_Olinorder__class_Osorted(_1752500, hAPP(hAPP(c_List_Omap(_1752502, _1752500), _1752504), _1752508)), hBOOL(hAPP(c_List_Odistinct(_1752500), hAPP(hAPP(c_List_Omap(_1752502, _1752500), _1752504), _1752508))), hAPP(c_List_Oset(_1752502), _1752506) = hAPP(c_List_Oset(_1752502), _1752508), -(_1752506 = _1752508)], (48023 ^ _782652) ^ [_1753083, _1753085, _1753087, _1753089] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1753083, tc_Nat_Onat), _1753083), c_Product__Type_Ofst(_1753083, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1753083, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1753083, 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(_1753083, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1753083, tc_Nat_Onat))), _1753085)), hAPP(hAPP(c_List_Ozip(_1753083, tc_Nat_Onat), _1753087), c_List_Oupt(_1753089, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1753089), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753083)), _1753087)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1753083, tc_Nat_Onat), _1753083), c_Product__Type_Ofst(_1753083, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1753083, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1753083, 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(_1753083, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1753083, 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(_1753083, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1753083, tc_Nat_Onat))), _1753089))), _1753085)), hAPP(hAPP(c_List_Ozip(_1753083, tc_Nat_Onat), _1753087), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753083)), _1753087))))))], (48025 ^ _782652) ^ [_1753288, _1753290, _1753292] : [48026 ^ _782652 : [(48027 ^ _782652) ^ [] : [-(_1753288 = c_List_Olist_ONil(tc_List_Olist(_1753290)))], (48029 ^ _782652) ^ [] : [_1753292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48033 ^ _782652 : [(48034 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48032 ^ [_1753288, _1753290, _1753292]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753290))), _1753288))))], (48036 ^ _782652) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753290)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1753290)), _1753288), 48032 ^ [_1753288, _1753290, _1753292])) = _1753292]], -(c_List_Otranspose(_1753290, _1753288) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1753290)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1753290)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1753290), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1753290)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1753290)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1753290), hAPP(hAPP(c_COMBB(tc_List_Olist(_1753290), tc_fun(tc_Nat_Onat, _1753290), tc_Nat_Onat), c_List_Onth(_1753290)), hAPP(c_List_Onth(tc_List_Olist(_1753290)), _1753288))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753290))), _1753288)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1753292)))], (48040 ^ _782652) ^ [_1753798, _1753800] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1753798)), c_List_Otranspose__rel(_1753798)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1753798)), c_List_Olist_ONil(_1753798)), _1753800))), -(c_List_Otranspose(_1753798, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1753798)), c_List_Olist_ONil(_1753798)), _1753800)) = c_List_Otranspose(_1753798, _1753800))], (48046 ^ _782652) ^ [_1753957] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1753957)), c_List_Otranspose__rel(_1753957)), c_List_Olist_ONil(tc_List_Olist(_1753957)))), -(c_List_Otranspose(_1753957, c_List_Olist_ONil(tc_List_Olist(_1753957))) = c_List_Olist_ONil(tc_List_Olist(_1753957)))], (48052 ^ _782652) ^ [_1754084, _1754086, _1754088] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754084), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1754084))), _1754086))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754088), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1754084))), _1754086))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754084), _1754084), hAPP(hAPP(c_COMBC(tc_List_Olist(_1754084), tc_Nat_Onat, _1754084), c_List_Onth(_1754084)), _1754088)), hAPP(c_List_Ofilter(tc_List_Olist(_1754084), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1754084)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754088)), c_Nat_Osize__class_Osize(tc_List_Olist(_1754084)))), c_List_Otranspose(_1754084, _1754086))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1754084)), _1754086), _1754088))], (48062 ^ _782652) ^ [_1754411, _1754413] : [-(c_List_Oconcat(_1754411, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754411), tc_List_Olist(_1754411)), c_List_Olist_Olist__case(tc_List_Olist(_1754411), _1754411, c_List_Olist_ONil(_1754411), hAPP(hAPP(c_COMBB(tc_List_Olist(_1754411), tc_fun(tc_List_Olist(_1754411), tc_List_Olist(_1754411)), _1754411), c_COMBK(tc_List_Olist(_1754411), tc_List_Olist(_1754411))), hAPP(hAPP(c_COMBC(_1754411, tc_List_Olist(_1754411), tc_List_Olist(_1754411)), c_List_Olist_OCons(_1754411)), c_List_Olist_ONil(_1754411))))), _1754413)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754411), _1754411), c_List_Ohd(_1754411)), hAPP(c_List_Ofilter(tc_List_Olist(_1754411), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1754411)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1754411), tc_List_Olist(_1754411), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1754411)))), _1754413)))], (48064 ^ _782652) ^ [_1754554, _1754556] : [-(c_Fun_Oinj__on(tc_List_Olist(_1754554), tc_List_Olist(_1754554), c_List_Orev(_1754554), _1754556))], (48066 ^ _782652) ^ [_1754587, _1754589, _1754591] : [-(hAPP(c_List_Ofilter(_1754587, _1754589), c_List_Oconcat(_1754587, _1754591)) = c_List_Oconcat(_1754587, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1754587), tc_List_Olist(_1754587)), c_List_Ofilter(_1754587, _1754589)), _1754591)))], (48068 ^ _782652) ^ [_1754660, _1754662, _1754664] : [hAPP(c_List_Orev(_1754660), _1754662) = hAPP(hAPP(c_List_Olist_OCons(_1754660), _1754664), c_List_Olist_ONil(_1754660)), -(_1754662 = hAPP(hAPP(c_List_Olist_OCons(_1754660), _1754664), c_List_Olist_ONil(_1754660)))], (48074 ^ _782652) ^ [_1754785, _1754787, _1754789] : [_1754787 = hAPP(hAPP(c_List_Olist_OCons(_1754785), _1754789), c_List_Olist_ONil(_1754785)), -(hAPP(c_List_Orev(_1754785), _1754787) = hAPP(hAPP(c_List_Olist_OCons(_1754785), _1754789), c_List_Olist_ONil(_1754785)))], (48080 ^ _782652) ^ [_1754934, _1754936, _1754938] : [hAPP(hAPP(c_List_Olist_OCons(_1754934), _1754936), c_List_Olist_ONil(_1754934)) = hAPP(c_List_Orev(_1754934), _1754938), -(_1754938 = hAPP(hAPP(c_List_Olist_OCons(_1754934), _1754936), c_List_Olist_ONil(_1754934)))], (48086 ^ _782652) ^ [_1755059, _1755061, _1755063] : [_1755063 = hAPP(hAPP(c_List_Olist_OCons(_1755059), _1755061), c_List_Olist_ONil(_1755059)), -(hAPP(hAPP(c_List_Olist_OCons(_1755059), _1755061), c_List_Olist_ONil(_1755059)) = hAPP(c_List_Orev(_1755059), _1755063))], (48102 ^ _782652) ^ [_1755411, _1755413] : [48104 ^ _782652 : [(48105 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1755411)), 48103 ^ [_1755411, _1755413]), hAPP(c_List_Oset(tc_List_Olist(_1755411)), _1755413))))], (48107 ^ _782652) ^ [] : [48103 ^ [_1755411, _1755413] = c_List_Olist_ONil(_1755411)]], -(c_List_Olist_ONil(_1755411) = c_List_Oconcat(_1755411, _1755413))], (48092 ^ _782652) ^ [_1755205, _1755207] : [c_List_Olist_ONil(_1755205) = c_List_Oconcat(_1755205, _1755207), 48095 ^ _782652 : [(48096 ^ _782652) ^ [_1755296] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1755205)), _1755296), hAPP(c_List_Oset(tc_List_Olist(_1755205)), _1755207))), -(_1755296 = c_List_Olist_ONil(_1755205))]]], (48121 ^ _782652) ^ [_1755823, _1755825] : [48123 ^ _782652 : [(48124 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1755823)), 48122 ^ [_1755823, _1755825]), hAPP(c_List_Oset(tc_List_Olist(_1755823)), _1755825))))], (48126 ^ _782652) ^ [] : [48122 ^ [_1755823, _1755825] = c_List_Olist_ONil(_1755823)]], -(c_List_Oconcat(_1755823, _1755825) = c_List_Olist_ONil(_1755823))], (48111 ^ _782652) ^ [_1755617, _1755619] : [c_List_Oconcat(_1755617, _1755619) = c_List_Olist_ONil(_1755617), 48114 ^ _782652 : [(48115 ^ _782652) ^ [_1755708] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1755617)), _1755708), hAPP(c_List_Oset(tc_List_Olist(_1755617)), _1755619))), -(_1755708 = c_List_Olist_ONil(_1755617))]]], (48130 ^ _782652) ^ [_1756014] : [-(hAPP(c_List_Orev(_1756014), c_List_Olist_ONil(_1756014)) = c_List_Olist_ONil(_1756014))], (48132 ^ _782652) ^ [_1756046] : [-(c_List_Oconcat(_1756046, c_List_Olist_ONil(tc_List_Olist(_1756046))) = c_List_Olist_ONil(_1756046))], (48134 ^ _782652) ^ [_1756093, _1756095] : [c_List_Olist_ONil(_1756093) = hAPP(c_List_Orev(_1756093), _1756095), -(_1756095 = c_List_Olist_ONil(_1756093))], (48140 ^ _782652) ^ [_1756184, _1756186] : [_1756186 = c_List_Olist_ONil(_1756184), -(c_List_Olist_ONil(_1756184) = hAPP(c_List_Orev(_1756184), _1756186))], (48146 ^ _782652) ^ [_1756296, _1756298] : [hAPP(c_List_Orev(_1756296), _1756298) = c_List_Olist_ONil(_1756296), -(_1756298 = c_List_Olist_ONil(_1756296))], (48152 ^ _782652) ^ [_1756387, _1756389] : [_1756389 = c_List_Olist_ONil(_1756387), -(hAPP(c_List_Orev(_1756387), _1756389) = c_List_Olist_ONil(_1756387))], (48158 ^ _782652) ^ [_1756484, _1756486, _1756488] : [-(c_List_Oconcat(_1756484, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1756484)), _1756486), _1756488)) = hAPP(hAPP(c_List_Oappend(_1756484), _1756486), c_List_Oconcat(_1756484, _1756488)))], (48160 ^ _782652) ^ [_1756535, _1756537] : [-(hAPP(c_List_Orev(_1756535), c_List_Oconcat(_1756535, _1756537)) = c_List_Oconcat(_1756535, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1756535), tc_List_Olist(_1756535)), c_List_Orev(_1756535)), hAPP(c_List_Orev(tc_List_Olist(_1756535)), _1756537))))], (48162 ^ _782652) ^ [_1756593, _1756595, _1756597, _1756599] : [-(hAPP(c_List_Orev(_1756593), hAPP(hAPP(c_List_Omap(_1756595, _1756593), _1756597), _1756599)) = hAPP(hAPP(c_List_Omap(_1756595, _1756593), _1756597), hAPP(c_List_Orev(_1756595), _1756599)))], (48164 ^ _782652) ^ [_1756650, _1756652, _1756654, _1756656] : [-(hAPP(hAPP(c_List_Omap(_1756650, _1756652), _1756654), c_List_Oconcat(_1756650, _1756656)) = c_List_Oconcat(_1756652, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1756650), tc_List_Olist(_1756652)), hAPP(c_List_Omap(_1756650, _1756652), _1756654)), _1756656)))], (48166 ^ _782652) ^ [_1756713, _1756715] : [-(hAPP(c_List_Orev(_1756713), _1756715) = hAPP(c_List_Ofoldl(tc_List_Olist(_1756713), _1756713, hAPP(c_COMBC(_1756713, tc_List_Olist(_1756713), tc_List_Olist(_1756713)), c_List_Olist_OCons(_1756713)), c_List_Olist_ONil(_1756713)), _1756715))], (48168 ^ _782652) ^ [_1756768, _1756770] : [-(c_List_Oconcat(_1756768, _1756770) = hAPP(c_List_Ofoldl(tc_List_Olist(_1756768), tc_List_Olist(_1756768), c_List_Oappend(_1756768), c_List_Olist_ONil(_1756768)), _1756770))], (48170 ^ _782652) ^ [_1756812, _1756814, _1756816] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1756812), tc_List_Olist(_1756812), c_List_Oappend(_1756812), _1756814), _1756816) = hAPP(hAPP(c_List_Oappend(_1756812), _1756814), c_List_Oconcat(_1756812, _1756816)))], (48172 ^ _782652) ^ [_1756864, _1756866, _1756868] : [-(hAPP(c_List_Orev(_1756864), hAPP(hAPP(c_List_Oappend(_1756864), _1756866), _1756868)) = hAPP(hAPP(c_List_Oappend(_1756864), hAPP(c_List_Orev(_1756864), _1756868)), hAPP(c_List_Orev(_1756864), _1756866)))], (48174 ^ _782652) ^ [_1756922, _1756924, _1756926] : [-(c_List_Oconcat(_1756922, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1756922)), _1756924), _1756926)) = hAPP(hAPP(c_List_Oappend(_1756922), c_List_Oconcat(_1756922, _1756924)), c_List_Oconcat(_1756922, _1756926)))], (48176 ^ _782652) ^ [_1756991, _1756993] : [hBOOL(hAPP(c_List_Odistinct(_1756991), hAPP(c_List_Orev(_1756991), _1756993))), -(hBOOL(hAPP(c_List_Odistinct(_1756991), _1756993)))], (48182 ^ _782652) ^ [_1757090, _1757092] : [hBOOL(hAPP(c_List_Odistinct(_1757090), _1757092)), -(hBOOL(hAPP(c_List_Odistinct(_1757090), hAPP(c_List_Orev(_1757090), _1757092))))], (48188 ^ _782652) ^ [_1757195, _1757197] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757195)), hAPP(c_List_Orev(_1757195), _1757197)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757195)), _1757197))], (48190 ^ _782652) ^ [_1757257, _1757259, _1757261] : [hAPP(c_List_Orev(_1757257), _1757259) = hAPP(c_List_Orev(_1757257), _1757261), -(_1757259 = _1757261)], (48196 ^ _782652) ^ [_1757352, _1757354, _1757356] : [_1757354 = _1757356, -(hAPP(c_List_Orev(_1757352), _1757354) = hAPP(c_List_Orev(_1757352), _1757356))], (48202 ^ _782652) ^ [_1757471, _1757473, _1757475] : [hAPP(c_List_Orev(_1757471), _1757473) = _1757475, -(_1757473 = hAPP(c_List_Orev(_1757471), _1757475))], (48208 ^ _782652) ^ [_1757566, _1757568, _1757570] : [_1757568 = hAPP(c_List_Orev(_1757566), _1757570), -(hAPP(c_List_Orev(_1757566), _1757568) = _1757570)], (48214 ^ _782652) ^ [_1757667, _1757669] : [-(hAPP(c_List_Orev(_1757667), hAPP(c_List_Orev(_1757667), _1757669)) = _1757669)], (48216 ^ _782652) ^ [_1757702, _1757704] : [class_Groups_Ocomm__monoid__add(_1757702), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1757702), hAPP(c_List_Orev(_1757702), _1757704)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1757702), _1757704))], (48222 ^ _782652) ^ [_1757807, _1757809, _1757811, _1757813, _1757815] : [-(hAPP(c_List_Ofoldl(_1757807, _1757809, _1757811, _1757813), _1757815) = c_List_Ofoldr(_1757809, _1757807, hAPP(c_COMBC(_1757807, _1757809, _1757807), _1757811), hAPP(c_List_Orev(_1757809), _1757815), _1757813))], (48224 ^ _782652) ^ [_1757864, _1757866, _1757868, _1757870, _1757872] : [-(c_List_Ofoldr(_1757864, _1757866, _1757868, _1757870, _1757872) = hAPP(c_List_Ofoldl(_1757866, _1757864, hAPP(c_COMBC(_1757864, _1757866, _1757866), _1757868), _1757872), hAPP(c_List_Orev(_1757864), _1757870)))], (48226 ^ _782652) ^ [_1757921, _1757923] : [-(hAPP(c_List_Oset(_1757921), hAPP(c_List_Orev(_1757921), _1757923)) = hAPP(c_List_Oset(_1757921), _1757923))], (48228 ^ _782652) ^ [_1757961, _1757963, _1757965, _1757967] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757961)), _1757963) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757965)), _1757967), -(hAPP(hAPP(c_List_Ozip(_1757961, _1757965), hAPP(c_List_Orev(_1757961), _1757963)), hAPP(c_List_Orev(_1757965), _1757967)) = hAPP(c_List_Orev(tc_prod(_1757961, _1757965)), hAPP(hAPP(c_List_Ozip(_1757961, _1757965), _1757963), _1757967)))], (48234 ^ _782652) ^ [_1758142, _1758144, _1758146] : [-(hAPP(c_List_Orev(_1758142), hAPP(c_List_Ofilter(_1758142, _1758144), _1758146)) = hAPP(c_List_Ofilter(_1758142, _1758144), hAPP(c_List_Orev(_1758142), _1758146)))], (48236 ^ _782652) ^ [_1758212, _1758214, _1758216, _1758218] : [hAPP(c_List_Orev(_1758212), _1758214) = hAPP(hAPP(c_List_Olist_OCons(_1758212), _1758216), _1758218), -(_1758214 = hAPP(hAPP(c_List_Oappend(_1758212), hAPP(c_List_Orev(_1758212), _1758218)), hAPP(hAPP(c_List_Olist_OCons(_1758212), _1758216), c_List_Olist_ONil(_1758212))))], (48242 ^ _782652) ^ [_1758361, _1758363, _1758365, _1758367] : [_1758363 = hAPP(hAPP(c_List_Oappend(_1758361), hAPP(c_List_Orev(_1758361), _1758367)), hAPP(hAPP(c_List_Olist_OCons(_1758361), _1758365), c_List_Olist_ONil(_1758361))), -(hAPP(c_List_Orev(_1758361), _1758363) = hAPP(hAPP(c_List_Olist_OCons(_1758361), _1758365), _1758367))], (48248 ^ _782652) ^ [_1758516, _1758518, _1758520] : [-(hAPP(c_List_Orev(_1758516), hAPP(hAPP(c_List_Olist_OCons(_1758516), _1758518), _1758520)) = hAPP(hAPP(c_List_Oappend(_1758516), hAPP(c_List_Orev(_1758516), _1758520)), hAPP(hAPP(c_List_Olist_OCons(_1758516), _1758518), c_List_Olist_ONil(_1758516))))], (48250 ^ _782652) ^ [_1758579, _1758581] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758579)), c_List_Oconcat(_1758579, _1758581)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1758579), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1758579))), _1758581)))], (48252 ^ _782652) ^ [_1758632, _1758634] : [-(hAPP(c_List_Oset(_1758632), c_List_Oconcat(_1758632, _1758634)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1758632), tc_fun(_1758632, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1758632)), _1758634)), c_List_Oset(_1758632)))], (48254 ^ _782652) ^ [_1758684, _1758686] : [-(_1758684 = c_List_Olist_ONil(_1758686)), -(c_List_Olast(_1758686, hAPP(c_List_Orev(_1758686), _1758684)) = hAPP(c_List_Ohd(_1758686), _1758684))], (48260 ^ _782652) ^ [_1758731, _1758733] : [-(_1758731 = c_List_Olist_ONil(_1758733)), -(hAPP(c_List_Ohd(_1758733), hAPP(c_List_Orev(_1758733), _1758731)) = c_List_Olast(_1758733, _1758731))], (48266 ^ _782652) ^ [_1758782, _1758784] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1758782), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1758782))), c_List_Otranspose(_1758782, _1758784)))))], (48268 ^ _782652) ^ [_1758828, _1758830, _1758832] : [-(hAPP(c_List_Orev(_1758828), hAPP(hAPP(c_List_Odrop(_1758828), _1758830), _1758832)) = hAPP(hAPP(c_List_Otake(_1758828), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758828)), _1758832)), _1758830)), hAPP(c_List_Orev(_1758828), _1758832)))], (48270 ^ _782652) ^ [_1758894, _1758896, _1758898] : [-(hAPP(c_List_Orev(_1758894), hAPP(hAPP(c_List_Otake(_1758894), _1758896), _1758898)) = hAPP(hAPP(c_List_Odrop(_1758894), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758894)), _1758898)), _1758896)), hAPP(c_List_Orev(_1758894), _1758898)))], (48272 ^ _782652) ^ [_1758960, _1758962, _1758964] : [-(hAPP(c_List_Orotate(_1758960, _1758962), hAPP(c_List_Orev(_1758960), _1758964)) = hAPP(c_List_Orev(_1758960), hAPP(c_List_Orotate(_1758960, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758960)), _1758964)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1758962, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758960)), _1758964)))), _1758964)))], (48274 ^ _782652) ^ [_1759033, _1759035, _1759037, _1759039] : [-(c_List_Otranspose(_1759033, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1759033)), hAPP(hAPP(c_List_Olist_OCons(_1759033), _1759035), _1759037)), _1759039)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1759033)), hAPP(hAPP(c_List_Olist_OCons(_1759033), _1759035), c_List_Oconcat(_1759033, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1759033), tc_List_Olist(_1759033)), c_List_Olist_Olist__case(tc_List_Olist(_1759033), _1759033, c_List_Olist_ONil(_1759033), hAPP(hAPP(c_COMBB(tc_List_Olist(_1759033), tc_fun(tc_List_Olist(_1759033), tc_List_Olist(_1759033)), _1759033), c_COMBK(tc_List_Olist(_1759033), tc_List_Olist(_1759033))), hAPP(hAPP(c_COMBC(_1759033, tc_List_Olist(_1759033), tc_List_Olist(_1759033)), c_List_Olist_OCons(_1759033)), c_List_Olist_ONil(_1759033))))), _1759039)))), c_List_Otranspose(_1759033, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1759033)), _1759037), c_List_Oconcat(tc_List_Olist(_1759033), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1759033), tc_List_Olist(tc_List_Olist(_1759033))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1759033)), _1759033, c_List_Olist_ONil(tc_List_Olist(_1759033)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1759033), tc_List_Olist(tc_List_Olist(_1759033))), _1759033), hAPP(hAPP(c_COMBC(tc_List_Olist(_1759033), tc_List_Olist(tc_List_Olist(_1759033)), tc_List_Olist(tc_List_Olist(_1759033))), c_List_Olist_OCons(tc_List_Olist(_1759033))), c_List_Olist_ONil(tc_List_Olist(_1759033)))))), _1759039))))))], (48276 ^ _782652) ^ [_1759259, _1759261, _1759263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1759259), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759261)), _1759263))), -(hAPP(hAPP(c_List_Onth(_1759261), hAPP(c_List_Orev(_1759261), _1759263)), _1759259) = hAPP(hAPP(c_List_Onth(_1759261), _1759263), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759261)), _1759263)), hAPP(c_Nat_OSuc, _1759259))))], (48282 ^ _782652) ^ [_1759436, _1759438, _1759440] : [c_List_Oconcat(_1759436, _1759438) = c_List_Oconcat(_1759436, _1759440), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1759436))), _1759438) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1759436))), _1759440), 48292 ^ _782652 : [(48293 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1759436), tc_List_Olist(_1759436))), 48291 ^ [_1759436, _1759438, _1759440]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1759436), tc_List_Olist(_1759436))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1759436), tc_List_Olist(_1759436)), _1759438), _1759440)))))], (48295 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1759436), tc_List_Olist(_1759436), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1759436), tc_fun(tc_List_Olist(_1759436), tc_Nat_Onat), tc_fun(tc_List_Olist(_1759436), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1759436), tc_Nat_Onat), tc_fun(tc_List_Olist(_1759436), tc_HOL_Obool)), tc_List_Olist(_1759436)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1759436))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1759436)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1759436))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1759436)))), 48291 ^ [_1759436, _1759438, _1759440]))]], -(_1759438 = _1759440)], (48299 ^ _782652) ^ [_1760077, _1760079, _1760081] : [48301 ^ _782652 : [(48302 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760077), tc_List_Olist(_1760077))), 48300 ^ [_1760077, _1760079, _1760081]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1760077), tc_List_Olist(_1760077))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1760077), tc_List_Olist(_1760077)), _1760079), _1760081)))))], (48304 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1760077), tc_List_Olist(_1760077), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1760077), tc_fun(tc_List_Olist(_1760077), tc_Nat_Onat), tc_fun(tc_List_Olist(_1760077), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1760077), tc_Nat_Onat), tc_fun(tc_List_Olist(_1760077), tc_HOL_Obool)), tc_List_Olist(_1760077)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1760077))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1760077)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1760077))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1760077)))), 48300 ^ [_1760077, _1760079, _1760081]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1760077))), _1760079) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1760077))), _1760081), 48309 ^ _782652 : [(48310 ^ _782652) ^ [] : [c_List_Oconcat(_1760077, _1760079) = c_List_Oconcat(_1760077, _1760081), -(_1760079 = _1760081)], (48316 ^ _782652) ^ [] : [_1760079 = _1760081, -(c_List_Oconcat(_1760077, _1760079) = c_List_Oconcat(_1760077, _1760081))]]], (48322 ^ _782652) ^ [_1760804, _1760806, _1760808, _1760810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1760804), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760806)), _1760808))), -(hAPP(c_List_Orev(_1760806), hAPP(hAPP(c_List_Olist__update(_1760806, _1760808), _1760804), _1760810)) = hAPP(hAPP(c_List_Olist__update(_1760806, hAPP(c_List_Orev(_1760806), _1760808)), 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(_1760806)), _1760808)), _1760804)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1760810))], (48328 ^ _782652) ^ [_1761003, _1761005, _1761007, _1761009] : [-(c_List_Oconcat(_1761003, hAPP(hAPP(c_List_Omap(_1761005, tc_List_Olist(_1761003)), hAPP(hAPP(c_COMBC(_1761005, tc_List_Olist(_1761003), tc_List_Olist(_1761003)), hAPP(hAPP(c_COMBB(_1761003, tc_fun(tc_List_Olist(_1761003), tc_List_Olist(_1761003)), _1761005), c_List_Olist_OCons(_1761003)), _1761007)), c_List_Olist_ONil(_1761003))), _1761009)) = hAPP(hAPP(c_List_Omap(_1761005, _1761003), _1761007), _1761009))], (48330 ^ _782652) ^ [_1761090, _1761092, _1761094, _1761096] : [class_Orderings_Olinorder(_1761090), c_List_Olinorder__class_Osorted(_1761090, hAPP(c_List_Orev(_1761090), _1761092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1761094), _1761096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761096), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761090)), _1761092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1761090), hAPP(hAPP(c_List_Onth(_1761090), _1761092), _1761096)), hAPP(hAPP(c_List_Onth(_1761090), _1761092), _1761094))))], (48348 ^ _782652) ^ [_1761427, _1761429, _1761431] : [class_Orderings_Olinorder(_1761427), c_List_Olinorder__class_Osorted(_1761427, hAPP(c_List_Orev(_1761427), _1761429)), 48355 ^ _782652 : [(48356 ^ _782652) ^ [] : [_1761429 = c_List_Olist_ONil(_1761427), -(c_List_Ofoldr(_1761427, _1761427, c_Orderings_Oord__class_Omax(_1761427), _1761429, _1761431) = _1761431)], (48362 ^ _782652) ^ [] : [-(_1761429 = c_List_Olist_ONil(_1761427)), -(c_List_Ofoldr(_1761427, _1761427, c_Orderings_Oord__class_Omax(_1761427), _1761429, _1761431) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1761427), hAPP(hAPP(c_List_Onth(_1761427), _1761429), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1761431))]]], (48368 ^ _782652) ^ [_1761741, _1761743, _1761745, _1761747] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1761741)), c_List_Otranspose__rel(_1761741)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1761741)), hAPP(hAPP(c_List_Olist_OCons(_1761741), _1761743), _1761745)), _1761747))), -(c_List_Otranspose(_1761741, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1761741)), hAPP(hAPP(c_List_Olist_OCons(_1761741), _1761743), _1761745)), _1761747)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1761741)), hAPP(hAPP(c_List_Olist_OCons(_1761741), _1761743), c_List_Oconcat(_1761741, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1761741), tc_List_Olist(_1761741)), c_List_Olist_Olist__case(tc_List_Olist(_1761741), _1761741, c_List_Olist_ONil(_1761741), hAPP(hAPP(c_COMBB(tc_List_Olist(_1761741), tc_fun(tc_List_Olist(_1761741), tc_List_Olist(_1761741)), _1761741), c_COMBK(tc_List_Olist(_1761741), tc_List_Olist(_1761741))), hAPP(hAPP(c_COMBC(_1761741, tc_List_Olist(_1761741), tc_List_Olist(_1761741)), c_List_Olist_OCons(_1761741)), c_List_Olist_ONil(_1761741))))), _1761747)))), c_List_Otranspose(_1761741, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1761741)), _1761745), c_List_Oconcat(tc_List_Olist(_1761741), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1761741), tc_List_Olist(tc_List_Olist(_1761741))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1761741)), _1761741, c_List_Olist_ONil(tc_List_Olist(_1761741)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1761741), tc_List_Olist(tc_List_Olist(_1761741))), _1761741), hAPP(hAPP(c_COMBC(tc_List_Olist(_1761741), tc_List_Olist(tc_List_Olist(_1761741)), tc_List_Olist(tc_List_Olist(_1761741))), c_List_Olist_OCons(tc_List_Olist(_1761741))), c_List_Olist_ONil(tc_List_Olist(_1761741)))))), _1761747))))))], (48374 ^ _782652) ^ [_1762274, _1762276] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1762274), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1762274))), _1762276))), 48377 ^ _782652 : [(48378 ^ _782652) ^ [] : [_1762276 = c_List_Olist_ONil(tc_List_Olist(_1762274)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1762274))), c_List_Otranspose(_1762274, _1762276)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48384 ^ _782652) ^ [] : [-(_1762276 = c_List_Olist_ONil(tc_List_Olist(_1762274))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1762274))), c_List_Otranspose(_1762274, _1762276)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762274)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1762274)), _1762276), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (48390 ^ _782652) ^ [_1762584, _1762586, _1762588] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1762584), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1762584))), _1762586))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762588), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1762584))), _1762586))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1762584))), hAPP(c_List_Ofilter(tc_List_Olist(_1762584), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1762584)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762588)), c_Nat_Osize__class_Osize(tc_List_Olist(_1762584)))), c_List_Otranspose(_1762584, _1762586))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762584)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1762584)), _1762586), _1762588)))], (48400 ^ _782652) ^ [_1762893, _1762895] : [-(c_List_Oconcat(tc_List_Olist(_1762893), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1762893), tc_List_Olist(tc_List_Olist(_1762893))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1762893)), _1762893, c_List_Olist_ONil(tc_List_Olist(_1762893)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1762893), tc_List_Olist(tc_List_Olist(_1762893))), _1762893), hAPP(hAPP(c_COMBC(tc_List_Olist(_1762893), tc_List_Olist(tc_List_Olist(_1762893)), tc_List_Olist(tc_List_Olist(_1762893))), c_List_Olist_OCons(tc_List_Olist(_1762893))), c_List_Olist_ONil(tc_List_Olist(_1762893)))))), _1762895)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1762893), tc_List_Olist(_1762893)), c_List_Otl(_1762893)), hAPP(c_List_Ofilter(tc_List_Olist(_1762893), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1762893)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1762893), tc_List_Olist(_1762893), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1762893)))), _1762895)))], (48402 ^ _782652) ^ [_1763045, _1763047, _1763049, _1763051] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1763045), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1763045))), _1763047))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763049), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1763045))), c_List_Otranspose(_1763045, _1763047)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763051), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1763045))), hAPP(c_List_Ofilter(tc_List_Olist(_1763045), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1763045)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763049)), c_Nat_Osize__class_Osize(tc_List_Olist(_1763045)))), _1763047)))), -(hAPP(hAPP(c_List_Onth(_1763045), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1763045)), c_List_Otranspose(_1763045, _1763047)), _1763049)), _1763051) = hAPP(hAPP(c_List_Onth(_1763045), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1763045)), _1763047), _1763051)), _1763049))], (48416 ^ _782652) ^ [_1763468, _1763470] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1763468), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1763468))), _1763470))), -(c_List_Otranspose(_1763468, c_List_Otranspose(_1763468, _1763470)) = c_List_OtakeWhile(tc_List_Olist(_1763468), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1763468)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1763468), tc_List_Olist(_1763468), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1763468))), _1763470))], (48422 ^ _782652) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (48424 ^ _782652) ^ [_1763679, _1763681, _1763683, _1763685, _1763687] : [-(c_List_OtakeWhile(_1763679, _1763681, hAPP(hAPP(c_List_Omap(_1763683, _1763679), _1763685), _1763687)) = hAPP(hAPP(c_List_Omap(_1763683, _1763679), _1763685), c_List_OtakeWhile(_1763683, hAPP(c_Fun_Ocomp(_1763679, tc_HOL_Obool, _1763683, _1763681), _1763685), _1763687)))], (48426 ^ _782652) ^ [_1763744, _1763746, _1763748, _1763750, _1763752] : [-(hAPP(hAPP(c_List_Ozip(_1763744, _1763746), c_List_OtakeWhile(_1763744, _1763748, _1763750)), _1763752) = c_List_OtakeWhile(tc_prod(_1763744, _1763746), hAPP(c_Fun_Ocomp(_1763744, tc_HOL_Obool, tc_prod(_1763744, _1763746), _1763748), c_Product__Type_Ofst(_1763744, _1763746)), hAPP(hAPP(c_List_Ozip(_1763744, _1763746), _1763750), _1763752)))], (48428 ^ _782652) ^ [_1763818, _1763820, _1763822, _1763824, _1763826] : [-(hAPP(hAPP(c_List_Ozip(_1763818, _1763820), _1763822), c_List_OtakeWhile(_1763820, _1763824, _1763826)) = c_List_OtakeWhile(tc_prod(_1763818, _1763820), hAPP(c_Fun_Ocomp(_1763820, tc_HOL_Obool, tc_prod(_1763818, _1763820), _1763824), c_Product__Type_Osnd(_1763818, _1763820)), hAPP(hAPP(c_List_Ozip(_1763818, _1763820), _1763822), _1763826)))], (48440 ^ _782652) ^ [_1764106, _1764108, _1764110] : [48442 ^ _782652 : [(48443 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764106), 48441 ^ [_1764106, _1764108, _1764110]), hAPP(c_List_Oset(_1764106), _1764110))))], (48445 ^ _782652) ^ [] : [hBOOL(hAPP(_1764108, 48441 ^ [_1764106, _1764108, _1764110]))]], -(c_List_OtakeWhile(_1764106, _1764108, _1764110) = _1764110)], (48430 ^ _782652) ^ [_1763910, _1763912, _1763914] : [c_List_OtakeWhile(_1763910, _1763912, _1763914) = _1763914, 48433 ^ _782652 : [(48434 ^ _782652) ^ [_1763997] : [hBOOL(hAPP(hAPP(c_member(_1763910), _1763997), hAPP(c_List_Oset(_1763910), _1763914))), -(hBOOL(hAPP(_1763912, _1763997)))]]], (48449 ^ _782652) ^ [_1764294, _1764296, _1764298, _1764300] : [hBOOL(hAPP(hAPP(c_member(_1764294), _1764296), hAPP(c_List_Oset(_1764294), c_List_OtakeWhile(_1764294, _1764298, _1764300)))), 48452 ^ _782652 : [(48453 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1764294), _1764296), hAPP(c_List_Oset(_1764294), _1764300))))], (48455 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1764298, _1764296)))]]], (48457 ^ _782652) ^ [_1764461, _1764463, _1764465] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764461)), c_List_OtakeWhile(_1764461, _1764463, _1764465))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764461)), _1764465))))], (48459 ^ _782652) ^ [_1764511, _1764513, _1764515] : [-(c_List_OtakeWhile(_1764511, _1764513, _1764515) = hAPP(hAPP(c_List_Otake(_1764511), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764511)), c_List_OtakeWhile(_1764511, _1764513, _1764515))), _1764515))], (48461 ^ _782652) ^ [_1764561, _1764563, _1764565] : [hBOOL(hAPP(c_List_Odistinct(_1764561), _1764563)), -(hBOOL(hAPP(c_List_Odistinct(_1764561), c_List_OtakeWhile(_1764561, _1764565, _1764563))))], (48467 ^ _782652) ^ [_1764660, _1764662, _1764664, _1764666, _1764668] : [-(hBOOL(hAPP(_1764660, _1764662))), -(c_List_OtakeWhile(_1764664, _1764660, hAPP(hAPP(c_List_Oappend(_1764664), _1764666), hAPP(hAPP(c_List_Olist_OCons(_1764664), _1764662), _1764668))) = c_List_OtakeWhile(_1764664, _1764660, _1764666))], (48473 ^ _782652) ^ [_1764728, _1764730] : [-(c_List_OtakeWhile(_1764728, _1764730, c_List_Olist_ONil(_1764728)) = c_List_Olist_ONil(_1764728))], (48475 ^ _782652) ^ [_1764761, _1764763, _1764765] : [class_Orderings_Olinorder(_1764761), c_List_Olinorder__class_Osorted(_1764761, _1764763), -(c_List_Olinorder__class_Osorted(_1764761, c_List_OtakeWhile(_1764761, _1764765, _1764763)))], (48485 ^ _782652) ^ [_1764915, _1764917, _1764919, _1764921] : [hBOOL(hAPP(_1764915, _1764917)), -(c_List_OtakeWhile(_1764919, _1764915, hAPP(hAPP(c_List_Olist_OCons(_1764919), _1764917), _1764921)) = hAPP(hAPP(c_List_Olist_OCons(_1764919), _1764917), c_List_OtakeWhile(_1764919, _1764915, _1764921)))], (48491 ^ _782652) ^ [_1765042, _1765044, _1765046, _1765048] : [-(hBOOL(hAPP(_1765042, _1765044))), -(c_List_OtakeWhile(_1765046, _1765042, hAPP(hAPP(c_List_Olist_OCons(_1765046), _1765044), _1765048)) = c_List_Olist_ONil(_1765046))], (48497 ^ _782652) ^ [_1765100] : [-(c_List_Oreturn__list(_1765100) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1765100))], (48499 ^ _782652) ^ [_1765128, _1765130, _1765132, _1765134, _1765136] : [hBOOL(hAPP(hAPP(c_member(_1765128), _1765130), hAPP(c_List_Oset(_1765128), _1765132))), -(hBOOL(hAPP(_1765134, _1765130))), -(c_List_OtakeWhile(_1765128, _1765134, hAPP(hAPP(c_List_Oappend(_1765128), _1765132), _1765136)) = c_List_OtakeWhile(_1765128, _1765134, _1765132))], (48509 ^ _782652) ^ [_1765286, _1765288, _1765290, _1765292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765286), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765288)), c_List_OtakeWhile(_1765288, _1765290, _1765292)))), -(hAPP(hAPP(c_List_Onth(_1765288), c_List_OtakeWhile(_1765288, _1765290, _1765292)), _1765286) = hAPP(hAPP(c_List_Onth(_1765288), _1765292), _1765286))], (48515 ^ _782652) ^ [_1765439, _1765441, _1765443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765439)), c_List_OtakeWhile(_1765439, _1765441, _1765443))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765439)), _1765443))), hBOOL(hAPP(_1765441, hAPP(hAPP(c_List_Onth(_1765439), _1765443), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765439)), c_List_OtakeWhile(_1765439, _1765441, _1765443)))))], (48521 ^ _782652) ^ [_1765607, _1765609, _1765611, _1765613, _1765615] : [-(c_Map_Omap__upds(_1765607, _1765609, _1765611, _1765613, _1765615) = c_Map_Omap__add(_1765607, _1765609, _1765611, hAPP(c_Map_Omap__of(_1765607, _1765609), hAPP(c_List_Orev(tc_prod(_1765607, _1765609)), hAPP(hAPP(c_List_Ozip(_1765607, _1765609), _1765613), _1765615)))))], (48523 ^ _782652) ^ [_1765671, _1765673] : [-(_1765671 = c_List_Olist_ONil(_1765673)), hBOOL(hAPP(c_List_Odistinct(_1765673), _1765671)), -(c_List_OtakeWhile(_1765673, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1765673), c_fNot), hAPP(hAPP(c_COMBC(_1765673, _1765673, tc_HOL_Obool), c_fequal), c_List_Olast(_1765673, _1765671))), _1765671) = c_List_Obutlast(_1765673, _1765671))], (48533 ^ _782652) ^ [_1765868, _1765870, _1765872, _1765874, _1765876] : [class_Orderings_Olinorder(_1765868), c_List_Olinorder__class_Osorted(_1765868, hAPP(c_List_Orev(_1765868), hAPP(hAPP(c_List_Omap(_1765870, _1765868), _1765872), _1765874))), -(hAPP(c_List_Ofilter(_1765870, hAPP(hAPP(c_COMBB(_1765868, tc_HOL_Obool, _1765870), hAPP(c_Orderings_Oord__class_Oless(_1765868), _1765876)), _1765872)), _1765874) = c_List_OtakeWhile(_1765870, hAPP(hAPP(c_COMBB(_1765868, tc_HOL_Obool, _1765870), hAPP(c_Orderings_Oord__class_Oless(_1765868), _1765876)), _1765872), _1765874))], (48543 ^ _782652) ^ [_1766115] : [c_List_Onat__list(_1766115), -(c_List_Oembed__list(c_List_Oreturn__list(_1766115)) = _1766115)], (48549 ^ _782652) ^ [_1766196, _1766198] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766196)), c_List_Oremdups(_1766196, c_List_Oconcat(_1766196, _1766198))) = hAPP(c_Finite__Set_Ocard(_1766196), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1766196), tc_fun(_1766196, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1766196)), _1766198)), c_List_Oset(_1766196))))], (48551 ^ _782652) ^ [_1766262, _1766264] : [-(hBOOL(hAPP(c_List_Odistinct(_1766262), c_List_Oremdups(_1766262, _1766264))))], (48553 ^ _782652) ^ [_1766294, _1766296] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766294)), c_List_Oremdups(_1766294, _1766296))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766294)), _1766296))))], (48555 ^ _782652) ^ [_1766341, _1766343, _1766345, _1766347] : [-(c_List_Oremdups(_1766341, hAPP(hAPP(c_List_Omap(_1766343, _1766341), _1766345), c_List_Oremdups(_1766343, _1766347))) = c_List_Oremdups(_1766341, hAPP(hAPP(c_List_Omap(_1766343, _1766341), _1766345), _1766347)))], (48557 ^ _782652) ^ [_1766397, _1766399] : [-(hAPP(c_List_Oset(_1766397), c_List_Oremdups(_1766397, _1766399)) = hAPP(c_List_Oset(_1766397), _1766399))], (48559 ^ _782652) ^ [_1766435, _1766437] : [class_Orderings_Olinorder(_1766435), c_List_Olinorder__class_Osorted(_1766435, _1766437), -(c_List_Olinorder__class_Osorted(_1766435, c_List_Oremdups(_1766435, _1766437)))], (48569 ^ _782652) ^ [_1766568] : [-(c_List_Oremdups(_1766568, c_List_Olist_ONil(_1766568)) = c_List_Olist_ONil(_1766568))], (48571 ^ _782652) ^ [_1766613, _1766615] : [c_List_Olist_ONil(_1766613) = c_List_Oremdups(_1766613, _1766615), -(_1766615 = c_List_Olist_ONil(_1766613))], (48577 ^ _782652) ^ [_1766700, _1766702] : [_1766702 = c_List_Olist_ONil(_1766700), -(c_List_Olist_ONil(_1766700) = c_List_Oremdups(_1766700, _1766702))], (48583 ^ _782652) ^ [_1766808, _1766810] : [c_List_Oremdups(_1766808, _1766810) = c_List_Olist_ONil(_1766808), -(_1766810 = c_List_Olist_ONil(_1766808))], (48589 ^ _782652) ^ [_1766895, _1766897] : [_1766897 = c_List_Olist_ONil(_1766895), -(c_List_Oremdups(_1766895, _1766897) = c_List_Olist_ONil(_1766895))], (48595 ^ _782652) ^ [_1766988, _1766990, _1766992] : [hBOOL(hAPP(c_List_Odistinct(_1766988), _1766990)), -(c_List_Oremove1(_1766988, _1766992, c_List_Oremdups(_1766988, _1766990)) = c_List_Oremdups(_1766988, c_List_Oremove1(_1766988, _1766992, _1766990)))], (48601 ^ _782652) ^ [_1767103, _1767105] : [hBOOL(hAPP(c_List_Odistinct(_1767103), _1767105)), -(c_List_Oremdups(_1767103, _1767105) = _1767105)], (48607 ^ _782652) ^ [_1767209, _1767211] : [c_List_Oremdups(_1767209, _1767211) = _1767211, -(hBOOL(hAPP(c_List_Odistinct(_1767209), _1767211)))], (48613 ^ _782652) ^ [_1767296, _1767298] : [hBOOL(hAPP(c_List_Odistinct(_1767296), _1767298)), -(c_List_Oremdups(_1767296, _1767298) = _1767298)], (48619 ^ _782652) ^ [_1767404, _1767406] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767404)), c_List_Oremdups(_1767404, _1767406)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767404)), _1767406), -(c_List_Oremdups(_1767404, _1767406) = _1767406)], (48625 ^ _782652) ^ [_1767517, _1767519] : [c_List_Oremdups(_1767517, _1767519) = _1767519, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767517)), c_List_Oremdups(_1767517, _1767519)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767517)), _1767519))], (48631 ^ _782652) ^ [_1767636, _1767638] : [-(c_List_Oremdups(_1767636, c_List_Oremdups(_1767636, _1767638)) = c_List_Oremdups(_1767636, _1767638))], (48633 ^ _782652) ^ [_1767670, _1767672, _1767674] : [-(c_List_Oremdups(_1767670, hAPP(c_List_Ofilter(_1767670, _1767672), _1767674)) = hAPP(c_List_Ofilter(_1767670, _1767672), c_List_Oremdups(_1767670, _1767674)))], (48635 ^ _782652) ^ [_1767715] : [-(c_List_Oembed__list(_1767715) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1767715))], (48637 ^ _782652) ^ [_1767755, _1767757, _1767759] : [hBOOL(hAPP(hAPP(c_member(_1767755), _1767757), hAPP(c_List_Oset(_1767755), _1767759))), -(c_List_Oremdups(_1767755, hAPP(hAPP(c_List_Olist_OCons(_1767755), _1767757), _1767759)) = c_List_Oremdups(_1767755, _1767759))], (48643 ^ _782652) ^ [_1767880, _1767882, _1767884] : [-(hBOOL(hAPP(hAPP(c_member(_1767880), _1767882), hAPP(c_List_Oset(_1767880), _1767884)))), -(c_List_Oremdups(_1767880, hAPP(hAPP(c_List_Olist_OCons(_1767880), _1767882), _1767884)) = hAPP(hAPP(c_List_Olist_OCons(_1767880), _1767882), c_List_Oremdups(_1767880, _1767884)))], (48649 ^ _782652) ^ [_1767954, _1767956] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767954)), c_List_Oremdups(_1767954, _1767956)) = hAPP(c_Finite__Set_Ocard(_1767954), hAPP(c_List_Oset(_1767954), _1767956)))], (48651 ^ _782652) ^ [_1767999, _1768001, _1768003, _1768005, _1768007] : [c_Finite__Set_Ofun__left__comm(_1767999, _1768001, _1768003), -(hAPP(hAPP(c_Finite__Set_Ofold(_1767999, _1768001, _1768003), _1768005), hAPP(c_List_Oset(_1767999), _1768007)) = hAPP(c_List_Ofoldl(_1768001, _1767999, hAPP(c_COMBC(_1767999, _1768001, _1768001), _1768003), _1768005), c_List_Oremdups(_1767999, _1768007)))], (48657 ^ _782652) ^ [_1768150, _1768152] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1768150), _1768152) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1768150)), c_List_Oembed__list(_1768152))))], (48659 ^ _782652) ^ [_1768193, _1768195, _1768197] : [hBOOL(hAPP(c_List_Odistinct(_1768193), _1768195)), hBOOL(hAPP(hAPP(c_member(_1768193), _1768197), hAPP(c_List_Oset(_1768193), _1768195))), -(c_List_OtakeWhile(_1768193, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1768193), c_fNot), hAPP(hAPP(c_COMBC(_1768193, _1768193, tc_HOL_Obool), c_fequal), _1768197)), hAPP(c_List_Orev(_1768193), _1768195)) = hAPP(c_List_Orev(_1768193), hAPP(c_List_Otl(_1768193), c_List_OdropWhile(_1768193, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1768193), c_fNot), hAPP(hAPP(c_COMBC(_1768193, _1768193, tc_HOL_Obool), c_fequal), _1768197)), _1768195))))], (48669 ^ _782652) ^ [_1768484, _1768486, _1768488] : [hBOOL(hAPP(c_List_Odistinct(_1768484), _1768486)), hBOOL(hAPP(hAPP(c_member(_1768484), _1768488), hAPP(c_List_Oset(_1768484), _1768486))), -(c_List_OdropWhile(_1768484, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1768484), c_fNot), hAPP(hAPP(c_COMBC(_1768484, _1768484, tc_HOL_Obool), c_fequal), _1768488)), hAPP(c_List_Orev(_1768484), _1768486)) = hAPP(hAPP(c_List_Olist_OCons(_1768484), _1768488), hAPP(c_List_Orev(_1768484), c_List_OtakeWhile(_1768484, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1768484), c_fNot), hAPP(hAPP(c_COMBC(_1768484, _1768484, tc_HOL_Obool), c_fequal), _1768488)), _1768486))))], (48679 ^ _782652) ^ [_1768781, _1768783, _1768785] : [-(hAPP(hAPP(c_List_Oappend(_1768781), c_List_OtakeWhile(_1768781, _1768783, _1768785)), c_List_OdropWhile(_1768781, _1768783, _1768785)) = _1768785)], (48681 ^ _782652) ^ [_1768824, _1768826, _1768828, _1768830, _1768832] : [-(c_List_OdropWhile(_1768824, _1768826, hAPP(hAPP(c_List_Omap(_1768828, _1768824), _1768830), _1768832)) = hAPP(hAPP(c_List_Omap(_1768828, _1768824), _1768830), c_List_OdropWhile(_1768828, hAPP(c_Fun_Ocomp(_1768824, tc_HOL_Obool, _1768828, _1768826), _1768830), _1768832)))], (48683 ^ _782652) ^ [_1768889, _1768891, _1768893] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768889)), c_List_OdropWhile(_1768889, _1768891, _1768893))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768889)), _1768893))))], (48685 ^ _782652) ^ [_1768939, _1768941, _1768943] : [hBOOL(hAPP(c_List_Odistinct(_1768939), _1768941)), -(hBOOL(hAPP(c_List_Odistinct(_1768939), c_List_OdropWhile(_1768939, _1768943, _1768941))))], (48691 ^ _782652) ^ [_1769042, _1769044] : [-(c_List_OdropWhile(_1769042, _1769044, c_List_Olist_ONil(_1769042)) = c_List_Olist_ONil(_1769042))], (48693 ^ _782652) ^ [_1769075, _1769077, _1769079] : [class_Orderings_Olinorder(_1769075), c_List_Olinorder__class_Osorted(_1769075, _1769077), -(c_List_Olinorder__class_Osorted(_1769075, c_List_OdropWhile(_1769075, _1769079, _1769077)))], (48703 ^ _782652) ^ [_1769229, _1769231, _1769233, _1769235] : [hBOOL(hAPP(_1769229, _1769231)), -(c_List_OdropWhile(_1769233, _1769229, hAPP(hAPP(c_List_Olist_OCons(_1769233), _1769231), _1769235)) = c_List_OdropWhile(_1769233, _1769229, _1769235))], (48709 ^ _782652) ^ [_1769340, _1769342, _1769344, _1769346] : [-(hBOOL(hAPP(_1769340, _1769342))), -(c_List_OdropWhile(_1769344, _1769340, hAPP(hAPP(c_List_Olist_OCons(_1769344), _1769342), _1769346)) = hAPP(hAPP(c_List_Olist_OCons(_1769344), _1769342), _1769346))], (48715 ^ _782652) ^ [_1769403, _1769405, _1769407] : [-(c_List_OdropWhile(_1769403, _1769405, _1769407) = c_List_Olist_ONil(_1769403)), hBOOL(hAPP(_1769405, hAPP(c_List_Ohd(_1769403), c_List_OdropWhile(_1769403, _1769405, _1769407))))], (48731 ^ _782652) ^ [_1769727, _1769729, _1769731] : [48733 ^ _782652 : [(48734 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769727), 48732 ^ [_1769727, _1769729, _1769731]), hAPP(c_List_Oset(_1769727), _1769731))))], (48736 ^ _782652) ^ [] : [hBOOL(hAPP(_1769729, 48732 ^ [_1769727, _1769729, _1769731]))]], -(c_List_OdropWhile(_1769727, _1769729, _1769731) = c_List_Olist_ONil(_1769727))], (48721 ^ _782652) ^ [_1769527, _1769529, _1769531] : [c_List_OdropWhile(_1769527, _1769529, _1769531) = c_List_Olist_ONil(_1769527), 48724 ^ _782652 : [(48725 ^ _782652) ^ [_1769618] : [hBOOL(hAPP(hAPP(c_member(_1769527), _1769618), hAPP(c_List_Oset(_1769527), _1769531))), -(hBOOL(hAPP(_1769529, _1769618)))]]], (48740 ^ _782652) ^ [_1769919, _1769921, _1769923, _1769925, _1769927] : [hBOOL(hAPP(hAPP(c_member(_1769919), _1769921), hAPP(c_List_Oset(_1769919), _1769923))), -(hBOOL(hAPP(_1769925, _1769921))), -(c_List_OdropWhile(_1769919, _1769925, hAPP(hAPP(c_List_Oappend(_1769919), _1769923), _1769927)) = hAPP(hAPP(c_List_Oappend(_1769919), c_List_OdropWhile(_1769919, _1769925, _1769923)), _1769927))], (48750 ^ _782652) ^ [_1770117, _1770119, _1770121, _1770123, _1770125] : [c_List_OdropWhile(_1770117, _1770119, _1770121) = hAPP(hAPP(c_List_Olist_OCons(_1770117), _1770123), _1770125), 48753 ^ _782652 : [(48754 ^ _782652) ^ [] : [-(_1770121 = hAPP(hAPP(c_List_Oappend(_1770117), c_List_OtakeWhile(_1770117, _1770119, _1770121)), hAPP(hAPP(c_List_Olist_OCons(_1770117), _1770123), _1770125)))], (48756 ^ _782652) ^ [] : [hBOOL(hAPP(_1770119, _1770123))]]], (48758 ^ _782652) ^ [_1770298, _1770300, _1770302, _1770304, _1770306] : [-(c_List_OdropWhile(_1770298, _1770300, _1770302) = hAPP(hAPP(c_List_Olist_OCons(_1770298), _1770304), _1770306)), _1770302 = hAPP(hAPP(c_List_Oappend(_1770298), c_List_OtakeWhile(_1770298, _1770300, _1770302)), hAPP(hAPP(c_List_Olist_OCons(_1770298), _1770304), _1770306)), -(hBOOL(hAPP(_1770300, _1770304)))], (48768 ^ _782652) ^ [_1770512, _1770514, _1770516] : [-(c_List_OdropWhile(_1770512, _1770514, _1770516) = hAPP(hAPP(c_List_Odrop(_1770512), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770512)), c_List_OtakeWhile(_1770512, _1770514, _1770516))), _1770516))], (48770 ^ _782652) ^ [_1770562, _1770564, _1770566, _1770568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770562), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770564)), c_List_OdropWhile(_1770564, _1770566, _1770568)))), -(hAPP(hAPP(c_List_Onth(_1770564), c_List_OdropWhile(_1770564, _1770566, _1770568)), _1770562) = hAPP(hAPP(c_List_Onth(_1770564), _1770568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1770562), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770564)), c_List_OtakeWhile(_1770564, _1770566, _1770568)))))], (48776 ^ _782652) ^ [_1770749, _1770751, _1770753, _1770755, _1770757] : [class_Groups_Omonoid__add(_1770749), 48782 ^ _782652 : [(48783 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770751), 48781 ^ [_1770749, _1770751, _1770753, _1770755, _1770757]), hAPP(c_List_Oset(_1770751), _1770753))))], (48785 ^ _782652) ^ [] : [hBOOL(hAPP(_1770755, 48781 ^ [_1770749, _1770751, _1770753, _1770755, _1770757]))], (48787 ^ _782652) ^ [] : [hAPP(_1770757, 48781 ^ [_1770749, _1770751, _1770753, _1770755, _1770757]) = c_Groups_Ozero__class_Ozero(_1770749)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1770749), hAPP(hAPP(c_List_Omap(_1770751, _1770749), _1770757), hAPP(c_List_Ofilter(_1770751, _1770755), _1770753))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1770749), hAPP(hAPP(c_List_Omap(_1770751, _1770749), _1770757), _1770753)))], (48791 ^ _782652) ^ [_1771140, _1771142] : [class_Orderings_Olinorder(_1771140), 48798 ^ _782652 : [(48799 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48796 ^ [_1771140, _1771142]), 48797 ^ [_1771140, _1771142])))], (48801 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48797 ^ [_1771140, _1771142]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771140)), _1771142))))], (48803 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1771140), hAPP(hAPP(c_List_Onth(_1771140), _1771142), 48796 ^ [_1771140, _1771142])), hAPP(hAPP(c_List_Onth(_1771140), _1771142), 48797 ^ [_1771140, _1771142])))]], -(c_List_Olinorder__class_Osorted(_1771140, _1771142))], (48807 ^ _782652) ^ [_1771515, _1771517, _1771519] : [-(c_Enum_On__lists(_1771515, hAPP(c_Nat_OSuc, _1771517), _1771519) = c_List_Oconcat(tc_List_Olist(_1771515), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1771515), tc_List_Olist(tc_List_Olist(_1771515))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1771515), tc_List_Olist(_1771515), tc_List_Olist(tc_List_Olist(_1771515))), hAPP(hAPP(c_COMBB(tc_fun(_1771515, tc_List_Olist(_1771515)), tc_fun(tc_List_Olist(_1771515), tc_List_Olist(tc_List_Olist(_1771515))), tc_List_Olist(_1771515)), c_List_Omap(_1771515, tc_List_Olist(_1771515))), hAPP(c_COMBC(_1771515, tc_List_Olist(_1771515), tc_List_Olist(_1771515)), c_List_Olist_OCons(_1771515)))), _1771519)), c_Enum_On__lists(_1771515, _1771517, _1771519))))], (48809 ^ _782652) ^ [_1771635, _1771637, _1771639] : [-(c_List_Opartition(_1771635, _1771637, _1771639) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1771635), tc_List_Olist(_1771635)), hAPP(c_List_Ofilter(_1771635, _1771637), _1771639)), hAPP(c_List_Ofilter(_1771635, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1771635, c_fNot), _1771637)), _1771639)))], (48811 ^ _782652) ^ [_1771699, _1771701, _1771703] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1771699), tc_List_Olist(_1771699)), c_List_Opartition(_1771699, _1771701, _1771703)) = hAPP(c_List_Ofilter(_1771699, _1771701), _1771703))], (48813 ^ _782652) ^ [_1771746, _1771748, _1771750] : [hBOOL(hAPP(c_List_Odistinct(_1771746), _1771748)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1771746)), c_Enum_On__lists(_1771746, _1771750, _1771748))))], (48819 ^ _782652) ^ [_1771853, _1771855, _1771857] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1771853))), c_Enum_On__lists(_1771853, _1771855, _1771857)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771853)), _1771857)), _1771855))], (48821 ^ _782652) ^ [_1771906, _1771908, _1771910, _1771912] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1771906)), _1771908), hAPP(c_List_Oset(tc_List_Olist(_1771906)), c_Enum_On__lists(_1771906, _1771910, _1771912)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771906)), _1771908) = _1771910)], (48827 ^ _782652) ^ [_1772041, _1772043, _1772045, _1772047, _1772049] : [c_List_Opartition(_1772041, _1772043, _1772045) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772041), tc_List_Olist(_1772041)), _1772047), _1772049), 48830 ^ _782652 : [(48831 ^ _782652) ^ [_1772194] : [hBOOL(hAPP(hAPP(c_member(_1772041), _1772194), hAPP(c_List_Oset(_1772041), _1772047))), -(hBOOL(hAPP(_1772043, _1772194)))], (48837 ^ _782652) ^ [_1772303] : [hBOOL(hAPP(hAPP(c_member(_1772041), _1772303), hAPP(c_List_Oset(_1772041), _1772049))), hBOOL(hAPP(_1772043, _1772303))]]], (48843 ^ _782652) ^ [_1772423, _1772425] : [-(c_List_Opartition(_1772423, _1772425, c_List_Olist_ONil(_1772423)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772423), tc_List_Olist(_1772423)), c_List_Olist_ONil(_1772423)), c_List_Olist_ONil(_1772423)))], (48845 ^ _782652) ^ [_1772471, _1772473] : [-(c_Enum_On__lists(_1772471, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1772473) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1772471)), c_List_Olist_ONil(_1772471)), c_List_Olist_ONil(tc_List_Olist(_1772471))))], (48847 ^ _782652) ^ [_1772525, _1772527] : [_1772525 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1772527, _1772525, c_List_Olist_ONil(_1772527)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1772527)), c_List_Olist_ONil(_1772527)), c_List_Olist_ONil(tc_List_Olist(_1772527))))], (48853 ^ _782652) ^ [_1772640, _1772642] : [-(_1772640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1772642, _1772640, c_List_Olist_ONil(_1772642)) = c_List_Olist_ONil(tc_List_Olist(_1772642)))], (48859 ^ _782652) ^ [_1772688, _1772690, _1772692, _1772694] : [-(c_List_Opartition(_1772688, _1772690, hAPP(hAPP(c_List_Olist_OCons(_1772688), _1772692), _1772694)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1772688), tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1772688), tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1772688), tc_fun(tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)))), tc_fun(tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)))), tc_List_Olist(_1772688)), c_COMBS(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), tc_fun(tc_List_Olist(_1772688), tc_fun(tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)))), tc_List_Olist(_1772688)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)), tc_fun(tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), tc_List_Olist(_1772688)), hAPP(c_If(tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), hAPP(_1772690, _1772692)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1772688), tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), tc_List_Olist(_1772688)), c_Product__Type_OPair(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), hAPP(c_List_Olist_OCons(_1772688), _1772692))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1772688), tc_fun(tc_List_Olist(_1772688), tc_List_Olist(_1772688)), tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688))), tc_fun(tc_fun(tc_List_Olist(_1772688), tc_List_Olist(_1772688)), tc_fun(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)))), tc_List_Olist(_1772688)), c_COMBB(tc_List_Olist(_1772688), tc_prod(tc_List_Olist(_1772688), tc_List_Olist(_1772688)), tc_List_Olist(_1772688))), c_Product__Type_OPair(tc_List_Olist(_1772688), tc_List_Olist(_1772688)))), hAPP(c_List_Olist_OCons(_1772688), _1772692)))), c_List_Opartition(_1772688, _1772690, _1772694)))], (48861 ^ _782652) ^ [_1773107, _1773109, _1773111] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1773107), tc_List_Olist(_1773107)), c_List_Opartition(_1773107, _1773109, _1773111)) = hAPP(c_List_Ofilter(_1773107, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1773107, c_fNot), _1773109)), _1773111))], (48863 ^ _782652) ^ [_1773162, _1773164, _1773166, _1773168, _1773170] : [c_List_Opartition(_1773162, _1773164, _1773166) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773162), tc_List_Olist(_1773162)), _1773168), _1773170), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1773162, tc_HOL_Obool)), hAPP(c_List_Oset(_1773162), _1773168)), hAPP(c_List_Oset(_1773162), _1773170)) = hAPP(c_List_Oset(_1773162), _1773166))], (48869 ^ _782652) ^ [_1773331, _1773333, _1773335] : [-(hAPP(c_List_Oset(tc_List_Olist(_1773331)), c_Enum_On__lists(_1773331, _1773333, _1773335)) = hAPP(c_Set_OCollect(tc_List_Olist(_1773331)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1773331), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1773331)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1773331), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1773331)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1773331)))), _1773333))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1773331), tc_fun(_1773331, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1773331, tc_HOL_Obool), tc_fun(tc_fun(_1773331, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1773331)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1773331, tc_HOL_Obool))), c_List_Oset(_1773331))), hAPP(c_List_Oset(_1773331), _1773335)))))], (48871 ^ _782652) ^ [_1773476, _1773478] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1773476), tc_fun(_1773476, tc_HOL_Obool), c_List_Oset(_1773476)), hAPP(c_List_Oset(tc_List_Olist(_1773476)), c_Enum_Osublists(_1773476, _1773478))) = hAPP(c_Set_OPow(_1773476), hAPP(c_List_Oset(_1773476), _1773478)))], (48873 ^ _782652) ^ [_1773535, _1773537] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1773535))), c_Enum_Osublists(_1773535, _1773537)) = 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(_1773535)), _1773537)))], (48875 ^ _782652) ^ [_1773582, _1773584] : [hBOOL(hAPP(c_List_Odistinct(_1773582), _1773584)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1773582, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1773582), tc_fun(_1773582, tc_HOL_Obool)), c_List_Oset(_1773582)), c_Enum_Osublists(_1773582, _1773584)))))], (48881 ^ _782652) ^ [_1773719] : [-(c_Enum_Osublists(_1773719, c_List_Olist_ONil(_1773719)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1773719)), c_List_Olist_ONil(_1773719)), c_List_Olist_ONil(tc_List_Olist(_1773719))))], (48883 ^ _782652) ^ [_1773763, _1773765, _1773767] : [-(c_Enum_Osublists(_1773763, hAPP(hAPP(c_List_Olist_OCons(_1773763), _1773765), _1773767)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1773763)), tc_List_Olist(tc_List_Olist(_1773763))), c_Enum_Osublists(_1773763, _1773767)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1773763)), tc_List_Olist(tc_List_Olist(_1773763)), tc_List_Olist(tc_List_Olist(_1773763))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1773763)), tc_fun(tc_List_Olist(tc_List_Olist(_1773763)), tc_List_Olist(tc_List_Olist(_1773763))), tc_List_Olist(tc_List_Olist(_1773763))), c_List_Oappend(tc_List_Olist(_1773763))), hAPP(c_List_Omap(tc_List_Olist(_1773763), tc_List_Olist(_1773763)), hAPP(c_List_Olist_OCons(_1773763), _1773765)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1773763))))))], (48885 ^ _782652) ^ [_1773897, _1773899, _1773901, _1773903, _1773905] : [-(c_Enum_Oproduct(_1773897, _1773899, hAPP(hAPP(c_List_Olist_OCons(_1773897), _1773901), _1773903), _1773905) = hAPP(hAPP(c_List_Oappend(tc_prod(_1773897, _1773899)), hAPP(hAPP(c_List_Omap(_1773899, tc_prod(_1773897, _1773899)), hAPP(c_Product__Type_OPair(_1773897, _1773899), _1773901)), _1773905)), c_Enum_Oproduct(_1773897, _1773899, _1773903, _1773905)))], (48887 ^ _782652) ^ [_1773975, _1773977] : [-(c_Enum_Oenum__the(_1773975, _1773977) = c_HOL_OThe(_1773975, _1773977))], (48889 ^ _782652) ^ [_1774006, _1774008, _1774010] : [-(c_Enum_Oproduct(_1774006, _1774008, c_List_Olist_ONil(_1774006), _1774010) = c_List_Olist_ONil(tc_prod(_1774006, _1774008)))], (48891 ^ _782652) ^ [_1774045, _1774047, _1774049, _1774051] : [hBOOL(hAPP(c_List_Odistinct(_1774045), _1774047)), hBOOL(hAPP(c_List_Odistinct(_1774049), _1774051)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1774045, _1774049)), c_Enum_Oproduct(_1774045, _1774049, _1774047, _1774051))))], (48901 ^ _782652) ^ [_1774222, _1774224, _1774226, _1774228] : [-(hAPP(c_List_Oset(tc_prod(_1774222, _1774224)), c_Enum_Oproduct(_1774222, _1774224, _1774226, _1774228)) = hAPP(hAPP(c_Product__Type_OSigma(_1774222, _1774224), hAPP(c_List_Oset(_1774222), _1774226)), hAPP(c_COMBK(tc_fun(_1774224, tc_HOL_Obool), _1774222), hAPP(c_List_Oset(_1774224), _1774228))))], (48903 ^ _782652) ^ [_1774292, _1774294, _1774296, _1774298] : [class_Enum_Oenum(_1774292), class_Enum_Oenum(_1774294), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774294)), _1774296) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774292)), c_Enum_Oenum__class_Oenum(_1774292)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774294)), _1774298) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1774292)), c_Enum_Oenum__class_Oenum(_1774292)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1774294), _1774294, _1774292, c_Option_Othe(_1774294)), hAPP(c_Map_Omap__of(_1774292, _1774294), hAPP(hAPP(c_List_Ozip(_1774292, _1774294), c_Enum_Oenum__class_Oenum(_1774292)), _1774296))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1774294), _1774294, _1774292, c_Option_Othe(_1774294)), hAPP(c_Map_Omap__of(_1774292, _1774294), hAPP(hAPP(c_List_Ozip(_1774292, _1774294), c_Enum_Oenum__class_Oenum(_1774292)), _1774298))), -(_1774296 = _1774298)], (48925 ^ _782652) ^ [_1774775, _1774777] : [class_Orderings_Olinorder(_1774775), -(c_List_Olinorder__class_Osort__key(_1774775, _1774775, c_COMBI(_1774775), _1774777) = hAPP(c_List_Ofoldl(tc_List_Olist(_1774775), _1774775, hAPP(c_COMBC(_1774775, tc_List_Olist(_1774775), tc_List_Olist(_1774775)), c_List_Olinorder__class_Oinsort__key(_1774775, _1774775, c_COMBI(_1774775))), c_List_Olist_ONil(_1774775)), _1774777))], (48931 ^ _782652) ^ [_1774922] : [class_Enum_Oenum(_1774922), -(hBOOL(hAPP(c_List_Odistinct(_1774922), c_Enum_Oenum__class_Oenum(_1774922))))], (48937 ^ _782652) ^ [_1775007, _1775009, _1775011, _1775013] : [class_Orderings_Olinorder(_1775007), 48940 ^ _782652 : [(48941 ^ _782652) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1775009), c_List_Olinorder__class_Osort__key(_1775009, _1775007, _1775011, _1775013))), -(hBOOL(hAPP(c_List_Odistinct(_1775009), _1775013)))], (48947 ^ _782652) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1775009), _1775013)), -(hBOOL(hAPP(c_List_Odistinct(_1775009), c_List_Olinorder__class_Osort__key(_1775009, _1775007, _1775011, _1775013))))]]], (48953 ^ _782652) ^ [_1775263] : [class_Enum_Oenum(_1775263), -(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(_1775263)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(_1775263)), c_Option_Ooption_ONone(_1775263)), hAPP(hAPP(c_List_Omap(_1775263, tc_Option_Ooption(_1775263)), c_Option_Ooption_OSome(_1775263)), c_Enum_Oenum__class_Oenum(_1775263))))], (48959 ^ _782652) ^ [_1775398, _1775400] : [-(c_Enum_Oenum__class_Oenum(tc_prod(_1775398, _1775400)) = c_Enum_Oproduct(_1775398, _1775400, c_Enum_Oenum__class_Oenum(_1775398), c_Enum_Oenum__class_Oenum(_1775400))), class_Enum_Oenum(_1775398), class_Enum_Oenum(_1775400)], (48969 ^ _782652) ^ [_1775551, _1775553] : [class_Enum_Oenum(_1775551), -(hBOOL(hAPP(hAPP(c_member(_1775551), _1775553), hAPP(c_List_Oset(_1775551), c_Enum_Oenum__class_Oenum(_1775551)))))], (48975 ^ _782652) ^ [_1775654] : [class_Enum_Oenum(_1775654), -(hAPP(c_List_Oset(_1775654), c_Enum_Oenum__class_Oenum(_1775654)) = c_Orderings_Otop__class_Otop(tc_fun(_1775654, tc_HOL_Obool)))], (48981 ^ _782652) ^ [_1775751] : [class_Enum_Oenum(_1775751), -(c_Orderings_Otop__class_Otop(tc_fun(_1775751, tc_HOL_Obool)) = hAPP(c_List_Oset(_1775751), c_Enum_Oenum__class_Oenum(_1775751)))], (48987 ^ _782652) ^ [_1775848, _1775850, _1775852, _1775854] : [class_Orderings_Olinorder(_1775848), -(hAPP(c_List_Oset(_1775850), c_List_Olinorder__class_Osort__key(_1775850, _1775848, _1775852, _1775854)) = hAPP(c_List_Oset(_1775850), _1775854))], (48993 ^ _782652) ^ [_1775957, _1775959] : [class_Orderings_Olinorder(_1775957), -(c_List_Olinorder__class_Osorted(_1775957, c_List_Olinorder__class_Osort__key(_1775957, _1775957, c_COMBI(_1775957), _1775959)))], (48999 ^ _782652) ^ [_1776046, _1776048, _1776050] : [class_Orderings_Olinorder(_1776046), -(c_List_Olinorder__class_Osort__key(_1776048, _1776046, _1776050, c_List_Olist_ONil(_1776048)) = c_List_Olist_ONil(_1776048))], (49005 ^ _782652) ^ [_1776141, _1776143, _1776145, _1776147] : [class_Orderings_Olinorder(_1776141), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776143)), c_List_Olinorder__class_Osort__key(_1776143, _1776141, _1776145, _1776147)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776143)), _1776147))], (49011 ^ _782652) ^ [_1776258, _1776260, _1776262, _1776264, _1776266] : [class_Orderings_Olinorder(_1776258), -(hAPP(c_List_Ofilter(_1776260, _1776262), c_List_Olinorder__class_Osort__key(_1776260, _1776258, _1776264, _1776266)) = c_List_Olinorder__class_Osort__key(_1776260, _1776258, _1776264, hAPP(c_List_Ofilter(_1776260, _1776262), _1776266)))], (49017 ^ _782652) ^ [_1776383, _1776385, _1776387, _1776389] : [class_Orderings_Olinorder(_1776383), -(c_List_Olinorder__class_Osorted(_1776383, hAPP(hAPP(c_List_Omap(_1776385, _1776383), _1776387), c_List_Olinorder__class_Osort__key(_1776385, _1776383, _1776387, _1776389))))], (49023 ^ _782652) ^ [_1776490, _1776492, _1776494, _1776496, _1776498] : [class_Orderings_Olinorder(_1776490), -(c_List_Olinorder__class_Osort__key(_1776492, _1776490, _1776494, hAPP(hAPP(c_List_Olist_OCons(_1776492), _1776496), _1776498)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1776492, _1776490, _1776494), _1776496), c_List_Olinorder__class_Osort__key(_1776492, _1776490, _1776494, _1776498)))], (49029 ^ _782652) ^ [_1776627, _1776629] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1776627, _1776629)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1776629), tc_fun(_1776627, _1776629)), hAPP(hAPP(c_COMBB(tc_fun(_1776627, tc_Option_Ooption(_1776629)), tc_fun(_1776627, _1776629), tc_List_Olist(_1776629)), c_Fun_Ocomp(tc_Option_Ooption(_1776629), _1776629, _1776627, c_Option_Othe(_1776629))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1776627, _1776629)), tc_fun(_1776627, tc_Option_Ooption(_1776629)), tc_List_Olist(_1776629)), c_Map_Omap__of(_1776627, _1776629)), hAPP(c_List_Ozip(_1776627, _1776629), c_Enum_Oenum__class_Oenum(_1776627))))), c_Enum_On__lists(_1776629, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776627)), c_Enum_Oenum__class_Oenum(_1776627)), c_Enum_Oenum__class_Oenum(_1776629)))), class_Enum_Oenum(_1776627), class_HOL_Oequal(_1776627), class_Enum_Oenum(_1776629)], (49043 ^ _782652) ^ [_1776994, _1776996] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1776994, _1776996)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1776996), tc_fun(_1776994, _1776996)), hAPP(hAPP(c_COMBB(tc_fun(_1776994, tc_Option_Ooption(_1776996)), tc_fun(_1776994, _1776996), tc_List_Olist(_1776996)), c_Fun_Ocomp(tc_Option_Ooption(_1776996), _1776996, _1776994, c_Option_Othe(_1776996))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1776994, _1776996)), tc_fun(_1776994, tc_Option_Ooption(_1776996)), tc_List_Olist(_1776996)), c_Map_Omap__of(_1776994, _1776996)), hAPP(c_List_Ozip(_1776994, _1776996), c_Enum_Oenum__class_Oenum(_1776994))))), c_Enum_On__lists(_1776996, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776994)), c_Enum_Oenum__class_Oenum(_1776994)), c_Enum_Oenum__class_Oenum(_1776996)))), class_Enum_Oenum(_1776994), class_Enum_Oenum(_1776996)], (49053 ^ _782652) ^ [_1777311, _1777313] : [class_Orderings_Olinorder(_1777311), -(c_List_Olinorder__class_Osorted__list__of__set(_1777311, hAPP(c_List_Oset(_1777311), _1777313)) = c_List_Olinorder__class_Osort__key(_1777311, _1777311, c_COMBI(_1777311), c_List_Oremdups(_1777311, _1777313)))], (49059 ^ _782652) ^ [_1777422, _1777424, _1777426] : [class_Enum_Oenum(_1777422), 49062 ^ _782652 : [(49073 ^ _782652) ^ [] : [49075 ^ _782652 : [(49076 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777422)), 49074 ^ [_1777422, _1777424, _1777426]), hAPP(c_List_Oset(tc_List_Olist(_1777422)), c_Enum_On__lists(_1777422, _1777426, c_Enum_Oenum__class_Oenum(_1777422))))))], (49078 ^ _782652) ^ [] : [hBOOL(hAPP(_1777424, 49074 ^ [_1777422, _1777424, _1777426]))]], -(c_Enum_Oall__n__lists(_1777422, _1777424, _1777426))], (49063 ^ _782652) ^ [] : [c_Enum_Oall__n__lists(_1777422, _1777424, _1777426), 49066 ^ _782652 : [(49067 ^ _782652) ^ [_1777572] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777422)), _1777572), hAPP(c_List_Oset(tc_List_Olist(_1777422)), c_Enum_On__lists(_1777422, _1777426, c_Enum_Oenum__class_Oenum(_1777422))))), -(hBOOL(hAPP(_1777424, _1777572)))]]]]], (49082 ^ _782652) ^ [_1777863, _1777865, _1777867] : [class_Enum_Oenum(_1777863), 49085 ^ _782652 : [(49086 ^ _782652) ^ [] : [c_Enum_Oex__n__lists(_1777863, _1777865, _1777867), 49090 ^ _782652 : [(49091 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777863)), 49089 ^ [_1777863, _1777865, _1777867]), hAPP(c_List_Oset(tc_List_Olist(_1777863)), c_Enum_On__lists(_1777863, _1777867, c_Enum_Oenum__class_Oenum(_1777863))))))], (49093 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1777865, 49089 ^ [_1777863, _1777865, _1777867])))]]], (49095 ^ _782652) ^ [] : [-(c_Enum_Oex__n__lists(_1777863, _1777865, _1777867)), 49096 ^ _782652 : [(49097 ^ _782652) ^ [_1778119] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777863)), _1778119), hAPP(c_List_Oset(tc_List_Olist(_1777863)), c_Enum_On__lists(_1777863, _1777867, c_Enum_Oenum__class_Oenum(_1777863))))), hBOOL(hAPP(_1777865, _1778119))]]]]], (49105 ^ _782652) ^ [_1778282, _1778284, _1778286] : [class_Enum_Oenum(_1778282), class_Enum_Oenum(_1778284), class_HOL_Oequal(_1778284), 49116 ^ _782652 : [(49117 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1778284, _1778282)), _1778286)), -(c_Enum_Oex__n__lists(_1778282, hAPP(hAPP(c_COMBB(tc_fun(_1778284, _1778282), tc_HOL_Obool, tc_List_Olist(_1778282)), _1778286), hAPP(hAPP(c_COMBB(tc_fun(_1778284, tc_Option_Ooption(_1778282)), tc_fun(_1778284, _1778282), tc_List_Olist(_1778282)), c_Fun_Ocomp(tc_Option_Ooption(_1778282), _1778282, _1778284, c_Option_Othe(_1778282))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1778284, _1778282)), tc_fun(_1778284, tc_Option_Ooption(_1778282)), tc_List_Olist(_1778282)), c_Map_Omap__of(_1778284, _1778282)), hAPP(c_List_Ozip(_1778284, _1778282), c_Enum_Oenum__class_Oenum(_1778284))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778284)), c_Enum_Oenum__class_Oenum(_1778284))))], (49123 ^ _782652) ^ [] : [c_Enum_Oex__n__lists(_1778282, hAPP(hAPP(c_COMBB(tc_fun(_1778284, _1778282), tc_HOL_Obool, tc_List_Olist(_1778282)), _1778286), hAPP(hAPP(c_COMBB(tc_fun(_1778284, tc_Option_Ooption(_1778282)), tc_fun(_1778284, _1778282), tc_List_Olist(_1778282)), c_Fun_Ocomp(tc_Option_Ooption(_1778282), _1778282, _1778284, c_Option_Othe(_1778282))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1778284, _1778282)), tc_fun(_1778284, tc_Option_Ooption(_1778282)), tc_List_Olist(_1778282)), c_Map_Omap__of(_1778284, _1778282)), hAPP(c_List_Ozip(_1778284, _1778282), c_Enum_Oenum__class_Oenum(_1778284))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778284)), c_Enum_Oenum__class_Oenum(_1778284))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1778284, _1778282)), _1778286)))]]], (49129 ^ _782652) ^ [_1778883, _1778885, _1778887] : [class_Enum_Oenum(_1778883), class_Enum_Oenum(_1778885), class_HOL_Oequal(_1778885), 49140 ^ _782652 : [(49141 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1778885, _1778883)), _1778887)), -(c_Enum_Oall__n__lists(_1778883, hAPP(hAPP(c_COMBB(tc_fun(_1778885, _1778883), tc_HOL_Obool, tc_List_Olist(_1778883)), _1778887), hAPP(hAPP(c_COMBB(tc_fun(_1778885, tc_Option_Ooption(_1778883)), tc_fun(_1778885, _1778883), tc_List_Olist(_1778883)), c_Fun_Ocomp(tc_Option_Ooption(_1778883), _1778883, _1778885, c_Option_Othe(_1778883))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1778885, _1778883)), tc_fun(_1778885, tc_Option_Ooption(_1778883)), tc_List_Olist(_1778883)), c_Map_Omap__of(_1778885, _1778883)), hAPP(c_List_Ozip(_1778885, _1778883), c_Enum_Oenum__class_Oenum(_1778885))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778885)), c_Enum_Oenum__class_Oenum(_1778885))))], (49147 ^ _782652) ^ [] : [c_Enum_Oall__n__lists(_1778883, hAPP(hAPP(c_COMBB(tc_fun(_1778885, _1778883), tc_HOL_Obool, tc_List_Olist(_1778883)), _1778887), hAPP(hAPP(c_COMBB(tc_fun(_1778885, tc_Option_Ooption(_1778883)), tc_fun(_1778885, _1778883), tc_List_Olist(_1778883)), c_Fun_Ocomp(tc_Option_Ooption(_1778883), _1778883, _1778885, c_Option_Othe(_1778883))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1778885, _1778883)), tc_fun(_1778885, tc_Option_Ooption(_1778883)), tc_List_Olist(_1778883)), c_Map_Omap__of(_1778885, _1778883)), hAPP(c_List_Ozip(_1778885, _1778883), c_Enum_Oenum__class_Oenum(_1778885))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778885)), c_Enum_Oenum__class_Oenum(_1778885))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1778885, _1778883)), _1778887)))]]], (49153 ^ _782652) ^ [_1779484, _1779486] : [class_Enum_Oenum(_1779484), 49156 ^ _782652 : [(49157 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1779484)), _1779486)), 49160 ^ _782652 : [(49161 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1779486, c_Option_Ooption_ONone(_1779484))))], (49163 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1779484), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1779484), tc_HOL_Obool, _1779484), _1779486), c_Option_Ooption_OSome(_1779484)))))]]], (49165 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1779484)), _1779486))), hBOOL(hAPP(_1779486, c_Option_Ooption_ONone(_1779484))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1779484), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1779484), tc_HOL_Obool, _1779484), _1779486), c_Option_Ooption_OSome(_1779484))))]]], (49175 ^ _782652) ^ [_1779845, _1779847] : [class_Enum_Oenum(_1779845), 49178 ^ _782652 : [(49189 ^ _782652) ^ [] : [49190 ^ _782652 : [(49191 ^ _782652) ^ [] : [hBOOL(hAPP(_1779847, c_Option_Ooption_ONone(_1779845)))], (49193 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1779845), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1779845), tc_HOL_Obool, _1779845), _1779847), c_Option_Ooption_OSome(_1779845))))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1779845)), _1779847)))], (49179 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1779845)), _1779847)), -(hBOOL(hAPP(_1779847, c_Option_Ooption_ONone(_1779845)))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1779845), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1779845), tc_HOL_Obool, _1779845), _1779847), c_Option_Ooption_OSome(_1779845)))))]]], (49197 ^ _782652) ^ [_1780179, _1780181] : [class_Enum_Oenum(_1780179), 49200 ^ _782652 : [(49201 ^ _782652) ^ [] : [hBOOL(hAPP(_1780181, 49202 ^ [_1780179, _1780181])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1780179), _1780181)))], (49208 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1780179), _1780181)), 49211 ^ _782652 : [(49212 ^ _782652) ^ [_1780397] : [-(hBOOL(hAPP(_1780181, _1780397)))]]]]], (49214 ^ _782652) ^ [_1780432, _1780434] : [class_Enum_Oenum(_1780432), 49217 ^ _782652 : [(49218 ^ _782652) ^ [] : [49219 ^ _782652 : [(49220 ^ _782652) ^ [_1780534] : [hBOOL(hAPP(_1780434, _1780534))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1780432), _1780434)))], (49224 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1780432), _1780434)), -(hBOOL(hAPP(_1780434, 49227 ^ [_1780432, _1780434])))]]], (49231 ^ _782652) ^ [_1780675, _1780677] : [class_Enum_Oenum(_1780675), 49234 ^ _782652 : [(49235 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1780675), _1780677)), 49238 ^ _782652 : [(49239 ^ _782652) ^ [_1780801] : [-(hBOOL(hAPP(_1780677, _1780801)))]]], (49241 ^ _782652) ^ [] : [hBOOL(hAPP(_1780677, 49242 ^ [_1780675, _1780677])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1780675), _1780677)))]]], (49248 ^ _782652) ^ [_1780928, _1780930] : [class_Enum_Oenum(_1780928), 49251 ^ _782652 : [(49252 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1780928), _1780930)), -(hBOOL(hAPP(_1780930, 49255 ^ [_1780928, _1780930])))], (49259 ^ _782652) ^ [] : [49260 ^ _782652 : [(49261 ^ _782652) ^ [_1781108] : [hBOOL(hAPP(_1780930, _1781108))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1780928), _1780930)))]]], (49265 ^ _782652) ^ [_1781171, _1781173, _1781175] : [class_Enum_Oenum(_1781171), class_Enum_Oenum(_1781173), 49272 ^ _782652 : [(49273 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1781173, _1781171)), _1781175)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1781173), hAPP(hAPP(c_COMBB(tc_fun(_1781171, tc_HOL_Obool), tc_HOL_Obool, _1781173), c_Enum_Oenum__class_Oenum__ex(_1781171)), hAPP(hAPP(c_COMBB(tc_fun(_1781171, tc_prod(_1781173, _1781171)), tc_fun(_1781171, tc_HOL_Obool), _1781173), hAPP(c_COMBB(tc_prod(_1781173, _1781171), tc_HOL_Obool, _1781171), _1781175)), c_Product__Type_OPair(_1781173, _1781171))))))], (49279 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1781173), hAPP(hAPP(c_COMBB(tc_fun(_1781171, tc_HOL_Obool), tc_HOL_Obool, _1781173), c_Enum_Oenum__class_Oenum__ex(_1781171)), hAPP(hAPP(c_COMBB(tc_fun(_1781171, tc_prod(_1781173, _1781171)), tc_fun(_1781171, tc_HOL_Obool), _1781173), hAPP(c_COMBB(tc_prod(_1781173, _1781171), tc_HOL_Obool, _1781171), _1781175)), c_Product__Type_OPair(_1781173, _1781171))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1781173, _1781171)), _1781175)))]]], (49285 ^ _782652) ^ [_1781610, _1781612, _1781614] : [class_Enum_Oenum(_1781610), class_Enum_Oenum(_1781612), 49292 ^ _782652 : [(49293 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1781612, _1781610)), _1781614)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1781612), hAPP(hAPP(c_COMBB(tc_fun(_1781610, tc_HOL_Obool), tc_HOL_Obool, _1781612), c_Enum_Oenum__class_Oenum__all(_1781610)), hAPP(hAPP(c_COMBB(tc_fun(_1781610, tc_prod(_1781612, _1781610)), tc_fun(_1781610, tc_HOL_Obool), _1781612), hAPP(c_COMBB(tc_prod(_1781612, _1781610), tc_HOL_Obool, _1781610), _1781614)), c_Product__Type_OPair(_1781612, _1781610))))))], (49299 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1781612), hAPP(hAPP(c_COMBB(tc_fun(_1781610, tc_HOL_Obool), tc_HOL_Obool, _1781612), c_Enum_Oenum__class_Oenum__all(_1781610)), hAPP(hAPP(c_COMBB(tc_fun(_1781610, tc_prod(_1781612, _1781610)), tc_fun(_1781610, tc_HOL_Obool), _1781612), hAPP(c_COMBB(tc_prod(_1781612, _1781610), tc_HOL_Obool, _1781610), _1781614)), c_Product__Type_OPair(_1781612, _1781610))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1781612, _1781610)), _1781614)))]]], (49305 ^ _782652) ^ [_1782049, _1782051, _1782053, _1782055] : [class_Orderings_Oorder(_1782049), class_Enum_Oenum(_1782051), 49312 ^ _782652 : [(49313 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1782051, _1782049)), _1782053), _1782055)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1782051), hAPP(hAPP(c_COMBS(_1782051, _1782049, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1782049, tc_fun(_1782049, tc_HOL_Obool), _1782051), c_Orderings_Oord__class_Oless__eq(_1782049)), _1782053)), _1782055))))], (49319 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1782051), hAPP(hAPP(c_COMBS(_1782051, _1782049, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1782049, tc_fun(_1782049, tc_HOL_Obool), _1782051), c_Orderings_Oord__class_Oless__eq(_1782049)), _1782053)), _1782055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1782051, _1782049)), _1782053), _1782055)))]]], (49325 ^ _782652) ^ [_1782439, _1782441, _1782443, _1782445] : [class_Orderings_Oorder(_1782439), class_Enum_Oenum(_1782441), 49332 ^ _782652 : [(49333 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1782441, _1782439)), _1782443), _1782445)), 49336 ^ _782652 : [(49337 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1782441, _1782439)), _1782443), _1782445)))], (49339 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1782441), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1782441), c_fNot), hAPP(hAPP(c_COMBS(_1782441, _1782439, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1782439, tc_fun(_1782439, tc_HOL_Obool), _1782441), c_fequal), _1782443)), _1782445)))))]]], (49341 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1782441, _1782439)), _1782443), _1782445))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1782441, _1782439)), _1782443), _1782445)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1782441), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1782441), c_fNot), hAPP(hAPP(c_COMBS(_1782441, _1782439, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1782439, tc_fun(_1782439, tc_HOL_Obool), _1782441), c_fequal), _1782443)), _1782445))))]]], (49351 ^ _782652) ^ [_1782959, _1782961, _1782963] : [class_Enum_Oenum(_1782959), class_Enum_Oenum(_1782961), 49358 ^ _782652 : [(49359 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1782961, _1782959)), _1782963)), -(c_Enum_Oall__n__lists(_1782959, hAPP(hAPP(c_COMBB(tc_fun(_1782961, _1782959), tc_HOL_Obool, tc_List_Olist(_1782959)), _1782963), hAPP(hAPP(c_COMBB(tc_fun(_1782961, tc_Option_Ooption(_1782959)), tc_fun(_1782961, _1782959), tc_List_Olist(_1782959)), c_Fun_Ocomp(tc_Option_Ooption(_1782959), _1782959, _1782961, c_Option_Othe(_1782959))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1782961, _1782959)), tc_fun(_1782961, tc_Option_Ooption(_1782959)), tc_List_Olist(_1782959)), c_Map_Omap__of(_1782961, _1782959)), hAPP(c_List_Ozip(_1782961, _1782959), c_Enum_Oenum__class_Oenum(_1782961))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782961)), c_Enum_Oenum__class_Oenum(_1782961))))], (49365 ^ _782652) ^ [] : [c_Enum_Oall__n__lists(_1782959, hAPP(hAPP(c_COMBB(tc_fun(_1782961, _1782959), tc_HOL_Obool, tc_List_Olist(_1782959)), _1782963), hAPP(hAPP(c_COMBB(tc_fun(_1782961, tc_Option_Ooption(_1782959)), tc_fun(_1782961, _1782959), tc_List_Olist(_1782959)), c_Fun_Ocomp(tc_Option_Ooption(_1782959), _1782959, _1782961, c_Option_Othe(_1782959))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1782961, _1782959)), tc_fun(_1782961, tc_Option_Ooption(_1782959)), tc_List_Olist(_1782959)), c_Map_Omap__of(_1782961, _1782959)), hAPP(c_List_Ozip(_1782961, _1782959), c_Enum_Oenum__class_Oenum(_1782961))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782961)), c_Enum_Oenum__class_Oenum(_1782961))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1782961, _1782959)), _1782963)))]]], (49371 ^ _782652) ^ [_1783506, _1783508, _1783510] : [class_Enum_Oenum(_1783506), class_Enum_Oenum(_1783508), 49378 ^ _782652 : [(49379 ^ _782652) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1783508, _1783506)), _1783510)), -(c_Enum_Oex__n__lists(_1783506, hAPP(hAPP(c_COMBB(tc_fun(_1783508, _1783506), tc_HOL_Obool, tc_List_Olist(_1783506)), _1783510), hAPP(hAPP(c_COMBB(tc_fun(_1783508, tc_Option_Ooption(_1783506)), tc_fun(_1783508, _1783506), tc_List_Olist(_1783506)), c_Fun_Ocomp(tc_Option_Ooption(_1783506), _1783506, _1783508, c_Option_Othe(_1783506))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1783508, _1783506)), tc_fun(_1783508, tc_Option_Ooption(_1783506)), tc_List_Olist(_1783506)), c_Map_Omap__of(_1783508, _1783506)), hAPP(c_List_Ozip(_1783508, _1783506), c_Enum_Oenum__class_Oenum(_1783508))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783508)), c_Enum_Oenum__class_Oenum(_1783508))))], (49385 ^ _782652) ^ [] : [c_Enum_Oex__n__lists(_1783506, hAPP(hAPP(c_COMBB(tc_fun(_1783508, _1783506), tc_HOL_Obool, tc_List_Olist(_1783506)), _1783510), hAPP(hAPP(c_COMBB(tc_fun(_1783508, tc_Option_Ooption(_1783506)), tc_fun(_1783508, _1783506), tc_List_Olist(_1783506)), c_Fun_Ocomp(tc_Option_Ooption(_1783506), _1783506, _1783508, c_Option_Othe(_1783506))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1783508, _1783506)), tc_fun(_1783508, tc_Option_Ooption(_1783506)), tc_List_Olist(_1783506)), c_Map_Omap__of(_1783508, _1783506)), hAPP(c_List_Ozip(_1783508, _1783506), c_Enum_Oenum__class_Oenum(_1783508))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783508)), c_Enum_Oenum__class_Oenum(_1783508))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1783508, _1783506)), _1783510)))]]], (49391 ^ _782652) ^ [_1784053, _1784055, _1784057, _1784059] : [class_Enum_Oenum(_1784053), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784055)), _1784057) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784053)), c_Enum_Oenum__class_Oenum(_1784053)), -(hAPP(hAPP(c_Map_Omap__of(_1784053, _1784055), hAPP(hAPP(c_List_Ozip(_1784053, _1784055), c_Enum_Oenum__class_Oenum(_1784053)), _1784057)), _1784059) = hAPP(c_Option_Ooption_OSome(_1784055), 49398 ^ [_1784053, _1784055, _1784057, _1784059]))], (49402 ^ _782652) ^ [_1784282, _1784284, _1784286] : [49404 ^ _782652 : [(49405 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784282), 49403 ^ [_1784282, _1784284, _1784286]), hAPP(c_List_Oset(_1784282), c_List_OdropWhile(_1784282, _1784284, _1784286)))))], (49407 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1784284, 49403 ^ [_1784282, _1784284, _1784286])))]], -(c_List_OtakeWhile(_1784282, _1784284, _1784286) = hAPP(c_List_Ofilter(_1784282, _1784284), _1784286))], (49411 ^ _782652) ^ [_1784403, _1784405, _1784407, _1784409] : [49413 ^ _782652 : [(49414 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49412 ^ [_1784403, _1784405, _1784407, _1784409]), _1784403)))], (49416 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49412 ^ [_1784403, _1784405, _1784407, _1784409]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784405)), _1784407))))], (49418 ^ _782652) ^ [] : [hBOOL(hAPP(_1784409, hAPP(hAPP(c_List_Onth(_1784405), _1784407), 49412 ^ [_1784403, _1784405, _1784407, _1784409])))]], 49421 ^ _782652 : [(49422 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1784403), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784405)), _1784407))))], (49424 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1784409, hAPP(hAPP(c_List_Onth(_1784405), _1784407), _1784403))))]], -(c_List_OtakeWhile(_1784405, _1784409, _1784407) = hAPP(hAPP(c_List_Otake(_1784405), _1784403), _1784407))], (49428 ^ _782652) ^ [_1784807, _1784809, _1784811, _1784813] : [49430 ^ _782652 : [(49431 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49429 ^ [_1784807, _1784809, _1784811, _1784813]), _1784807)))], (49433 ^ _782652) ^ [] : [hBOOL(hAPP(_1784809, hAPP(hAPP(c_List_Onth(_1784811), _1784813), 49429 ^ [_1784807, _1784809, _1784811, _1784813])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1784807), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784811)), _1784813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1784807), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784811)), c_List_OtakeWhile(_1784811, _1784809, _1784813)))))], (49441 ^ _782652) ^ [_1785115, _1785117, _1785119] : [-(c_List_Olistsp(_1785115, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785115, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1785115, tc_fun(_1785115, tc_HOL_Obool), tc_HOL_Obool), c_member(_1785115)), _1785117)), hAPP(hAPP(c_COMBC(_1785115, tc_fun(_1785115, tc_HOL_Obool), tc_HOL_Obool), c_member(_1785115)), _1785119))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1785115), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1785115), tc_fun(tc_List_Olist(_1785115), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1785115))), c_List_Olists(_1785115, _1785117))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1785115), tc_fun(tc_List_Olist(_1785115), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1785115))), c_List_Olists(_1785115, _1785119))))], (49443 ^ _782652) ^ [_1785247, _1785249, _1785251, _1785253] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1785247)), _1785249), c_List_Olists(_1785247, _1785251))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1785247)), _1785249), c_List_Olists(_1785247, _1785253))), -(hBOOL(hAPP(c_List_Olistsp(_1785247, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785247, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1785247, tc_fun(_1785247, tc_HOL_Obool), tc_HOL_Obool), c_member(_1785247)), _1785251)), hAPP(hAPP(c_COMBC(_1785247, tc_fun(_1785247, tc_HOL_Obool), tc_HOL_Obool), c_member(_1785247)), _1785253))), _1785249)))], (49453 ^ _782652) ^ [_1785524, _1785526] : [-(hBOOL(hAPP(c_List_Olistsp(_1785524, _1785526), c_List_Olist_ONil(_1785524))))], (49455 ^ _782652) ^ [_1785556, _1785558, _1785560] : [-(c_List_Olistsp(_1785556, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785556, tc_HOL_Obool)), _1785558), _1785560)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1785556), tc_HOL_Obool)), c_List_Olistsp(_1785556, _1785558)), c_List_Olistsp(_1785556, _1785560)))], (49457 ^ _782652) ^ [_1785616, _1785618, _1785620, _1785622] : [hBOOL(hAPP(c_List_Olistsp(_1785616, _1785618), _1785620)), hBOOL(hAPP(c_List_Olistsp(_1785616, _1785622), _1785620)), -(hBOOL(hAPP(c_List_Olistsp(_1785616, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785616, tc_HOL_Obool)), _1785618), _1785622)), _1785620)))], (49467 ^ _782652) ^ [_1785826, _1785828, _1785830, _1785832] : [hBOOL(hAPP(c_List_Olistsp(_1785826, hAPP(hAPP(c_COMBS(_1785826, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785826), c_fconj), _1785828)), _1785830)), _1785832)), 49470 ^ _782652 : [(49471 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1785826, _1785828), _1785832)))], (49473 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1785826, _1785830), _1785832)))]]], (49475 ^ _782652) ^ [_1785999, _1786001, _1786003, _1786005] : [-(hBOOL(hAPP(c_List_Olistsp(_1785999, hAPP(hAPP(c_COMBS(_1785999, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785999), c_fconj), _1786001)), _1786003)), _1786005))), hBOOL(hAPP(c_List_Olistsp(_1785999, _1786001), _1786005)), hBOOL(hAPP(c_List_Olistsp(_1785999, _1786003), _1786005))], (49485 ^ _782652) ^ [_1786208, _1786210] : [-(hBOOL(hAPP(c_List_Olistsp(_1786208, _1786210), c_List_Olist_ONil(_1786208))))], (49497 ^ _782652) ^ [_1786456, _1786458, _1786460] : [49499 ^ _782652 : [(49500 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786456), 49498 ^ [_1786456, _1786458, _1786460]), hAPP(c_List_Oset(_1786456), _1786460))))], (49502 ^ _782652) ^ [] : [hBOOL(hAPP(_1786458, 49498 ^ [_1786456, _1786458, _1786460]))]], -(hBOOL(hAPP(c_List_Olistsp(_1786456, _1786458), _1786460)))], (49487 ^ _782652) ^ [_1786258, _1786260, _1786262] : [hBOOL(hAPP(c_List_Olistsp(_1786258, _1786260), _1786262)), 49490 ^ _782652 : [(49491 ^ _782652) ^ [_1786347] : [hBOOL(hAPP(hAPP(c_member(_1786258), _1786347), hAPP(c_List_Oset(_1786258), _1786262))), -(hBOOL(hAPP(_1786260, _1786347)))]]], (49506 ^ _782652) ^ [_1786667, _1786669, _1786671, _1786673] : [hBOOL(hAPP(c_List_Olistsp(_1786667, _1786669), hAPP(hAPP(c_List_Oappend(_1786667), _1786671), _1786673))), 49509 ^ _782652 : [(49510 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1786667, _1786669), _1786671)))], (49512 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1786667, _1786669), _1786673)))]]], (49514 ^ _782652) ^ [_1786816, _1786818, _1786820, _1786822] : [-(hBOOL(hAPP(c_List_Olistsp(_1786816, _1786818), hAPP(hAPP(c_List_Oappend(_1786816), _1786820), _1786822)))), hBOOL(hAPP(c_List_Olistsp(_1786816, _1786818), _1786820)), hBOOL(hAPP(c_List_Olistsp(_1786816, _1786818), _1786822))], (49524 ^ _782652) ^ [_1787022, _1787024, _1787026, _1787028] : [hBOOL(hAPP(c_List_Olistsp(_1787022, _1787024), hAPP(hAPP(c_List_Olist_OCons(_1787022), _1787026), _1787028))), 49527 ^ _782652 : [(49528 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1787024, _1787026)))], (49530 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1787022, _1787024), _1787028)))]]], (49532 ^ _782652) ^ [_1787165, _1787167, _1787169, _1787171] : [-(hBOOL(hAPP(c_List_Olistsp(_1787165, _1787167), hAPP(hAPP(c_List_Olist_OCons(_1787165), _1787169), _1787171)))), hBOOL(hAPP(_1787167, _1787169)), hBOOL(hAPP(c_List_Olistsp(_1787165, _1787167), _1787171))], (49542 ^ _782652) ^ [_1787344, _1787346, _1787348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1787344, tc_HOL_Obool)), _1787346), _1787348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1787344), tc_HOL_Obool)), c_List_Olistsp(_1787344, _1787346)), c_List_Olistsp(_1787344, _1787348))))], (49548 ^ _782652) ^ [_1787497, _1787499, _1787501] : [hBOOL(hAPP(c_List_Olistsp(_1787497, hAPP(hAPP(c_COMBC(_1787497, tc_fun(_1787497, tc_HOL_Obool), tc_HOL_Obool), c_member(_1787497)), _1787499)), _1787501)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1787497)), _1787501), c_List_Olists(_1787497, _1787499))))], (49554 ^ _782652) ^ [_1787636, _1787638, _1787640] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1787636)), _1787640), c_List_Olists(_1787636, _1787638))), -(hBOOL(hAPP(c_List_Olistsp(_1787636, hAPP(hAPP(c_COMBC(_1787636, tc_fun(_1787636, tc_HOL_Obool), tc_HOL_Obool), c_member(_1787636)), _1787638)), _1787640)))], (49560 ^ _782652) ^ [_1787807, _1787809, _1787811, _1787813, _1787815] : [c_List_Olist__all2(_1787807, _1787809, _1787811, _1787813, _1787815), 49563 ^ _782652 : [(49564 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787807)), _1787813) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787809)), _1787815))], (49566 ^ _782652) ^ [_1788098] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1787807, _1787809)), _1788098), hAPP(c_List_Oset(tc_prod(_1787807, _1787809)), hAPP(hAPP(c_List_Ozip(_1787807, _1787809), _1787813), _1787815)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1787807, _1787809, tc_HOL_Obool), _1787811), _1788098)))]]], (49572 ^ _782652) ^ [_1788373, _1788375, _1788377, _1788379, _1788381] : [-(c_List_Olist__all2(_1788373, _1788375, _1788377, _1788379, _1788381)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788373)), _1788379) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788375)), _1788381), 49578 ^ _782652 : [(49579 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788373, _1788375)), 49577 ^ [_1788373, _1788375, _1788377, _1788379, _1788381]), hAPP(c_List_Oset(tc_prod(_1788373, _1788375)), hAPP(hAPP(c_List_Ozip(_1788373, _1788375), _1788379), _1788381)))))], (49581 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1788373, _1788375, tc_HOL_Obool), _1788377), 49577 ^ [_1788373, _1788375, _1788377, _1788379, _1788381]))]]], (49585 ^ _782652) ^ [_1789021, _1789023] : [class_Orderings_Olinorder(_1789021), 49588 ^ _782652 : [(49589 ^ _782652) ^ [] : [c_List_Olinorder__class_Osorted(_1789021, _1789023), -(_1789023 = c_List_Olist_ONil(_1789021)), 49598 ^ _782652 : [(49599 ^ _782652) ^ [] : [-(_1789023 = hAPP(hAPP(c_List_Olist_OCons(_1789021), 49597 ^ [_1789021, _1789023]), 49596 ^ [_1789021, _1789023]))], (49607 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1789021, 49596 ^ [_1789021, _1789023]))], (49601 ^ _782652) ^ [_1789733] : [hBOOL(hAPP(hAPP(c_member(_1789021), _1789733), hAPP(c_List_Oset(_1789021), 49596 ^ [_1789021, _1789023]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789021), 49597 ^ [_1789021, _1789023]), _1789733)))]]], (49609 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1789021, _1789023)), 49610 ^ _782652 : [(49611 ^ _782652) ^ [] : [_1789023 = c_List_Olist_ONil(_1789021)], (49613 ^ _782652) ^ [_1790166, _1790168] : [_1789023 = hAPP(hAPP(c_List_Olist_OCons(_1789021), _1790166), _1790168), 49619 ^ _782652 : [(49620 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789021), 49618 ^ [_1789021, _1789023, _1790166, _1790168]), hAPP(c_List_Oset(_1789021), _1790168))))], (49622 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1789021), _1790166), 49618 ^ [_1789021, _1789023, _1790166, _1790168]))]], c_List_Olinorder__class_Osorted(_1789021, _1790168)]]]]], (49628 ^ _782652) ^ [_1790885, _1790887, _1790889, _1790891, _1790893, _1790895, _1790897] : [c_List_Olist__all2(_1790885, _1790887, _1790889, hAPP(hAPP(c_List_Olist_OCons(_1790885), _1790891), _1790893), hAPP(hAPP(c_List_Olist_OCons(_1790887), _1790895), _1790897)), 49631 ^ _782652 : [(49632 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(_1790889, _1790891), _1790895)))], (49634 ^ _782652) ^ [] : [-(c_List_Olist__all2(_1790885, _1790887, _1790889, _1790893, _1790897))]]], (49636 ^ _782652) ^ [_1791216, _1791218, _1791220, _1791222, _1791224, _1791226, _1791228] : [-(c_List_Olist__all2(_1791216, _1791218, _1791220, hAPP(hAPP(c_List_Olist_OCons(_1791216), _1791222), _1791224), hAPP(hAPP(c_List_Olist_OCons(_1791218), _1791226), _1791228))), hBOOL(hAPP(hAPP(_1791220, _1791222), _1791226)), c_List_Olist__all2(_1791216, _1791218, _1791220, _1791224, _1791228)], (49646 ^ _782652) ^ [_1791720, _1791722, _1791724, _1791726, _1791728, _1791730, _1791732] : [c_List_Olist__all2(_1791720, _1791722, _1791724, hAPP(hAPP(c_List_Omap(_1791726, _1791720), _1791728), _1791730), _1791732), -(c_List_Olist__all2(_1791726, _1791722, hAPP(hAPP(c_COMBB(_1791720, tc_fun(_1791722, tc_HOL_Obool), _1791726), _1791724), _1791728), _1791730, _1791732))], (49652 ^ _782652) ^ [_1791968, _1791970, _1791972, _1791974, _1791976, _1791978, _1791980] : [c_List_Olist__all2(_1791974, _1791970, hAPP(hAPP(c_COMBB(_1791968, tc_fun(_1791970, tc_HOL_Obool), _1791974), _1791972), _1791976), _1791978, _1791980), -(c_List_Olist__all2(_1791968, _1791970, _1791972, hAPP(hAPP(c_List_Omap(_1791974, _1791968), _1791976), _1791978), _1791980))], (49658 ^ _782652) ^ [_1792365, _1792367, _1792369, _1792371, _1792373, _1792375, _1792377] : [c_List_Olist__all2(_1792365, _1792367, _1792369, _1792371, hAPP(hAPP(c_List_Omap(_1792373, _1792367), _1792375), _1792377)), -(c_List_Olist__all2(_1792365, _1792373, hAPP(hAPP(c_COMBC(_1792365, tc_fun(_1792373, _1792367), tc_fun(_1792373, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1792367, tc_HOL_Obool), tc_fun(tc_fun(_1792373, _1792367), tc_fun(_1792373, tc_HOL_Obool)), _1792365), c_COMBB(_1792367, tc_HOL_Obool, _1792373)), _1792369)), _1792375), _1792371, _1792377))], (49664 ^ _782652) ^ [_1792671, _1792673, _1792675, _1792677, _1792679, _1792681, _1792683] : [c_List_Olist__all2(_1792671, _1792679, hAPP(hAPP(c_COMBC(_1792671, tc_fun(_1792679, _1792673), tc_fun(_1792679, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1792673, tc_HOL_Obool), tc_fun(tc_fun(_1792679, _1792673), tc_fun(_1792679, tc_HOL_Obool)), _1792671), c_COMBB(_1792673, tc_HOL_Obool, _1792679)), _1792675)), _1792681), _1792677, _1792683), -(c_List_Olist__all2(_1792671, _1792673, _1792675, _1792677, hAPP(hAPP(c_List_Omap(_1792679, _1792673), _1792681), _1792683)))], (49670 ^ _782652) ^ [_1793097, _1793099, _1793101, _1793103, _1793105, _1793107, _1793109] : [c_List_Olist__all2(_1793097, _1793099, _1793101, _1793103, _1793105), c_List_Olist__all2(_1793097, _1793099, _1793101, _1793107, _1793109), -(c_List_Olist__all2(_1793097, _1793099, _1793101, hAPP(hAPP(c_List_Oappend(_1793097), _1793103), _1793107), hAPP(hAPP(c_List_Oappend(_1793099), _1793105), _1793109)))], (49680 ^ _782652) ^ [_1793566, _1793568, _1793570, _1793572, _1793574, _1793576, _1793578] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793566)), _1793568) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1793570)), _1793572), 49683 ^ _782652 : [(49684 ^ _782652) ^ [] : [c_List_Olist__all2(_1793566, _1793570, _1793574, hAPP(hAPP(c_List_Oappend(_1793566), _1793568), _1793576), hAPP(hAPP(c_List_Oappend(_1793570), _1793572), _1793578)), 49687 ^ _782652 : [(49688 ^ _782652) ^ [] : [-(c_List_Olist__all2(_1793566, _1793570, _1793574, _1793568, _1793572))], (49690 ^ _782652) ^ [] : [-(c_List_Olist__all2(_1793566, _1793570, _1793574, _1793576, _1793578))]]], (49692 ^ _782652) ^ [] : [-(c_List_Olist__all2(_1793566, _1793570, _1793574, hAPP(hAPP(c_List_Oappend(_1793566), _1793568), _1793576), hAPP(hAPP(c_List_Oappend(_1793570), _1793572), _1793578))), c_List_Olist__all2(_1793566, _1793570, _1793574, _1793568, _1793572), c_List_Olist__all2(_1793566, _1793570, _1793574, _1793576, _1793578)]]], (49702 ^ _782652) ^ [_1794468, _1794470, _1794472, _1794474, _1794476] : [c_List_Olist__all2(_1794468, _1794470, _1794472, hAPP(c_List_Orev(_1794468), _1794474), hAPP(c_List_Orev(_1794470), _1794476)), -(c_List_Olist__all2(_1794468, _1794470, _1794472, _1794474, _1794476))], (49708 ^ _782652) ^ [_1794680, _1794682, _1794684, _1794686, _1794688] : [c_List_Olist__all2(_1794680, _1794682, _1794684, _1794686, _1794688), -(c_List_Olist__all2(_1794680, _1794682, _1794684, hAPP(c_List_Orev(_1794680), _1794686), hAPP(c_List_Orev(_1794682), _1794688)))], (49714 ^ _782652) ^ [_1795013, _1795015, _1795017, _1795019, _1795021] : [c_List_Olist__all2(_1795013, _1795015, _1795017, hAPP(c_List_Orev(_1795013), _1795019), _1795021), -(c_List_Olist__all2(_1795013, _1795015, _1795017, _1795019, hAPP(c_List_Orev(_1795015), _1795021)))], (49720 ^ _782652) ^ [_1795225, _1795227, _1795229, _1795231, _1795233] : [c_List_Olist__all2(_1795225, _1795227, _1795229, _1795231, hAPP(c_List_Orev(_1795227), _1795233)), -(c_List_Olist__all2(_1795225, _1795227, _1795229, hAPP(c_List_Orev(_1795225), _1795231), _1795233))], (49726 ^ _782652) ^ [_1795558, _1795560, _1795562, _1795564, _1795566] : [c_List_Olist__all2(_1795558, _1795560, _1795562, _1795564, _1795566), 49729 ^ _782652 : [(49730 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795558)), _1795564) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795560)), _1795566))], (49732 ^ _782652) ^ [_1795852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1795852), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1795558)), _1795564))), -(hBOOL(hAPP(hAPP(_1795562, hAPP(hAPP(c_List_Onth(_1795558), _1795564), _1795852)), hAPP(hAPP(c_List_Onth(_1795560), _1795566), _1795852))))]]], (49738 ^ _782652) ^ [_1796121, _1796123, _1796125, _1796127, _1796129] : [-(c_List_Olist__all2(_1796121, _1796123, _1796125, _1796127, _1796129)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796121)), _1796127) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796123)), _1796129), 49744 ^ _782652 : [(49745 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49743 ^ [_1796121, _1796123, _1796125, _1796127, _1796129]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796121)), _1796127))))], (49747 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1796125, hAPP(hAPP(c_List_Onth(_1796121), _1796127), 49743 ^ [_1796121, _1796123, _1796125, _1796127, _1796129])), hAPP(hAPP(c_List_Onth(_1796123), _1796129), 49743 ^ [_1796121, _1796123, _1796125, _1796127, _1796129])))]]], (49751 ^ _782652) ^ [_1796829, _1796831, _1796833, _1796835, _1796837, _1796839] : [c_List_Olist__all2(_1796829, _1796831, _1796833, _1796835, _1796837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796839), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796829)), _1796835))), -(hBOOL(hAPP(hAPP(_1796833, hAPP(hAPP(c_List_Onth(_1796829), _1796835), _1796839)), hAPP(hAPP(c_List_Onth(_1796831), _1796837), _1796839))))], (49761 ^ _782652) ^ [_1797296, _1797298, _1797300, _1797302, _1797304, _1797306] : [c_List_Olist__all2(_1797296, _1797298, _1797300, _1797302, _1797304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1797306), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1797298)), _1797304))), -(hBOOL(hAPP(hAPP(_1797300, hAPP(hAPP(c_List_Onth(_1797296), _1797302), _1797306)), hAPP(hAPP(c_List_Onth(_1797298), _1797304), _1797306))))], (49771 ^ _782652) ^ [_1797764, _1797766, _1797768, _1797770] : [c_List_Olist__all2(_1797764, _1797766, _1797768, c_List_Olist_ONil(_1797764), _1797770), -(_1797770 = c_List_Olist_ONil(_1797766))], (49777 ^ _782652) ^ [_1797952, _1797954, _1797956, _1797958] : [_1797958 = c_List_Olist_ONil(_1797954), -(c_List_Olist__all2(_1797952, _1797954, _1797956, c_List_Olist_ONil(_1797952), _1797958))], (49783 ^ _782652) ^ [_1798247, _1798249, _1798251, _1798253] : [c_List_Olist__all2(_1798247, _1798249, _1798251, _1798253, c_List_Olist_ONil(_1798249)), -(_1798253 = c_List_Olist_ONil(_1798247))], (49789 ^ _782652) ^ [_1798435, _1798437, _1798439, _1798441] : [_1798441 = c_List_Olist_ONil(_1798435), -(c_List_Olist__all2(_1798435, _1798437, _1798439, _1798441, c_List_Olist_ONil(_1798437)))], (49795 ^ _782652) ^ [_1798729, _1798731, _1798733, _1798735, _1798737, _1798739] : [c_List_Olist__all2(_1798729, _1798731, _1798733, _1798735, _1798737), -(c_List_Olist__all2(_1798729, _1798731, _1798733, hAPP(hAPP(c_List_Otake(_1798729), _1798739), _1798735), hAPP(hAPP(c_List_Otake(_1798731), _1798739), _1798737)))], (49801 ^ _782652) ^ [_1799063, _1799065, _1799067, _1799069, _1799071, _1799073] : [c_List_Olist__all2(_1799063, _1799065, _1799067, _1799069, _1799071), -(c_List_Olist__all2(_1799063, _1799065, _1799067, hAPP(hAPP(c_List_Odrop(_1799063), _1799073), _1799069), hAPP(hAPP(c_List_Odrop(_1799065), _1799073), _1799071)))], (49807 ^ _782652) ^ [_1799383, _1799385, _1799387, _1799389, _1799391] : [c_List_Olist__all2(_1799383, _1799385, _1799387, _1799389, _1799391), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799383)), _1799389) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799385)), _1799391))], (49813 ^ _782652) ^ [_1799688, _1799690, _1799692] : [_1799688 = _1799690, -(c_List_Olist__all2(_1799692, _1799692, c_fequal, _1799688, _1799690))], (49819 ^ _782652) ^ [_1799862, _1799864, _1799866] : [c_List_Olist__all2(_1799866, _1799866, c_fequal, _1799862, _1799864), -(_1799862 = _1799864)], (49825 ^ _782652) ^ [_1800170, _1800172, _1800174, _1800176, _1800178, _1800180, _1800182, _1800184] : [c_List_Olist__all2(_1800170, _1800172, _1800174, _1800176, _1800178), hBOOL(hAPP(hAPP(_1800174, _1800180), _1800182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800184), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800172)), _1800178))), -(c_List_Olist__all2(_1800170, _1800172, _1800174, hAPP(hAPP(c_List_Olist__update(_1800170, _1800176), _1800184), _1800180), hAPP(hAPP(c_List_Olist__update(_1800172, _1800178), _1800184), _1800182)))], (49839 ^ _782652) ^ [_1800808, _1800810, _1800812, _1800814, _1800816, _1800818, _1800820, _1800822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800808), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800810)), _1800812))), c_List_Olist__all2(_1800810, _1800814, _1800816, _1800812, _1800818), hBOOL(hAPP(hAPP(_1800816, _1800820), _1800822)), -(c_List_Olist__all2(_1800810, _1800814, _1800816, hAPP(hAPP(c_List_Olist__update(_1800810, _1800812), _1800808), _1800820), hAPP(hAPP(c_List_Olist__update(_1800814, _1800818), _1800808), _1800822)))], (49853 ^ _782652) ^ [_1801404, _1801406, _1801408, _1801410, _1801412] : [49855 ^ _782652 : [(49856 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801404, _1801406)), 49854 ^ [_1801404, _1801406, _1801408, _1801410, _1801412]), hAPP(c_List_Oset(tc_prod(_1801404, _1801406)), hAPP(hAPP(c_List_Ozip(_1801404, _1801406), _1801408), _1801410)))))], (49858 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1801404, _1801406, tc_HOL_Obool), _1801412), 49854 ^ [_1801404, _1801406, _1801408, _1801410, _1801412]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801404)), _1801408) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801406)), _1801410), -(c_List_Olist__all2(_1801404, _1801406, _1801412, _1801408, _1801410))], (49866 ^ _782652) ^ [_1802078, _1802080, _1802082, _1802084] : [49868 ^ _782652 : [(49869 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49867 ^ [_1802078, _1802080, _1802082, _1802084]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1802078)), _1802080))))], (49871 ^ _782652) ^ [] : [hBOOL(hAPP(_1802082, hAPP(hAPP(c_List_Onth(_1802078), _1802080), 49867 ^ [_1802078, _1802080, _1802082, _1802084])))]], hBOOL(hAPP(hAPP(c_member(_1802078), _1802084), hAPP(c_List_Oset(_1802078), _1802080))), -(hBOOL(hAPP(_1802082, _1802084)))], (49879 ^ _782652) ^ [_1802698, _1802700, _1802702, _1802704, _1802706] : [c_Fun_Oinj__on(_1802698, _1802700, _1802702, hAPP(hAPP(c_Set_Oinsert(_1802698), _1802704), hAPP(c_List_Oset(_1802698), _1802706))), -(hAPP(hAPP(c_List_Omap(_1802698, _1802700), _1802702), hAPP(c_List_OremoveAll(_1802698, _1802704), _1802706)) = hAPP(c_List_OremoveAll(_1802700, hAPP(_1802702, _1802704)), hAPP(hAPP(c_List_Omap(_1802698, _1802700), _1802702), _1802706)))], (49885 ^ _782652) ^ [_1803036, _1803038, _1803040] : [-(hBOOL(hAPP(hAPP(c_member(_1803036), _1803038), hAPP(c_List_Oset(_1803036), _1803040)))), -(c_List_Oinsert(_1803036, _1803038, _1803040) = hAPP(hAPP(c_List_Olist_OCons(_1803036), _1803038), _1803040))], (49891 ^ _782652) ^ [_1803351, _1803353, _1803355, _1803357] : [_1803351 = _1803353, -(hAPP(c_List_OremoveAll(_1803355, _1803351), hAPP(hAPP(c_List_Olist_OCons(_1803355), _1803353), _1803357)) = hAPP(c_List_OremoveAll(_1803355, _1803351), _1803357))], (49897 ^ _782652) ^ [_1803565, _1803567, _1803569, _1803571] : [-(_1803565 = _1803567), -(hAPP(c_List_OremoveAll(_1803569, _1803565), hAPP(hAPP(c_List_Olist_OCons(_1803569), _1803567), _1803571)) = hAPP(hAPP(c_List_Olist_OCons(_1803569), _1803567), hAPP(c_List_OremoveAll(_1803569, _1803565), _1803571)))], (49903 ^ _782652) ^ [_1803862, _1803864, _1803866] : [hBOOL(hAPP(c_List_Odistinct(_1803862), _1803864)), -(hBOOL(hAPP(c_List_Odistinct(_1803862), hAPP(c_List_OremoveAll(_1803862, _1803866), _1803864))))], (49909 ^ _782652) ^ [_1804120, _1804122, _1804124] : [hBOOL(hAPP(c_List_Odistinct(_1804120), _1804122)), -(hBOOL(hAPP(c_List_Odistinct(_1804120), c_List_Oinsert(_1804120, _1804124, _1804122))))], (49915 ^ _782652) ^ [_1804373, _1804375, _1804377, _1804379] : [-(hAPP(c_List_OremoveAll(_1804373, _1804375), hAPP(hAPP(c_List_Oappend(_1804373), _1804377), _1804379)) = hAPP(hAPP(c_List_Oappend(_1804373), hAPP(c_List_OremoveAll(_1804373, _1804375), _1804377)), hAPP(c_List_OremoveAll(_1804373, _1804375), _1804379)))], (49917 ^ _782652) ^ [_1804534, _1804536, _1804538] : [-(hBOOL(hAPP(hAPP(c_member(_1804534), _1804536), hAPP(c_List_Oset(_1804534), _1804538)))), -(hAPP(c_List_OremoveAll(_1804534, _1804536), _1804538) = _1804538)], (49923 ^ _782652) ^ [_1804774, _1804776] : [-(hAPP(c_List_OremoveAll(_1804774, _1804776), c_List_Olist_ONil(_1804774)) = c_List_Olist_ONil(_1804774))], (49925 ^ _782652) ^ [_1804878, _1804880] : [-(c_List_OremoveAll(_1804878, _1804880) = c_List_Ofilter(_1804878, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1804878), c_fNot), hAPP(c_fequal, _1804880))))], (49927 ^ _782652) ^ [_1805034, _1805036, _1805038, _1805040] : [-(hBOOL(hAPP(_1805034, _1805036))), -(hAPP(c_List_OremoveAll(_1805038, _1805036), hAPP(c_List_Ofilter(_1805038, _1805034), _1805040)) = hAPP(c_List_Ofilter(_1805038, _1805034), _1805040))], (49933 ^ _782652) ^ [_1805298, _1805300, _1805302] : [-(c_List_Oinsert(_1805298, _1805300, c_List_Oremdups(_1805298, _1805302)) = c_List_Oremdups(_1805298, c_List_Oinsert(_1805298, _1805300, _1805302)))], (49935 ^ _782652) ^ [_1805437, _1805439, _1805441] : [hBOOL(hAPP(c_List_Odistinct(_1805437), _1805439)), -(c_List_Oremove1(_1805437, _1805441, _1805439) = hAPP(c_List_OremoveAll(_1805437, _1805441), _1805439))], (49941 ^ _782652) ^ [_1805695, _1805697, _1805699] : [hBOOL(hAPP(hAPP(c_member(_1805695), _1805697), hAPP(c_List_Oset(_1805695), _1805699))), -(c_List_Oinsert(_1805695, _1805697, _1805699) = _1805699)], (49947 ^ _782652) ^ [_1805942, _1805944, _1805946] : [-(hAPP(c_List_Oset(_1805942), c_List_Oinsert(_1805942, _1805944, _1805946)) = hAPP(hAPP(c_Set_Oinsert(_1805942), _1805944), hAPP(c_List_Oset(_1805942), _1805946)))], (49949 ^ _782652) ^ [_1806060, _1806062] : [-(c_List_Oinsert(_1806060, _1806062, c_List_Olist_ONil(_1806060)) = hAPP(hAPP(c_List_Olist_OCons(_1806060), _1806062), c_List_Olist_ONil(_1806060)))], (49951 ^ _782652) ^ [_1806227, _1806229, _1806231, _1806233, _1806235] : [c_Fun_Oinj__on(_1806227, _1806229, _1806231, c_Orderings_Otop__class_Otop(tc_fun(_1806227, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1806227, _1806229), _1806231), hAPP(c_List_OremoveAll(_1806227, _1806233), _1806235)) = hAPP(c_List_OremoveAll(_1806229, hAPP(_1806231, _1806233)), hAPP(hAPP(c_List_Omap(_1806227, _1806229), _1806231), _1806235)))], (49957 ^ _782652) ^ [_1806534, _1806536, _1806538] : [-(hAPP(c_List_Oset(_1806534), hAPP(c_List_OremoveAll(_1806534, _1806536), _1806538)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1806534, tc_HOL_Obool)), hAPP(c_List_Oset(_1806534), _1806538)), hAPP(hAPP(c_Set_Oinsert(_1806534), _1806536), c_Orderings_Obot__class_Obot(tc_fun(_1806534, tc_HOL_Obool)))))], (49959 ^ _782652) ^ [_1806719, _1806721, _1806723] : [hBOOL(hAPP(hAPP(c_member(_1806719), _1806721), hAPP(c_List_Oset(_1806719), _1806723))), -(c_List_Oinsert(_1806719, _1806721, _1806723) = _1806723)], (49965 ^ _782652) ^ [_1806919, _1806921, _1806923] : [-(hBOOL(hAPP(hAPP(c_member(_1806919), _1806921), hAPP(c_List_Oset(_1806919), _1806923)))), -(c_List_Oinsert(_1806919, _1806921, _1806923) = hAPP(hAPP(c_List_Olist_OCons(_1806919), _1806921), _1806923))], (49971 ^ _782652) ^ [_1807201, _1807203, _1807205, _1807207] : [-(c_List_Oconcat(_1807201, hAPP(hAPP(c_List_Omap(_1807203, tc_List_Olist(_1807201)), _1807205), _1807207)) = c_List_Omaps(_1807203, _1807201, _1807205, _1807207))], (49973 ^ _782652) ^ [_1807346, _1807348, _1807350, _1807352] : [-(c_List_Omaps(_1807346, _1807348, _1807350, _1807352) = c_List_Oconcat(_1807348, hAPP(hAPP(c_List_Omap(_1807346, tc_List_Olist(_1807348)), _1807350), _1807352)))], (49975 ^ _782652) ^ [_1807477, _1807479, _1807481] : [-(c_List_Omaps(_1807477, _1807479, _1807481, c_List_Olist_ONil(_1807477)) = c_List_Olist_ONil(_1807479))], (49977 ^ _782652) ^ [_1807624, _1807626, _1807628, _1807630, _1807632] : [-(c_List_Omaps(_1807624, _1807626, _1807628, hAPP(hAPP(c_List_Olist_OCons(_1807624), _1807630), _1807632)) = hAPP(hAPP(c_List_Oappend(_1807626), hAPP(_1807628, _1807630)), c_List_Omaps(_1807624, _1807626, _1807628, _1807632)))], (49979 ^ _782652) ^ [_1807768, _1807770] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1807768)), _1807770)), 49985 ^ _782652 : [(49986 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1807768)), 49984 ^ [_1807768, _1807770]), hAPP(c_List_Oset(tc_List_Olist(_1807768)), _1807770))))], (49988 ^ _782652) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1807768), 49984 ^ [_1807768, _1807770]))]], 49992 ^ _782652 : [(49993 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1807768)), 49991 ^ [_1807768, _1807770]), hAPP(c_List_Oset(tc_List_Olist(_1807768)), _1807770))))], (49996 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1807768)), 49994 ^ [_1807768, _1807770]), hAPP(c_List_Oset(tc_List_Olist(_1807768)), _1807770))))], (49998 ^ _782652) ^ [] : [49991 ^ [_1807768, _1807770] = 49994 ^ [_1807768, _1807770]], (50000 ^ _782652) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1807768, tc_HOL_Obool)), hAPP(c_List_Oset(_1807768), 49991 ^ [_1807768, _1807770])), hAPP(c_List_Oset(_1807768), 49994 ^ [_1807768, _1807770])) = c_Orderings_Obot__class_Obot(tc_fun(_1807768, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1807768), c_List_Oconcat(_1807768, _1807770))))], (50004 ^ _782652) ^ [_1809064, _1809066, _1809068, _1809070, _1809072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1809064, _1809066)), hAPP(_1809064, _1809068))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1809070, _1809070)), hAPP(hAPP(c_Product__Type_OPair(_1809070, _1809070), _1809066), _1809068)), c_List_Omeasures(_1809070, _1809072))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1809070, _1809070)), hAPP(hAPP(c_Product__Type_OPair(_1809070, _1809070), _1809066), _1809068)), c_List_Omeasures(_1809070, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1809070, tc_Nat_Onat)), _1809064), _1809072)))))], (50014 ^ _782652) ^ [_1809510, _1809512] : [-(c_Wellfounded_Owf(_1809510, c_List_Omeasures(_1809510, _1809512)))], (50016 ^ _782652) ^ [_1809620, _1809622, _1809624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1809620, _1809620)), hAPP(hAPP(c_Product__Type_OPair(_1809620, _1809620), _1809622), _1809624)), c_List_Omeasures(_1809620, c_List_Olist_ONil(tc_fun(_1809620, tc_Nat_Onat)))))], (50018 ^ _782652) ^ [_1809743, _1809745] : [-(c_List_Omeasures(_1809743, _1809745) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1809743), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1809743, tc_List_Olist(tc_fun(_1809743, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809743, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1809743, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1809743), c_List_Omap(tc_fun(_1809743, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1809743, tc_Nat_Onat), _1809743, tc_Nat_Onat), c_COMBI(tc_fun(_1809743, tc_Nat_Onat))))), _1809745)))], (50020 ^ _782652) ^ [_1809995, _1809997, _1809999, _1810001, _1810003] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1809995, _1809995)), hAPP(hAPP(c_Product__Type_OPair(_1809995, _1809995), _1809997), _1809999)), c_List_Omeasures(_1809995, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1809995, tc_Nat_Onat)), _1810001), _1810003)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1810001, _1809997)), hAPP(_1810001, _1809999)))), 50027 ^ _782652 : [(50028 ^ _782652) ^ [] : [-(hAPP(_1810001, _1809997) = hAPP(_1810001, _1809999))], (50030 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1809995, _1809995)), hAPP(hAPP(c_Product__Type_OPair(_1809995, _1809995), _1809997), _1809999)), c_List_Omeasures(_1809995, _1810003))))]]], (50032 ^ _782652) ^ [_1810502, _1810504, _1810506, _1810508, _1810510] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1810502, _1810502)), hAPP(hAPP(c_Product__Type_OPair(_1810502, _1810502), _1810504), _1810506)), c_List_Omeasures(_1810502, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1810502, tc_Nat_Onat)), _1810508), _1810510))))), 50033 ^ _782652 : [(50034 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1810508, _1810504)), hAPP(_1810508, _1810506)))], (50036 ^ _782652) ^ [] : [hAPP(_1810508, _1810504) = hAPP(_1810508, _1810506), hBOOL(hAPP(hAPP(c_member(tc_prod(_1810502, _1810502)), hAPP(hAPP(c_Product__Type_OPair(_1810502, _1810502), _1810504), _1810506)), c_List_Omeasures(_1810502, _1810510)))]]], (50044 ^ _782652) ^ [_1811099, _1811101, _1811103, _1811105, _1811107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1811099, _1811101)), hAPP(_1811099, _1811103))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1811105, _1811105)), hAPP(hAPP(c_Product__Type_OPair(_1811105, _1811105), _1811101), _1811103)), c_List_Omeasures(_1811105, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1811105, tc_Nat_Onat)), _1811099), _1811107)))))], (50050 ^ _782652) ^ [_1811499, _1811501, _1811503, _1811505, _1811507, _1811509, _1811511, _1811513] : [50052 ^ _782652 : [(50053 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811499), 50051 ^ [_1811499, _1811501, _1811503, _1811505, _1811507, _1811509, _1811511, _1811513]), hAPP(c_List_Oset(_1811499), _1811501))))], (50055 ^ _782652) ^ [] : [hAPP(c_Fun_Ocomp(_1811503, _1811503, _1811505, hAPP(_1811507, 50051 ^ [_1811499, _1811501, _1811503, _1811505, _1811507, _1811509, _1811511, _1811513])), _1811509) = hAPP(c_Fun_Ocomp(_1811505, _1811503, _1811505, _1811509), hAPP(_1811511, 50051 ^ [_1811499, _1811501, _1811503, _1811505, _1811507, _1811509, _1811511, _1811513]))]], -(hAPP(c_List_Ofoldl(_1811503, _1811499, hAPP(c_COMBC(_1811499, _1811503, _1811503), _1811507), hAPP(_1811509, _1811513)), _1811501) = hAPP(_1811509, hAPP(c_List_Ofoldl(_1811505, _1811499, hAPP(c_COMBC(_1811499, _1811505, _1811505), _1811511), _1811513), _1811501)))], (50059 ^ _782652) ^ [_1812185, _1812187, _1812189, _1812191, _1812193] : [50060 ^ _782652 : [(50061 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812185)), hAPP(hAPP(c_List_Otake(_1812185), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812185)), _1812187)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812189)), _1812191))), _1812187)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812189)), hAPP(hAPP(c_List_Otake(_1812189), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812185)), _1812187)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812189)), _1812191))), _1812191)))], (50063 ^ _782652) ^ [] : [hBOOL(hAPP(_1812193, hAPP(hAPP(c_List_Ozip(_1812185, _1812189), hAPP(hAPP(c_List_Otake(_1812185), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812185)), _1812187)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812189)), _1812191))), _1812187)), hAPP(hAPP(c_List_Otake(_1812189), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812185)), _1812187)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1812189)), _1812191))), _1812191))))]], -(hBOOL(hAPP(_1812193, hAPP(hAPP(c_List_Ozip(_1812185, _1812189), _1812187), _1812191))))], (50067 ^ _782652) ^ [_1812818, _1812820, _1812822, _1812824] : [hAPP(c_List_Oset(_1812818), hAPP(hAPP(c_List_Omap(tc_prod(_1812818, _1812820), _1812818), c_Product__Type_Ofst(_1812818, _1812820)), _1812822)) = hAPP(c_List_Oset(_1812818), hAPP(hAPP(c_List_Omap(tc_prod(_1812818, _1812820), _1812818), c_Product__Type_Ofst(_1812818, _1812820)), _1812824)), 50073 ^ _782652 : [(50074 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812818), 50072 ^ [_1812818, _1812820, _1812822, _1812824]), hAPP(c_List_Oset(_1812818), hAPP(hAPP(c_List_Omap(tc_prod(_1812818, _1812820), _1812818), c_Product__Type_Ofst(_1812818, _1812820)), _1812822)))))], (50076 ^ _782652) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1812818, _1812820), _1812822), 50072 ^ [_1812818, _1812820, _1812822, _1812824]) = hAPP(hAPP(c_Map_Omap__of(_1812818, _1812820), _1812824), 50072 ^ [_1812818, _1812820, _1812822, _1812824])]], -(hAPP(c_Map_Omap__of(_1812818, _1812820), _1812822) = hAPP(c_Map_Omap__of(_1812818, _1812820), _1812824))], (50080 ^ _782652) ^ [_1813565, _1813567, _1813569, _1813571] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1813565, _1813567, _1813569, _1813571) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1813565, _1813567), _1813569), _1813571)))], (50082 ^ _782652) ^ [_1813722, _1813724, _1813726, _1813728] : [50084 ^ _782652 : [(50085 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1813722), 50083 ^ [_1813722, _1813724, _1813726, _1813728]), hAPP(c_List_Oset(_1813722), _1813724))))], (50087 ^ _782652) ^ [] : [hBOOL(hAPP(_1813726, 50083 ^ [_1813722, _1813724, _1813726, _1813728]))]], -(c_List_OdropWhile(_1813722, _1813726, hAPP(hAPP(c_List_Oappend(_1813722), _1813724), _1813728)) = c_List_OdropWhile(_1813722, _1813726, _1813728))], (50091 ^ _782652) ^ [_1814225, _1814227, _1814229, _1814231, _1814233] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814225)), _1814227) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814229)), _1814231), 50097 ^ _782652 : [(50098 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50096 ^ [_1814225, _1814227, _1814229, _1814231, _1814233]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814225)), _1814227))))], (50100 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1814233, hAPP(hAPP(c_List_Onth(_1814225), _1814227), 50096 ^ [_1814225, _1814227, _1814229, _1814231, _1814233])), hAPP(hAPP(c_List_Onth(_1814229), _1814231), 50096 ^ [_1814225, _1814227, _1814229, _1814231, _1814233])))]], -(c_List_Olist__all2(_1814225, _1814229, _1814233, _1814227, _1814231))], (50104 ^ _782652) ^ [_1814875, _1814877] : [class_Orderings_Olinorder(_1814875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1814875), _1814877)), 50112 ^ _782652 : [(50113 ^ _782652) ^ [] : [-(hAPP(c_List_Oset(_1814875), 50111 ^ [_1814875, _1814877]) = _1814877)], (50115 ^ _782652) ^ [] : [-(c_List_Olinorder__class_Osorted(_1814875, 50111 ^ [_1814875, _1814877]))], (50117 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1814875), 50111 ^ [_1814875, _1814877])))], (50119 ^ _782652) ^ [_1815488] : [-(_1815488 = 50111 ^ [_1814875, _1814877]), hAPP(c_List_Oset(_1814875), _1815488) = _1814877, c_List_Olinorder__class_Osorted(_1814875, _1815488), hBOOL(hAPP(c_List_Odistinct(_1814875), _1815488))]]], (50133 ^ _782652) ^ [_1815969, _1815971, _1815973, _1815975] : [50135 ^ _782652 : [(50136 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1815969), 50134 ^ [_1815969, _1815971, _1815973, _1815975]), hAPP(c_List_Oset(_1815969), _1815971))))], (50138 ^ _782652) ^ [] : [hBOOL(hAPP(_1815973, 50134 ^ [_1815969, _1815971, _1815973, _1815975]))]], -(c_List_OtakeWhile(_1815969, _1815973, hAPP(hAPP(c_List_Oappend(_1815969), _1815971), _1815975)) = hAPP(hAPP(c_List_Oappend(_1815969), _1815971), c_List_OtakeWhile(_1815969, _1815973, _1815975)))], (50142 ^ _782652) ^ [_1816488, _1816490, _1816492, _1816494, _1816496] : [class_Orderings_Olinorder(_1816488), 50148 ^ _782652 : [(50149 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1816490), 50147 ^ [_1816488, _1816490, _1816492, _1816494, _1816496]), hAPP(c_List_Oset(_1816490), _1816492))))], (50151 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1816488), hAPP(_1816494, _1816496)), hAPP(_1816494, 50147 ^ [_1816488, _1816490, _1816492, _1816494, _1816496])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1816490, _1816488, _1816494), _1816496), _1816492) = hAPP(hAPP(c_List_Olist_OCons(_1816490), _1816496), _1816492))], (50155 ^ _782652) ^ [_1817172, _1817174, _1817176, _1817178, _1817180] : [hAPP(hAPP(c_List_Olist_OCons(_1817172), _1817174), _1817176) = hAPP(c_List_Ofilter(_1817172, _1817178), _1817180), 50160 ^ _782652 : [(50161 ^ _782652) ^ [] : [-(_1817180 = hAPP(hAPP(c_List_Oappend(_1817172), 50158 ^ [_1817172, _1817174, _1817176, _1817178, _1817180]), hAPP(hAPP(c_List_Olist_OCons(_1817172), _1817174), 50159 ^ [_1817172, _1817174, _1817176, _1817178, _1817180])))], (50169 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1817178, _1817174)))], (50171 ^ _782652) ^ [] : [-(_1817176 = hAPP(c_List_Ofilter(_1817172, _1817178), 50159 ^ [_1817172, _1817174, _1817176, _1817178, _1817180]))], (50163 ^ _782652) ^ [_1817834] : [hBOOL(hAPP(hAPP(c_member(_1817172), _1817834), hAPP(c_List_Oset(_1817172), 50158 ^ [_1817172, _1817174, _1817176, _1817178, _1817180]))), hBOOL(hAPP(_1817178, _1817834))]]], (50173 ^ _782652) ^ [_1818243, _1818245, _1818247, _1818249, _1818251] : [-(hAPP(hAPP(c_List_Olist_OCons(_1818243), _1818245), _1818247) = hAPP(c_List_Ofilter(_1818243, _1818249), _1818251)), 50174 ^ _782652 : [(50175 ^ _782652) ^ [_1818437, _1818439] : [_1818251 = hAPP(hAPP(c_List_Oappend(_1818243), _1818439), hAPP(hAPP(c_List_Olist_OCons(_1818243), _1818245), _1818437)), 50181 ^ _782652 : [(50182 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1818243), 50180 ^ [_1818243, _1818245, _1818247, _1818249, _1818251, _1818437, _1818439]), hAPP(c_List_Oset(_1818243), _1818439))))], (50184 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1818249, 50180 ^ [_1818243, _1818245, _1818247, _1818249, _1818251, _1818437, _1818439])))]], hBOOL(hAPP(_1818249, _1818245)), _1818247 = hAPP(c_List_Ofilter(_1818243, _1818249), _1818437)]]], (50194 ^ _782652) ^ [_1819338, _1819340, _1819342, _1819344, _1819346] : [hAPP(c_List_Ofilter(_1819338, _1819340), _1819342) = hAPP(hAPP(c_List_Olist_OCons(_1819338), _1819344), _1819346), 50199 ^ _782652 : [(50200 ^ _782652) ^ [] : [-(_1819342 = hAPP(hAPP(c_List_Oappend(_1819338), 50197 ^ [_1819338, _1819340, _1819342, _1819344, _1819346]), hAPP(hAPP(c_List_Olist_OCons(_1819338), _1819344), 50198 ^ [_1819338, _1819340, _1819342, _1819344, _1819346])))], (50208 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1819340, _1819344)))], (50210 ^ _782652) ^ [] : [-(_1819346 = hAPP(c_List_Ofilter(_1819338, _1819340), 50198 ^ [_1819338, _1819340, _1819342, _1819344, _1819346]))], (50202 ^ _782652) ^ [_1820000] : [hBOOL(hAPP(hAPP(c_member(_1819338), _1820000), hAPP(c_List_Oset(_1819338), 50197 ^ [_1819338, _1819340, _1819342, _1819344, _1819346]))), hBOOL(hAPP(_1819340, _1820000))]]], (50212 ^ _782652) ^ [_1820409, _1820411, _1820413, _1820415, _1820417] : [-(hAPP(c_List_Ofilter(_1820409, _1820411), _1820413) = hAPP(hAPP(c_List_Olist_OCons(_1820409), _1820415), _1820417)), 50213 ^ _782652 : [(50214 ^ _782652) ^ [_1820603, _1820605] : [_1820413 = hAPP(hAPP(c_List_Oappend(_1820409), _1820605), hAPP(hAPP(c_List_Olist_OCons(_1820409), _1820415), _1820603)), 50220 ^ _782652 : [(50221 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1820409), 50219 ^ [_1820409, _1820411, _1820413, _1820415, _1820417, _1820603, _1820605]), hAPP(c_List_Oset(_1820409), _1820605))))], (50223 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1820411, 50219 ^ [_1820409, _1820411, _1820413, _1820415, _1820417, _1820603, _1820605])))]], hBOOL(hAPP(_1820411, _1820415)), _1820417 = hAPP(c_List_Ofilter(_1820409, _1820411), _1820603)]]], (50233 ^ _782652) ^ [_1821461, _1821463, _1821465, _1821467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1821461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1821463)), _1821465))), 50239 ^ _782652 : [(50240 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1821463), 50238 ^ [_1821461, _1821463, _1821465, _1821467]), hAPP(c_List_Oset(_1821463), _1821465))))], (50242 ^ _782652) ^ [] : [hBOOL(hAPP(_1821467, 50238 ^ [_1821461, _1821463, _1821465, _1821467]))]], -(hBOOL(hAPP(_1821467, hAPP(hAPP(c_List_Onth(_1821463), _1821465), _1821461))))], (50246 ^ _782652) ^ [_1822045, _1822047, _1822049] : [class_Orderings_Olinorder(_1822045), 50252 ^ _782652 : [(50253 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822045), 50251 ^ [_1822045, _1822047, _1822049]), hAPP(c_List_Oset(_1822045), _1822047))))], (50255 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1822045), _1822049), 50251 ^ [_1822045, _1822047, _1822049]))]], c_List_Olinorder__class_Osorted(_1822045, _1822047), -(c_List_Olinorder__class_Osorted(_1822045, hAPP(hAPP(c_List_Olist_OCons(_1822045), _1822049), _1822047)))], (50263 ^ _782652) ^ [_1822716, _1822718, _1822720] : [c_List_Olist__ex(_1822716, _1822718, _1822720), 50267 ^ _782652 : [(50268 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50266 ^ [_1822716, _1822718, _1822720]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1822716)), _1822720))))], (50270 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1822718, hAPP(hAPP(c_List_Onth(_1822716), _1822720), 50266 ^ [_1822716, _1822718, _1822720]))))]]], (50272 ^ _782652) ^ [_1823107, _1823109, _1823111] : [-(c_List_Olist__ex(_1823107, _1823109, _1823111)), 50273 ^ _782652 : [(50274 ^ _782652) ^ [_1823224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1823224), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1823107)), _1823111))), hBOOL(hAPP(_1823109, hAPP(hAPP(c_List_Onth(_1823107), _1823111), _1823224)))]]], (50292 ^ _782652) ^ [_1823904, _1823906, _1823908, _1823910] : [50293 ^ _782652 : [(50294 ^ _782652) ^ [] : [hBOOL(hAPP(_1823906, _1823908))], (50296 ^ _782652) ^ [] : [c_List_Olist__ex(_1823904, _1823906, _1823910)]], -(c_List_Olist__ex(_1823904, _1823906, hAPP(hAPP(c_List_Olist_OCons(_1823904), _1823908), _1823910)))], (50282 ^ _782652) ^ [_1823608, _1823610, _1823612, _1823614] : [c_List_Olist__ex(_1823608, _1823610, hAPP(hAPP(c_List_Olist_OCons(_1823608), _1823612), _1823614)), -(hBOOL(hAPP(_1823610, _1823612))), -(c_List_Olist__ex(_1823608, _1823610, _1823614))], (50300 ^ _782652) ^ [_1824273, _1824275, _1824277] : [c_List_Olist__ex(_1824273, _1824275, _1824277), 50304 ^ _782652 : [(50305 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1824273), 50303 ^ [_1824273, _1824275, _1824277]), hAPP(c_List_Oset(_1824273), _1824277))))], (50307 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1824275, 50303 ^ [_1824273, _1824275, _1824277])))]]], (50309 ^ _782652) ^ [_1824640, _1824642, _1824644] : [-(c_List_Olist__ex(_1824640, _1824642, _1824644)), 50310 ^ _782652 : [(50311 ^ _782652) ^ [_1824749] : [hBOOL(hAPP(hAPP(c_member(_1824640), _1824749), hAPP(c_List_Oset(_1824640), _1824644))), hBOOL(hAPP(_1824642, _1824749))]]], (50319 ^ _782652) ^ [_1825103, _1825105, _1825107] : [c_List_Olist__ex(_1825103, _1825105, hAPP(c_List_Orev(_1825103), _1825107)), -(c_List_Olist__ex(_1825103, _1825105, _1825107))], (50325 ^ _782652) ^ [_1825285, _1825287, _1825289] : [c_List_Olist__ex(_1825285, _1825287, _1825289), -(c_List_Olist__ex(_1825285, _1825287, hAPP(c_List_Orev(_1825285), _1825289)))], (50341 ^ _782652) ^ [_1825868, _1825870, _1825872, _1825874] : [50342 ^ _782652 : [(50343 ^ _782652) ^ [] : [c_List_Olist__ex(_1825868, _1825870, _1825872)], (50345 ^ _782652) ^ [] : [c_List_Olist__ex(_1825868, _1825870, _1825874)]], -(c_List_Olist__ex(_1825868, _1825870, hAPP(hAPP(c_List_Oappend(_1825868), _1825872), _1825874)))], (50331 ^ _782652) ^ [_1825574, _1825576, _1825578, _1825580] : [c_List_Olist__ex(_1825574, _1825576, hAPP(hAPP(c_List_Oappend(_1825574), _1825578), _1825580)), -(c_List_Olist__ex(_1825574, _1825576, _1825578)), -(c_List_Olist__ex(_1825574, _1825576, _1825580))], (50349 ^ _782652) ^ [_1826176, _1826178] : [c_List_Olist__ex(_1826176, _1826178, c_List_Olist_ONil(_1826176))], (50351 ^ _782652) ^ [_1826331, _1826333, _1826335] : [hBOOL(hAPP(hAPP(c_member(_1826331), _1826333), hAPP(c_List_Oset(_1826331), _1826335))), -(_1826335 = hAPP(hAPP(c_List_Oappend(_1826331), 50354 ^ [_1826331, _1826333, _1826335]), hAPP(hAPP(c_List_Olist_OCons(_1826331), _1826333), 50355 ^ [_1826331, _1826333, _1826335])))], (50359 ^ _782652) ^ [_1826727, _1826729, _1826731] : [50360 ^ _782652 : [(50361 ^ _782652) ^ [_1826846, _1826848] : [_1826731 = hAPP(hAPP(c_List_Oappend(_1826727), _1826848), hAPP(hAPP(c_List_Olist_OCons(_1826727), _1826729), _1826846))]], -(hBOOL(hAPP(hAPP(c_member(_1826727), _1826729), hAPP(c_List_Oset(_1826727), _1826731))))], (50365 ^ _782652) ^ [_1827087, _1827089, _1827091] : [hBOOL(hAPP(hAPP(c_member(_1827087), _1827089), hAPP(c_List_Oset(_1827087), _1827091))), 50370 ^ _782652 : [(50371 ^ _782652) ^ [] : [-(_1827091 = hAPP(hAPP(c_List_Oappend(_1827087), 50368 ^ [_1827087, _1827089, _1827091]), hAPP(hAPP(c_List_Olist_OCons(_1827087), _1827089), 50369 ^ [_1827087, _1827089, _1827091])))], (50373 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1827087), _1827089), hAPP(c_List_Oset(_1827087), 50369 ^ [_1827087, _1827089, _1827091])))]]], (50375 ^ _782652) ^ [_1827634, _1827636, _1827638] : [-(hBOOL(hAPP(hAPP(c_member(_1827634), _1827636), hAPP(c_List_Oset(_1827634), _1827638)))), 50376 ^ _782652 : [(50377 ^ _782652) ^ [_1827789, _1827791] : [_1827638 = hAPP(hAPP(c_List_Oappend(_1827634), _1827791), hAPP(hAPP(c_List_Olist_OCons(_1827634), _1827636), _1827789)), -(hBOOL(hAPP(hAPP(c_member(_1827634), _1827636), hAPP(c_List_Oset(_1827634), _1827789))))]]], (50385 ^ _782652) ^ [_1828191, _1828193, _1828195] : [hBOOL(hAPP(hAPP(c_member(_1828191), _1828193), hAPP(c_List_Oset(_1828191), _1828195))), 50390 ^ _782652 : [(50391 ^ _782652) ^ [] : [-(_1828195 = hAPP(hAPP(c_List_Oappend(_1828191), 50388 ^ [_1828191, _1828193, _1828195]), hAPP(hAPP(c_List_Olist_OCons(_1828191), _1828193), 50389 ^ [_1828191, _1828193, _1828195])))], (50393 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1828191), _1828193), hAPP(c_List_Oset(_1828191), 50388 ^ [_1828191, _1828193, _1828195])))]]], (50395 ^ _782652) ^ [_1828718, _1828720, _1828722] : [-(hBOOL(hAPP(hAPP(c_member(_1828718), _1828720), hAPP(c_List_Oset(_1828718), _1828722)))), 50396 ^ _782652 : [(50397 ^ _782652) ^ [_1828859] : [50398 ^ _782652 : [(50399 ^ _782652) ^ [_1828969] : [_1828722 = hAPP(hAPP(c_List_Oappend(_1828718), _1828859), hAPP(hAPP(c_List_Olist_OCons(_1828718), _1828720), _1828969))]], -(hBOOL(hAPP(hAPP(c_member(_1828718), _1828720), hAPP(c_List_Oset(_1828718), _1828859))))]]], (50415 ^ _782652) ^ [_1829671, _1829673, _1829675] : [50417 ^ _782652 : [(50418 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50416 ^ [_1829671, _1829673, _1829675]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1829671)), _1829675))))], (50420 ^ _782652) ^ [] : [hBOOL(hAPP(_1829673, hAPP(hAPP(c_List_Onth(_1829671), _1829675), 50416 ^ [_1829671, _1829673, _1829675])))]], -(c_List_Olist__all(_1829671, _1829673, _1829675))], (50405 ^ _782652) ^ [_1829277, _1829279, _1829281] : [c_List_Olist__all(_1829277, _1829279, _1829281), 50408 ^ _782652 : [(50409 ^ _782652) ^ [_1829442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1829442), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1829277)), _1829281))), -(hBOOL(hAPP(_1829279, hAPP(hAPP(c_List_Onth(_1829277), _1829281), _1829442))))]]], (50424 ^ _782652) ^ [_1830169, _1830171, _1830173, _1830175] : [c_List_Olist__all(_1830169, _1830171, hAPP(hAPP(c_List_Olist_OCons(_1830169), _1830173), _1830175)), 50427 ^ _782652 : [(50428 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1830171, _1830173)))], (50430 ^ _782652) ^ [] : [-(c_List_Olist__all(_1830169, _1830171, _1830175))]]], (50432 ^ _782652) ^ [_1830446, _1830448, _1830450, _1830452] : [-(c_List_Olist__all(_1830446, _1830448, hAPP(hAPP(c_List_Olist_OCons(_1830446), _1830450), _1830452))), hBOOL(hAPP(_1830448, _1830450)), c_List_Olist__all(_1830446, _1830448, _1830452)], (50452 ^ _782652) ^ [_1831204, _1831206, _1831208] : [50454 ^ _782652 : [(50455 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1831204), 50453 ^ [_1831204, _1831206, _1831208]), hAPP(c_List_Oset(_1831204), _1831208))))], (50457 ^ _782652) ^ [] : [hBOOL(hAPP(_1831206, 50453 ^ [_1831204, _1831206, _1831208]))]], -(c_List_Olist__all(_1831204, _1831206, _1831208))], (50442 ^ _782652) ^ [_1830834, _1830836, _1830838] : [c_List_Olist__all(_1830834, _1830836, _1830838), 50445 ^ _782652 : [(50446 ^ _782652) ^ [_1830991] : [hBOOL(hAPP(hAPP(c_member(_1830834), _1830991), hAPP(c_List_Oset(_1830834), _1830838))), -(hBOOL(hAPP(_1830836, _1830991)))]]], (50461 ^ _782652) ^ [_1831664, _1831666, _1831668] : [c_List_Olist__all(_1831664, _1831666, hAPP(c_List_Orev(_1831664), _1831668)), -(c_List_Olist__all(_1831664, _1831666, _1831668))], (50467 ^ _782652) ^ [_1831846, _1831848, _1831850] : [c_List_Olist__all(_1831846, _1831848, _1831850), -(c_List_Olist__all(_1831846, _1831848, hAPP(c_List_Orev(_1831846), _1831850)))], (50473 ^ _782652) ^ [_1832135, _1832137, _1832139, _1832141] : [c_List_Olist__all(_1832135, _1832137, hAPP(hAPP(c_List_Oappend(_1832135), _1832139), _1832141)), 50476 ^ _782652 : [(50477 ^ _782652) ^ [] : [-(c_List_Olist__all(_1832135, _1832137, _1832139))], (50479 ^ _782652) ^ [] : [-(c_List_Olist__all(_1832135, _1832137, _1832141))]]], (50481 ^ _782652) ^ [_1832410, _1832412, _1832414, _1832416] : [-(c_List_Olist__all(_1832410, _1832412, hAPP(hAPP(c_List_Oappend(_1832410), _1832414), _1832416))), c_List_Olist__all(_1832410, _1832412, _1832414), c_List_Olist__all(_1832410, _1832412, _1832416)], (50491 ^ _782652) ^ [_1832796, _1832798, _1832800] : [50493 ^ _782652 : [(50494 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1832796), 50492 ^ [_1832796, _1832798, _1832800]), hAPP(c_List_Oset(_1832796), _1832798))))], (50496 ^ _782652) ^ [] : [hBOOL(hAPP(_1832800, 50492 ^ [_1832796, _1832798, _1832800]))]], -(c_List_Olist__all(_1832796, _1832800, _1832798))], (50500 ^ _782652) ^ [_1833163, _1833165, _1833167] : [c_List_Olist__all(_1833163, _1833167, _1833165), 50503 ^ _782652 : [(50504 ^ _782652) ^ [_1833320] : [hBOOL(hAPP(hAPP(c_member(_1833163), _1833320), hAPP(c_List_Oset(_1833163), _1833165))), -(hBOOL(hAPP(_1833167, _1833320)))]]], (50510 ^ _782652) ^ [_1833568, _1833570] : [-(c_List_Olist__all(_1833568, _1833570, c_List_Olist_ONil(_1833568)))], (50522 ^ _782652) ^ [_1834093, _1834095, _1834097] : [50524 ^ _782652 : [(50525 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1834093), 50523 ^ [_1834093, _1834095, _1834097]), hAPP(c_List_Oset(_1834093), _1834097))))], (50527 ^ _782652) ^ [] : [hBOOL(hAPP(_1834095, 50523 ^ [_1834093, _1834095, _1834097]))]], -(c_List_Olist__all(_1834093, _1834095, _1834097))], (50512 ^ _782652) ^ [_1833723, _1833725, _1833727] : [c_List_Olist__all(_1833723, _1833725, _1833727), 50515 ^ _782652 : [(50516 ^ _782652) ^ [_1833880] : [hBOOL(hAPP(hAPP(c_member(_1833723), _1833880), hAPP(c_List_Oset(_1833723), _1833727))), -(hBOOL(hAPP(_1833725, _1833880)))]]], (50547 ^ _782652) ^ [_1835113, _1835115, _1835117, _1835119] : [-(c_List_Olist__ex1(_1835113, _1835115, hAPP(hAPP(c_List_Olist_OCons(_1835113), _1835117), _1835119))), 50550 ^ _782652 : [(50551 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1835115, _1835117)))], (50553 ^ _782652) ^ [] : [c_List_Olist__all(_1835113, hAPP(hAPP(c_COMBS(_1835113, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1835113), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1835113), c_fNot), _1835115))), hAPP(c_fequal, _1835117)), _1835119)]], 50554 ^ _782652 : [(50555 ^ _782652) ^ [] : [hBOOL(hAPP(_1835115, _1835117))], (50557 ^ _782652) ^ [] : [c_List_Olist__ex1(_1835113, _1835115, _1835119)]]], (50531 ^ _782652) ^ [_1834567, _1834569, _1834571, _1834573] : [c_List_Olist__ex1(_1834567, _1834569, hAPP(hAPP(c_List_Olist_OCons(_1834567), _1834571), _1834573)), 50534 ^ _782652 : [(50535 ^ _782652) ^ [] : [hBOOL(hAPP(_1834569, _1834571)), -(c_List_Olist__all(_1834567, hAPP(hAPP(c_COMBS(_1834567, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1834567), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1834567), c_fNot), _1834569))), hAPP(c_fequal, _1834571)), _1834573))], (50541 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1834569, _1834571))), -(c_List_Olist__ex1(_1834567, _1834569, _1834573))]]], (50561 ^ _782652) ^ [_1835688, _1835690, _1835692] : [-(c_Product__Type_Ointernal__split(_1835688, _1835690, _1835692) = c_Product__Type_Oprod_Oprod__case(_1835688, _1835690, _1835692))], (50563 ^ _782652) ^ [_1835791, _1835793] : [c_List_Olist__ex1(_1835791, _1835793, c_List_Olist_ONil(_1835791))], (50565 ^ _782652) ^ [_1835903, _1835905] : [class_Enum_Oenum(_1835903), 50568 ^ _782652 : [(50569 ^ _782652) ^ [] : [-(c_List_Olist__ex1(_1835903, _1835905, c_Enum_Oenum__class_Oenum(_1835903))), 50570 ^ _782652 : [(50571 ^ _782652) ^ [_1836125] : [hBOOL(hAPP(_1835905, _1836125)), 50575 ^ _782652 : [(50576 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1835905, 50574 ^ [_1835903, _1835905, _1836125])))], (50578 ^ _782652) ^ [] : [50574 ^ [_1835903, _1835905, _1836125] = _1836125]]]]], (50582 ^ _782652) ^ [] : [c_List_Olist__ex1(_1835903, _1835905, c_Enum_Oenum__class_Oenum(_1835903)), 50586 ^ _782652 : [(50587 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1835905, 50585 ^ [_1835903, _1835905])))], (50589 ^ _782652) ^ [_1836752] : [hBOOL(hAPP(_1835905, _1836752)), -(_1836752 = 50585 ^ [_1835903, _1835905])]]]]], (50595 ^ _782652) ^ [_1837045, _1837047, _1837049, _1837051, _1837053, _1837055] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1837045, _1837047, _1837049), _1837051), hAPP(hAPP(c_Product__Type_OPair(_1837045, _1837047), _1837053), _1837055)) = hAPP(hAPP(_1837051, _1837053), _1837055))], (50597 ^ _782652) ^ [_1837230, _1837232, _1837234] : [c_List_Olist__ex1(_1837230, _1837232, _1837234), 50601 ^ _782652 : [(50602 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1837230), 50600 ^ [_1837230, _1837232, _1837234]), hAPP(c_List_Oset(_1837230), _1837234))))], (50604 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1837232, 50600 ^ [_1837230, _1837232, _1837234])))], (50606 ^ _782652) ^ [_1837698] : [-(_1837698 = 50600 ^ [_1837230, _1837232, _1837234]), hBOOL(hAPP(hAPP(c_member(_1837230), _1837698), hAPP(c_List_Oset(_1837230), _1837234))), hBOOL(hAPP(_1837232, _1837698))]]], (50616 ^ _782652) ^ [_1838030, _1838032, _1838034] : [-(c_List_Olist__ex1(_1838030, _1838032, _1838034)), 50617 ^ _782652 : [(50618 ^ _782652) ^ [_1838176] : [hBOOL(hAPP(hAPP(c_member(_1838030), _1838176), hAPP(c_List_Oset(_1838030), _1838034))), hBOOL(hAPP(_1838032, _1838176)), 50626 ^ _782652 : [(50627 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1838030), 50625 ^ [_1838030, _1838032, _1838034, _1838176]), hAPP(c_List_Oset(_1838030), _1838034))))], (50629 ^ _782652) ^ [] : [-(hBOOL(hAPP(_1838032, 50625 ^ [_1838030, _1838032, _1838034, _1838176])))], (50631 ^ _782652) ^ [] : [50625 ^ [_1838030, _1838032, _1838034, _1838176] = _1838176]]]]], (50635 ^ _782652) ^ [_1838916, _1838918, _1838920, _1838922] : [class_Rings_Olinordered__semidom(_1838916), 50641 ^ _782652 : [(50642 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1838918), 50640 ^ [_1838916, _1838918, _1838920, _1838922]), _1838920)))], (50644 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1838916), c_Groups_Ozero__class_Ozero(_1838916)), hAPP(_1838922, 50640 ^ [_1838916, _1838918, _1838920, _1838922])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1838916), c_Groups_Ozero__class_Ozero(_1838916)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1838918, _1838916), _1838922), _1838920))))], (50648 ^ _782652) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50650 ^ _782652) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50652 ^ _782652) ^ [_1839597, _1839599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50653 ^ [_1839597, _1839599]), hAPP(_1839597, 50653 ^ [_1839597, _1839599]))), -(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)), _1839597)), _1839599)))))], (50659 ^ _782652) ^ [] : [-(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))))], (50661 ^ _782652) ^ [_1839962] : [class_Nat_Osize(_1839962), -(c_FunDef_Ois__measure(_1839962, c_Nat_Osize__class_Osize(_1839962)))], (50667 ^ _782652) ^ [_1840153, _1840155] : [-(c_FunDef_Ois__measure(_1840153, _1840155))], (50669 ^ _782652) ^ [_1840247, _1840249] : [-(c_FunDef_Ois__measure(_1840247, _1840249))], (50671 ^ _782652) ^ [_1840341, _1840343] : [-(c_FunDef_Ois__measure(_1840341, _1840343))], (50673 ^ _782652) ^ [_1840464, _1840466, _1840468] : [c_FunDef_Ois__measure(_1840464, _1840466), -(c_FunDef_Ois__measure(tc_prod(_1840464, _1840468), hAPP(hAPP(c_COMBB(_1840464, tc_Nat_Onat, tc_prod(_1840464, _1840468)), _1840466), c_Product__Type_Ofst(_1840464, _1840468))))], (50679 ^ _782652) ^ [_1840732, _1840734, _1840736] : [c_FunDef_Ois__measure(_1840732, _1840734), -(c_FunDef_Ois__measure(tc_prod(_1840736, _1840732), hAPP(hAPP(c_COMBB(_1840732, tc_Nat_Onat, tc_prod(_1840736, _1840732)), _1840734), c_Product__Type_Osnd(_1840736, _1840732))))], (50685 ^ _782652) ^ [_1841014, _1841016, _1841018, _1841020] : [class_HOL_Oequal(_1841014), class_Enum_Oenum(_1841016), 50692 ^ _782652 : [(50703 ^ _782652) ^ [] : [50705 ^ _782652 : [(50706 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1841016), 50704 ^ [_1841014, _1841016, _1841018, _1841020]), hAPP(c_List_Oset(_1841016), c_Enum_Oenum__class_Oenum(_1841016)))))], (50708 ^ _782652) ^ [] : [hAPP(_1841018, 50704 ^ [_1841014, _1841016, _1841018, _1841020]) = hAPP(_1841020, 50704 ^ [_1841014, _1841016, _1841018, _1841020])]], -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1841016, _1841014)), _1841018), _1841020)))], (50693 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1841016, _1841014)), _1841018), _1841020)), 50696 ^ _782652 : [(50697 ^ _782652) ^ [_1841414] : [hBOOL(hAPP(hAPP(c_member(_1841016), _1841414), hAPP(c_List_Oset(_1841016), c_Enum_Oenum__class_Oenum(_1841016)))), -(hAPP(_1841018, _1841414) = hAPP(_1841020, _1841414))]]]]], (50712 ^ _782652) ^ [] : [-(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)))], (50714 ^ _782652) ^ [_1842099] : [class_HOL_Oequal(_1842099), -(c_HOL_Oequal__class_Oequal(_1842099) = c_fequal)], (50720 ^ _782652) ^ [_1842305, _1842307] : [class_HOL_Oequal(_1842305), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1842305), _1842307), _1842307)))], (50726 ^ _782652) ^ [_1842541, _1842543, _1842545] : [class_HOL_Oequal(_1842541), 50729 ^ _782652 : [(50730 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1842541), _1842543), _1842545)), -(_1842543 = _1842545)], (50736 ^ _782652) ^ [] : [_1842543 = _1842545, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1842541), _1842543), _1842545)))]]], (50742 ^ _782652) ^ [_1843022] : [class_HOL_Oequal(_1843022), -(c_fequal = c_HOL_Oequal__class_Oequal(_1843022))], (50748 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50750 ^ _782652) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50752 ^ _782652) ^ [_1843319, _1843321] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1843319)), _1843321) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1843319, tc_Lazy__Sequence_Olazy__sequence(_1843319)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1843319, tc_Lazy__Sequence_Olazy__sequence(_1843319), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1843319), tc_Nat_Onat), _1843319), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1843319), 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(_1843319)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1843319)))), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), hAPP(c_Lazy__Sequence_Oyield(_1843319), _1843321)))], (50754 ^ _782652) ^ [_1843563, _1843565, _1843567, _1843569, _1843571] : [_1843563 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1843565, _1843567, _1843569, _1843571), _1843563) = c_Lazy__Sequence_Oempty(_1843567))], (50760 ^ _782652) ^ [_1843763, _1843765, _1843767, _1843769, _1843771] : [-(_1843763 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1843765, _1843767, _1843769, _1843771), _1843763) = hAPP(c_Lazy__Sequence_Obind(_1843765, _1843767, hAPP(_1843769, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1843763), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1843765, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1843767)), _1843771), _1843763)))], (50766 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (50768 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (50770 ^ _782652) ^ [_1844187] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1844187))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1844187)))], (50776 ^ _782652) ^ [_1844355] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1844355)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1844355))))], (50782 ^ _782652) ^ [_1844588] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1844588)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1844588), c_Int_OMin)))], (50788 ^ _782652) ^ [_1844768] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1844768), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1844768)), c_Int_OMin)))], (50794 ^ _782652) ^ [_1845013] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1845013))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1845013)))], (50800 ^ _782652) ^ [_1845181] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1845181)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1845181))))], (50806 ^ _782652) ^ [_1845414] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1845414)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1845414), c_Int_OPls)))], (50812 ^ _782652) ^ [_1845594] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1845594), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1845594)), c_Int_OPls)))], (50818 ^ _782652) ^ [_1845808, _1845810] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1845808)), c_Int_OBit1(_1845810)))], (50820 ^ _782652) ^ [_1845910, _1845912] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1845910)), c_Int_OBit0(_1845912)))], (50822 ^ _782652) ^ [_1846057, _1846059] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1846057)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1846059))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1846057), _1846059)))], (50828 ^ _782652) ^ [_1846251, _1846253] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1846251), _1846253)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1846251)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1846253))))], (50834 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (50836 ^ _782652) ^ [_1846577, _1846579] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1846577)), c_Int_OBit1(_1846579))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1846577), _1846579)))], (50842 ^ _782652) ^ [_1846767, _1846769] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1846767), _1846769)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1846767)), c_Int_OBit1(_1846769))))], (50848 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (50850 ^ _782652) ^ [_1847089, _1847091] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1847089)), c_Int_OBit0(_1847091))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1847089), _1847091)))], (50856 ^ _782652) ^ [_1847279, _1847281] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1847279), _1847281)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1847279)), c_Int_OBit0(_1847281))))], (50862 ^ _782652) ^ [_1847489] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1847489)))], (50864 ^ _782652) ^ [_1847570] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1847570)), c_Int_OPls))], (50866 ^ _782652) ^ [_1847713, _1847715] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1847713), _1847715)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1847713), _1847715) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50872 ^ _782652) ^ [_1847897, _1847899] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1847897), _1847899) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1847897), _1847899)))], (50878 ^ _782652) ^ [_1848101] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1848101)))], (50880 ^ _782652) ^ [_1848182] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1848182)), c_Int_OMin))], (50882 ^ _782652) ^ [_1848295, _1848297, _1848299] : 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tc_Lazy__Sequence_Olazy__sequence(_1850296))), hAPP(hAPP(c_Product__Type_OPair(_1850296, tc_Lazy__Sequence_Olazy__sequence(_1850296)), _1850298), _1850300)))], (50908 ^ _782652) ^ [_1850508, _1850510, _1850512, _1850514, _1850516] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1850508, _1850510, _1850512) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1850508, _1850514, _1850516), 50911 ^ _782652 : [(50912 ^ _782652) ^ [] : [-(_1850510 = _1850514)], (50914 ^ _782652) ^ [] : [-(_1850512 = _1850516)]]], (50916 ^ _782652) ^ [_1850785, _1850787, _1850789, _1850791, _1850793] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1850785, _1850787, _1850789) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1850785, _1850791, _1850793)), _1850787 = _1850791, _1850789 = _1850793], (50926 ^ _782652) ^ [_1851145, _1851147, _1851149, _1851151] : [-(c_New__Random__Sequence_Opos__map(_1851145, _1851147, _1851149, _1851151) = c_New__Random__Sequence_Opos__bind(_1851145, _1851147, _1851151, hAPP(c_Fun_Ocomp(_1851147, 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(_1851147))))), _1851145, c_New__Random__Sequence_Opos__single(_1851147)), _1851149)))], (50928 ^ _782652) ^ [_1851354, _1851356, _1851358, _1851360, _1851362] : [_1851354 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1851356, _1851358, _1851360, _1851362), _1851354) = c_Lazy__Sequence_Ohit__bound(_1851358))], (50934 ^ _782652) ^ [_1851554, _1851556, _1851558, _1851560, _1851562] : [-(_1851554 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1851556, _1851558, _1851560, _1851562), _1851554) = c_Lazy__Sequence_Ohb__bind(_1851556, _1851558, hAPP(_1851560, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1851554), 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hAPP(hAPP(c_COMBC(_1851914, 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(_1851916)))))), _1851920), _1851922)), _1851924)), _1851926)))], (50942 ^ _782652) ^ [_1852142, _1852144, _1852146, _1852148, _1852150] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1852142), _1852144), _1852146), _1852148), _1852150) = c_New__DSequence_Opos__single(_1852142, _1852144))], (50944 ^ _782652) ^ [_1852273, _1852275, _1852277] : [-(hAPP(c_New__DSequence_Opos__single(_1852273, _1852275), _1852277) = hAPP(c_Lazy__Sequence_Osingle(_1852273), _1852275))], (50946 ^ _782652) ^ [_1852422, _1852424, _1852426, _1852428, _1852430] : [-(hAPP(c_New__DSequence_Oneg__bind(_1852422, _1852424, _1852426, _1852428), _1852430) = c_Lazy__Sequence_Ohb__bind(_1852422, _1852424, hAPP(_1852426, _1852430), hAPP(hAPP(c_COMBC(_1852422, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1852424))), _1852428), _1852430)))], (50948 ^ _782652) ^ [_1852622, _1852624, _1852626, _1852628, _1852630, _1852632, _1852634] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1852622, _1852624, _1852626, _1852628), _1852630), _1852632), _1852634) = c_New__DSequence_Oneg__bind(_1852622, _1852624, hAPP(hAPP(hAPP(_1852626, _1852630), _1852632), _1852634), hAPP(hAPP(c_COMBC(_1852622, 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(_1852624)))), hAPP(hAPP(c_COMBC(_1852622, 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(_1852624))))), hAPP(hAPP(c_COMBC(_1852622, tc_Code__Numeral_Ocode__numeral, 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c_List_Olist_ONil(_1853209)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1853209))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1853211)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1853209, tc_List_Olist(_1853209)), tc_List_Olist(_1853209), c_Lazy__Sequence_Oproduct(_1853209, tc_List_Olist(_1853209), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1853209, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1853211), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1853209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1853211), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1853209, tc_List_Olist(_1853209), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1853209))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1853209), tc_List_Olist(_1853209)), tc_fun(tc_List_Olist(_1853209), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1853209))), _1853209), hAPP(c_COMBB(tc_List_Olist(_1853209), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1853209)), tc_List_Olist(_1853209)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1853209)))), c_List_Olist_OCons(_1853209))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1853209)))))], (50960 ^ _782652) ^ [_1853717, _1853719, _1853721] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1853717, _1853719), _1853721) = c_Lazy__Sequence_Oproduct(_1853717, _1853719, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1853717, _1853721), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1853719, _1853721))), class_Lazy__Sequence_Osmall__lazy(_1853717), class_Lazy__Sequence_Osmall__lazy(_1853719)], (50970 ^ _782652) ^ [_1854069, _1854071, _1854073, _1854075] : [-(c_Lazy__Sequence_Oappend(_1854069, c_Lazy__Sequence_Olazy__sequence_OInsert(_1854069, _1854071, _1854073), _1854075) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1854069, _1854071, c_Lazy__Sequence_Oappend(_1854069, _1854073, _1854075)))], (50972 ^ _782652) ^ [_1854225, _1854227, _1854229, _1854231, _1854233] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1854225), _1854227), _1854229), _1854231), _1854233) = c_New__DSequence_Oneg__single(_1854225, _1854227))], (50974 ^ _782652) ^ [_1854370, _1854372, _1854374, _1854376] : [-(hAPP(c_New__DSequence_Opos__union(_1854370, _1854372, _1854374), _1854376) = c_Lazy__Sequence_Oappend(_1854370, hAPP(_1854372, _1854376), hAPP(_1854374, _1854376)))], (50976 ^ _782652) ^ [_1854499, _1854501, _1854503] : [-(hAPP(c_New__DSequence_Oneg__single(_1854499, _1854501), _1854503) = c_Lazy__Sequence_Ohb__single(_1854499, _1854501))], (50978 ^ _782652) ^ [_1854660, _1854662, _1854664, _1854666, _1854668, _1854670] : [-(c_New__Random__Sequence_Opos__union(_1854660, _1854662, _1854664, _1854666, _1854668, _1854670) = c_New__DSequence_Opos__union(_1854660, hAPP(hAPP(hAPP(_1854662, _1854666), _1854668), _1854670), hAPP(hAPP(hAPP(_1854664, _1854666), _1854668), _1854670)))], (50980 ^ _782652) ^ [_1854826, _1854828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1854826), _1854828)), -(c_Lazy__Sequence_Osmall__lazy_H(_1854826, _1854828) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (50986 ^ _782652) ^ [_1855004, _1855006] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1855004), _1855006))), -(c_Lazy__Sequence_Osmall__lazy_H(_1855004, _1855006) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1855006), c_Lazy__Sequence_Osmall__lazy_H(_1855004, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1855006), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50992 ^ _782652) ^ [_1855267, _1855269] : [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), _1855267), _1855269))), 50995 ^ _782652 : [(50996 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1855267), _1855269)), -(c_Lazy__Sequence_Osmall__lazy_H(_1855267, _1855269) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (51002 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1855267), _1855269))), -(c_Lazy__Sequence_Osmall__lazy_H(_1855267, _1855269) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1855269), c_Lazy__Sequence_Osmall__lazy_H(_1855267, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1855269), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (51008 ^ _782652) ^ [_1855784] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1855784) = c_Lazy__Sequence_Osmall__lazy_H(_1855784, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1855784)))], (51010 ^ _782652) ^ [_1855914, _1855916, _1855918] : [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), _1855914), _1855916))), -(hBOOL(hAPP(hAPP(_1855918, _1855914), _1855916))), 51017 ^ _782652 : [(51018 ^ _782652) ^ [] : [-(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), 51015 ^ [_1855914, _1855916, _1855918]), 51016 ^ [_1855914, _1855916, _1855918]))))], (51026 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(_1855918, 51015 ^ [_1855914, _1855916, _1855918]), 51016 ^ [_1855914, _1855916, _1855918]))], (51020 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 51015 ^ [_1855914, _1855916, _1855918]), 51016 ^ [_1855914, _1855916, _1855918]))), -(hBOOL(hAPP(hAPP(_1855918, 51015 ^ [_1855914, _1855916, _1855918]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 51016 ^ [_1855914, _1855916, _1855918]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (51030 ^ _782652) ^ [_1856874, _1856876, _1856878] : [-(c_Lazy__Sequence_Ohb__flat(_1856874, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1856874))), _1856876, _1856878)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(_1856874), hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1856874)), tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1856874)), c_Lazy__Sequence_Ohit__bound(_1856874), c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1856874)))), _1856876), c_Lazy__Sequence_Ohb__flat(_1856874, _1856878)))], (51032 ^ _782652) ^ [_1857044, _1857046, _1857048, _1857050] : [-(hAPP(c_New__DSequence_Oneg__union(_1857044, _1857046, _1857048), _1857050) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(_1857044), hAPP(_1857046, _1857050), hAPP(_1857048, _1857050)))], (51034 ^ _782652) ^ [_1857189, _1857191, _1857193, _1857195] : [-(c_Lazy__Sequence_Ohb__bind(_1857189, _1857191, _1857193, _1857195) = c_Lazy__Sequence_Ohb__flat(_1857191, c_Lazy__Sequence_Ohb__map(_1857189, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1857191)), _1857195, _1857193)))], (51036 ^ _782652) ^ [_1857346, _1857348, _1857350, _1857352, _1857354] : [-(c_Lazy__Sequence_Ohb__map(_1857346, _1857348, _1857350, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(_1857346), _1857352, _1857354)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(_1857348), hAPP(hAPP(c_Option_Omap(_1857346, _1857348), _1857350), _1857352), c_Lazy__Sequence_Ohb__map(_1857346, _1857348, _1857350, _1857354)))], (51038 ^ _782652) ^ [_1857533, _1857535, _1857537, _1857539, _1857541, _1857543] : [-(c_New__Random__Sequence_Oneg__union(_1857533, _1857535, _1857537, _1857539, _1857541, _1857543) = c_New__DSequence_Oneg__union(_1857533, hAPP(hAPP(hAPP(_1857535, _1857539), _1857541), _1857543), hAPP(hAPP(hAPP(_1857537, _1857539), _1857541), _1857543)))], (51040 ^ _782652) ^ [_1857706, _1857708, _1857710, _1857712, _1857714] : [-(c_New__DSequence_Oneg__map(_1857706, _1857708, _1857710, _1857712, _1857714) = c_Lazy__Sequence_Ohb__map(_1857706, _1857708, _1857710, hAPP(_1857712, _1857714)))], (51042 ^ _782652) ^ [_1857834, _1857836, _1857838] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1857834)), c_List_Osplice(_1857834, _1857836, _1857838)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1857834)), _1857836)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1857834)), _1857838)))], (51044 ^ _782652) ^ [_1858005, _1858007] : [c_Wellfounded_Oacyclic(_1858005, hAPP(c_Set_OCollect(tc_prod(_1858005, _1858005)), hAPP(c_Product__Type_Oprod_Oprod__case(_1858005, _1858005, tc_HOL_Obool), c_Predicate_Oconversep(_1858005, _1858005, _1858007)))), -(c_Wellfounded_Oacyclic(_1858005, hAPP(c_Set_OCollect(tc_prod(_1858005, _1858005)), hAPP(c_Product__Type_Oprod_Oprod__case(_1858005, _1858005, tc_HOL_Obool), _1858007))))], (51050 ^ _782652) ^ [_1858235, _1858237] : [c_Wellfounded_Oacyclic(_1858235, hAPP(c_Set_OCollect(tc_prod(_1858235, _1858235)), hAPP(c_Product__Type_Oprod_Oprod__case(_1858235, _1858235, tc_HOL_Obool), _1858237))), -(c_Wellfounded_Oacyclic(_1858235, hAPP(c_Set_OCollect(tc_prod(_1858235, _1858235)), hAPP(c_Product__Type_Oprod_Oprod__case(_1858235, _1858235, tc_HOL_Obool), c_Predicate_Oconversep(_1858235, _1858235, _1858237)))))], (51056 ^ _782652) ^ [_1858542, _1858544, _1858546, _1858548, _1858550] : [-(c_List_Osplice(_1858542, hAPP(hAPP(c_List_Olist_OCons(_1858542), _1858544), _1858546), hAPP(hAPP(c_List_Olist_OCons(_1858542), _1858548), _1858550)) = hAPP(hAPP(c_List_Olist_OCons(_1858542), _1858544), hAPP(hAPP(c_List_Olist_OCons(_1858542), _1858548), c_List_Osplice(_1858542, _1858546, _1858550))))], (51058 ^ _782652) ^ [_1858710, _1858712, _1858714, _1858716] : [-(c_Predicate_Oconversep(_1858710, _1858712, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1858710, tc_fun(_1858712, tc_HOL_Obool))), _1858714), _1858716)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1858712, tc_fun(_1858710, tc_HOL_Obool))), c_Predicate_Oconversep(_1858710, _1858712, _1858714)), c_Predicate_Oconversep(_1858710, _1858712, _1858716)))], (51060 ^ _782652) ^ [_1858890, _1858892, _1858894, _1858896, _1858898] : [-(c_Predicate_Oconversep(_1858890, _1858892, c_Predicate_Opred__comp(_1858890, _1858894, _1858892, _1858896, _1858898)) = c_Predicate_Opred__comp(_1858892, _1858894, _1858890, c_Predicate_Oconversep(_1858894, _1858892, _1858898), c_Predicate_Oconversep(_1858890, _1858894, _1858896)))], (51062 ^ _782652) ^ [_1859000] : [-(c_Predicate_Oconversep(_1859000, _1859000, c_fequal) = c_fequal)], (51064 ^ _782652) ^ [_1859110, _1859112, _1859114] : [-(c_Predicate_Oconversep(_1859110, _1859112, c_Predicate_Oconversep(_1859112, _1859110, _1859114)) = _1859114)], (51066 ^ _782652) ^ [_1859300, _1859302, _1859304, _1859306, _1859308] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1859300, _1859302, _1859304), _1859306), _1859308)), -(hBOOL(hAPP(hAPP(_1859304, _1859308), _1859306)))], (51072 ^ _782652) ^ [_1859508, _1859510, _1859512, _1859514, _1859516] : [hBOOL(hAPP(hAPP(_1859512, _1859516), _1859514)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1859508, _1859510, _1859512), _1859514), _1859516)))], (51078 ^ _782652) ^ [_1859837, _1859839, _1859841, _1859843, _1859845] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1859837, _1859839, _1859841), _1859843), _1859845)), -(hBOOL(hAPP(hAPP(_1859841, _1859845), _1859843)))], (51084 ^ _782652) ^ [_1860045, _1860047, _1860049, _1860051, _1860053] : [hBOOL(hAPP(hAPP(_1860049, _1860053), _1860051)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1860045, _1860047, _1860049), _1860051), _1860053)))], (51090 ^ _782652) ^ [_1860345, _1860347, _1860349, _1860351, _1860353] : [hBOOL(hAPP(hAPP(_1860345, _1860347), _1860349)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1860351, _1860353, _1860345), _1860349), _1860347)))], (51096 ^ _782652) ^ [_1860643, _1860645, _1860647, _1860649, _1860651] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1860643, _1860645, _1860647), _1860649), _1860651)), -(hBOOL(hAPP(hAPP(_1860647, _1860651), _1860649)))], (51102 ^ _782652) ^ [_1860942, _1860944, _1860946] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1860942, _1860942, hAPP(hAPP(c_COMBB(tc_fun(_1860942, tc_HOL_Obool), tc_fun(_1860942, tc_HOL_Obool), _1860942), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1860942), c_fNot)), c_fequal)), _1860944), _1860946)), _1860944 = _1860946], (51108 ^ _782652) ^ [_1861175, _1861177, _1861179] : [-(_1861177 = _1861179), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1861175, _1861175, hAPP(hAPP(c_COMBB(tc_fun(_1861175, tc_HOL_Obool), tc_fun(_1861175, tc_HOL_Obool), _1861175), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1861175), c_fNot)), c_fequal)), _1861177), _1861179)))], (51114 ^ _782652) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (51116 ^ _782652) ^ [_1861513, _1861515] : [class_Lattices_Obounded__lattice(_1861513), -(class_Lattices_Obounded__lattice(tc_fun(_1861515, _1861513)))], (51122 ^ _782652) ^ [_1861725, _1861727] : [class_Complete__Lattice_Ocomplete__lattice(_1861725), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1861727, _1861725)))], (51128 ^ _782652) ^ [_1861937, _1861939] : [class_Lattices_Obounded__lattice(_1861937), -(class_Lattices_Obounded__lattice__top(tc_fun(_1861939, _1861937)))], (51134 ^ _782652) ^ [_1862149, _1862151] : [class_Lattices_Obounded__lattice(_1862149), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1862151, _1862149)))], (51140 ^ _782652) ^ [_1862361, _1862363] : [class_Lattices_Olattice(_1862361), -(class_Lattices_Osemilattice__sup(tc_fun(_1862363, _1862361)))], (51146 ^ _782652) ^ [_1862573, _1862575] : [class_Lattices_Olattice(_1862573), -(class_Lattices_Osemilattice__inf(tc_fun(_1862575, _1862573)))], (51152 ^ _782652) ^ [_1862785, _1862787] : [class_Lattices_Odistrib__lattice(_1862785), -(class_Lattices_Odistrib__lattice(tc_fun(_1862787, _1862785)))], (51158 ^ _782652) ^ [_1862997, _1862999] : [class_Lattices_Oboolean__algebra(_1862997), -(class_Lattices_Oboolean__algebra(tc_fun(_1862999, _1862997)))], (51164 ^ _782652) ^ [_1863209, _1863211] : [class_Orderings_Opreorder(_1863209), -(class_Orderings_Opreorder(tc_fun(_1863211, _1863209)))], (51170 ^ _782652) ^ [_1863421, _1863423] : [-(class_Finite__Set_Ofinite(tc_fun(_1863421, _1863423))), class_Finite__Set_Ofinite(_1863421), class_Finite__Set_Ofinite(_1863423)], (51180 ^ _782652) ^ [_1863720, _1863722] : [class_Lattices_Olattice(_1863720), -(class_Lattices_Olattice(tc_fun(_1863722, _1863720)))], (51186 ^ _782652) ^ [_1863932, _1863934] : [class_Orderings_Oorder(_1863932), -(class_Orderings_Oorder(tc_fun(_1863934, _1863932)))], (51192 ^ _782652) ^ [_1864144, _1864146] : [class_Orderings_Otop(_1864144), -(class_Orderings_Otop(tc_fun(_1864146, _1864144)))], (51198 ^ _782652) ^ [_1864356, _1864358] : [class_Orderings_Oord(_1864356), -(class_Orderings_Oord(tc_fun(_1864358, _1864356)))], (51204 ^ _782652) ^ [_1864568, _1864570] : [class_Orderings_Obot(_1864568), -(class_Orderings_Obot(tc_fun(_1864570, _1864568)))], (51210 ^ _782652) ^ [_1864780, _1864782] : [class_Groups_Ouminus(_1864780), -(class_Groups_Ouminus(tc_fun(_1864782, _1864780)))], (51216 ^ _782652) ^ [_1864992, _1864994] : [class_Groups_Ominus(_1864992), -(class_Groups_Ominus(tc_fun(_1864994, _1864992)))], (51222 ^ _782652) ^ [_1865204, _1865206] : [-(class_HOL_Oequal(tc_fun(_1865204, _1865206))), class_Enum_Oenum(_1865204), class_HOL_Oequal(_1865206)], (51232 ^ _782652) ^ [_1865503, _1865505] : [-(class_Enum_Oenum(tc_fun(_1865503, _1865505))), class_Enum_Oenum(_1865503), class_Enum_Oenum(_1865505)], (51242 ^ _782652) ^ [] : [-(class_HOL_Oequal(tc_Com_Ocom))], (51244 ^ _782652) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (51246 ^ _782652) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (51248 ^ _782652) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (51250 ^ _782652) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (51252 ^ _782652) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (51254 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (51256 ^ _782652) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (51258 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (51260 ^ _782652) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (51262 ^ _782652) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (51264 ^ _782652) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (51266 ^ _782652) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (51268 ^ _782652) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (51270 ^ _782652) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (51272 ^ _782652) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (51274 ^ _782652) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (51276 ^ _782652) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (51278 ^ _782652) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (51280 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (51282 ^ _782652) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (51284 ^ _782652) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (51286 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (51288 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (51290 ^ _782652) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (51292 ^ _782652) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (51294 ^ _782652) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (51296 ^ _782652) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (51298 ^ _782652) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (51300 ^ _782652) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (51302 ^ _782652) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (51304 ^ _782652) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (51306 ^ _782652) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (51308 ^ _782652) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (51310 ^ _782652) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (51312 ^ _782652) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (51314 ^ _782652) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (51316 ^ _782652) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (51318 ^ _782652) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (51320 ^ _782652) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (51322 ^ _782652) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (51324 ^ _782652) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (51326 ^ _782652) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (51328 ^ _782652) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (51330 ^ _782652) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (51332 ^ _782652) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (51334 ^ _782652) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (51336 ^ _782652) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (51338 ^ _782652) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (51340 ^ _782652) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (51342 ^ _782652) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (51344 ^ _782652) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (51346 ^ _782652) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (51348 ^ _782652) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (51350 ^ _782652) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (51352 ^ _782652) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (51354 ^ _782652) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (51356 ^ _782652) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (51358 ^ _782652) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (51360 ^ _782652) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (51362 ^ _782652) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (51364 ^ _782652) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (51366 ^ _782652) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (51368 ^ _782652) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (51370 ^ _782652) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (51372 ^ _782652) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (51374 ^ _782652) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (51376 ^ _782652) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (51378 ^ _782652) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (51380 ^ _782652) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (51382 ^ _782652) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (51384 ^ _782652) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (51386 ^ _782652) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (51388 ^ _782652) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (51390 ^ _782652) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (51392 ^ _782652) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (51394 ^ _782652) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (51396 ^ _782652) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (51398 ^ _782652) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (51400 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (51402 ^ _782652) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (51404 ^ _782652) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (51406 ^ _782652) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (51408 ^ _782652) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (51410 ^ _782652) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (51412 ^ _782652) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (51414 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (51416 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (51418 ^ _782652) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (51420 ^ _782652) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (51422 ^ _782652) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (51424 ^ _782652) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (51426 ^ _782652) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (51428 ^ _782652) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (51430 ^ _782652) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (51432 ^ _782652) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (51434 ^ _782652) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (51436 ^ _782652) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (51438 ^ _782652) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (51440 ^ _782652) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (51442 ^ _782652) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (51444 ^ _782652) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (51446 ^ _782652) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (51448 ^ _782652) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (51450 ^ _782652) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (51452 ^ _782652) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (51454 ^ _782652) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (51456 ^ _782652) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (51458 ^ _782652) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (51460 ^ _782652) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (51462 ^ _782652) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (51464 ^ _782652) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (51466 ^ _782652) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (51468 ^ _782652) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (51470 ^ _782652) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (51472 ^ _782652) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (51474 ^ _782652) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (51476 ^ _782652) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (51478 ^ _782652) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (51480 ^ _782652) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (51482 ^ _782652) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (51484 ^ _782652) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (51486 ^ _782652) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (51488 ^ _782652) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (51490 ^ _782652) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (51492 ^ _782652) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (51494 ^ _782652) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (51496 ^ _782652) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (51498 ^ _782652) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (51500 ^ _782652) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (51502 ^ _782652) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (51504 ^ _782652) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (51506 ^ _782652) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (51508 ^ _782652) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (51510 ^ _782652) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (51512 ^ _782652) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (51514 ^ _782652) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (51516 ^ _782652) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (51518 ^ _782652) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (51520 ^ _782652) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (51522 ^ _782652) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (51524 ^ _782652) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (51526 ^ _782652) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (51528 ^ _782652) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (51530 ^ _782652) ^ [_1873420] : [class_Lazy__Sequence_Osmall__lazy(_1873420), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1873420)))], (51536 ^ _782652) ^ [_1873595] : [-(class_HOL_Oequal(tc_List_Olist(_1873595)))], (51538 ^ _782652) ^ [_1873674] : [-(class_Nat_Osize(tc_List_Olist(_1873674)))], (51540 ^ _782652) ^ [_1873782, _1873784] : [-(class_Finite__Set_Ofinite(tc_sum(_1873782, _1873784))), class_Finite__Set_Ofinite(_1873782), class_Finite__Set_Ofinite(_1873784)], (51550 ^ _782652) ^ [_1874066, _1874068] : [-(class_HOL_Oequal(tc_sum(_1874066, _1874068)))], (51552 ^ _782652) ^ [_1874177, _1874179] : [-(class_Enum_Oenum(tc_sum(_1874177, _1874179))), class_Enum_Oenum(_1874177), class_Enum_Oenum(_1874179)], (51562 ^ _782652) ^ [_1874461, _1874463] : [-(class_Nat_Osize(tc_sum(_1874461, _1874463)))], (51564 ^ _782652) ^ [_1874558] : [class_Finite__Set_Ofinite(_1874558), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1874558)))], (51570 ^ _782652) ^ [_1874733] : [-(class_HOL_Oequal(tc_Option_Ooption(_1874733)))], (51572 ^ _782652) ^ [_1874827] : [class_Enum_Oenum(_1874827), -(class_Enum_Oenum(tc_Option_Ooption(_1874827)))], (51578 ^ _782652) ^ [_1875002] : [-(class_Nat_Osize(tc_Option_Ooption(_1875002)))], (51580 ^ _782652) ^ [_1875110, _1875112] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1875110, _1875112))), class_Lazy__Sequence_Osmall__lazy(_1875110), class_Lazy__Sequence_Osmall__lazy(_1875112)], (51590 ^ _782652) ^ [_1875409, _1875411] : [-(class_Finite__Set_Ofinite(tc_prod(_1875409, _1875411))), class_Finite__Set_Ofinite(_1875409), class_Finite__Set_Ofinite(_1875411)], (51600 ^ _782652) ^ [_1875708, _1875710] : [-(class_Smallcheck_Osmall(tc_prod(_1875708, _1875710))), class_Smallcheck_Osmall(_1875708), class_Smallcheck_Osmall(_1875710)], (51610 ^ _782652) ^ [_1875992, _1875994] : [-(class_HOL_Oequal(tc_prod(_1875992, _1875994)))], (51612 ^ _782652) ^ [_1876103, _1876105] : [-(class_Enum_Oenum(tc_prod(_1876103, _1876105))), class_Enum_Oenum(_1876103), class_Enum_Oenum(_1876105)], (51622 ^ _782652) ^ [_1876387, _1876389] : [-(class_Nat_Osize(tc_prod(_1876387, _1876389)))], (51624 ^ _782652) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (51626 ^ _782652) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (51628 ^ _782652) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (51630 ^ _782652) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (51632 ^ _782652) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (51634 ^ _782652) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (51636 ^ _782652) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (51638 ^ _782652) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (51640 ^ _782652) ^ [_1876893] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1876893)))], (51642 ^ _782652) ^ [_1876972] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1876972)))], (51644 ^ _782652) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51646 ^ _782652) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (51648 ^ _782652) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (51650 ^ _782652) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51652 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (51654 ^ _782652) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51656 ^ _782652) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (51658 ^ _782652) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51660 ^ _782652) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (51662 ^ _782652) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (51664 ^ _782652) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51666 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (51668 ^ _782652) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (51670 ^ _782652) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (51672 ^ _782652) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (51674 ^ _782652) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51676 ^ _782652) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (51678 ^ _782652) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (51680 ^ _782652) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (51682 ^ _782652) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (51684 ^ _782652) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (51686 ^ _782652) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (51688 ^ _782652) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (51690 ^ _782652) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (51692 ^ _782652) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (51694 ^ _782652) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (51696 ^ _782652) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (51698 ^ _782652) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (51700 ^ _782652) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (51702 ^ _782652) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (51704 ^ _782652) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (51706 ^ _782652) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (51708 ^ _782652) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (51710 ^ _782652) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (51712 ^ _782652) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (51714 ^ _782652) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (51716 ^ _782652) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (51718 ^ _782652) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (51720 ^ _782652) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (51722 ^ _782652) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (51724 ^ _782652) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (51726 ^ _782652) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (51728 ^ _782652) ^ [_1879277] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1879277)))], (51730 ^ _782652) ^ [_1879356] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1879356)))], (51732 ^ _782652) ^ [_1879449, _1879451] : [-(hAPP(c_COMBI(_1879449), _1879451) = _1879451)], (51734 ^ _782652) ^ [_1879576, _1879578, _1879580, _1879582] : [-(hAPP(hAPP(c_COMBK(_1879576, _1879578), _1879580), _1879582) = _1879580)], (51736 ^ _782652) ^ [_1879739, _1879741, _1879743, _1879745, _1879747, _1879749] : [-(hAPP(hAPP(hAPP(c_COMBB(_1879739, _1879741, _1879743), _1879745), _1879747), _1879749) = hAPP(_1879745, hAPP(_1879747, _1879749)))], (51738 ^ _782652) ^ [_1879916, _1879918, _1879920, _1879922, _1879924, _1879926] : [-(hAPP(hAPP(hAPP(c_COMBC(_1879916, _1879918, _1879920), _1879922), _1879924), _1879926) = hAPP(hAPP(_1879922, _1879926), _1879924))], (51740 ^ _782652) ^ [_1880093, _1880095, _1880097, _1880099, _1880101, _1880103] : [-(hAPP(hAPP(hAPP(c_COMBS(_1880093, _1880095, _1880097), _1880099), _1880101), _1880103) = hAPP(hAPP(_1880099, _1880103), hAPP(_1880101, _1880103)))], (51742 ^ _782652) ^ [_1880232, _1880234] : [hBOOL(hAPP(hAPP(c_fequal, _1880232), _1880234)), -(_1880232 = _1880234)], (51748 ^ _782652) ^ [_1880454, _1880456] : [_1880454 = _1880456, -(hBOOL(hAPP(hAPP(c_fequal, _1880454), _1880456)))], (51754 ^ _782652) ^ [] : [hBOOL(c_fFalse)], (51756 ^ _782652) ^ [] : [-(hBOOL(c_fTrue))], (51758 ^ _782652) ^ [_1880767] : [hBOOL(hAPP(c_fNot, _1880767)), hBOOL(_1880767)], (51764 ^ _782652) ^ [_1880962] : [-(hBOOL(_1880962)), -(hBOOL(hAPP(c_fNot, _1880962)))], (51770 ^ _782652) ^ [_1881173, _1881175] : [hBOOL(_1881173), hBOOL(_1881175), -(hBOOL(hAPP(hAPP(c_fconj, _1881173), _1881175)))], (51780 ^ _782652) ^ [_1881482, _1881484] : [hBOOL(hAPP(hAPP(c_fconj, _1881482), _1881484)), -(hBOOL(_1881482))], (51786 ^ _782652) ^ [_1881702, _1881704] : [hBOOL(hAPP(hAPP(c_fconj, _1881702), _1881704)), -(hBOOL(_1881704))], (51792 ^ _782652) ^ [_1881922, _1881924] : [hBOOL(_1881922), -(hBOOL(hAPP(hAPP(c_fdisj, _1881922), _1881924)))], (51798 ^ _782652) ^ [_1882142, _1882144] : [hBOOL(_1882142), -(hBOOL(hAPP(hAPP(c_fdisj, _1882144), _1882142)))], (51804 ^ _782652) ^ [_1882362, _1882364] : [hBOOL(hAPP(hAPP(c_fdisj, _1882362), _1882364)), -(hBOOL(_1882362)), -(hBOOL(_1882364))], (51814 ^ _782652) ^ [_1882670, _1882672] : [-(hBOOL(_1882670)), -(hBOOL(hAPP(hAPP(c_fimplies, _1882670), _1882672)))], (51820 ^ _782652) ^ [_1882889, _1882891] : [hBOOL(_1882889), -(hBOOL(hAPP(hAPP(c_fimplies, _1882891), _1882889)))], (51836 ^ _782652) ^ [] : [-(c_Com_OWT__bodies)], (51838 ^ _782652) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), v_F)))], (51840 ^ _782652) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, v_y)), v_F))], (51842 ^ _782652) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), v_F), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))))], (51844 ^ _782652) ^ [] : [-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))], (51846 ^ _782652) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), v_F))], (51826 ^ _782652) ^ [_1883109, _1883111] : [hBOOL(hAPP(hAPP(c_fimplies, _1883109), _1883111)), hBOOL(_1883109), -(hBOOL(_1883111))]], input).
% 1.69/2.50  ncf('1',plain,[hBOOL(hAPP(c_Com_OWT, v_y))],start(51848 ^ 0)).
% 1.69/2.50  ncf('1.1',plain,[-(hBOOL(hAPP(c_Com_OWT, v_y))), c_Com_OWT__bodies, hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y)],extension(5711 ^ 1,bind([[_872822, _872824], [v_pn, v_y]]))).
% 1.69/2.50  ncf('1.1.1',plain,[-(c_Com_OWT__bodies)],extension(51836 ^ 2)).
% 1.69/2.50  ncf('1.1.2',plain,[-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))],extension(51844 ^ 2)).
% 1.69/2.50  %-----------------------------------------------------
% 1.69/2.50  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------