%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW342+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:59 EDT 2023

% Result   : Theorem 106.20s 102.97s
% Output   : Proof 106.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW342+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n031.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 23:12:25 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 106.20/102.97  
% 106.20/102.97  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 106.20/102.97  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 106.20/102.97  %-----------------------------------------------------
% 106.20/102.97  ncf(matrix, plain, [(51691 ^ _780461) ^ [] : [-(v_P(51688 ^ [], 51689 ^ []))], (51694 ^ _780461) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, 51689 ^ [], v_n, 51692 ^ []))], (51696 ^ _780461) ^ [] : [v_P(51688 ^ [], 51692 ^ [])], (2 ^ _780461) ^ [_780491] : [-(_780491 = _780491)], (4 ^ _780461) ^ [_780514, _780516] : [_780516 = _780514, -(_780514 = _780516)], (10 ^ _780461) ^ [_780587, _780589, _780591] : [-(_780591 = _780587), _780591 = _780589, _780589 = _780587], (20 ^ _780461) ^ [_780724, _780726, _780728, _780730] : [-(c_Option_Ois__none(_780728, _780724)), c_Option_Ois__none(_780730, _780726), _780730 = _780728, _780726 = _780724], (34 ^ _780461) ^ [_780917, _780919, _780921, _780923] : [-(c_Int_Oiszero(_780921, _780917)), c_Int_Oiszero(_780923, _780919), _780923 = _780921, _780919 = _780917], (48 ^ _780461) ^ [_781110, _781112] : [-(class_Rings_Odivision__ring__inverse__zero(_781110)), _781112 = _781110, class_Rings_Odivision__ring__inverse__zero(_781112)], (58 ^ _780461) ^ [_781235, _781237] : [-(class_Rings_Odivision__ring(_781235)), _781237 = _781235, class_Rings_Odivision__ring(_781237)], (68 ^ _780461) ^ [_781360, _781362] : [-(class_Fields_Olinordered__field__inverse__zero(_781360)), _781362 = _781360, class_Fields_Olinordered__field__inverse__zero(_781362)], (78 ^ _780461) ^ [_781485, _781487, _781489, _781491, _781493, _781495, _781497, _781499] : [-(c_Nat__Transfer_Otransfer__morphism(_781497, _781493, _781489, _781485)), c_Nat__Transfer_Otransfer__morphism(_781499, _781495, _781491, _781487), _781499 = _781497, _781495 = _781493, _781491 = _781489, _781487 = _781485], (100 ^ _780461) ^ [_781838, _781840] : [-(class_Rings_Oinverse(_781838)), _781840 = _781838, class_Rings_Oinverse(_781840)], (110 ^ _780461) ^ [_781963, _781965, _781967, _781969, _781971, _781973] : [-(c_Nitpick_Oless__frac(_781971, _781967, _781963)), c_Nitpick_Oless__frac(_781973, _781969, _781965), _781973 = _781971, _781969 = _781967, _781965 = _781963], (128 ^ _780461) ^ [_782232, _782234, _782236, _782238, _782240, _782242] : [-(c_Nitpick_Oless__eq__frac(_782240, _782236, _782232)), c_Nitpick_Oless__eq__frac(_782242, _782238, _782234), _782242 = _782240, _782238 = _782236, _782234 = _782232], (146 ^ _780461) ^ [_782501, _782503, _782505, _782507, _782509, _782511, _782513, _782515] : [-(c_Orderings_Oorder_Omono(_782513, _782509, _782505, _782501)), c_Orderings_Oorder_Omono(_782515, _782511, _782507, _782503), _782515 = _782513, _782511 = _782509, _782507 = _782505, _782503 = _782501], (168 ^ _780461) ^ [_782854, _782856, _782858, _782860] : [-(c_Nitpick_Orefl_H(_782858, _782854)), c_Nitpick_Orefl_H(_782860, _782856), _782860 = _782858, _782856 = _782854], (182 ^ _780461) ^ [_783047, _783049, _783051, _783053, _783055, _783057, _783059, _783061, _783063, _783065, _783067, _783069] : [-(c_Nitpick_Ofold__graph_H(_783067, _783063, _783059, _783055, _783051, _783047)), c_Nitpick_Ofold__graph_H(_783069, _783065, _783061, _783057, _783053, _783049), _783069 = _783067, _783065 = _783063, _783061 = _783059, _783057 = _783055, _783053 = _783051, _783049 = _783047], (212 ^ _780461) ^ [_783592, _783594] : [-(class_Fields_Olinordered__field(_783592)), _783594 = _783592, class_Fields_Olinordered__field(_783594)], (222 ^ _780461) ^ [_783717, _783719] : [-(class_Fields_Ofield__inverse__zero(_783717)), _783719 = _783717, class_Fields_Ofield__inverse__zero(_783719)], (232 ^ _780461) ^ [_783842, _783844, _783846, _783848, _783850, _783852, _783854, _783856, _783858, _783860, _783862, _783864] : [-(c_Equiv__Relations_Ocongruent2(_783862, _783858, _783854, _783850, _783846, _783842)), c_Equiv__Relations_Ocongruent2(_783864, _783860, _783856, _783852, _783848, _783844), _783864 = _783862, _783860 = _783858, _783856 = _783854, _783852 = _783850, _783848 = _783846, _783844 = _783842], (262 ^ _780461) ^ [_784387, _784389, _784391, _784393, _784395, _784397, _784399, _784401] : [-(c_Equiv__Relations_Ocongruent(_784399, _784395, _784391, _784387)), c_Equiv__Relations_Ocongruent(_784401, _784397, _784393, _784389), _784401 = _784399, _784397 = _784395, _784393 = _784391, _784389 = _784387], (284 ^ _780461) ^ [_784740, _784742, _784744, _784746, _784748, _784750, _784752, _784754, _784756, _784758] : [-(c_Big__Operators_Ocomm__monoid__big(_784756, _784752, _784748, _784744, _784740)), c_Big__Operators_Ocomm__monoid__big(_784758, _784754, _784750, _784746, _784742), _784758 = _784756, _784754 = _784752, _784750 = _784748, _784746 = _784744, _784742 = _784740], (310 ^ _780461) ^ [_785185, _785187] : [-(class_Fields_Ofield(_785185)), _785187 = _785185, class_Fields_Ofield(_785187)], (320 ^ _780461) ^ [_785310, _785312] : [-(c_Nat__Transfer_Ois__nat(_785310)), _785312 = _785310, c_Nat__Transfer_Ois__nat(_785312)], (330 ^ _780461) ^ [_785435, _785437, _785439, _785441, _785443, _785445, _785447, _785449, _785451, _785453] : [-(c_Finite__Set_Ofolding__image(_785451, _785447, _785443, _785439, _785435)), c_Finite__Set_Ofolding__image(_785453, _785449, _785445, _785441, _785437), _785453 = _785451, _785449 = _785447, _785445 = _785443, _785441 = _785439, _785437 = _785435], (356 ^ _780461) ^ [_785880, _785882, _785884, _785886, _785888, _785890] : [-(c_Hoare__Mirabelle_Ohoare__valids(_785888, _785884, _785880)), c_Hoare__Mirabelle_Ohoare__valids(_785890, _785886, _785882), _785890 = _785888, _785886 = _785884, _785882 = _785880], (374 ^ _780461) ^ [_786149, _786151, _786153, _786155, _786157, _786159] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_786157, _786153, _786149)), c_Hoare__Mirabelle_Ohoare__derivs(_786159, _786155, _786151), _786159 = _786157, _786155 = _786153, _786151 = _786149], (392 ^ _780461) ^ [_786418, _786420, _786422, _786424, _786426, _786428, _786430, _786432] : [-(c_Finite__Set_Ofolding__idem(_786430, _786426, _786422, _786418)), c_Finite__Set_Ofolding__idem(_786432, _786428, _786424, _786420), _786432 = _786430, _786428 = _786426, _786424 = _786422, _786420 = _786418], (414 ^ _780461) ^ [_786771, _786773, _786775, _786777] : [-(c_Equiv__Relations_Oequivp(_786775, _786771)), c_Equiv__Relations_Oequivp(_786777, _786773), _786777 = _786775, _786773 = _786771], (428 ^ _780461) ^ [_786964, _786966, _786968, _786970, _786972, _786974, _786976, _786978, _786980, _786982] : [-(c_Typedef_Otype__definition(_786980, _786976, _786972, _786968, _786964)), c_Typedef_Otype__definition(_786982, _786978, _786974, _786970, _786966), _786982 = _786980, _786978 = _786976, _786974 = _786972, _786970 = _786968, _786966 = _786964], (454 ^ _780461) ^ [_787409, _787411, _787413, _787415, _787417, _787419, _787421, _787423] : [-(c_Wellfounded_Omax__extp(_787421, _787417, _787413, _787409)), c_Wellfounded_Omax__extp(_787423, _787419, _787415, _787411), _787423 = _787421, _787419 = _787417, _787415 = _787413, _787411 = _787409], (476 ^ _780461) ^ [_787762, _787764, _787766, _787768, _787770, _787772] : [-(c_Big__Operators_Osemilattice__big(_787770, _787766, _787762)), c_Big__Operators_Osemilattice__big(_787772, _787768, _787764), _787772 = _787770, _787768 = _787766, _787764 = _787762], (494 ^ _780461) ^ [_788031, _788033, _788035, _788037, _788039, _788041, _788043, _788045, _788047, _788049, _788051, _788053] : [-(c_Finite__Set_Ofolding__image__simple(_788051, _788047, _788043, _788039, _788035, _788031)), c_Finite__Set_Ofolding__image__simple(_788053, _788049, _788045, _788041, _788037, _788033), _788053 = _788051, _788049 = _788047, _788045 = _788043, _788041 = _788039, _788037 = _788035, _788033 = _788031], (524 ^ _780461) ^ [_788576, _788578, _788580, _788582] : [-(c_Predicate_Oreflp(_788580, _788576)), c_Predicate_Oreflp(_788582, _788578), _788582 = _788580, _788578 = _788576], (538 ^ _780461) ^ [_788769, _788771, _788773, _788775, _788777, _788779, _788781, _788783, _788785, _788787, _788789, _788791, _788793, _788795] : [-(c_Predicate_Opred__comp(_788793, _788789, _788785, _788781, _788777, _788773, _788769)), c_Predicate_Opred__comp(_788795, _788791, _788787, _788783, _788779, _788775, _788771), _788795 = _788793, _788791 = _788789, _788787 = _788785, _788783 = _788781, _788779 = _788777, _788775 = _788773, _788771 = _788769], (572 ^ _780461) ^ [_789422, _789424, _789426, _789428] : [-(c_FunDef_Oreduction__pair(_789426, _789422)), c_FunDef_Oreduction__pair(_789428, _789424), _789428 = _789426, _789424 = _789422], (586 ^ _780461) ^ [_789615, _789617, _789619, _789621] : [-(c_Nitpick_Owf_H(_789619, _789615)), c_Nitpick_Owf_H(_789621, _789617), _789621 = _789619, _789617 = _789615], (600 ^ _780461) ^ [_789808, _789810] : [-(c_Nitpick_Ounknown(_789808)), _789810 = _789808, c_Nitpick_Ounknown(_789810)], (610 ^ _780461) ^ [_789933, _789935, _789937, _789939] : [-(c_Wellfounded_OwfP(_789937, _789933)), c_Wellfounded_OwfP(_789939, _789935), _789939 = _789937, _789935 = _789933], (624 ^ _780461) ^ [_790126, _790128, _790130, _790132, _790134, _790136, _790138, _790140] : [-(c_Orderings_Oorder_Ostrict__mono(_790138, _790134, _790130, _790126)), c_Orderings_Oorder_Ostrict__mono(_790140, _790136, _790132, _790128), _790140 = _790138, _790136 = _790134, _790132 = _790130, _790128 = _790126], (646 ^ _780461) ^ [_790479, _790481, _790483, _790485, _790487, _790489, _790491, _790493] : [-(c_Finite__Set_Ofolding(_790491, _790487, _790483, _790479)), c_Finite__Set_Ofolding(_790493, _790489, _790485, _790481), _790493 = _790491, _790489 = _790487, _790485 = _790483, _790481 = _790479], (668 ^ _780461) ^ [_790832, _790834, _790836, _790838, _790840, _790842] : [-(c_Finite__Set_Ofolding__one__idem(_790840, _790836, _790832)), c_Finite__Set_Ofolding__one__idem(_790842, _790838, _790834), _790842 = _790840, _790838 = _790836, _790834 = _790832], (686 ^ _780461) ^ [_791101, _791103, _791105, _791107, _791109, _791111] : [-(c_Finite__Set_Ofolding__one(_791109, _791105, _791101)), c_Finite__Set_Ofolding__one(_791111, _791107, _791103), _791111 = _791109, _791107 = _791105, _791103 = _791101], (704 ^ _780461) ^ [_791370, _791372, _791374, _791376] : [-(c_Relation_Oirrefl(_791374, _791370)), c_Relation_Oirrefl(_791376, _791372), _791376 = _791374, _791372 = _791370], (718 ^ _780461) ^ [_791563, _791565, _791567, _791569, _791571, _791573] : [-(c_Relation_Osingle__valued(_791571, _791567, _791563)), c_Relation_Osingle__valued(_791573, _791569, _791565), _791573 = _791571, _791569 = _791567, _791565 = _791563], (736 ^ _780461) ^ [_791832, _791834, _791836, _791838, _791840, _791842] : [-(c_Relation_Ototal__on(_791840, _791836, _791832)), c_Relation_Ototal__on(_791842, _791838, _791834), _791842 = _791840, _791838 = _791836, _791834 = _791832], (754 ^ _780461) ^ [_792101, _792103, _792105, _792107] : [-(c_Wellfounded_Oacyclic(_792105, _792101)), c_Wellfounded_Oacyclic(_792107, _792103), _792107 = _792105, _792103 = _792101], (768 ^ _780461) ^ [_792294, _792296, _792298, _792300] : [-(c_Wellfounded_Owf(_792298, _792294)), c_Wellfounded_Owf(_792300, _792296), _792300 = _792298, _792296 = _792294], (782 ^ _780461) ^ [_792487, _792489, _792491, _792493, _792495, _792497, _792499, _792501, _792503, _792505, _792507, _792509] : [-(c_Finite__Set_Ofolding__image__simple__idem(_792507, _792503, _792499, _792495, _792491, _792487)), c_Finite__Set_Ofolding__image__simple__idem(_792509, _792505, _792501, _792497, _792493, _792489), _792509 = _792507, _792505 = _792503, _792501 = _792499, _792497 = _792495, _792493 = _792491, _792489 = _792487], (812 ^ _780461) ^ [_793032, _793034] : [-(c_List_Onat__list(_793032)), _793034 = _793032, c_List_Onat__list(_793034)], (822 ^ _780461) ^ [_793157, _793159] : [-(c_Nat__Transfer_Onat__set(_793157)), _793159 = _793157, c_Nat__Transfer_Onat__set(_793159)], (832 ^ _780461) ^ [_793282, _793284, _793286, _793288, _793290, _793292] : [-(c_Finite__Set_Ofun__left__comm(_793290, _793286, _793282)), c_Finite__Set_Ofun__left__comm(_793292, _793288, _793284), _793292 = _793290, _793288 = _793286, _793284 = _793282], (850 ^ _780461) ^ [_793551, _793553, _793555, _793557, _793559, _793561, _793563, _793565] : [-(c_List_Olistrelp(_793563, _793559, _793555, _793551)), c_List_Olistrelp(_793565, _793561, _793557, _793553), _793565 = _793563, _793561 = _793559, _793557 = _793555, _793553 = _793551], (872 ^ _780461) ^ [_793904, _793906] : [-(class_Lattices_Oab__semigroup__idem__mult(_793904)), _793906 = _793904, class_Lattices_Oab__semigroup__idem__mult(_793906)], (882 ^ _780461) ^ [_794029, _794031, _794033, _794035, _794037, _794039] : [-(c_Finite__Set_Ofun__left__comm__idem(_794037, _794033, _794029)), c_Finite__Set_Ofun__left__comm__idem(_794039, _794035, _794031), _794039 = _794037, _794035 = _794033, _794031 = _794029], (900 ^ _780461) ^ [_794298, _794300, _794302, _794304, _794306, _794308] : [-(c_Relation_Orefl__on(_794306, _794302, _794298)), c_Relation_Orefl__on(_794308, _794304, _794300), _794308 = _794306, _794304 = _794302, _794300 = _794298], (918 ^ _780461) ^ [_794567, _794569, _794571, _794573, _794575, _794577] : [-(c_Equiv__Relations_Oequiv(_794575, _794571, _794567)), c_Equiv__Relations_Oequiv(_794577, _794573, _794569), _794577 = _794575, _794573 = _794571, _794569 = _794567], (936 ^ _780461) ^ [_794836, _794838, _794840, _794842, _794844, _794846, _794848, _794850] : [-(c_Fun_Oinj__on(_794848, _794844, _794840, _794836)), c_Fun_Oinj__on(_794850, _794846, _794842, _794838), _794850 = _794848, _794846 = _794844, _794842 = _794840, _794838 = _794836], (958 ^ _780461) ^ [_795189, _795191, _795193, _795195] : [-(c_List_Olinorder__class_Osorted(_795193, _795189)), c_List_Olinorder__class_Osorted(_795195, _795191), _795195 = _795193, _795191 = _795189], (972 ^ _780461) ^ [_795382, _795384] : [-(class_Lattices_Obounded__lattice(_795382)), _795384 = _795382, class_Lattices_Obounded__lattice(_795384)], (982 ^ _780461) ^ [_795507, _795509] : [-(class_Rings_Olinordered__semiring__1__strict(_795507)), _795509 = _795507, class_Rings_Olinordered__semiring__1__strict(_795509)], (992 ^ _780461) ^ [_795632, _795634] : [-(class_Groups_Oordered__ab__group__add__abs(_795632)), _795634 = _795632, class_Groups_Oordered__ab__group__add__abs(_795634)], (1002 ^ _780461) ^ [_795757, _795759] : [-(class_Groups_Olinordered__ab__group__add(_795757)), _795759 = _795757, class_Groups_Olinordered__ab__group__add(_795759)], (1012 ^ _780461) ^ [_795882, _795884] : [-(class_Rings_Oring__1__no__zero__divisors(_795882)), _795884 = _795882, class_Rings_Oring__1__no__zero__divisors(_795884)], (1022 ^ _780461) ^ [_796007, _796009] : [-(class_Rings_Olinordered__ring__strict(_796007)), _796009 = _796007, class_Rings_Olinordered__ring__strict(_796009)], (1032 ^ _780461) ^ [_796132, _796134] : [-(class_Rings_Oring__no__zero__divisors(_796132)), _796134 = _796132, class_Rings_Oring__no__zero__divisors(_796134)], (1042 ^ _780461) ^ [_796257, _796259] : [-(class_Rings_Olinordered__semiring__1(_796257)), _796259 = _796257, class_Rings_Olinordered__semiring__1(_796259)], (1052 ^ _780461) ^ [_796382, _796384] : [-(class_Groups_Oordered__ab__group__add(_796382)), _796384 = _796382, class_Groups_Oordered__ab__group__add(_796384)], (1062 ^ _780461) ^ [_796507, _796509] : [-(class_Rings_Oordered__ring__abs(_796507)), _796509 = _796507, class_Rings_Oordered__ring__abs(_796509)], (1072 ^ _780461) ^ [_796632, _796634] : [-(class_Rings_Olinordered__ring(_796632)), _796634 = _796632, class_Rings_Olinordered__ring(_796634)], (1082 ^ _780461) ^ [_796757, _796759] : [-(class_Rings_Olinordered__idom(_796757)), _796759 = _796757, class_Rings_Olinordered__idom(_796759)], (1092 ^ _780461) ^ [_796882, _796884] : [-(class_Groups_Oab__group__add(_796882)), _796884 = _796882, class_Groups_Oab__group__add(_796884)], (1102 ^ _780461) ^ [_797007, _797009] : [-(class_Rings_Oordered__ring(_797007)), _797009 = _797007, class_Rings_Oordered__ring(_797009)], (1112 ^ _780461) ^ [_797132, _797134] : [-(class_Rings_Ocomm__ring__1(_797132)), _797134 = _797132, class_Rings_Ocomm__ring__1(_797134)], (1122 ^ _780461) ^ [_797257, _797259] : [-(class_Groups_Ogroup__add(_797257)), _797259 = _797257, class_Groups_Ogroup__add(_797259)], (1132 ^ _780461) ^ [_797382, _797384] : [-(class_Divides_Oring__div(_797382)), _797384 = _797382, class_Divides_Oring__div(_797384)], (1142 ^ _780461) ^ [_797507, _797509] : [-(class_Rings_Ocomm__ring(_797507)), _797509 = _797507, class_Rings_Ocomm__ring(_797509)], (1152 ^ _780461) ^ [_797632, _797634] : [-(class_Int_Oring__char__0(_797632)), _797634 = _797632, class_Int_Oring__char__0(_797634)], (1162 ^ _780461) ^ [_797757, _797759] : [-(class_Int_Onumber__ring(_797757)), _797759 = _797757, class_Int_Onumber__ring(_797759)], (1172 ^ _780461) ^ [_797882, _797884] : [-(class_Groups_Osgn__if(_797882)), _797884 = _797882, class_Groups_Osgn__if(_797884)], (1182 ^ _780461) ^ [_798007, _798009] : [-(class_Groups_Oabs__if(_798007)), _798009 = _798007, class_Groups_Oabs__if(_798009)], (1192 ^ _780461) ^ [_798132, _798134] : [-(class_Rings_Oring__1(_798132)), _798134 = _798132, class_Rings_Oring__1(_798134)], (1202 ^ _780461) ^ [_798257, _798259] : [-(class_Rings_Oring(_798257)), _798259 = _798257, class_Rings_Oring(_798259)], (1212 ^ _780461) ^ [_798382, _798384] : [-(class_Rings_Oidom(_798382)), _798384 = _798382, class_Rings_Oidom(_798384)], (1222 ^ _780461) ^ [_798507, _798509] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_798507)), _798509 = _798507, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_798509)], (1232 ^ _780461) ^ [_798632, _798634] : [-(class_Orderings_Owellorder(_798632)), _798634 = _798632, class_Orderings_Owellorder(_798634)], (1242 ^ _780461) ^ [_798757, _798759] : [-(class_Complete__Lattice_Ocomplete__lattice(_798757)), _798759 = _798757, class_Complete__Lattice_Ocomplete__lattice(_798759)], (1252 ^ _780461) ^ [_798882, _798884] : [-(class_Lattices_Obounded__lattice__top(_798882)), _798884 = _798882, class_Lattices_Obounded__lattice__top(_798884)], (1262 ^ _780461) ^ [_799007, _799009] : [-(class_Lattices_Obounded__lattice__bot(_799007)), _799009 = _799007, class_Lattices_Obounded__lattice__bot(_799009)], (1272 ^ _780461) ^ [_799132, _799134] : [-(class_Lattices_Osemilattice__sup(_799132)), _799134 = _799132, class_Lattices_Osemilattice__sup(_799134)], (1282 ^ _780461) ^ [_799257, _799259] : [-(class_Lattices_Osemilattice__inf(_799257)), _799259 = _799257, class_Lattices_Osemilattice__inf(_799259)], (1292 ^ _780461) ^ [_799382, _799384] : [-(class_Lattices_Odistrib__lattice(_799382)), _799384 = _799382, class_Lattices_Odistrib__lattice(_799384)], (1302 ^ _780461) ^ [_799507, _799509] : [-(class_Lattices_Oboolean__algebra(_799507)), _799509 = _799507, class_Lattices_Oboolean__algebra(_799509)], (1312 ^ _780461) ^ [_799632, _799634] : [-(class_Lattices_Olattice(_799632)), _799634 = _799632, class_Lattices_Olattice(_799634)], (1322 ^ _780461) ^ [_799757, _799759] : [-(class_Orderings_Otop(_799757)), _799759 = _799757, class_Orderings_Otop(_799759)], (1332 ^ _780461) ^ [_799882, _799884] : [-(class_Orderings_Obot(_799882)), _799884 = _799882, class_Orderings_Obot(_799884)], (1342 ^ _780461) ^ [_800007, _800009] : [-(class_Groups_Ouminus(_800007)), _800009 = _800007, class_Groups_Ouminus(_800009)], (1352 ^ _780461) ^ [_800132, _800134] : [-(class_Finite__Set_Ofinite(_800132)), _800134 = _800132, class_Finite__Set_Ofinite(_800134)], (1362 ^ _780461) ^ [_800257, _800259] : [-(class_Smallcheck_Osmall(_800257)), _800259 = _800257, class_Smallcheck_Osmall(_800259)], (1372 ^ _780461) ^ [_800382, _800384] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_800382)), _800384 = _800382, class_Groups_Oordered__cancel__ab__semigroup__add(_800384)], (1382 ^ _780461) ^ [_800507, _800509] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_800507)), _800509 = _800507, class_Groups_Oordered__ab__semigroup__add__imp__le(_800509)], (1392 ^ _780461) ^ [_800632, _800634] : [-(class_Rings_Olinordered__comm__semiring__strict(_800632)), _800634 = _800632, class_Rings_Olinordered__comm__semiring__strict(_800634)], (1402 ^ _780461) ^ [_800757, _800759] : [-(class_Groups_Olinordered__ab__semigroup__add(_800757)), _800759 = _800757, class_Groups_Olinordered__ab__semigroup__add(_800759)], (1412 ^ _780461) ^ [_800882, _800884] : [-(class_Rings_Olinordered__semiring__strict(_800882)), _800884 = _800882, class_Rings_Olinordered__semiring__strict(_800884)], (1422 ^ _780461) ^ [_801007, _801009] : [-(class_Groups_Oordered__ab__semigroup__add(_801007)), _801009 = _801007, class_Groups_Oordered__ab__semigroup__add(_801009)], (1432 ^ _780461) ^ [_801132, _801134] : [-(class_Groups_Oordered__comm__monoid__add(_801132)), _801134 = _801132, class_Groups_Oordered__comm__monoid__add(_801134)], (1442 ^ _780461) ^ [_801257, _801259] : [-(class_Groups_Ocancel__ab__semigroup__add(_801257)), _801259 = _801257, class_Groups_Ocancel__ab__semigroup__add(_801259)], (1452 ^ _780461) ^ [_801382, _801384] : [-(class_Rings_Oordered__cancel__semiring(_801382)), _801384 = _801382, class_Rings_Oordered__cancel__semiring(_801384)], (1462 ^ _780461) ^ [_801507, _801509] : [-(class_Rings_Oordered__comm__semiring(_801507)), _801509 = _801507, class_Rings_Oordered__comm__semiring(_801509)], (1472 ^ _780461) ^ [_801632, _801634] : [-(class_Groups_Ocancel__semigroup__add(_801632)), _801634 = _801632, class_Groups_Ocancel__semigroup__add(_801634)], (1482 ^ _780461) ^ [_801757, _801759] : [-(class_Rings_Olinordered__semiring(_801757)), _801759 = _801757, class_Rings_Olinordered__semiring(_801759)], (1492 ^ _780461) ^ [_801882, _801884] : [-(class_Rings_Olinordered__semidom(_801882)), _801884 = _801882, class_Rings_Olinordered__semidom(_801884)], (1502 ^ _780461) ^ [_802007, _802009] : [-(class_Groups_Oab__semigroup__mult(_802007)), _802009 = _802007, class_Groups_Oab__semigroup__mult(_802009)], (1512 ^ _780461) ^ [_802132, _802134] : [-(class_Groups_Ocomm__monoid__mult(_802132)), _802134 = _802132, class_Groups_Ocomm__monoid__mult(_802134)], (1522 ^ _780461) ^ [_802257, _802259] : [-(class_Groups_Oab__semigroup__add(_802257)), _802259 = _802257, class_Groups_Oab__semigroup__add(_802259)], (1532 ^ _780461) ^ [_802382, _802384] : [-(class_Rings_Oordered__semiring(_802382)), _802384 = _802382, class_Rings_Oordered__semiring(_802384)], (1542 ^ _780461) ^ [_802507, _802509] : [-(class_Rings_Ono__zero__divisors(_802507)), _802509 = _802507, class_Rings_Ono__zero__divisors(_802509)], (1552 ^ _780461) ^ [_802632, _802634] : [-(class_Groups_Ocomm__monoid__add(_802632)), _802634 = _802632, class_Groups_Ocomm__monoid__add(_802634)], (1562 ^ _780461) ^ [_802757, _802759] : [-(class_Rings_Ocomm__semiring__1(_802757)), _802759 = _802757, class_Rings_Ocomm__semiring__1(_802759)], (1572 ^ _780461) ^ [_802882, _802884] : [-(class_Groups_Osemigroup__add(_802882)), _802884 = _802882, class_Groups_Osemigroup__add(_802884)], (1582 ^ _780461) ^ [_803007, _803009] : [-(class_Divides_Osemiring__div(_803007)), _803009 = _803007, class_Divides_Osemiring__div(_803009)], (1592 ^ _780461) ^ [_803132, _803134] : [-(class_Rings_Ocomm__semiring(_803132)), _803134 = _803132, class_Rings_Ocomm__semiring(_803134)], (1602 ^ _780461) ^ [_803257, _803259] : [-(class_Nat_Osemiring__char__0(_803257)), _803259 = _803257, class_Nat_Osemiring__char__0(_803259)], (1612 ^ _780461) ^ [_803382, _803384] : [-(class_Rings_Ozero__neq__one(_803382)), _803384 = _803382, class_Rings_Ozero__neq__one(_803384)], (1622 ^ _780461) ^ [_803507, _803509] : [-(class_Orderings_Opreorder(_803507)), _803509 = _803507, class_Orderings_Opreorder(_803509)], (1632 ^ _780461) ^ [_803632, _803634] : [-(class_Orderings_Olinorder(_803632)), _803634 = _803632, class_Orderings_Olinorder(_803634)], (1642 ^ _780461) ^ [_803757, _803759] : [-(class_Groups_Omonoid__mult(_803757)), _803759 = _803757, class_Groups_Omonoid__mult(_803759)], (1652 ^ _780461) ^ [_803882, _803884] : [-(class_Groups_Omonoid__add(_803882)), _803884 = _803882, class_Groups_Omonoid__add(_803884)], (1662 ^ _780461) ^ [_804007, _804009] : [-(class_Rings_Osemiring__1(_804007)), _804009 = _804007, class_Rings_Osemiring__1(_804009)], (1672 ^ _780461) ^ [_804132, _804134] : [-(class_Rings_Osemiring__0(_804132)), _804134 = _804132, class_Rings_Osemiring__0(_804134)], (1682 ^ _780461) ^ [_804257, _804259] : [-(class_Rings_Omult__zero(_804257)), _804259 = _804257, class_Rings_Omult__zero(_804259)], (1692 ^ _780461) ^ [_804382, _804384] : [-(class_Orderings_Oorder(_804382)), _804384 = _804382, class_Orderings_Oorder(_804384)], (1702 ^ _780461) ^ [_804507, _804509] : [-(class_Rings_Osemiring(_804507)), _804509 = _804507, class_Rings_Osemiring(_804509)], (1712 ^ _780461) ^ [_804632, _804634] : [-(class_Orderings_Oord(_804632)), _804634 = _804632, class_Orderings_Oord(_804634)], (1722 ^ _780461) ^ [_804757, _804759] : [-(class_Groups_Ominus(_804757)), _804759 = _804757, class_Groups_Ominus(_804759)], (1732 ^ _780461) ^ [_804882, _804884] : [-(class_Power_Opower(_804882)), _804884 = _804882, class_Power_Opower(_804884)], (1742 ^ _780461) ^ [_805007, _805009] : [-(class_Groups_Ozero(_805007)), _805009 = _805007, class_Groups_Ozero(_805009)], (1752 ^ _780461) ^ [_805132, _805134] : [-(class_Int_Onumber(_805132)), _805134 = _805132, class_Int_Onumber(_805134)], (1762 ^ _780461) ^ [_805257, _805259] : [-(class_Groups_Oone(_805257)), _805259 = _805257, class_Groups_Oone(_805259)], (1772 ^ _780461) ^ [_805382, _805384] : [-(class_Rings_Odvd(_805382)), _805384 = _805382, class_Rings_Odvd(_805384)], (1782 ^ _780461) ^ [_805507, _805509] : [-(hBOOL(_805507)), _805509 = _805507, hBOOL(_805509)], (1792 ^ _780461) ^ [_805632, _805634, _805636, _805638, _805640, _805642] : [-(c_Hoare__Mirabelle_Otriple__valid(_805640, _805636, _805632)), c_Hoare__Mirabelle_Otriple__valid(_805642, _805638, _805634), _805642 = _805640, _805638 = _805636, _805634 = _805632], (1832 ^ _780461) ^ [_806250, _806252, _806254, _806256] : [-(v_P(_806254, _806250)), v_P(_806256, _806252), _806256 = _806254, _806252 = _806250], (1810 ^ _780461) ^ [_805901, _805903, _805905, _805907, _805909, _805911, _805913, _805915] : [-(c_Natural_Oevaln(_805913, _805909, _805905, _805901)), c_Natural_Oevaln(_805915, _805911, _805907, _805903), _805915 = _805913, _805911 = _805909, _805907 = _805905, _805903 = _805901], (1846 ^ _780461) ^ [_807166, _807168, _807170, _807172, _807174, _807176, _807178, _807180] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_807180, _807176, _807172, _807168) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_807178, _807174, _807170, _807166)), _807180 = _807178, _807176 = _807174, _807172 = _807170, _807168 = _807166], (1864 ^ _780461) ^ [_807467, _807469, _807471, _807473, _807475, _807477, _807479, _807481] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_807481, _807477, _807473, _807469) = c_Hoare__Mirabelle_Otriple_Otriple__case(_807479, _807475, _807471, _807467)), _807481 = _807479, _807477 = _807475, _807473 = _807471, _807469 = _807467], (1882 ^ _780461) ^ [_807768, _807770, _807772, _807774, _807776, _807778, _807780, _807782, _807784, _807786, _807788, _807790, _807792, _807794, _807796, _807798, _807800, _807802, _807804, _807806] : [-(c_Com_Ocom_Ocom__rec(_807806, _807802, _807798, _807794, _807790, _807786, _807782, _807778, _807774, _807770) = c_Com_Ocom_Ocom__rec(_807804, _807800, _807796, _807792, _807788, _807784, _807780, _807776, _807772, _807768)), _807806 = _807804, _807802 = _807800, _807798 = _807796, _807794 = _807792, _807790 = _807788, _807786 = _807784, _807782 = _807780, _807778 = _807776, _807774 = _807772, _807770 = _807768], (1924 ^ _780461) ^ [_808717, _808719, _808721, _808723, _808725, _808727, _808729, _808731, _808733, _808735, _808737, _808739, _808741, _808743, _808745, _808747, _808749, _808751, _808753, _808755] : [-(c_Com_Ocom_Ocom__case(_808755, _808751, _808747, _808743, _808739, _808735, _808731, _808727, _808723, _808719) = c_Com_Ocom_Ocom__case(_808753, _808749, _808745, _808741, _808737, _808733, _808729, _808725, _808721, _808717)), _808755 = _808753, _808751 = _808749, _808747 = _808745, _808743 = _808741, _808739 = _808737, _808735 = _808733, _808731 = _808729, _808727 = _808725, _808723 = _808721, _808719 = _808717], (1966 ^ _780461) ^ [_809666, _809668, _809670, _809672, _809674, _809676] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_809676, _809672, _809668) = c_Hoare__Mirabelle_Otriple_Otriple__size(_809674, _809670, _809666)), _809676 = _809674, _809672 = _809670, _809668 = _809666], (1980 ^ _780461) ^ [_809887, _809889] : [_809889 = _809887, -(c_Com_Ovname_Ovname__size(_809889) = c_Com_Ovname_Ovname__size(_809887))], (1986 ^ _780461) ^ [_809972, _809974] : [_809974 = _809972, -(c_Com_Ocom_Ocom__size(_809974) = c_Com_Ocom_Ocom__size(_809972))], (1992 ^ _780461) ^ [_810057, _810059, _810061, _810063, _810065, _810067, _810069, _810071] : [-(c_Com_Ovname_Ovname__case(_810071, _810067, _810063, _810059) = c_Com_Ovname_Ovname__case(_810069, _810065, _810061, _810057)), _810071 = _810069, _810067 = _810065, _810063 = _810061, _810059 = _810057], (2010 ^ _780461) ^ [_810358, _810360, _810362, _810364, _810366, _810368, _810370, _810372] : [-(c_Com_Ovname_Ovname__rec(_810372, _810368, _810364, _810360) = c_Com_Ovname_Ovname__rec(_810370, _810366, _810362, _810358)), _810372 = _810370, _810368 = _810366, _810364 = _810362, _810360 = _810358], (2028 ^ _780461) ^ [_810659, _810661] : [_810661 = _810659, -(c_Com_Ovname_OGlb(_810661) = c_Com_Ovname_OGlb(_810659))], (2034 ^ _780461) ^ [_810744, _810746] : [_810746 = _810744, -(c_Nat_Onat_Onat__size(_810746) = c_Nat_Onat_Onat__size(_810744))], (2040 ^ _780461) ^ [_810829, _810831] : [_810831 = _810829, -(c_HOL_Obool_Obool__size(_810831) = c_HOL_Obool_Obool__size(_810829))], (2046 ^ _780461) ^ [_810914, _810916, _810918, _810920, _810922, _810924] : [-(c_Option_Ooption_Ooption__size(_810924, _810920, _810916) = c_Option_Ooption_Ooption__size(_810922, _810918, _810914)), _810924 = _810922, _810920 = _810918, _810916 = _810914], (2060 ^ _780461) ^ [_811135, _811137, _811139, _811141, _811143, _811145, _811147, _811149, _811151, _811153] : [-(c_Option_Ooption_Ooption__rec(_811153, _811149, _811145, _811141, _811137) = c_Option_Ooption_Ooption__rec(_811151, _811147, _811143, _811139, _811135)), _811153 = _811151, _811149 = _811147, _811145 = _811143, _811141 = _811139, _811137 = _811135], (2082 ^ _780461) ^ [_811524, _811526, _811528, _811530, _811532, _811534, _811536, _811538, _811540, _811542] : [-(c_Nitpick_Opair__box_Opair__box__size(_811542, _811538, _811534, _811530, _811526) = c_Nitpick_Opair__box_Opair__box__size(_811540, _811536, _811532, _811528, _811524)), _811542 = _811540, _811538 = _811536, _811534 = _811532, _811530 = _811528, _811526 = _811524], (2104 ^ _780461) ^ [_811913, _811915, _811917, _811919] : [-(tc_Nitpick_Opair__box(_811919, _811915) = tc_Nitpick_Opair__box(_811917, _811913)), _811919 = _811917, _811915 = _811913], (2114 ^ _780461) ^ [_812062, _812064, _812066, _812068, _812070, _812072, _812074, _812076, _812078, _812080] : [-(c_Nitpick_Opair__box_Opair__box__case(_812080, _812076, _812072, _812068, _812064) = c_Nitpick_Opair__box_Opair__box__case(_812078, _812074, _812070, _812066, _812062)), _812080 = _812078, _812076 = _812074, _812072 = _812070, _812068 = _812066, _812064 = _812062], (2136 ^ _780461) ^ [_812451, _812453, _812455, _812457, _812459, _812461, _812463, _812465, _812467, _812469] : [-(c_Nitpick_Opair__box_Opair__box__rec(_812469, _812465, _812461, _812457, _812453) = c_Nitpick_Opair__box_Opair__box__rec(_812467, _812463, _812459, _812455, _812451)), _812469 = _812467, _812465 = _812463, _812461 = _812459, _812457 = _812455, _812453 = _812451], (2158 ^ _780461) ^ [_812840, _812842, _812844, _812846, _812848, _812850, _812852, _812854] : [-(c_Nitpick_Opair__box_OPairBox(_812854, _812850, _812846, _812842) = c_Nitpick_Opair__box_OPairBox(_812852, _812848, _812844, _812840)), _812854 = _812852, _812850 = _812848, _812846 = _812844, _812842 = _812840], (2176 ^ _780461) ^ [_813141, _813143, _813145, _813147, _813149, _813151, _813153, _813155, _813157, _813159] : [-(c_Sum__Type_Osum_Osum__size(_813159, _813155, _813151, _813147, _813143) = c_Sum__Type_Osum_Osum__size(_813157, _813153, _813149, _813145, _813141)), _813159 = _813157, _813155 = _813153, _813151 = _813149, _813147 = _813145, _813143 = _813141], (2198 ^ _780461) ^ [_813530, _813532, _813534, _813536, _813538, _813540] : [-(c_Sum__Type_OProjl(_813540, _813536, _813532) = c_Sum__Type_OProjl(_813538, _813534, _813530)), _813540 = _813538, _813536 = _813534, _813532 = _813530], (2212 ^ _780461) ^ [_813751, _813753, _813755, _813757, _813759, _813761] : [-(c_Sum__Type_OProjr(_813761, _813757, _813753) = c_Sum__Type_OProjr(_813759, _813755, _813751)), _813761 = _813759, _813757 = _813755, _813753 = _813751], (2226 ^ _780461) ^ [_813972, _813974, _813976, _813978, _813980, _813982, _813984, _813986, _813988, _813990, _813992, _813994] : [-(c_Sum__Type_Osum_Osum__rec(_813994, _813990, _813986, _813982, _813978, _813974) = c_Sum__Type_Osum_Osum__rec(_813992, _813988, _813984, _813980, _813976, _813972)), _813994 = _813992, _813990 = _813988, _813986 = _813984, _813982 = _813980, _813978 = _813976, _813974 = _813972], (2252 ^ _780461) ^ [_814457, _814459, _814461, _814463, _814465, _814467, _814469, _814471] : [-(c_Sum__Type_OSuml(_814471, _814467, _814463, _814459) = c_Sum__Type_OSuml(_814469, _814465, _814461, _814457)), _814471 = _814469, _814467 = _814465, _814463 = _814461, _814459 = _814457], (2270 ^ _780461) ^ [_814758, _814760, _814762, _814764, _814766, _814768, _814770, _814772] : [-(c_Sum__Type_OSumr(_814772, _814768, _814764, _814760) = c_Sum__Type_OSumr(_814770, _814766, _814762, _814758)), _814772 = _814770, _814768 = _814766, _814764 = _814762, _814760 = _814758], (2288 ^ _780461) ^ [_815059, _815061, _815063, _815065] : [-(c_Int_Onat__aux(_815065, _815061) = c_Int_Onat__aux(_815063, _815059)), _815065 = _815063, _815061 = _815059], (2298 ^ _780461) ^ [_815208, _815210, _815212, _815214] : [-(c_SMT_Oz3mod(_815214, _815210) = c_SMT_Oz3mod(_815212, _815208)), _815214 = _815212, _815210 = _815208], (2308 ^ _780461) ^ [_815357, _815359, _815361, _815363] : [-(c_SMT_Oz3div(_815363, _815359) = c_SMT_Oz3div(_815361, _815357)), _815363 = _815361, _815359 = _815357], (2318 ^ _780461) ^ [_815506, _815508, _815510, _815512, _815514, _815516] : [-(c_Power_Opower_Opower(_815516, _815512, _815508) = c_Power_Opower_Opower(_815514, _815510, _815506)), _815516 = _815514, _815512 = _815510, _815508 = _815506], (2332 ^ _780461) ^ [_815727, _815729, _815731, _815733] : [-(c_Nitpick_Onat__lcm(_815733, _815729) = c_Nitpick_Onat__lcm(_815731, _815727)), _815733 = _815731, _815729 = _815727], (2342 ^ _780461) ^ [_815876, _815878] : [_815878 = _815876, -(c_Int_Osucc(_815878) = c_Int_Osucc(_815876))], (2348 ^ _780461) ^ [_815961, _815963, _815965, _815967] : [-(c_Nat__Transfer_Otsub(_815967, _815963) = c_Nat__Transfer_Otsub(_815965, _815961)), _815967 = _815965, _815963 = _815961], (2358 ^ _780461) ^ [_816110, _816112, _816114, _816116] : [-(c_Random_Olog(_816116, _816112) = c_Random_Olog(_816114, _816110)), _816116 = _816114, _816112 = _816110], (2368 ^ _780461) ^ [_816259, _816261, _816263, _816265, _816267, _816269] : [-(c_Random_Ominus__shift(_816269, _816265, _816261) = c_Random_Ominus__shift(_816267, _816263, _816259)), _816269 = _816267, _816265 = _816263, _816261 = _816259], (2382 ^ _780461) ^ [_816480, _816482, _816484, _816486] : [-(c_Random_Oinc__shift(_816486, _816482) = c_Random_Oinc__shift(_816484, _816480)), _816486 = _816484, _816482 = _816480], (2392 ^ _780461) ^ [_816629, _816631] : [_816631 = _816629, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_816631) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_816629))], (2398 ^ _780461) ^ [_816714, _816716, _816718, _816720, _816722, _816724, _816726, _816728] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_816728, _816724, _816720, _816716) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_816726, _816722, _816718, _816714)), _816728 = _816726, _816724 = _816722, _816720 = _816718, _816716 = _816714], (2416 ^ _780461) ^ [_817015, _817017, _817019, _817021, _817023, _817025, _817027, _817029] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_817029, _817025, _817021, _817017) = c_Nat_Osemiring__1__class_Oof__nat__aux(_817027, _817023, _817019, _817015)), _817029 = _817027, _817025 = _817023, _817021 = _817019, _817017 = _817015], (2434 ^ _780461) ^ [_817316, _817318, _817320, _817322, _817324, _817326] : [-(c_Nat_Onat_Onat__rec(_817326, _817322, _817318) = c_Nat_Onat_Onat__rec(_817324, _817320, _817316)), _817326 = _817324, _817322 = _817320, _817318 = _817316], (2448 ^ _780461) ^ [_817537, _817539, _817541, _817543, _817545, _817547, _817549, _817551] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_817551, _817547, _817543, _817539) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_817549, _817545, _817541, _817537)), _817551 = _817549, _817547 = _817545, _817543 = _817541, _817539 = _817537], (2466 ^ _780461) ^ [_817838, _817840] : [_817840 = _817838, -(c_Hoare__Mirabelle_OMGT(_817840) = c_Hoare__Mirabelle_OMGT(_817838))], (2472 ^ _780461) ^ [_817923, _817925] : [_817925 = _817923, -(c_Natural_Oevalc(_817925) = c_Natural_Oevalc(_817923))], (2478 ^ _780461) ^ [_818008, _818010] : [_818010 = _818008, -(c_Divides_Oadjust(_818010) = c_Divides_Oadjust(_818008))], (2484 ^ _780461) ^ [_818093, _818095, _818097, _818099] : [-(c_Nitpick_Onat__gcd(_818099, _818095) = c_Nitpick_Onat__gcd(_818097, _818093)), _818099 = _818097, _818095 = _818093], (2494 ^ _780461) ^ [_818242, _818244, _818246, _818248] : [-(c_Groups_Osgn__class_Osgn(_818248, _818244) = c_Groups_Osgn__class_Osgn(_818246, _818242)), _818248 = _818246, _818244 = _818242], (2504 ^ _780461) ^ [_818391, _818393, _818395, _818397] : [-(c_Divides_Opdivmod(_818397, _818393) = c_Divides_Opdivmod(_818395, _818391)), _818397 = _818395, _818393 = _818391], (2514 ^ _780461) ^ [_818540, _818542, _818544, _818546] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_818546, _818542) = c_Code__Numeral_Odiv__mod__code__numeral(_818544, _818540)), _818546 = _818544, _818542 = _818540], (2524 ^ _780461) ^ [_818689, _818691, _818693, _818695] : [-(c_Divides_Odivmod__int__rel(_818695, _818691) = c_Divides_Odivmod__int__rel(_818693, _818689)), _818695 = _818693, _818691 = _818689], (2534 ^ _780461) ^ [_818838, _818840, _818842, _818844] : [-(c_Divides_Odivmod__int(_818844, _818840) = c_Divides_Odivmod__int(_818842, _818838)), _818844 = _818842, _818840 = _818838], (2544 ^ _780461) ^ [_818987, _818989, _818991, _818993] : [-(c_Divides_OposDivAlg(_818993, _818989) = c_Divides_OposDivAlg(_818991, _818987)), _818993 = _818991, _818989 = _818987], (2554 ^ _780461) ^ [_819136, _819138, _819140, _819142] : [-(c_Divides_OnegDivAlg(_819142, _819138) = c_Divides_OnegDivAlg(_819140, _819136)), _819142 = _819140, _819138 = _819136], (2564 ^ _780461) ^ [_819285, _819287, _819289, _819291, _819293, _819295, _819297, _819299, _819301, _819303] : [-(c_Product__Type_Oprod_Oprod__size(_819303, _819299, _819295, _819291, _819287) = c_Product__Type_Oprod_Oprod__size(_819301, _819297, _819293, _819289, _819285)), _819303 = _819301, _819299 = _819297, _819295 = _819293, _819291 = _819289, _819287 = _819285], (2586 ^ _780461) ^ [_819674, _819676, _819678, _819680, _819682, _819684, _819686, _819688, _819690, _819692] : [-(c_Product__Type_Oprod_Oprod__rec(_819692, _819688, _819684, _819680, _819676) = c_Product__Type_Oprod_Oprod__rec(_819690, _819686, _819682, _819678, _819674)), _819692 = _819690, _819688 = _819686, _819684 = _819682, _819680 = _819678, _819676 = _819674], (2608 ^ _780461) ^ [_820063, _820065] : [_820065 = _820063, -(c_Lazy__Sequence_Ohb__not__seq(_820065) = c_Lazy__Sequence_Ohb__not__seq(_820063))], (2614 ^ _780461) ^ [_820148, _820150] : [_820150 = _820148, -(c_Int_Opred(_820150) = c_Int_Opred(_820148))], (2620 ^ _780461) ^ [_820233, _820235, _820237, _820239] : [-(c_Orderings_Oord_Omin(_820239, _820235) = c_Orderings_Oord_Omin(_820237, _820233)), _820239 = _820237, _820235 = _820233], (2630 ^ _780461) ^ [_820382, _820384] : [_820384 = _820382, -(c_Nitpick_Ozero__frac(_820384) = c_Nitpick_Ozero__frac(_820382))], (2636 ^ _780461) ^ [_820467, _820469, _820471, _820473, _820475, _820477, _820479, _820481] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_820481, _820477, _820473, _820469) = c_New__Random__Sequence_Opos__not__random__dseq(_820479, _820475, _820471, _820467)), _820481 = _820479, _820477 = _820475, _820473 = _820471, _820469 = _820467], (2654 ^ _780461) ^ [_820768, _820770] : [_820770 = _820768, -(c_New__DSequence_Opos__not__seq(_820770) = c_New__DSequence_Opos__not__seq(_820768))], (2660 ^ _780461) ^ [_820853, _820855, _820857, _820859] : [-(c_Code__Numeral_Onat__of__aux(_820859, _820855) = c_Code__Numeral_Onat__of__aux(_820857, _820853)), _820859 = _820857, _820855 = _820853], (2670 ^ _780461) ^ [_821002, _821004, _821006, _821008] : [-(c_Orderings_Oord_Omax(_821008, _821004) = c_Orderings_Oord_Omax(_821006, _821002)), _821008 = _821006, _821004 = _821002], (2680 ^ _780461) ^ [_821151, _821153] : [_821153 = _821151, -(c_Code__Numeral_OSuc__code__numeral(_821153) = c_Code__Numeral_OSuc__code__numeral(_821151))], (2686 ^ _780461) ^ [_821236, _821238] : [_821238 = _821236, -(c_Nitpick_Oone__frac(_821238) = c_Nitpick_Oone__frac(_821236))], (2692 ^ _780461) ^ [_821321, _821323, _821325, _821327] : [-(c_Nitpick_Onumber__of__frac(_821327, _821323) = c_Nitpick_Onumber__of__frac(_821325, _821321)), _821327 = _821325, _821323 = _821321], (2702 ^ _780461) ^ [_821470, _821472, _821474, _821476] : [-(c_Nitpick_Onorm__frac(_821476, _821472) = c_Nitpick_Onorm__frac(_821474, _821470)), _821476 = _821474, _821472 = _821470], (2712 ^ _780461) ^ [_821619, _821621, _821623, _821625, _821627, _821629, _821631, _821633] : [-(c_Random_Oiterate(_821633, _821629, _821625, _821621) = c_Random_Oiterate(_821631, _821627, _821623, _821619)), _821633 = _821631, _821629 = _821627, _821625 = _821623, _821621 = _821619], (2730 ^ _780461) ^ [_821920, _821922, _821924, _821926] : [-(c_HOL_OLet(_821926, _821922) = c_HOL_OLet(_821924, _821920)), _821926 = _821924, _821922 = _821920], (2740 ^ _780461) ^ [_822069, _822071, _822073, _822075] : [-(c_Nitpick_Oint__lcm(_822075, _822071) = c_Nitpick_Oint__lcm(_822073, _822069)), _822075 = _822073, _822071 = _822069], (2750 ^ _780461) ^ [_822218, _822220] : [_822220 = _822218, -(c_Lazy__Sequence_Ohit__bound(_822220) = c_Lazy__Sequence_Ohit__bound(_822218))], (2756 ^ _780461) ^ [_822303, _822305, _822307, _822309, _822311, _822313] : [-(c_Product__Type_Ointernal__split(_822313, _822309, _822305) = c_Product__Type_Ointernal__split(_822311, _822307, _822303)), _822313 = _822311, _822309 = _822307, _822305 = _822303], (2770 ^ _780461) ^ [_822524, _822526, _822528, _822530, _822532, _822534] : [-(c_Nitpick_Otimes__frac(_822534, _822530, _822526) = c_Nitpick_Otimes__frac(_822532, _822528, _822524)), _822534 = _822532, _822530 = _822528, _822526 = _822524], (2784 ^ _780461) ^ [_822745, _822747, _822749, _822751, _822753, _822755] : [-(c_Nitpick_Oof__frac(_822755, _822751, _822747) = c_Nitpick_Oof__frac(_822753, _822749, _822745)), _822755 = _822753, _822751 = _822749, _822747 = _822745], (2798 ^ _780461) ^ [_822966, _822968, _822970, _822972] : [-(c_Nitpick_Oinverse__frac(_822972, _822968) = c_Nitpick_Oinverse__frac(_822970, _822966)), _822972 = _822970, _822968 = _822966], (2808 ^ _780461) ^ [_823115, _823117] : [_823117 = _823115, -(c_Nitpick_Ofrac(_823117) = c_Nitpick_Ofrac(_823115))], (2814 ^ _780461) ^ [_823200, _823202, _823204, _823206] : [-(c_Nitpick_OAbs__Frac(_823206, _823202) = c_Nitpick_OAbs__Frac(_823204, _823200)), _823206 = _823204, _823202 = _823200], (2824 ^ _780461) ^ [_823349, _823351, _823353, _823355, _823357, _823359, _823361, _823363, _823365, _823367, _823369, _823371, _823373, _823375] : [-(c_New__Random__Sequence_Opos__decr__bind(_823375, _823371, _823367, _823363, _823359, _823355, _823351) = c_New__Random__Sequence_Opos__decr__bind(_823373, _823369, _823365, _823361, _823357, _823353, _823349)), _823375 = _823373, _823371 = _823369, _823367 = _823365, _823363 = _823361, _823359 = _823357, _823355 = _823353, _823351 = _823349], (2854 ^ _780461) ^ [_823938, _823940, _823942, _823944, _823946, _823948, _823950, _823952] : [-(c_New__DSequence_Opos__decr__bind(_823952, _823948, _823944, _823940) = c_New__DSequence_Opos__decr__bind(_823950, _823946, _823942, _823938)), _823952 = _823950, _823948 = _823946, _823944 = _823942, _823940 = _823938], (2872 ^ _780461) ^ [_824239, _824241, _824243, _824245, _824247, _824249] : [-(c_Nitpick_Oplus__frac(_824249, _824245, _824241) = c_Nitpick_Oplus__frac(_824247, _824243, _824239)), _824249 = _824247, _824245 = _824243, _824241 = _824239], (2886 ^ _780461) ^ [_824460, _824462, _824464, _824466] : [-(c_Nitpick_Ouminus__frac(_824466, _824462) = c_Nitpick_Ouminus__frac(_824464, _824460)), _824466 = _824464, _824462 = _824460], (2896 ^ _780461) ^ [_824609, _824611, _824613, _824615, _824617, _824619, _824621, _824623, _824625, _824627, _824629, _824631, _824633, _824635] : [-(c_New__Random__Sequence_Oneg__decr__bind(_824635, _824631, _824627, _824623, _824619, _824615, _824611) = c_New__Random__Sequence_Oneg__decr__bind(_824633, _824629, _824625, _824621, _824617, _824613, _824609)), _824635 = _824633, _824631 = _824629, _824627 = _824625, _824623 = _824621, _824619 = _824617, _824615 = _824613, _824611 = _824609], (2926 ^ _780461) ^ [_825198, _825200, _825202, _825204, _825206, _825208, _825210, _825212] : [-(c_New__DSequence_Oneg__decr__bind(_825212, _825208, _825204, _825200) = c_New__DSequence_Oneg__decr__bind(_825210, _825206, _825202, _825198)), _825212 = _825210, _825208 = _825206, _825204 = _825202, _825200 = _825198], (2944 ^ _780461) ^ [_825499, _825501, _825503, _825505, _825507, _825509, _825511, _825513] : [-(c_Lazy__Sequence_Ohb__bind(_825513, _825509, _825505, _825501) = c_Lazy__Sequence_Ohb__bind(_825511, _825507, _825503, _825499)), _825513 = _825511, _825509 = _825507, _825505 = _825503, _825501 = _825499], (2962 ^ _780461) ^ [_825800, _825802] : [_825802 = _825800, -(c_Lazy__Sequence_Oempty(_825802) = c_Lazy__Sequence_Oempty(_825800))], (2968 ^ _780461) ^ [_825885, _825887, _825889, _825891, _825893, _825895, _825897, _825899] : [-(c_New__Random__Sequence_Opos__empty(_825899, _825895, _825891, _825887) = c_New__Random__Sequence_Opos__empty(_825897, _825893, _825889, _825885)), _825899 = _825897, _825895 = _825893, _825891 = _825889, _825887 = _825885], (2986 ^ _780461) ^ [_826186, _826188] : [_826188 = _826186, -(c_New__DSequence_Opos__empty(_826188) = c_New__DSequence_Opos__empty(_826186))], (2992 ^ _780461) ^ [_826271, _826273, _826275, _826277, _826279, _826281, _826283, _826285] : [-(c_New__DSequence_Oneg__bind(_826285, _826281, _826277, _826273) = c_New__DSequence_Oneg__bind(_826283, _826279, _826275, _826271)), _826285 = _826283, _826281 = _826279, _826277 = _826275, _826273 = _826271], (3010 ^ _780461) ^ [_826572, _826574, _826576, _826578, _826580, _826582, _826584, _826586] : [-(c_Lazy__Sequence_Obind(_826586, _826582, _826578, _826574) = c_Lazy__Sequence_Obind(_826584, _826580, _826576, _826572)), _826586 = _826584, _826582 = _826580, _826578 = _826576, _826574 = _826572], (3028 ^ _780461) ^ [_826873, _826875, _826877, _826879, _826881, _826883, _826885, _826887] : [-(c_New__DSequence_Opos__bind(_826887, _826883, _826879, _826875) = c_New__DSequence_Opos__bind(_826885, _826881, _826877, _826873)), _826887 = _826885, _826883 = _826881, _826879 = _826877, _826875 = _826873], (3046 ^ _780461) ^ [_827174, _827176, _827178, _827180, _827182, _827184, _827186, _827188] : [-(c_Random__Sequence_ORandom(_827188, _827184, _827180, _827176) = c_Random__Sequence_ORandom(_827186, _827182, _827178, _827174)), _827188 = _827186, _827184 = _827182, _827180 = _827178, _827176 = _827174], (3064 ^ _780461) ^ [_827475, _827477] : [_827477 = _827475, -(c_DSequence_Ounion(_827477) = c_DSequence_Ounion(_827475))], (3070 ^ _780461) ^ [_827560, _827562, _827564, _827566] : [-(c_Quickcheck_Obeyond(_827566, _827562) = c_Quickcheck_Obeyond(_827564, _827560)), _827566 = _827564, _827562 = _827560], (3080 ^ _780461) ^ [_827709, _827711, _827713, _827715] : [-(c_Divides_Odivmod__nat(_827715, _827711) = c_Divides_Odivmod__nat(_827713, _827709)), _827715 = _827713, _827711 = _827709], (3090 ^ _780461) ^ [_827858, _827860, _827862, _827864] : [-(c_Divides_Odivmod__nat__rel(_827864, _827860) = c_Divides_Odivmod__nat__rel(_827862, _827858)), _827864 = _827862, _827860 = _827858], (3100 ^ _780461) ^ [_828007, _828009, _828011, _828013, _828015, _828017] : [-(c_Random__Sequence_Oempty(_828017, _828013, _828009) = c_Random__Sequence_Oempty(_828015, _828011, _828007)), _828017 = _828015, _828013 = _828011, _828009 = _828007], (3114 ^ _780461) ^ [_828228, _828230] : [_828230 = _828228, -(c_DSequence_Oempty(_828230) = c_DSequence_Oempty(_828228))], (3120 ^ _780461) ^ [_828313, _828315] : [_828315 = _828313, -(c_DSequence_Osingle(_828315) = c_DSequence_Osingle(_828313))], (3126 ^ _780461) ^ [_828398, _828400, _828402, _828404, _828406, _828408, _828410, _828412] : [-(c_Product__Type_Ocurry(_828412, _828408, _828404, _828400) = c_Product__Type_Ocurry(_828410, _828406, _828402, _828398)), _828412 = _828410, _828408 = _828406, _828404 = _828402, _828400 = _828398], (3144 ^ _780461) ^ [_828699, _828701, _828703, _828705, _828707, _828709] : [-(c_Com_Ocom_OCall(_828709, _828705, _828701) = c_Com_Ocom_OCall(_828707, _828703, _828699)), _828709 = _828707, _828705 = _828703, _828701 = _828699], (3158 ^ _780461) ^ [_828920, _828922, _828924, _828926] : [-(c_Com_Ocom_OAss(_828926, _828922) = c_Com_Ocom_OAss(_828924, _828920)), _828926 = _828924, _828922 = _828920], (3168 ^ _780461) ^ [_829069, _829071, _829073, _829075] : [-(c_Com_Ocom_OSemi(_829075, _829071) = c_Com_Ocom_OSemi(_829073, _829069)), _829075 = _829073, _829071 = _829069], (3178 ^ _780461) ^ [_829218, _829220] : [_829220 = _829218, -(c_Com_Ovname_OLoc(_829220) = c_Com_Ovname_OLoc(_829218))], (3184 ^ _780461) ^ [_829303, _829305, _829307, _829309, _829311, _829313] : [-(c_Com_Ocom_OLocal(_829313, _829309, _829305) = c_Com_Ocom_OLocal(_829311, _829307, _829303)), _829313 = _829311, _829309 = _829307, _829305 = _829303], (3198 ^ _780461) ^ [_829524, _829526] : [_829526 = _829524, -(c_Divides_Odiv__class_Odiv(_829526) = c_Divides_Odiv__class_Odiv(_829524))], (3204 ^ _780461) ^ [_829609, _829611, _829613, _829615] : [-(c_Option_Oset(_829615, _829611) = c_Option_Oset(_829613, _829609)), _829615 = _829613, _829611 = _829609], (3214 ^ _780461) ^ [_829758, _829760, _829762, _829764, _829766, _829768] : [-(c_Partial__Function_Oflat__lub(_829768, _829764, _829760) = c_Partial__Function_Oflat__lub(_829766, _829762, _829758)), _829768 = _829766, _829764 = _829762, _829760 = _829758], (3228 ^ _780461) ^ [_829979, _829981] : [_829981 = _829979, -(c_Nat_Osemiring__1__class_ONats(_829981) = c_Nat_Osemiring__1__class_ONats(_829979))], (3234 ^ _780461) ^ [_830064, _830066] : [_830066 = _830064, -(c_Int_Oring__1__class_OInts(_830066) = c_Int_Oring__1__class_OInts(_830064))], (3240 ^ _780461) ^ [_830149, _830151, _830153, _830155] : [-(c_FunDef_Orp__inv__image(_830155, _830151) = c_FunDef_Orp__inv__image(_830153, _830149)), _830155 = _830153, _830151 = _830149], (3250 ^ _780461) ^ [_830298, _830300, _830302, _830304, _830306, _830308, _830310, _830312] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_830312, _830308, _830304, _830300) = c_SetInterval_Oord_OgreaterThanLessThan(_830310, _830306, _830302, _830298)), _830312 = _830310, _830308 = _830306, _830304 = _830302, _830300 = _830298], (3268 ^ _780461) ^ [_830599, _830601, _830603, _830605, _830607, _830609] : [-(c_SetInterval_Oord_OgreaterThan(_830609, _830605, _830601) = c_SetInterval_Oord_OgreaterThan(_830607, _830603, _830599)), _830609 = _830607, _830605 = _830603, _830601 = _830599], (3282 ^ _780461) ^ [_830820, _830822, _830824, _830826, _830828, _830830] : [-(c_SetInterval_Oord_OlessThan(_830830, _830826, _830822) = c_SetInterval_Oord_OlessThan(_830828, _830824, _830820)), _830830 = _830828, _830826 = _830824, _830822 = _830820], (3296 ^ _780461) ^ [_831041, _831043, _831045, _831047, _831049, _831051] : [-(c_SetInterval_Oord_OatMost(_831051, _831047, _831043) = c_SetInterval_Oord_OatMost(_831049, _831045, _831041)), _831051 = _831049, _831047 = _831045, _831043 = _831041], (3310 ^ _780461) ^ [_831262, _831264, _831266, _831268, _831270, _831272, _831274, _831276, _831278, _831280] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_831280, _831276, _831272, _831268, _831264) = c_SetInterval_Oord_OgreaterThanAtMost(_831278, _831274, _831270, _831266, _831262)), _831280 = _831278, _831276 = _831274, _831272 = _831270, _831268 = _831266, _831264 = _831262], (3332 ^ _780461) ^ [_831651, _831653, _831655, _831657, _831659, _831661, _831663, _831665, _831667, _831669] : [-(c_SetInterval_Oord_OatLeastLessThan(_831669, _831665, _831661, _831657, _831653) = c_SetInterval_Oord_OatLeastLessThan(_831667, _831663, _831659, _831655, _831651)), _831669 = _831667, _831665 = _831663, _831661 = _831659, _831657 = _831655, _831653 = _831651], (3354 ^ _780461) ^ [_832040, _832042, _832044, _832046, _832048, _832050] : [-(c_SetInterval_Oord_OatLeast(_832050, _832046, _832042) = c_SetInterval_Oord_OatLeast(_832048, _832044, _832040)), _832050 = _832048, _832046 = _832044, _832042 = _832040], (3368 ^ _780461) ^ [_832261, _832263, _832265, _832267, _832269, _832271, _832273, _832275] : [-(c_SetInterval_Oord_OatLeastAtMost(_832275, _832271, _832267, _832263) = c_SetInterval_Oord_OatLeastAtMost(_832273, _832269, _832265, _832261)), _832275 = _832273, _832271 = _832269, _832267 = _832265, _832263 = _832261], (3386 ^ _780461) ^ [_832562, _832564, _832566, _832568] : [-(c_Set_Othe__elem(_832568, _832564) = c_Set_Othe__elem(_832566, _832562)), _832568 = _832566, _832564 = _832562], (3396 ^ _780461) ^ [_832711, _832713, _832715, _832717] : [-(c_Predicate_OPowp(_832717, _832713) = c_Predicate_OPowp(_832715, _832711)), _832717 = _832715, _832713 = _832711], (3406 ^ _780461) ^ [_832860, _832862] : [_832862 = _832860, -(c_Rings_Oinverse__class_Odivide(_832862) = c_Rings_Oinverse__class_Odivide(_832860))], (3412 ^ _780461) ^ [_832945, _832947] : [_832947 = _832945, -(c_Power_Opower__class_Opower(_832947) = c_Power_Opower__class_Opower(_832945))], (3418 ^ _780461) ^ [_833030, _833032, _833034, _833036] : [-(c_Sum__Type_OInl(_833036, _833032) = c_Sum__Type_OInl(_833034, _833030)), _833036 = _833034, _833032 = _833030], (3428 ^ _780461) ^ [_833179, _833181, _833183, _833185] : [-(c_Sum__Type_OInr(_833185, _833181) = c_Sum__Type_OInr(_833183, _833179)), _833185 = _833183, _833181 = _833179], (3438 ^ _780461) ^ [_833328, _833330] : [_833330 = _833328, -(c_Nitpick_Onum(_833330) = c_Nitpick_Onum(_833328))], (3444 ^ _780461) ^ [_833413, _833415] : [_833415 = _833413, -(c_Nitpick_Odenom(_833415) = c_Nitpick_Odenom(_833413))], (3450 ^ _780461) ^ [_833498, _833500] : [_833500 = _833498, -(c_Nitpick_ORep__Frac(_833500) = c_Nitpick_ORep__Frac(_833498))], (3456 ^ _780461) ^ [_833583, _833585, _833587, _833589] : [-(c_Com_Ocom_OWhile(_833589, _833585) = c_Com_Ocom_OWhile(_833587, _833583)), _833589 = _833587, _833585 = _833583], (3466 ^ _780461) ^ [_833732, _833734, _833736, _833738, _833740, _833742] : [-(c_Hoare__Mirabelle_Opeek__and(_833742, _833738, _833734) = c_Hoare__Mirabelle_Opeek__and(_833740, _833736, _833732)), _833742 = _833740, _833738 = _833736, _833734 = _833732], (3480 ^ _780461) ^ [_833953, _833955] : [_833955 = _833953, -(c_Hoare__Mirabelle_Otriple_Otriple(_833955) = c_Hoare__Mirabelle_Otriple_Otriple(_833953))], (3486 ^ _780461) ^ [_834038, _834040, _834042, _834044, _834046, _834048] : [-(c_Com_Ocom_OCond(_834048, _834044, _834040) = c_Com_Ocom_OCond(_834046, _834042, _834038)), _834048 = _834046, _834044 = _834042, _834040 = _834038], (3500 ^ _780461) ^ [_834259, _834261, _834263, _834265, _834267, _834269, _834271, _834273] : [-(c_Random__Sequence_Omap(_834273, _834269, _834265, _834261) = c_Random__Sequence_Omap(_834271, _834267, _834263, _834259)), _834273 = _834271, _834269 = _834267, _834265 = _834263, _834261 = _834259], (3518 ^ _780461) ^ [_834560, _834562, _834564, _834566, _834568, _834570, _834572, _834574] : [-(c_Random__Sequence_Obind(_834574, _834570, _834566, _834562) = c_Random__Sequence_Obind(_834572, _834568, _834564, _834560)), _834574 = _834572, _834570 = _834568, _834566 = _834564, _834562 = _834560], (3536 ^ _780461) ^ [_834861, _834863] : [_834863 = _834861, -(c_Random__Sequence_Osingle(_834863) = c_Random__Sequence_Osingle(_834861))], (3542 ^ _780461) ^ [_834946, _834948, _834950, _834952, _834954, _834956, _834958, _834960] : [-(c_Sum__Type_OPlus(_834960, _834956, _834952, _834948) = c_Sum__Type_OPlus(_834958, _834954, _834950, _834946)), _834960 = _834958, _834956 = _834954, _834952 = _834950, _834948 = _834946], (3560 ^ _780461) ^ [_835247, _835249, _835251, _835253, _835255, _835257, _835259, _835261] : [-(c_Fun_Othe__inv__into(_835261, _835257, _835253, _835249) = c_Fun_Othe__inv__into(_835259, _835255, _835251, _835247)), _835261 = _835259, _835257 = _835255, _835253 = _835251, _835249 = _835247], (3578 ^ _780461) ^ [_835548, _835550] : [_835550 = _835548, -(c_SetInterval_Oord__class_OatLeast(_835550) = c_SetInterval_Oord__class_OatLeast(_835548))], (3584 ^ _780461) ^ [_835633, _835635] : [_835635 = _835633, -(c_Int_OBit0(_835635) = c_Int_OBit0(_835633))], (3590 ^ _780461) ^ [_835718, _835720] : [_835720 = _835718, -(c_Int_OBit1(_835720) = c_Int_OBit1(_835718))], (3596 ^ _780461) ^ [_835803, _835805, _835807, _835809, _835811, _835813] : [-(c_Finite__Set_Ofold1Set(_835813, _835809, _835805) = c_Finite__Set_Ofold1Set(_835811, _835807, _835803)), _835813 = _835811, _835809 = _835807, _835805 = _835803], (3610 ^ _780461) ^ [_836024, _836026, _836028, _836030, _836032, _836034, _836036, _836038, _836040, _836042] : [-(c_Fun_Ooverride__on(_836042, _836038, _836034, _836030, _836026) = c_Fun_Ooverride__on(_836040, _836036, _836032, _836028, _836024)), _836042 = _836040, _836038 = _836036, _836034 = _836032, _836030 = _836028, _836026 = _836024], (3632 ^ _780461) ^ [_836413, _836415, _836417, _836419, _836421, _836423, _836425, _836427] : [-(c_Nitpick_Oprod(_836427, _836423, _836419, _836415) = c_Nitpick_Oprod(_836425, _836421, _836417, _836413)), _836427 = _836425, _836423 = _836421, _836419 = _836417, _836415 = _836413], (3650 ^ _780461) ^ [_836714, _836716] : [_836716 = _836714, -(c_Int_Oring__1__class_Oof__int(_836716) = c_Int_Oring__1__class_Oof__int(_836714))], (3656 ^ _780461) ^ [_836799, _836801, _836803, _836805, _836807, _836809, _836811, _836813] : [-(c_Product__Type_Oapsnd(_836813, _836809, _836805, _836801) = c_Product__Type_Oapsnd(_836811, _836807, _836803, _836799)), _836813 = _836811, _836809 = _836807, _836805 = _836803, _836801 = _836799], (3674 ^ _780461) ^ [_837100, _837102, _837104, _837106, _837108, _837110, _837112, _837114] : [-(c_Product__Type_Oapfst(_837114, _837110, _837106, _837102) = c_Product__Type_Oapfst(_837112, _837108, _837104, _837100)), _837114 = _837112, _837110 = _837108, _837106 = _837104, _837102 = _837100], (3692 ^ _780461) ^ [_837401, _837403] : [_837403 = _837401, -(c_Wellfounded_Omeasure(_837403) = c_Wellfounded_Omeasure(_837401))], (3698 ^ _780461) ^ [_837486, _837488] : [_837488 = _837486, -(c_Int_Oint__ge__less__than2(_837488) = c_Int_Oint__ge__less__than2(_837486))], (3704 ^ _780461) ^ [_837571, _837573, _837575, _837577] : [-(c_Wellfounded_Omin__ext(_837577, _837573) = c_Wellfounded_Omin__ext(_837575, _837571)), _837577 = _837575, _837573 = _837571], (3714 ^ _780461) ^ [_837720, _837722] : [_837722 = _837720, -(c_Wellfounded_Ofinite__psubset(_837722) = c_Wellfounded_Ofinite__psubset(_837720))], (3720 ^ _780461) ^ [_837805, _837807, _837809, _837811, _837813, _837815] : [-(c_Wellfounded_Omlex__prod(_837815, _837811, _837807) = c_Wellfounded_Omlex__prod(_837813, _837809, _837805)), _837815 = _837813, _837811 = _837809, _837807 = _837805], (3734 ^ _780461) ^ [_838026, _838028] : [_838028 = _838026, -(c_Int_Oint__ge__less__than(_838028) = c_Int_Oint__ge__less__than(_838026))], (3740 ^ _780461) ^ [_838111, _838113, _838115, _838117, _838119, _838121, _838123, _838125] : [-(c_Recdef_Osame__fst(_838125, _838121, _838117, _838113) = c_Recdef_Osame__fst(_838123, _838119, _838115, _838111)), _838125 = _838123, _838121 = _838119, _838117 = _838115, _838113 = _838111], (3758 ^ _780461) ^ [_838412, _838414, _838416, _838418, _838420, _838422] : [-(c_FunDef_Oin__rel(_838422, _838418, _838414) = c_FunDef_Oin__rel(_838420, _838416, _838412)), _838422 = _838420, _838418 = _838416, _838414 = _838412], (3772 ^ _780461) ^ [_838633, _838635, _838637, _838639, _838641, _838643, _838645, _838647] : [-(c_New__Random__Sequence_Opos__map(_838647, _838643, _838639, _838635) = c_New__Random__Sequence_Opos__map(_838645, _838641, _838637, _838633)), _838647 = _838645, _838643 = _838641, _838639 = _838637, _838635 = _838633], (3790 ^ _780461) ^ [_838934, _838936, _838938, _838940, _838942, _838944, _838946, _838948] : [-(c_New__Random__Sequence_Opos__bind(_838948, _838944, _838940, _838936) = c_New__Random__Sequence_Opos__bind(_838946, _838942, _838938, _838934)), _838948 = _838946, _838944 = _838942, _838940 = _838938, _838936 = _838934], (3808 ^ _780461) ^ [_839235, _839237] : [_839237 = _839235, -(c_New__Random__Sequence_Opos__single(_839237) = c_New__Random__Sequence_Opos__single(_839235))], (3814 ^ _780461) ^ [_839320, _839322, _839324, _839326] : [-(c_New__DSequence_Opos__single(_839326, _839322) = c_New__DSequence_Opos__single(_839324, _839320)), _839326 = _839324, _839322 = _839320], (3824 ^ _780461) ^ [_839469, _839471, _839473, _839475] : [-(c_Lazy__Sequence_Osingle(_839475, _839471) = c_Lazy__Sequence_Osingle(_839473, _839469)), _839475 = _839473, _839471 = _839469], (3834 ^ _780461) ^ [_839618, _839620, _839622, _839624, _839626, _839628, _839630, _839632] : [-(c_New__Random__Sequence_Oneg__map(_839632, _839628, _839624, _839620) = c_New__Random__Sequence_Oneg__map(_839630, _839626, _839622, _839618)), _839632 = _839630, _839628 = _839626, _839624 = _839622, _839620 = _839618], (3852 ^ _780461) ^ [_839919, _839921, _839923, _839925, _839927, _839929, _839931, _839933] : [-(c_New__Random__Sequence_Oneg__bind(_839933, _839929, _839925, _839921) = c_New__Random__Sequence_Oneg__bind(_839931, _839927, _839923, _839919)), _839933 = _839931, _839929 = _839927, _839925 = _839923, _839921 = _839919], (3870 ^ _780461) ^ [_840220, _840222] : [_840222 = _840220, -(tc_Lazy__Sequence_Olazy__sequence(_840222) = tc_Lazy__Sequence_Olazy__sequence(_840220))], (3876 ^ _780461) ^ [_840305, _840307] : [_840307 = _840305, -(c_New__Random__Sequence_Oneg__single(_840307) = c_New__Random__Sequence_Oneg__single(_840305))], (3882 ^ _780461) ^ [_840390, _840392, _840394, _840396] : [-(c_New__DSequence_Oneg__single(_840396, _840392) = c_New__DSequence_Oneg__single(_840394, _840390)), _840396 = _840394, _840392 = _840390], (3892 ^ _780461) ^ [_840539, _840541, _840543, _840545] : [-(c_Lazy__Sequence_Ohb__single(_840545, _840541) = c_Lazy__Sequence_Ohb__single(_840543, _840539)), _840545 = _840543, _840541 = _840539], (3902 ^ _780461) ^ [_840688, _840690, _840692, _840694, _840696, _840698] : [-(c_Predicate_ODomainP(_840698, _840694, _840690) = c_Predicate_ODomainP(_840696, _840692, _840688)), _840698 = _840696, _840694 = _840692, _840690 = _840688], (3916 ^ _780461) ^ [_840909, _840911, _840913, _840915, _840917, _840919] : [-(c_Predicate_ORangeP(_840919, _840915, _840911) = c_Predicate_ORangeP(_840917, _840913, _840909)), _840919 = _840917, _840915 = _840913, _840911 = _840909], (3930 ^ _780461) ^ [_841130, _841132, _841134, _841136] : [-(c_Wellfounded_Omax__ext(_841136, _841132) = c_Wellfounded_Omax__ext(_841134, _841130)), _841136 = _841134, _841132 = _841130], (3940 ^ _780461) ^ [_841279, _841281] : [_841281 = _841279, -(c_Rings_Odvd__class_Odvd(_841281) = c_Rings_Odvd__class_Odvd(_841279))], (3946 ^ _780461) ^ [_841364, _841366, _841368, _841370] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_841370, _841366) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_841368, _841364)), _841370 = _841368, _841366 = _841364], (3956 ^ _780461) ^ [_841513, _841515, _841517, _841519, _841521, _841523] : [-(c_Finite__Set_Ofold__image(_841523, _841519, _841515) = c_Finite__Set_Ofold__image(_841521, _841517, _841513)), _841523 = _841521, _841519 = _841517, _841515 = _841513], (3970 ^ _780461) ^ [_841734, _841736, _841738, _841740] : [-(c_HOL_OThe(_841740, _841736) = c_HOL_OThe(_841738, _841734)), _841740 = _841738, _841736 = _841734], (3980 ^ _780461) ^ [_841883, _841885] : [_841885 = _841883, -(c_Set_OBall(_841885) = c_Set_OBall(_841883))], (3986 ^ _780461) ^ [_841968, _841970] : [_841970 = _841968, -(c_SetInterval_Oord__class_OgreaterThan(_841970) = c_SetInterval_Oord__class_OgreaterThan(_841968))], (3992 ^ _780461) ^ [_842053, _842055, _842057, _842059] : [-(c_Relation_OId__on(_842059, _842055) = c_Relation_OId__on(_842057, _842053)), _842059 = _842057, _842055 = _842053], (4002 ^ _780461) ^ [_842202, _842204] : [_842204 = _842202, -(c_Nat_Ofunpow(_842204) = c_Nat_Ofunpow(_842202))], (4008 ^ _780461) ^ [_842287, _842289] : [_842289 = _842287, -(c_HOL_OAll(_842289) = c_HOL_OAll(_842287))], (4014 ^ _780461) ^ [_842372, _842374, _842376, _842378, _842380, _842382] : [-(c_Set_Ovimage(_842382, _842378, _842374) = c_Set_Ovimage(_842380, _842376, _842372)), _842382 = _842380, _842378 = _842376, _842374 = _842372], (4028 ^ _780461) ^ [_842593, _842595, _842597, _842599] : [-(c_Relation_ORange(_842599, _842595) = c_Relation_ORange(_842597, _842593)), _842599 = _842597, _842595 = _842593], (4038 ^ _780461) ^ [_842742, _842744, _842746, _842748] : [-(c_Relation_ODomain(_842748, _842744) = c_Relation_ODomain(_842746, _842742)), _842748 = _842746, _842744 = _842742], (4048 ^ _780461) ^ [_842891, _842893] : [_842893 = _842891, -(c_Relation_OField(_842893) = c_Relation_OField(_842891))], (4054 ^ _780461) ^ [_842976, _842978] : [_842978 = _842976, -(c_Set_OPow(_842978) = c_Set_OPow(_842976))], (4060 ^ _780461) ^ [_843061, _843063] : [_843063 = _843061, -(c_Equiv__Relations_Oquotient(_843063) = c_Equiv__Relations_Oquotient(_843061))], (4066 ^ _780461) ^ [_843146, _843148, _843150, _843152, _843154, _843156, _843158, _843160, _843162, _843164] : [-(c_Finite__Set_Ofold__graph(_843164, _843160, _843156, _843152, _843148) = c_Finite__Set_Ofold__graph(_843162, _843158, _843154, _843150, _843146)), _843164 = _843162, _843160 = _843158, _843156 = _843154, _843152 = _843150, _843148 = _843146], (4088 ^ _780461) ^ [_843535, _843537, _843539, _843541] : [-(c_Transitive__Closure_Otrancl(_843541, _843537) = c_Transitive__Closure_Otrancl(_843539, _843535)), _843541 = _843539, _843537 = _843535], (4098 ^ _780461) ^ [_843684, _843686] : [_843686 = _843684, -(c_Relation_OId(_843686) = c_Relation_OId(_843684))], (4104 ^ _780461) ^ [_843769, _843771, _843773, _843775, _843777, _843779] : [-(c_Relation_Orel__comp(_843779, _843775, _843771) = c_Relation_Orel__comp(_843777, _843773, _843769)), _843779 = _843777, _843775 = _843773, _843771 = _843769], (4118 ^ _780461) ^ [_843990, _843992, _843994, _843996, _843998, _844000] : [-(c_Smallcheck_Oorelse(_844000, _843996, _843992) = c_Smallcheck_Oorelse(_843998, _843994, _843990)), _844000 = _843998, _843996 = _843994, _843992 = _843990], (4132 ^ _780461) ^ [_844211, _844213, _844215, _844217, _844219, _844221] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_844221, _844217, _844213) = c_Smallcheck_Ofull__small__class_Ofull__small(_844219, _844215, _844211)), _844221 = _844219, _844217 = _844215, _844213 = _844211], (4146 ^ _780461) ^ [_844432, _844434, _844436, _844438, _844440, _844442] : [-(c_Smallcheck_Ofull__small_H(_844442, _844438, _844434) = c_Smallcheck_Ofull__small_H(_844440, _844436, _844432)), _844442 = _844440, _844438 = _844436, _844434 = _844432], (4160 ^ _780461) ^ [_844653, _844655, _844657, _844659, _844661, _844663] : [-(c_Smallcheck_Osmall_H(_844663, _844659, _844655) = c_Smallcheck_Osmall_H(_844661, _844657, _844653)), _844663 = _844661, _844659 = _844657, _844655 = _844653], (4174 ^ _780461) ^ [_844874, _844876] : [_844876 = _844874, -(c_Smallcheck_Osmall__class_Osmall(_844876) = c_Smallcheck_Osmall__class_Osmall(_844874))], (4180 ^ _780461) ^ [_844959, _844961, _844963, _844965, _844967, _844969, _844971, _844973, _844975, _844977, _844979, _844981] : [-(c_Map_Omap__comp(_844981, _844977, _844973, _844969, _844965, _844961) = c_Map_Omap__comp(_844979, _844975, _844971, _844967, _844963, _844959)), _844981 = _844979, _844977 = _844975, _844973 = _844971, _844969 = _844967, _844965 = _844963, _844961 = _844959], (4206 ^ _780461) ^ [_845444, _845446, _845448, _845450, _845452, _845454, _845456, _845458, _845460, _845462] : [-(c_Sum__Type_Osum_Osum__case(_845462, _845458, _845454, _845450, _845446) = c_Sum__Type_Osum_Osum__case(_845460, _845456, _845452, _845448, _845444)), _845462 = _845460, _845458 = _845456, _845454 = _845452, _845450 = _845448, _845446 = _845444], (4228 ^ _780461) ^ [_845833, _845835, _845837, _845839] : [-(c_Option_Omap(_845839, _845835) = c_Option_Omap(_845837, _845833)), _845839 = _845837, _845835 = _845833], (4238 ^ _780461) ^ [_845982, _845984, _845986, _845988, _845990, _845992] : [-(c_Map_Oran(_845992, _845988, _845984) = c_Map_Oran(_845990, _845986, _845982)), _845992 = _845990, _845988 = _845986, _845984 = _845982], (4252 ^ _780461) ^ [_846203, _846205, _846207, _846209] : [-(c_List_Olenlex(_846209, _846205) = c_List_Olenlex(_846207, _846203)), _846209 = _846207, _846205 = _846203], (4262 ^ _780461) ^ [_846352, _846354, _846356, _846358] : [-(c_Relation_Oinv__image(_846358, _846354) = c_Relation_Oinv__image(_846356, _846352)), _846358 = _846356, _846354 = _846352], (4272 ^ _780461) ^ [_846501, _846503, _846505, _846507] : [-(c_Nitpick_Ocard_H(_846507, _846503) = c_Nitpick_Ocard_H(_846505, _846501)), _846507 = _846505, _846503 = _846501], (4282 ^ _780461) ^ [_846650, _846652, _846654, _846656, _846658, _846660, _846662, _846664, _846666, _846668, _846670, _846672] : [-(c_Product__Type_Omap__pair(_846672, _846668, _846664, _846660, _846656, _846652) = c_Product__Type_Omap__pair(_846670, _846666, _846662, _846658, _846654, _846650)), _846672 = _846670, _846668 = _846666, _846664 = _846662, _846660 = _846658, _846656 = _846654, _846652 = _846650], (4308 ^ _780461) ^ [_847135, _847137, _847139, _847141, _847143, _847145, _847147, _847149] : [-(c_Wellfounded_Olex__prod(_847149, _847145, _847141, _847137) = c_Wellfounded_Olex__prod(_847147, _847143, _847139, _847135)), _847149 = _847147, _847145 = _847143, _847141 = _847139, _847137 = _847135], (4326 ^ _780461) ^ [_847436, _847438, _847440, _847442] : [-(c_List_Olexn(_847442, _847438) = c_List_Olexn(_847440, _847436)), _847442 = _847440, _847438 = _847436], (4336 ^ _780461) ^ [_847585, _847587] : [_847587 = _847585, -(c_Groups_Oabs__class_Oabs(_847587) = c_Groups_Oabs__class_Oabs(_847585))], (4342 ^ _780461) ^ [_847670, _847672] : [_847672 = _847670, -(c_Groups_Ouminus__class_Ouminus(_847672) = c_Groups_Ouminus__class_Ouminus(_847670))], (4348 ^ _780461) ^ [_847755, _847757] : [_847757 = _847755, -(c_Nat_Osemiring__1__class_Oof__nat(_847757) = c_Nat_Osemiring__1__class_Oof__nat(_847755))], (4354 ^ _780461) ^ [_847840, _847842, _847844, _847846] : [-(c_Hilbert__Choice_OEps(_847846, _847842) = c_Hilbert__Choice_OEps(_847844, _847840)), _847846 = _847844, _847842 = _847840], (4364 ^ _780461) ^ [_847989, _847991, _847993, _847995, _847997, _847999, _848001, _848003] : [-(c_Nitpick_Osetsum_H(_848003, _847999, _847995, _847991) = c_Nitpick_Osetsum_H(_848001, _847997, _847993, _847989)), _848003 = _848001, _847999 = _847997, _847995 = _847993, _847991 = _847989], (4382 ^ _780461) ^ [_848290, _848292] : [_848292 = _848290, -(c_HOL_OEx(_848292) = c_HOL_OEx(_848290))], (4388 ^ _780461) ^ [_848375, _848377, _848379, _848381, _848383, _848385, _848387, _848389] : [-(c_Product__Type_Oscomp(_848389, _848385, _848381, _848377) = c_Product__Type_Oscomp(_848387, _848383, _848379, _848375)), _848389 = _848387, _848385 = _848383, _848381 = _848379, _848377 = _848375], (4406 ^ _780461) ^ [_848676, _848678] : [_848678 = _848676, -(c_Random_Orange(_848678) = c_Random_Orange(_848676))], (4412 ^ _780461) ^ [_848761, _848763, _848765, _848767] : [-(c_List_Olex(_848767, _848763) = c_List_Olex(_848765, _848761)), _848767 = _848765, _848763 = _848761], (4422 ^ _780461) ^ [_848910, _848912, _848914, _848916] : [-(c_Random_Oselect(_848916, _848912) = c_Random_Oselect(_848914, _848910)), _848916 = _848914, _848912 = _848910], (4432 ^ _780461) ^ [_849059, _849061, _849063, _849065, _849067, _849069] : [-(c_Relation_OImage(_849069, _849065, _849061) = c_Relation_OImage(_849067, _849063, _849059)), _849069 = _849067, _849065 = _849063, _849061 = _849059], (4446 ^ _780461) ^ [_849280, _849282, _849284, _849286, _849288, _849290] : [-(c_Set_Oimage(_849290, _849286, _849282) = c_Set_Oimage(_849288, _849284, _849280)), _849290 = _849288, _849286 = _849284, _849282 = _849280], (4460 ^ _780461) ^ [_849501, _849503, _849505, _849507, _849509, _849511, _849513, _849515] : [-(c_Lazy__Sequence_Oanamorph(_849515, _849511, _849507, _849503) = c_Lazy__Sequence_Oanamorph(_849513, _849509, _849505, _849501)), _849515 = _849513, _849511 = _849509, _849507 = _849505, _849503 = _849501], (4478 ^ _780461) ^ [_849802, _849804, _849806, _849808, _849810, _849812] : [-(c_List_Oset__Cons(_849812, _849808, _849804) = c_List_Oset__Cons(_849810, _849806, _849802)), _849812 = _849810, _849808 = _849806, _849804 = _849802], (4492 ^ _780461) ^ [_850023, _850025, _850027, _850029] : [-(c_List_Olistset(_850029, _850025) = c_List_Olistset(_850027, _850023)), _850029 = _850027, _850025 = _850023], (4502 ^ _780461) ^ [_850172, _850174, _850176, _850178, _850180, _850182, _850184, _850186] : [-(c_Map_Orestrict__map(_850186, _850182, _850178, _850174) = c_Map_Orestrict__map(_850184, _850180, _850176, _850172)), _850186 = _850184, _850182 = _850180, _850178 = _850176, _850174 = _850172], (4520 ^ _780461) ^ [_850473, _850475, _850477, _850479, _850481, _850483] : [-(c_Map_Odom(_850483, _850479, _850475) = c_Map_Odom(_850481, _850477, _850473)), _850483 = _850481, _850479 = _850477, _850475 = _850473], (4534 ^ _780461) ^ [_850694, _850696, _850698, _850700, _850702, _850704, _850706, _850708] : [-(c_Map_Omap__add(_850708, _850704, _850700, _850696) = c_Map_Omap__add(_850706, _850702, _850698, _850694)), _850708 = _850706, _850704 = _850702, _850700 = _850698, _850696 = _850694], (4552 ^ _780461) ^ [_850995, _850997, _850999, _851001] : [-(c_Relation_Oconverse(_851001, _850997) = c_Relation_Oconverse(_850999, _850995)), _851001 = _850999, _850997 = _850995], (4562 ^ _780461) ^ [_851144, _851146, _851148, _851150] : [-(c_Transitive__Closure_Ortrancl(_851150, _851146) = c_Transitive__Closure_Ortrancl(_851148, _851144)), _851150 = _851148, _851146 = _851144], (4572 ^ _780461) ^ [_851293, _851295, _851297, _851299, _851301, _851303, _851305, _851307] : [-(c_Nat_Onat_Onat__case(_851307, _851303, _851299, _851295) = c_Nat_Onat_Onat__case(_851305, _851301, _851297, _851293)), _851307 = _851305, _851303 = _851301, _851299 = _851297, _851295 = _851293], (4590 ^ _780461) ^ [_851594, _851596, _851598, _851600] : [-(c_Nat_Ocompow(_851600, _851596) = c_Nat_Ocompow(_851598, _851594)), _851600 = _851598, _851596 = _851594], (4600 ^ _780461) ^ [_851743, _851745] : [_851745 = _851743, -(c_List_Orotate1(_851745) = c_List_Orotate1(_851743))], (4606 ^ _780461) ^ [_851828, _851830] : [_851830 = _851828, -(c_Fun_Oid(_851830) = c_Fun_Oid(_851828))], (4612 ^ _780461) ^ [_851913, _851915, _851917, _851919] : [-(c_Finite__Set_Ofold1(_851919, _851915) = c_Finite__Set_Ofold1(_851917, _851913)), _851919 = _851917, _851915 = _851913], (4622 ^ _780461) ^ [_852062, _852064] : [_852064 = _852062, -(c_Groups_Otimes__class_Otimes(_852064) = c_Groups_Otimes__class_Otimes(_852062))], (4628 ^ _780461) ^ [_852147, _852149, _852151, _852153, _852155, _852157] : [-(c_Finite__Set_Ofold(_852157, _852153, _852149) = c_Finite__Set_Ofold(_852155, _852151, _852147)), _852157 = _852155, _852153 = _852151, _852149 = _852147], (4642 ^ _780461) ^ [_852368, _852370, _852372, _852374] : [-(c_Complete__Lattice_OSup__class_OSup(_852374, _852370) = c_Complete__Lattice_OSup__class_OSup(_852372, _852368)), _852374 = _852372, _852370 = _852368], (4652 ^ _780461) ^ [_852517, _852519, _852521, _852523] : [-(c_Complete__Lattice_OInf__class_OInf(_852523, _852519) = c_Complete__Lattice_OInf__class_OInf(_852521, _852517)), _852523 = _852521, _852519 = _852517], (4662 ^ _780461) ^ [_852666, _852668, _852670, _852672] : [-(c_Big__Operators_Olattice__class_OSup__fin(_852672, _852668) = c_Big__Operators_Olattice__class_OSup__fin(_852670, _852666)), _852672 = _852670, _852668 = _852666], (4672 ^ _780461) ^ [_852815, _852817, _852819, _852821] : [-(c_Big__Operators_Olattice__class_OInf__fin(_852821, _852817) = c_Big__Operators_Olattice__class_OInf__fin(_852819, _852815)), _852821 = _852819, _852817 = _852815], (4682 ^ _780461) ^ [_852964, _852966, _852968, _852970] : [-(c_Big__Operators_Olinorder__class_OMin(_852970, _852966) = c_Big__Operators_Olinorder__class_OMin(_852968, _852964)), _852970 = _852968, _852966 = _852964], (4692 ^ _780461) ^ [_853113, _853115, _853117, _853119] : [-(c_Big__Operators_Olinorder__class_OMax(_853119, _853115) = c_Big__Operators_Olinorder__class_OMax(_853117, _853113)), _853119 = _853117, _853115 = _853113], (4702 ^ _780461) ^ [_853262, _853264, _853266, _853268, _853270, _853272] : [-(c_Big__Operators_Olattice_OInf__fin(_853272, _853268, _853264) = c_Big__Operators_Olattice_OInf__fin(_853270, _853266, _853262)), _853272 = _853270, _853268 = _853266, _853264 = _853262], (4716 ^ _780461) ^ [_853483, _853485] : [_853485 = _853483, -(c_Orderings_Oord__class_Omin(_853485) = c_Orderings_Oord__class_Omin(_853483))], (4722 ^ _780461) ^ [_853568, _853570, _853572, _853574, _853576, _853578] : [-(c_Big__Operators_Olattice_OSup__fin(_853578, _853574, _853570) = c_Big__Operators_Olattice_OSup__fin(_853576, _853572, _853568)), _853578 = _853576, _853574 = _853572, _853570 = _853568], (4736 ^ _780461) ^ [_853789, _853791, _853793, _853795] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_853795, _853791) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_853793, _853789)), _853795 = _853793, _853791 = _853789], (4746 ^ _780461) ^ [_853938, _853940] : [_853940 = _853938, -(c_Lattices_Osemilattice__inf__class_Oinf(_853940) = c_Lattices_Osemilattice__inf__class_Oinf(_853938))], (4752 ^ _780461) ^ [_854023, _854025, _854027, _854029, _854031, _854033, _854035, _854037, _854039, _854041] : [-(c_Map_Omap__upds(_854041, _854037, _854033, _854029, _854025) = c_Map_Omap__upds(_854039, _854035, _854031, _854027, _854023)), _854041 = _854039, _854037 = _854035, _854033 = _854031, _854029 = _854027, _854025 = _854023], (4774 ^ _780461) ^ [_854412, _854414, _854416, _854418] : [-(c_Fun_Ofun__upd(_854418, _854414) = c_Fun_Ofun__upd(_854416, _854412)), _854418 = _854416, _854414 = _854412], (4784 ^ _780461) ^ [_854561, _854563, _854565, _854567] : [-(c_Product__Type_OSigma(_854567, _854563) = c_Product__Type_OSigma(_854565, _854561)), _854567 = _854565, _854563 = _854561], (4794 ^ _780461) ^ [_854710, _854712, _854714, _854716] : [-(c_List_Olistrel(_854716, _854712) = c_List_Olistrel(_854714, _854710)), _854716 = _854714, _854712 = _854710], (4804 ^ _780461) ^ [_854859, _854861] : [_854861 = _854859, -(c_Orderings_Otop__class_Otop(_854861) = c_Orderings_Otop__class_Otop(_854859))], (4810 ^ _780461) ^ [_854944, _854946, _854948, _854950] : [-(c_List_Olistrel1(_854950, _854946) = c_List_Olistrel1(_854948, _854944)), _854950 = _854948, _854946 = _854944], (4820 ^ _780461) ^ [_855093, _855095, _855097, _855099] : [-(c_Wellfounded_Oacc(_855099, _855095) = c_Wellfounded_Oacc(_855097, _855093)), _855099 = _855097, _855095 = _855093], (4830 ^ _780461) ^ [_855242, _855244, _855246, _855248] : [-(c_List_Olexord(_855248, _855244) = c_List_Olexord(_855246, _855242)), _855248 = _855246, _855244 = _855242], (4840 ^ _780461) ^ [_855391, _855393, _855395, _855397] : [-(c_List_Olists(_855397, _855393) = c_List_Olists(_855395, _855391)), _855397 = _855395, _855393 = _855391], (4850 ^ _780461) ^ [_855540, _855542, _855544, _855546, _855548, _855550] : [-(c_List_Olist_Olist__size(_855550, _855546, _855542) = c_List_Olist_Olist__size(_855548, _855544, _855540)), _855550 = _855548, _855546 = _855544, _855542 = _855540], (4864 ^ _780461) ^ [_855761, _855763] : [_855763 = _855761, -(c_Set_Oinsert(_855763) = c_Set_Oinsert(_855761))], (4870 ^ _780461) ^ [_855846, _855848] : [_855848 = _855846, -(c_Orderings_Obot__class_Obot(_855848) = c_Orderings_Obot__class_Obot(_855846))], (4876 ^ _780461) ^ [_855931, _855933, _855935, _855937] : [-(c_Product__Type_OPair(_855937, _855933) = c_Product__Type_OPair(_855935, _855931)), _855937 = _855935, _855933 = _855931], (4886 ^ _780461) ^ [_856080, _856082, _856084, _856086, _856088, _856090] : [-(c_List_Opartition(_856090, _856086, _856082) = c_List_Opartition(_856088, _856084, _856080)), _856090 = _856088, _856086 = _856084, _856082 = _856080], (4900 ^ _780461) ^ [_856301, _856303] : [_856303 = _856301, -(c_Finite__Set_Ocard(_856303) = c_Finite__Set_Ocard(_856301))], (4906 ^ _780461) ^ [_856386, _856388] : [_856388 = _856386, -(c_Set_OCollect(_856388) = c_Set_OCollect(_856386))], (4912 ^ _780461) ^ [_856471, _856473, _856475, _856477, _856479, _856481, _856483, _856485] : [-(c_Fun_Ocomp(_856485, _856481, _856477, _856473) = c_Fun_Ocomp(_856483, _856479, _856475, _856471)), _856485 = _856483, _856481 = _856479, _856477 = _856475, _856473 = _856471], (4930 ^ _780461) ^ [_856772, _856774] : [_856774 = _856772, -(c_Option_Othe(_856774) = c_Option_Othe(_856772))], (4936 ^ _780461) ^ [_856857, _856859, _856861, _856863, _856865, _856867] : [-(c_Map_Omap__of(_856867, _856863, _856859) = c_Map_Omap__of(_856865, _856861, _856857)), _856867 = _856865, _856863 = _856861, _856859 = _856857], (4950 ^ _780461) ^ [_857078, _857080, _857082, _857084, _857086, _857088, _857090, _857092] : [-(c_Option_Ooption_Ooption__case(_857092, _857088, _857084, _857080) = c_Option_Ooption_Ooption__case(_857090, _857086, _857082, _857078)), _857092 = _857090, _857088 = _857086, _857084 = _857082, _857080 = _857078], (4968 ^ _780461) ^ [_857379, _857381, _857383, _857385] : [-(c_Random_Oselect__weight(_857385, _857381) = c_Random_Oselect__weight(_857383, _857379)), _857385 = _857383, _857381 = _857379], (4978 ^ _780461) ^ [_857528, _857530, _857532, _857534] : [-(c_Random_Opick(_857534, _857530) = c_Random_Opick(_857532, _857528)), _857534 = _857532, _857530 = _857528], (4988 ^ _780461) ^ [_857677, _857679, _857681, _857683, _857685, _857687, _857689, _857691] : [-(c_List_Omap__filter(_857691, _857687, _857683, _857679) = c_List_Omap__filter(_857689, _857685, _857681, _857677)), _857691 = _857689, _857687 = _857685, _857683 = _857681, _857679 = _857677], (5006 ^ _780461) ^ [_857978, _857980] : [_857980 = _857978, -(c_If(_857980) = c_If(_857978))], (5012 ^ _780461) ^ [_858063, _858065] : [_858065 = _858063, -(c_Option_Ooption_OSome(_858065) = c_Option_Ooption_OSome(_858063))], (5018 ^ _780461) ^ [_858148, _858150] : [_858150 = _858148, -(c_Option_Ooption_ONone(_858150) = c_Option_Ooption_ONone(_858148))], (5024 ^ _780461) ^ [_858233, _858235, _858237, _858239, _858241, _858243] : [-(c_List_Osublist(_858243, _858239, _858235) = c_List_Osublist(_858241, _858237, _858233)), _858243 = _858241, _858239 = _858237, _858235 = _858233], (5038 ^ _780461) ^ [_858454, _858456, _858458, _858460] : [-(c_List_Obutlast(_858460, _858456) = c_List_Obutlast(_858458, _858454)), _858460 = _858458, _858456 = _858454], (5048 ^ _780461) ^ [_858603, _858605] : [_858605 = _858603, -(c_Int_Onumber__class_Onumber__of(_858605) = c_Int_Onumber__class_Onumber__of(_858603))], (5054 ^ _780461) ^ [_858688, _858690, _858692, _858694] : [-(c_List_Oupto(_858694, _858690) = c_List_Oupto(_858692, _858688)), _858694 = _858692, _858690 = _858688], (5064 ^ _780461) ^ [_858837, _858839, _858841, _858843] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_858843, _858839) = c_SetInterval_Oord__class_OatLeastLessThan(_858841, _858837)), _858843 = _858841, _858839 = _858837], (5074 ^ _780461) ^ [_858986, _858988, _858990, _858992] : [-(c_List_Otl(_858992, _858988) = c_List_Otl(_858990, _858986)), _858992 = _858990, _858988 = _858986], (5084 ^ _780461) ^ [_859135, _859137, _859139, _859141, _859143, _859145, _859147, _859149, _859151, _859153] : [-(c_List_Olinorder__class_Oinsort__insert__key(_859153, _859149, _859145, _859141, _859137) = c_List_Olinorder__class_Oinsort__insert__key(_859151, _859147, _859143, _859139, _859135)), _859153 = _859151, _859149 = _859147, _859145 = _859143, _859141 = _859139, _859137 = _859135], (5106 ^ _780461) ^ [_859524, _859526, _859528, _859530, _859532, _859534] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_859534, _859530, _859526) = c_SetInterval_Oord__class_OatLeastAtMost(_859532, _859528, _859524)), _859534 = _859532, _859530 = _859528, _859526 = _859524], (5120 ^ _780461) ^ [_859745, _859747] : [_859747 = _859745, -(c_SetInterval_Oord__class_OlessThan(_859747) = c_SetInterval_Oord__class_OlessThan(_859745))], (5126 ^ _780461) ^ [_859830, _859832, _859834, _859836] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_859836, _859832) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_859834, _859830)), _859836 = _859834, _859832 = _859830], (5136 ^ _780461) ^ [_859979, _859981, _859983, _859985, _859987, _859989] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_859989, _859985, _859981) = c_SetInterval_Oord__class_OgreaterThanAtMost(_859987, _859983, _859979)), _859989 = _859987, _859985 = _859983, _859981 = _859979], (5150 ^ _780461) ^ [_860200, _860202, _860204, _860206, _860208, _860210] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_860210, _860206, _860202) = c_SetInterval_Oord__class_OgreaterThanLessThan(_860208, _860204, _860200)), _860210 = _860208, _860206 = _860204, _860202 = _860200], (5164 ^ _780461) ^ [_860421, _860423] : [_860423 = _860421, -(c_Finite__Set_Ofinite(_860423) = c_Finite__Set_Ofinite(_860421))], (5170 ^ _780461) ^ [_860506, _860508, _860510, _860512] : [-(c_List_Olinorder__class_Osorted__list__of__set(_860512, _860508) = c_List_Olinorder__class_Osorted__list__of__set(_860510, _860506)), _860512 = _860510, _860508 = _860506], (5180 ^ _780461) ^ [_860655, _860657] : [_860657 = _860655, -(c_SetInterval_Oord__class_OatMost(_860657) = c_SetInterval_Oord__class_OatMost(_860655))], (5186 ^ _780461) ^ [_860740, _860742, _860744, _860746, _860748, _860750] : [-(c_List_Olinorder__class_Oinsort__key(_860750, _860746, _860742) = c_List_Olinorder__class_Oinsort__key(_860748, _860744, _860740)), _860750 = _860748, _860746 = _860744, _860742 = _860740], (5200 ^ _780461) ^ [_860961, _860963, _860965, _860967, _860969, _860971] : [-(c_List_Oremove1(_860971, _860967, _860963) = c_List_Oremove1(_860969, _860965, _860961)), _860971 = _860969, _860967 = _860965, _860963 = _860961], (5214 ^ _780461) ^ [_861182, _861184] : [_861184 = _861182, -(c_Lattices_Osemilattice__sup__class_Osup(_861184) = c_Lattices_Osemilattice__sup__class_Osup(_861182))], (5220 ^ _780461) ^ [_861267, _861269, _861271, _861273] : [-(c_Product__Type_Ofst(_861273, _861269) = c_Product__Type_Ofst(_861271, _861267)), _861273 = _861271, _861269 = _861267], (5230 ^ _780461) ^ [_861416, _861418] : [_861418 = _861416, -(c_Groups_Oplus__class_Oplus(_861418) = c_Groups_Oplus__class_Oplus(_861416))], (5236 ^ _780461) ^ [_861501, _861503, _861505, _861507] : [-(c_Product__Type_Osnd(_861507, _861503) = c_Product__Type_Osnd(_861505, _861501)), _861507 = _861505, _861503 = _861501], (5246 ^ _780461) ^ [_861650, _861652, _861654, _861656] : [-(c_List_Oupt(_861656, _861652) = c_List_Oupt(_861654, _861650)), _861656 = _861654, _861652 = _861650], (5256 ^ _780461) ^ [_861799, _861801] : [_861801 = _861799, -(c_List_Oappend(_861801) = c_List_Oappend(_861799))], (5262 ^ _780461) ^ [_861884, _861886] : [_861886 = _861884, -(c_List_Odistinct(_861886) = c_List_Odistinct(_861884))], (5268 ^ _780461) ^ [_861969, _861971] : [_861971 = _861969, -(c_List_Omonoid__add__class_Olistsum(_861971) = c_List_Omonoid__add__class_Olistsum(_861969))], (5274 ^ _780461) ^ [_862054, _862056, _862058, _862060, _862062, _862064, _862066, _862068] : [-(c_List_Ofoldl(_862068, _862064, _862060, _862056) = c_List_Ofoldl(_862066, _862062, _862058, _862054)), _862068 = _862066, _862064 = _862062, _862060 = _862058, _862056 = _862054], (5292 ^ _780461) ^ [_862355, _862357, _862359, _862361] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_862361, _862357) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_862359, _862355)), _862361 = _862359, _862357 = _862355], (5302 ^ _780461) ^ [_862504, _862506, _862508, _862510] : [-(c_List_Ofilter(_862510, _862506) = c_List_Ofilter(_862508, _862504)), _862510 = _862508, _862506 = _862504], (5312 ^ _780461) ^ [_862653, _862655] : [_862655 = _862653, -(c_List_Ohd(_862655) = c_List_Ohd(_862653))], (5318 ^ _780461) ^ [_862738, _862740, _862742, _862744] : [-(c_List_Olast(_862744, _862740) = c_List_Olast(_862742, _862738)), _862744 = _862742, _862740 = _862738], (5328 ^ _780461) ^ [_862887, _862889] : [_862889 = _862887, -(c_List_Odrop(_862889) = c_List_Odrop(_862887))], (5334 ^ _780461) ^ [_862972, _862974] : [_862974 = _862972, -(c_List_Otake(_862974) = c_List_Otake(_862972))], (5340 ^ _780461) ^ [_863057, _863059, _863061, _863063] : [-(c_List_Orotate(_863063, _863059) = c_List_Orotate(_863061, _863057)), _863063 = _863061, _863059 = _863057], (5350 ^ _780461) ^ [_863206, _863208, _863210, _863212, _863214, _863216] : [-(c_Divides_Odiv__class_Omod(_863216, _863212, _863208) = c_Divides_Odiv__class_Omod(_863214, _863210, _863206)), _863216 = _863214, _863212 = _863210, _863208 = _863206], (5364 ^ _780461) ^ [_863427, _863429] : [_863429 = _863427, -(c_List_Oset(_863429) = c_List_Oset(_863427))], (5370 ^ _780461) ^ [_863512, _863514, _863516, _863518] : [-(c_List_Ozip(_863518, _863514) = c_List_Ozip(_863516, _863512)), _863518 = _863516, _863514 = _863512], (5380 ^ _780461) ^ [_863661, _863663, _863665, _863667, _863669, _863671] : [-(c_Product__Type_Oprod_Oprod__case(_863671, _863667, _863663) = c_Product__Type_Oprod_Oprod__case(_863669, _863665, _863661)), _863671 = _863669, _863667 = _863665, _863663 = _863661], (5394 ^ _780461) ^ [_863882, _863884, _863886, _863888] : [-(c_List_Olist__update(_863888, _863884) = c_List_Olist__update(_863886, _863882)), _863888 = _863886, _863884 = _863882], (5404 ^ _780461) ^ [_864031, _864033] : [_864033 = _864031, -(c_Groups_Ominus__class_Ominus(_864033) = c_Groups_Ominus__class_Ominus(_864031))], (5410 ^ _780461) ^ [_864116, _864118] : [_864118 = _864116, -(c_Groups_Oone__class_Oone(_864118) = c_Groups_Oone__class_Oone(_864116))], (5416 ^ _780461) ^ [_864201, _864203] : [_864203 = _864201, -(c_Orderings_Oord__class_Oless(_864203) = c_Orderings_Oord__class_Oless(_864201))], (5422 ^ _780461) ^ [_864286, _864288] : [_864288 = _864286, -(c_Orderings_Oord__class_Oless__eq(_864288) = c_Orderings_Oord__class_Oless__eq(_864286))], (5428 ^ _780461) ^ [_864371, _864373, _864375, _864377, _864379, _864381, _864383, _864385, _864387, _864389] : [-(c_List_Ofoldr(_864389, _864385, _864381, _864377, _864373) = c_List_Ofoldr(_864387, _864383, _864379, _864375, _864371)), _864389 = _864387, _864385 = _864383, _864381 = _864379, _864377 = _864375, _864373 = _864371], (5450 ^ _780461) ^ [_864760, _864762] : [_864762 = _864760, -(c_Orderings_Oord__class_Omax(_864762) = c_Orderings_Oord__class_Omax(_864760))], (5456 ^ _780461) ^ [_864845, _864847, _864849, _864851] : [-(c_Wellfounded_Oaccp(_864851, _864847) = c_Wellfounded_Oaccp(_864849, _864845)), _864851 = _864849, _864847 = _864845], (5466 ^ _780461) ^ [_864994, _864996] : [_864996 = _864994, -(c_List_Otranspose__rel(_864996) = c_List_Otranspose__rel(_864994))], (5472 ^ _780461) ^ [_865079, _865081, _865083, _865085] : [-(c_List_Oconcat(_865085, _865081) = c_List_Oconcat(_865083, _865079)), _865085 = _865083, _865081 = _865079], (5482 ^ _780461) ^ [_865228, _865230, _865232, _865234, _865236, _865238, _865240, _865242] : [-(c_List_Olist_Olist__case(_865242, _865238, _865234, _865230) = c_List_Olist_Olist__case(_865240, _865236, _865232, _865228)), _865242 = _865240, _865238 = _865236, _865234 = _865232, _865230 = _865228], (5500 ^ _780461) ^ [_865529, _865531] : [_865531 = _865529, -(c_List_Olist_OCons(_865531) = c_List_Olist_OCons(_865529))], (5506 ^ _780461) ^ [_865614, _865616] : [_865616 = _865614, -(c_List_Orev(_865616) = c_List_Orev(_865614))], (5512 ^ _780461) ^ [_865699, _865701, _865703, _865705] : [-(c_List_Omap(_865705, _865701) = c_List_Omap(_865703, _865699)), _865705 = _865703, _865701 = _865699], (5522 ^ _780461) ^ [_865848, _865850] : [_865850 = _865848, -(c_List_Olist_ONil(_865850) = c_List_Olist_ONil(_865848))], (5528 ^ _780461) ^ [_865933, _865935, _865937, _865939] : [-(c_List_Otranspose(_865939, _865935) = c_List_Otranspose(_865937, _865933)), _865939 = _865937, _865935 = _865933], (5538 ^ _780461) ^ [_866082, _866084] : [_866084 = _866082, -(c_Nat_Osize__class_Osize(_866084) = c_Nat_Osize__class_Osize(_866082))], (5544 ^ _780461) ^ [_866167, _866169] : [_866169 = _866167, -(c_List_Onth(_866169) = c_List_Onth(_866167))], (5550 ^ _780461) ^ [_866252, _866254] : [_866254 = _866252, -(tc_List_Olist(_866254) = tc_List_Olist(_866252))], (5556 ^ _780461) ^ [_866337, _866339] : [_866339 = _866337, -(c_Groups_Ozero__class_Ozero(_866339) = c_Groups_Ozero__class_Ozero(_866337))], (5562 ^ _780461) ^ [_866422, _866424, _866426, _866428] : [-(tc_fun(_866428, _866424) = tc_fun(_866426, _866422)), _866428 = _866426, _866424 = _866422], (5572 ^ _780461) ^ [_866571, _866573, _866575, _866577] : [-(tc_sum(_866577, _866573) = tc_sum(_866575, _866571)), _866577 = _866575, _866573 = _866571], (5582 ^ _780461) ^ [_866720, _866722] : [_866722 = _866720, -(tc_Option_Ooption(_866722) = tc_Option_Ooption(_866720))], (5588 ^ _780461) ^ [_866805, _866807, _866809, _866811] : [-(tc_prod(_866811, _866807) = tc_prod(_866809, _866805)), _866811 = _866809, _866807 = _866805], (5598 ^ _780461) ^ [_866954, _866956] : [_866956 = _866954, -(c_COMBI(_866956) = c_COMBI(_866954))], (5604 ^ _780461) ^ [_867039, _867041, _867043, _867045] : [-(c_COMBK(_867045, _867041) = c_COMBK(_867043, _867039)), _867045 = _867043, _867041 = _867039], (5614 ^ _780461) ^ [_867188, _867190, _867192, _867194, _867196, _867198] : [-(c_COMBB(_867198, _867194, _867190) = c_COMBB(_867196, _867192, _867188)), _867198 = _867196, _867194 = _867192, _867190 = _867188], (5628 ^ _780461) ^ [_867409, _867411, _867413, _867415, _867417, _867419] : [-(c_COMBC(_867419, _867415, _867411) = c_COMBC(_867417, _867413, _867409)), _867419 = _867417, _867415 = _867413, _867411 = _867409], (5642 ^ _780461) ^ [_867630, _867632, _867634, _867636, _867638, _867640] : [-(c_COMBS(_867640, _867636, _867632) = c_COMBS(_867638, _867634, _867630)), _867640 = _867638, _867636 = _867634, _867632 = _867630], (5656 ^ _780461) ^ [_867851, _867853, _867855, _867857] : [-(hAPP(_867857, _867853) = hAPP(_867855, _867851)), _867857 = _867855, _867853 = _867851], (5666 ^ _780461) ^ [_868000, _868002] : [_868002 = _868000, -(c_member(_868002) = c_member(_868000))], (5672 ^ _780461) ^ [_868081, _868083] : [_868083 = _868081, -(tc_Hoare__Mirabelle_Otriple(_868083) = tc_Hoare__Mirabelle_Otriple(_868081))], (5678 ^ _780461) ^ [_870944, _870946] : [hAPP(_870944, 5679 ^ [_870944, _870946]) = hAPP(_870946, 5679 ^ [_870944, _870946]), -(_870944 = _870946)], (5685 ^ _780461) ^ [_871070, _871072] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _871070, _871072, _871070))], (5687 ^ _780461) ^ [_871097, _871099, _871101] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _871097, _871099, _871101), -(_871101 = _871097)], (5693 ^ _780461) ^ [_871180, _871182] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _871180, _871182, _871180))], (5709 ^ _780461) ^ [_871549, _871551, _871553, _871555, _871557] : [5712 ^ _780461 : [(5713 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_871553, 5710 ^ [_871549, _871551, _871553, _871555, _871557]), 5711 ^ [_871549, _871551, _871553, _871555, _871557])))], (5716 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_871555, 5711 ^ [_871549, _871551, _871553, _871555, _871557], _871551, 5714 ^ [_871549, _871551, _871553, _871555, _871557]))], (5718 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_871557, 5710 ^ [_871549, _871551, _871553, _871555, _871557]), 5714 ^ [_871549, _871551, _871553, _871555, _871557]))]], -(c_Hoare__Mirabelle_Otriple__valid(_871549, _871551, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871549), _871553), _871555), _871557)))], (5695 ^ _780461) ^ [_871231, _871233, _871235, _871237, _871239] : [c_Hoare__Mirabelle_Otriple__valid(_871231, _871233, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871231), _871235), _871237), _871239)), 5698 ^ _780461 : [(5699 ^ _780461) ^ [_871352, _871354] : [hBOOL(hAPP(hAPP(_871235, _871354), _871352)), 5702 ^ _780461 : [(5703 ^ _780461) ^ [_871442] : [c_Natural_Oevaln(_871237, _871352, _871233, _871442), -(hBOOL(hAPP(hAPP(_871239, _871354), _871442)))]]]]], (5722 ^ _780461) ^ [_871930, _871932, _871934] : [c_Hoare__Mirabelle_Otriple__valid(_871930, hAPP(c_Nat_OSuc, _871932), _871934), -(c_Hoare__Mirabelle_Otriple__valid(_871930, _871932, _871934))], (5728 ^ _780461) ^ [_872019, _872021, _872023, _872025, _872027, _872029, _872031, _872033, _872035] : [-(c_Com_Ocom_Ocom__case(_872019, _872021, _872023, _872025, _872027, _872029, _872031, _872033, _872035, c_Com_Ocom_OSKIP) = _872021)], (5730 ^ _780461) ^ [_872069, _872071, _872073, _872075, _872077, _872079, _872081, _872083, _872085] : [-(c_Com_Ocom_Ocom__rec(_872069, _872071, _872073, _872075, _872077, _872079, _872081, _872083, _872085, c_Com_Ocom_OSKIP) = _872071)], (5749 ^ _780461) ^ [_872527, _872529, _872531] : [-(c_Hoare__Mirabelle_Ohoare__valids(_872527, _872529, _872531)), 5751 ^ _780461 : [(5759 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_872527)), 5757 ^ [_872527, _872529, _872531]), _872531)))], (5761 ^ _780461) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_872527, 5750 ^ [_872527, _872529, _872531], 5757 ^ [_872527, _872529, _872531])], (5752 ^ _780461) ^ [_872673] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_872527)), _872673), _872529)), -(c_Hoare__Mirabelle_Otriple__valid(_872527, 5750 ^ [_872527, _872529, _872531], _872673))]]], (5732 ^ _780461) ^ [_872137, _872139, _872141] : [c_Hoare__Mirabelle_Ohoare__valids(_872137, _872139, _872141), 5735 ^ _780461 : [(5736 ^ _780461) ^ [_872246] : [5738 ^ _780461 : [(5739 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_872137)), 5737 ^ [_872137, _872139, _872141, _872246]), _872139)))], (5741 ^ _780461) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_872137, _872246, 5737 ^ [_872137, _872139, _872141, _872246])]], 5742 ^ _780461 : [(5743 ^ _780461) ^ [_872418] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_872137)), _872418), _872141)), -(c_Hoare__Mirabelle_Otriple__valid(_872137, _872246, _872418))]]]]], (5765 ^ _780461) ^ [_872928, _872930, _872932, _872934, _872936, _872938] : [c_Natural_Oevaln(_872928, _872930, _872932, _872934), c_Natural_Oevaln(_872936, _872934, _872932, _872938), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_872928, _872936), _872930, _872932, _872938))], (5775 ^ _780461) ^ [_873090, _873092, _873094, _873096, _873098, _873100] : [-(hBOOL(hAPP(_873090, _873092))), c_Natural_Oevaln(_873094, _873092, _873096, _873098), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_873090, _873100, _873094), _873092, _873096, _873098))], (5785 ^ _780461) ^ [_873251, _873253, _873255, _873257, _873259, _873261] : [hBOOL(hAPP(_873251, _873253)), c_Natural_Oevaln(_873255, _873253, _873257, _873259), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_873251, _873255, _873261), _873253, _873257, _873259))], (5795 ^ _780461) ^ [_873416, _873418, _873420, _873422, _873424, _873426] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_873416, _873418, _873420), _873422, _873424, _873426), 5800 ^ _780461 : [(5801 ^ _780461) ^ [] : [-(hBOOL(hAPP(_873416, _873422)))], (5803 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_873418, _873422, _873424, _873426))]], 5804 ^ _780461 : [(5805 ^ _780461) ^ [] : [hBOOL(hAPP(_873416, _873422))], (5807 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_873420, _873422, _873424, _873426))]]], (5809 ^ _780461) ^ [_873658, _873660, _873662] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_873658, _873660, _873662))), 5812 ^ _780461 : [(5813 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _873660)))], (5815 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _873662)))]]], (5817 ^ _780461) ^ [_873787, _873789] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_873787, _873789))), 5820 ^ _780461 : [(5821 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _873787)))], (5823 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _873789)))]]], (5825 ^ _780461) ^ [_873933, _873935, _873937, _873939, _873941] : [c_Com_Ocom_OSemi(_873933, _873935) = c_Com_Ocom_OCond(_873937, _873939, _873941)], (5827 ^ _780461) ^ [_873992, _873994, _873996, _873998, _874000] : [c_Com_Ocom_OCond(_873992, _873994, _873996) = c_Com_Ocom_OSemi(_873998, _874000)], (5829 ^ _780461) ^ [_874045, _874047] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_874045, _874047))), 5832 ^ _780461 : [(5833 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _874045)))], (5835 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _874047)))]]], (5837 ^ _780461) ^ [_874162, _874164] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_874162, _874164)))), hBOOL(hAPP(c_Com_OWT, _874162)), hBOOL(hAPP(c_Com_OWT, _874164))], (5847 ^ _780461) ^ [_874329, _874331, _874333] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_874329, _874331, _874333))), 5850 ^ _780461 : [(5851 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _874331)))], (5853 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _874333)))]]], (5855 ^ _780461) ^ [_874450, _874452, _874454] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_874450, _874452, _874454)))), hBOOL(hAPP(c_Com_OWT, _874452)), hBOOL(hAPP(c_Com_OWT, _874454))], (5865 ^ _780461) ^ [_874626, _874628, _874630, _874632] : [c_Com_Ocom_OSemi(_874626, _874628) = c_Com_Ocom_OSemi(_874630, _874632), 5868 ^ _780461 : [(5869 ^ _780461) ^ [] : [-(_874626 = _874630)], (5871 ^ _780461) ^ [] : [-(_874628 = _874632)]]], (5873 ^ _780461) ^ [_874741, _874743, _874745, _874747] : [-(c_Com_Ocom_OSemi(_874741, _874743) = c_Com_Ocom_OSemi(_874745, _874747)), _874741 = _874745, _874743 = _874747], (5883 ^ _780461) ^ [_874919, _874921, _874923, _874925, _874927, _874929] : [c_Com_Ocom_OCond(_874919, _874921, _874923) = c_Com_Ocom_OCond(_874925, _874927, _874929), 5886 ^ _780461 : [(5887 ^ _780461) ^ [] : [-(_874919 = _874925)], (5889 ^ _780461) ^ [] : [-(_874921 = _874927)], (5891 ^ _780461) ^ [] : [-(_874923 = _874929)]]], (5893 ^ _780461) ^ [_875066, _875068, _875070, _875072, _875074, _875076] : [-(c_Com_Ocom_OCond(_875066, _875068, _875070) = c_Com_Ocom_OCond(_875072, _875074, _875076)), _875066 = _875072, _875068 = _875074, _875070 = _875076], (5907 ^ _780461) ^ [_875319, _875321, _875323, _875325, _875327, _875329, _875331] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_875319), _875321), _875323), _875325) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_875319), _875327), _875329), _875331), 5910 ^ _780461 : [(5911 ^ _780461) ^ [] : [-(_875321 = _875327)], (5913 ^ _780461) ^ [] : [-(_875323 = _875329)], (5915 ^ _780461) ^ [] : [-(_875325 = _875331)]]], (5917 ^ _780461) ^ [_875496, _875498, _875500, _875502, _875504, _875506, _875508] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_875496), _875498), _875500), _875502) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_875496), _875504), _875506), _875508)), _875498 = _875504, _875500 = _875506, _875502 = _875508], (5931 ^ _780461) ^ [_875753, _875755, _875757, _875759, _875761, _875763, _875765, _875767, _875769, _875771, _875773] : [-(c_Com_Ocom_Ocom__case(_875753, _875755, _875757, _875759, _875761, _875763, _875765, _875767, _875769, c_Com_Ocom_OSemi(_875771, _875773)) = hAPP(hAPP(_875761, _875771), _875773))], (5933 ^ _780461) ^ [_875816, _875818, _875820, _875822, _875824, _875826, _875828, _875830, _875832, _875834, _875836] : [-(c_Com_Ocom_Ocom__rec(_875816, _875818, _875820, _875822, _875824, _875826, _875828, _875830, _875832, c_Com_Ocom_OSemi(_875834, _875836)) = hAPP(hAPP(hAPP(hAPP(_875824, _875834), _875836), c_Com_Ocom_Ocom__rec(_875816, _875818, _875820, _875822, _875824, _875826, _875828, _875830, _875832, _875834)), c_Com_Ocom_Ocom__rec(_875816, _875818, _875820, _875822, _875824, _875826, _875828, _875830, _875832, _875836)))], (5935 ^ _780461) ^ [_875907, _875909, _875911, _875913, _875915, _875917, _875919, _875921, _875923, _875925, _875927, _875929] : [-(c_Com_Ocom_Ocom__case(_875907, _875909, _875911, _875913, _875915, _875917, _875919, _875921, _875923, c_Com_Ocom_OCond(_875925, _875927, _875929)) = hAPP(hAPP(hAPP(_875917, _875925), _875927), _875929))], (5937 ^ _780461) ^ [_875976, _875978, _875980, _875982, _875984, _875986, _875988, _875990, _875992, _875994, _875996, _875998] : [-(c_Com_Ocom_Ocom__rec(_875976, _875978, _875980, _875982, _875984, _875986, _875988, _875990, _875992, c_Com_Ocom_OCond(_875994, _875996, _875998)) = hAPP(hAPP(hAPP(hAPP(hAPP(_875986, _875994), _875996), _875998), c_Com_Ocom_Ocom__rec(_875976, _875978, _875980, _875982, _875984, _875986, _875988, _875990, _875992, _875996)), c_Com_Ocom_Ocom__rec(_875976, _875978, _875980, _875982, _875984, _875986, _875988, _875990, _875992, _875998)))], (5939 ^ _780461) ^ [_876073, _876075] : [hBOOL(hAPP(c_Com_OWT, _876073)), hBOOL(hAPP(c_Com_OWT, _876075)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_876073, _876075))))], (5949 ^ _780461) ^ [_876220, _876222, _876224] : [hBOOL(hAPP(c_Com_OWT, _876220)), hBOOL(hAPP(c_Com_OWT, _876222)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_876224, _876220, _876222))))], (5959 ^ _780461) ^ [_876373, _876375, _876377] : [5961 ^ _780461 : [(5962 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_876373)), 5960 ^ [_876373, _876375, _876377]), _876375)))], (5964 ^ _780461) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_876373, hAPP(c_Nat_OSuc, _876377), 5960 ^ [_876373, _876375, _876377])]], 5965 ^ _780461 : [(5966 ^ _780461) ^ [_876546] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_876373)), _876546), _876375)), -(c_Hoare__Mirabelle_Otriple__valid(_876373, _876377, _876546))]]], (5972 ^ _780461) ^ [_876653, _876655, _876657, _876659] : [c_Natural_Oevaln(_876653, _876655, _876657, _876659), -(c_Natural_Oevaln(_876653, _876655, hAPP(c_Nat_OSuc, _876657), _876659))], (5978 ^ _780461) ^ [_876775, _876777, _876779, _876781, _876783, _876785] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_876775, _876777, _876779), _876781, _876783, _876785), 5983 ^ _780461 : [(5984 ^ _780461) ^ [] : [-(hBOOL(hAPP(_876775, _876781)))], (5986 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_876777, _876781, _876783, _876785))]], 5987 ^ _780461 : [(5988 ^ _780461) ^ [] : [hBOOL(hAPP(_876775, _876781))], (5990 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_876779, _876781, _876783, _876785))]]], (5992 ^ _780461) ^ [_877007, _877009, _877011, _877013, _877015, _877017] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_877007, _877009, _877011), _877013, _877015, _877017)), 5993 ^ _780461 : [(5994 ^ _780461) ^ [] : [hBOOL(hAPP(_877007, _877013)), c_Natural_Oevaln(_877009, _877013, _877015, _877017)], (6000 ^ _780461) ^ [] : [-(hBOOL(hAPP(_877007, _877013))), c_Natural_Oevaln(_877011, _877013, _877015, _877017)]]], (6008 ^ _780461) ^ [_877303, _877305, _877307, _877309, _877311, _877313] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_877303, _877305, _877307), _877309, _877311, _877313), 6013 ^ _780461 : [(6014 ^ _780461) ^ [] : [-(hBOOL(hAPP(_877303, _877309)))], (6016 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_877305, _877309, _877311, _877313))]], 6017 ^ _780461 : [(6018 ^ _780461) ^ [] : [hBOOL(hAPP(_877303, _877309))], (6020 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_877307, _877309, _877311, _877313))]]], (6022 ^ _780461) ^ [_877535, _877537, _877539, _877541, _877543, _877545] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_877535, _877537, _877539), _877541, _877543, _877545)), 6023 ^ _780461 : [(6024 ^ _780461) ^ [] : [hBOOL(hAPP(_877535, _877541)), c_Natural_Oevaln(_877537, _877541, _877543, _877545)], (6030 ^ _780461) ^ [] : [-(hBOOL(hAPP(_877535, _877541))), c_Natural_Oevaln(_877539, _877541, _877543, _877545)]]], (6038 ^ _780461) ^ [_877828, _877830, _877832, _877834, _877836] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_877828, _877830), _877832, _877834, _877836), 6042 ^ _780461 : [(6043 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_877828, _877832, _877834, 6041 ^ [_877828, _877830, _877832, _877834, _877836]))], (6045 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_877830, 6041 ^ [_877828, _877830, _877832, _877834, _877836], _877834, _877836))]]], (6047 ^ _780461) ^ [_877982, _877984, _877986, _877988, _877990] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_877982, _877984), _877986, _877988, _877990)), 6048 ^ _780461 : [(6049 ^ _780461) ^ [_878037] : [c_Natural_Oevaln(_877982, _877986, _877988, _878037), c_Natural_Oevaln(_877984, _878037, _877988, _877990)]]], (6057 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (6059 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (6061 ^ _780461) ^ [_878215, _878217, _878219] : [c_Com_Ocom_OCond(_878215, _878217, _878219) = c_Com_Ocom_OSKIP], (6063 ^ _780461) ^ [_878261, _878263, _878265] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_878261, _878263, _878265)], (6065 ^ _780461) ^ [_878304, _878306] : [c_Com_Ocom_OSemi(_878304, _878306) = c_Com_Ocom_OSKIP], (6067 ^ _780461) ^ [_878344, _878346] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_878344, _878346)], (6069 ^ _780461) ^ [_878372, _878374, _878376, _878378, _878380, _878382] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_878372, _878374, _878376, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_878372), _878378), _878380), _878382)) = hAPP(hAPP(hAPP(_878376, _878378), _878380), _878382))], (6071 ^ _780461) ^ [_878430, _878432, _878434, _878436, _878438, _878440] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_878430, _878432, _878434, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_878430), _878436), _878438), _878440)) = hAPP(hAPP(hAPP(_878434, _878436), _878438), _878440))], (6073 ^ _780461) ^ [_878488, _878490, _878492, _878494, _878496] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_878488, _878490), _878492, _878494, _878496), 6077 ^ _780461 : [(6078 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_878488, _878492, _878494, 6076 ^ [_878488, _878490, _878492, _878494, _878496]))], (6080 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_878490, 6076 ^ [_878488, _878490, _878492, _878494, _878496], _878494, _878496))]]], (6082 ^ _780461) ^ [_878659] : [_878659 = hAPP(c_Nat_OSuc, _878659)], (6084 ^ _780461) ^ [_878694] : [hAPP(c_Nat_OSuc, _878694) = _878694], (6086 ^ _780461) ^ [_878735, _878737] : [hAPP(c_Nat_OSuc, _878735) = hAPP(c_Nat_OSuc, _878737), -(_878735 = _878737)], (6092 ^ _780461) ^ [_878820, _878822] : [_878820 = _878822, -(hAPP(c_Nat_OSuc, _878820) = hAPP(c_Nat_OSuc, _878822))], (6098 ^ _780461) ^ [_878911, _878913] : [hAPP(c_Nat_OSuc, _878911) = hAPP(c_Nat_OSuc, _878913), -(_878911 = _878913)], (6104 ^ _780461) ^ [_879000, _879002, _879004] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_879000, _879002, _879004))), -(hBOOL(hAPP(c_Com_OWT, _879004)))], (6110 ^ _780461) ^ [_879095, _879097, _879099, _879101, _879103, _879105, _879107, _879109, _879111, _879113, _879115, _879117] : [-(c_Com_Ocom_Ocom__case(_879095, _879097, _879099, _879101, _879103, _879105, _879107, _879109, _879111, c_Com_Ocom_OCall(_879113, _879115, _879117)) = hAPP(hAPP(hAPP(_879111, _879113), _879115), _879117))], (6112 ^ _780461) ^ [_879164, _879166, _879168, _879170, _879172, _879174, _879176, _879178, _879180, _879182, _879184, _879186] : [-(c_Com_Ocom_Ocom__case(_879164, _879166, _879168, _879170, _879172, _879174, _879176, _879178, _879180, c_Com_Ocom_OLocal(_879182, _879184, _879186)) = hAPP(hAPP(hAPP(_879170, _879182), _879184), _879186))], (6114 ^ _780461) ^ [_879254, _879256, _879258, _879260, _879262] : [c_Com_Ocom_OAss(_879254, _879256) = c_Com_Ocom_OCall(_879258, _879260, _879262)], (6116 ^ _780461) ^ [_879313, _879315, _879317, _879319, _879321] : [c_Com_Ocom_OAss(_879313, _879315) = c_Com_Ocom_OLocal(_879317, _879319, _879321)], (6118 ^ _780461) ^ [_879372, _879374, _879376, _879378, _879380] : [c_Com_Ocom_OCall(_879372, _879374, _879376) = c_Com_Ocom_OAss(_879378, _879380)], (6120 ^ _780461) ^ [_879431, _879433, _879435, _879437, _879439] : [c_Com_Ocom_OLocal(_879431, _879433, _879435) = c_Com_Ocom_OAss(_879437, _879439)], (6122 ^ _780461) ^ [_879493, _879495, _879497, _879499, _879501, _879503] : [c_Com_Ocom_OCall(_879493, _879495, _879497) = c_Com_Ocom_OLocal(_879499, _879501, _879503)], (6124 ^ _780461) ^ [_879558, _879560, _879562, _879564, _879566, _879568] : [c_Com_Ocom_OLocal(_879558, _879560, _879562) = c_Com_Ocom_OCall(_879564, _879566, _879568)], (6126 ^ _780461) ^ [_879620, _879622, _879624, _879626] : [c_Com_Ocom_OAss(_879620, _879622) = c_Com_Ocom_OAss(_879624, _879626), 6129 ^ _780461 : [(6130 ^ _780461) ^ [] : [-(_879620 = _879624)], (6132 ^ _780461) ^ [] : [-(_879622 = _879626)]]], (6134 ^ _780461) ^ [_879735, _879737, _879739, _879741] : [-(c_Com_Ocom_OAss(_879735, _879737) = c_Com_Ocom_OAss(_879739, _879741)), _879735 = _879739, _879737 = _879741], (6144 ^ _780461) ^ [_879913, _879915, _879917, _879919, _879921, _879923] : [c_Com_Ocom_OCall(_879913, _879915, _879917) = c_Com_Ocom_OCall(_879919, _879921, _879923), 6147 ^ _780461 : [(6148 ^ _780461) ^ [] : [-(_879913 = _879919)], (6150 ^ _780461) ^ [] : [-(_879915 = _879921)], (6152 ^ _780461) ^ [] : [-(_879917 = _879923)]]], (6154 ^ _780461) ^ [_880060, _880062, _880064, _880066, _880068, _880070] : [-(c_Com_Ocom_OCall(_880060, _880062, _880064) = c_Com_Ocom_OCall(_880066, _880068, _880070)), _880060 = _880066, _880062 = _880068, _880064 = _880070], (6168 ^ _780461) ^ [_880310, _880312, _880314, _880316, _880318, _880320] : [c_Com_Ocom_OLocal(_880310, _880312, _880314) = c_Com_Ocom_OLocal(_880316, _880318, _880320), 6171 ^ _780461 : [(6172 ^ _780461) ^ [] : [-(_880310 = _880316)], (6174 ^ _780461) ^ [] : [-(_880312 = _880318)], (6176 ^ _780461) ^ [] : [-(_880314 = _880320)]]], (6178 ^ _780461) ^ [_880457, _880459, _880461, _880463, _880465, _880467] : [-(c_Com_Ocom_OLocal(_880457, _880459, _880461) = c_Com_Ocom_OLocal(_880463, _880465, _880467)), _880457 = _880463, _880459 = _880465, _880461 = _880467], (6192 ^ _780461) ^ [_880680, _880682] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_880680, _880682))))], (6194 ^ _780461) ^ [_880710, _880712] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_880710, _880712))))], (6196 ^ _780461) ^ [_880740, _880742, _880744] : [hBOOL(hAPP(c_Com_OWT, _880740)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_880742, _880744, _880740))))], (6202 ^ _780461) ^ [_880853, _880855, _880857] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_880853, _880855, _880857))), -(hBOOL(hAPP(c_Com_OWT, _880857)))], (6208 ^ _780461) ^ [_880944, _880946, _880948] : [hBOOL(hAPP(c_Com_OWT, _880948)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_880944, _880946, _880948))))], (6214 ^ _780461) ^ [_881062, _881064, _881066, _881068, _881070] : [c_Com_Ocom_OCond(_881062, _881064, _881066) = c_Com_Ocom_OAss(_881068, _881070)], (6216 ^ _780461) ^ [_881121, _881123, _881125, _881127, _881129] : [c_Com_Ocom_OAss(_881121, _881123) = c_Com_Ocom_OCond(_881125, _881127, _881129)], (6218 ^ _780461) ^ [_881183, _881185, _881187, _881189, _881191, _881193] : [c_Com_Ocom_OLocal(_881183, _881185, _881187) = c_Com_Ocom_OCond(_881189, _881191, _881193)], (6220 ^ _780461) ^ [_881248, _881250, _881252, _881254, _881256, _881258] : [c_Com_Ocom_OCond(_881248, _881250, _881252) = c_Com_Ocom_OLocal(_881254, _881256, _881258)], (6222 ^ _780461) ^ [_881313, _881315, _881317, _881319, _881321, _881323] : [c_Com_Ocom_OCond(_881313, _881315, _881317) = c_Com_Ocom_OCall(_881319, _881321, _881323)], (6224 ^ _780461) ^ [_881378, _881380, _881382, _881384, _881386, _881388] : [c_Com_Ocom_OCall(_881378, _881380, _881382) = c_Com_Ocom_OCond(_881384, _881386, _881388)], (6226 ^ _780461) ^ [_881437, _881439, _881441, _881443] : [c_Com_Ocom_OSemi(_881437, _881439) = c_Com_Ocom_OAss(_881441, _881443)], (6228 ^ _780461) ^ [_881490, _881492, _881494, _881496] : [c_Com_Ocom_OAss(_881490, _881492) = c_Com_Ocom_OSemi(_881494, _881496)], (6230 ^ _780461) ^ [_881537, _881539] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_881537, _881539)], (6232 ^ _780461) ^ [_881577, _881579] : [c_Com_Ocom_OAss(_881577, _881579) = c_Com_Ocom_OSKIP], (6234 ^ _780461) ^ [_881626, _881628, _881630, _881632, _881634] : [c_Com_Ocom_OLocal(_881626, _881628, _881630) = c_Com_Ocom_OSemi(_881632, _881634)], (6236 ^ _780461) ^ [_881685, _881687, _881689, _881691, _881693] : [c_Com_Ocom_OCall(_881685, _881687, _881689) = c_Com_Ocom_OSemi(_881691, _881693)], (6238 ^ _780461) ^ [_881744, _881746, _881748, _881750, _881752] : [c_Com_Ocom_OSemi(_881744, _881746) = c_Com_Ocom_OLocal(_881748, _881750, _881752)], (6240 ^ _780461) ^ [_881803, _881805, _881807, _881809, _881811] : [c_Com_Ocom_OSemi(_881803, _881805) = c_Com_Ocom_OCall(_881807, _881809, _881811)], (6242 ^ _780461) ^ [_881856, _881858, _881860] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_881856, _881858, _881860)], (6244 ^ _780461) ^ [_881902, _881904, _881906] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_881902, _881904, _881906)], (6246 ^ _780461) ^ [_881948, _881950, _881952] : [c_Com_Ocom_OCall(_881948, _881950, _881952) = c_Com_Ocom_OSKIP], (6248 ^ _780461) ^ [_881994, _881996, _881998] : [c_Com_Ocom_OLocal(_881994, _881996, _881998) = c_Com_Ocom_OSKIP], (6250 ^ _780461) ^ [_882025, _882027, _882029, _882031, _882033, _882035, _882037, _882039, _882041, _882043, _882045] : [-(c_Com_Ocom_Ocom__rec(_882025, _882027, _882029, _882031, _882033, _882035, _882037, _882039, _882041, c_Com_Ocom_OAss(_882043, _882045)) = hAPP(hAPP(_882029, _882043), _882045))], (6252 ^ _780461) ^ [_882088, _882090, _882092, _882094, _882096, _882098, _882100, _882102, _882104, _882106, _882108, _882110] : [-(c_Com_Ocom_Ocom__rec(_882088, _882090, _882092, _882094, _882096, _882098, _882100, _882102, _882104, c_Com_Ocom_OLocal(_882106, _882108, _882110)) = hAPP(hAPP(hAPP(hAPP(_882094, _882106), _882108), _882110), c_Com_Ocom_Ocom__rec(_882088, _882090, _882092, _882094, _882096, _882098, _882100, _882102, _882104, _882110)))], (6254 ^ _780461) ^ [_882171, _882173, _882175, _882177, _882179, _882181, _882183, _882185, _882187, _882189, _882191, _882193] : [-(c_Com_Ocom_Ocom__rec(_882171, _882173, _882175, _882177, _882179, _882181, _882183, _882185, _882187, c_Com_Ocom_OCall(_882189, _882191, _882193)) = hAPP(hAPP(hAPP(_882187, _882189), _882191), _882193))], (6256 ^ _780461) ^ [_882240, _882242, _882244, _882246, _882248, _882250, _882252, _882254, _882256, _882258, _882260] : [-(c_Com_Ocom_Ocom__case(_882240, _882242, _882244, _882246, _882248, _882250, _882252, _882254, _882256, c_Com_Ocom_OAss(_882258, _882260)) = hAPP(hAPP(_882244, _882258), _882260))], (6258 ^ _780461) ^ [_882303, _882305, _882307, _882309] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_882303, _882305), _882307, _882309, hAPP(hAPP(hAPP(c_Natural_Oupdate, _882307), _882303), hAPP(_882305, _882307))))], (6260 ^ _780461) ^ [_882349, _882351, _882353, _882355, _882357] : [c_Natural_Oevaln(c_Com_Ocom_OAss(_882349, _882351), _882353, _882355, _882357), -(_882357 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _882353), _882349), hAPP(_882351, _882353)))], (6266 ^ _780461) ^ [_882466, _882468, _882470] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_882466, _882468, _882470))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _882468))))], (6272 ^ _780461) ^ [_882567, _882569, _882571, _882573] : [class_Rings_Osemiring__1(_882567), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_882567, _882569, hAPP(c_Nat_OSuc, _882571), _882573) = c_Nat_Osemiring__1__class_Oof__nat__aux(_882567, _882569, _882571, hAPP(_882569, _882573)))], (6278 ^ _780461) ^ [_882678, _882680, _882682, _882684] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_882678, _882680), _882682, _882684, hAPP(hAPP(hAPP(c_Natural_Oupdate, _882682), _882678), hAPP(_882680, _882682))))], (6280 ^ _780461) ^ [_882724, _882726, _882728] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _882724))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_882726, _882724, _882728))))], (6286 ^ _780461) ^ [_882843, _882845, _882847] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_882843, _882845, _882847))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _882845))))], (6292 ^ _780461) ^ [_882940, _882942, _882944] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _882942))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_882940, _882942, _882944))))], (6298 ^ _780461) ^ [_883043, _883045, _883047, _883049] : [-(c_Nat_Onat_Onat__case(_883043, _883045, _883047, hAPP(c_Nat_OSuc, _883049)) = hAPP(_883047, _883049))], (6300 ^ _780461) ^ [_883083, _883085, _883087, _883089] : [-(hAPP(c_Nat_Onat_Onat__rec(_883083, _883085, _883087), hAPP(c_Nat_OSuc, _883089)) = hAPP(hAPP(_883087, _883089), hAPP(c_Nat_Onat_Onat__rec(_883083, _883085, _883087), _883089)))], (6302 ^ _780461) ^ [_883135, _883137] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_883135, _883137))), -(hBOOL(hAPP(c_Com_OWT, _883137)))], (6308 ^ _780461) ^ [_883226, _883228, _883230, _883232, _883234, _883236, _883238, _883240, _883242, _883244, _883246] : [-(c_Com_Ocom_Ocom__case(_883226, _883228, _883230, _883232, _883234, _883236, _883238, _883240, _883242, c_Com_Ocom_OWhile(_883244, _883246)) = hAPP(hAPP(_883238, _883244), _883246))], (6310 ^ _780461) ^ [_883285, _883287, _883289, _883291] : [-(hBOOL(hAPP(_883285, _883287))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_883285, _883289), _883287, _883291, _883287))], (6316 ^ _780461) ^ [_883332, _883334, _883336, _883338, _883340, _883342] : [hBOOL(hAPP(_883332, _883334)), c_Natural_Oevaln(_883336, _883334, _883338, _883340), c_Natural_Oevaln(c_Com_Ocom_OWhile(_883332, _883336), _883340, _883338, _883342), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_883332, _883336), _883334, _883338, _883342))], (6330 ^ _780461) ^ [_883586, _883588, _883590, _883592] : [c_Com_Ocom_OWhile(_883586, _883588) = c_Com_Ocom_OWhile(_883590, _883592), 6333 ^ _780461 : [(6334 ^ _780461) ^ [] : [-(_883586 = _883590)], (6336 ^ _780461) ^ [] : [-(_883588 = _883592)]]], (6338 ^ _780461) ^ [_883701, _883703, _883705, _883707] : [-(c_Com_Ocom_OWhile(_883701, _883703) = c_Com_Ocom_OWhile(_883705, _883707)), _883701 = _883705, _883703 = _883707], (6348 ^ _780461) ^ [_883867, _883869] : [hAPP(c_Com_Ocom_OBODY, _883867) = hAPP(c_Com_Ocom_OBODY, _883869), -(_883867 = _883869)], (6354 ^ _780461) ^ [_883952, _883954] : [_883952 = _883954, -(hAPP(c_Com_Ocom_OBODY, _883952) = hAPP(c_Com_Ocom_OBODY, _883954))], (6360 ^ _780461) ^ [_884058, _884060, _884062] : [c_Com_Ocom_OWhile(_884058, _884060) = hAPP(c_Com_Ocom_OBODY, _884062)], (6362 ^ _780461) ^ [_884106, _884108, _884110] : [hAPP(c_Com_Ocom_OBODY, _884106) = c_Com_Ocom_OWhile(_884108, _884110)], (6364 ^ _780461) ^ [_884163, _884165, _884167, _884169, _884171] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_884163, _884165), _884167, _884169, _884171), 6369 ^ _780461 : [(6370 ^ _780461) ^ [] : [-(_884171 = _884167)], (6372 ^ _780461) ^ [] : [hBOOL(hAPP(_884163, _884167))]], 6373 ^ _780461 : [(6374 ^ _780461) ^ [] : [-(hBOOL(hAPP(_884163, _884167)))], (6377 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_884165, _884167, _884169, 6375 ^ [_884163, _884165, _884167, _884169, _884171]))], (6379 ^ _780461) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_884163, _884165), 6375 ^ [_884163, _884165, _884167, _884169, _884171], _884169, _884171))]]], (6381 ^ _780461) ^ [_884448, _884450, _884452, _884454, _884456] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_884448, _884450), _884452, _884454, _884456)), 6382 ^ _780461 : [(6383 ^ _780461) ^ [] : [_884456 = _884452, -(hBOOL(hAPP(_884448, _884452)))], (6389 ^ _780461) ^ [] : [hBOOL(hAPP(_884448, _884452)), 6392 ^ _780461 : [(6393 ^ _780461) ^ [_884658] : [c_Natural_Oevaln(_884450, _884452, _884454, _884658), c_Natural_Oevaln(c_Com_Ocom_OWhile(_884448, _884450), _884658, _884454, _884456)]]]]], (6401 ^ _780461) ^ [_884818, _884820, _884822, _884824] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_884818, _884820), _884822, _884824, _884822), hBOOL(hAPP(_884818, _884822)), 6409 ^ _780461 : [(6410 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_884820, _884822, _884824, 6408 ^ [_884818, _884820, _884822, _884824]))], (6412 ^ _780461) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_884818, _884820), 6408 ^ [_884818, _884820, _884822, _884824], _884824, _884822))]]], (6414 ^ _780461) ^ [_885032, _885034, _885036, _885038] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_885032, _885034), _885036, _885038, _885036)), 6415 ^ _780461 : [(6416 ^ _780461) ^ [] : [-(hBOOL(hAPP(_885032, _885036)))], (6418 ^ _780461) ^ [_885119] : [c_Natural_Oevaln(_885034, _885036, _885038, _885119), c_Natural_Oevaln(c_Com_Ocom_OWhile(_885032, _885034), _885119, _885038, _885036)]]], (6426 ^ _780461) ^ [_885270, _885272, _885274, _885276] : [hAPP(c_Com_Ocom_OBODY, _885270) = c_Com_Ocom_OCond(_885272, _885274, _885276)], (6428 ^ _780461) ^ [_885324, _885326, _885328, _885330] : [c_Com_Ocom_OCond(_885324, _885326, _885328) = hAPP(c_Com_Ocom_OBODY, _885330)], (6430 ^ _780461) ^ [_885375, _885377, _885379] : [c_Com_Ocom_OAss(_885375, _885377) = hAPP(c_Com_Ocom_OBODY, _885379)], (6432 ^ _780461) ^ [_885423, _885425, _885427] : [hAPP(c_Com_Ocom_OBODY, _885423) = c_Com_Ocom_OAss(_885425, _885427)], (6434 ^ _780461) ^ [_885471, _885473] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_885471, _885473))), -(hBOOL(hAPP(c_Com_OWT, _885473)))], (6440 ^ _780461) ^ [_885558, _885560] : [hBOOL(hAPP(c_Com_OWT, _885560)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_885558, _885560))))], (6446 ^ _780461) ^ [_885651, _885653] : [hBOOL(hAPP(c_Com_OWT, _885651)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_885653, _885651))))], (6452 ^ _780461) ^ [_885757, _885759, _885761] : [hAPP(c_Com_Ocom_OBODY, _885757) = c_Com_Ocom_OSemi(_885759, _885761)], (6454 ^ _780461) ^ [_885805, _885807, _885809] : [c_Com_Ocom_OSemi(_885805, _885807) = hAPP(c_Com_Ocom_OBODY, _885809)], (6456 ^ _780461) ^ [_885856, _885858, _885860, _885862] : [c_Com_Ocom_OLocal(_885856, _885858, _885860) = hAPP(c_Com_Ocom_OBODY, _885862)], (6458 ^ _780461) ^ [_885910, _885912, _885914, _885916] : [c_Com_Ocom_OCall(_885910, _885912, _885914) = hAPP(c_Com_Ocom_OBODY, _885916)], (6460 ^ _780461) ^ [_885964, _885966, _885968, _885970] : [hAPP(c_Com_Ocom_OBODY, _885964) = c_Com_Ocom_OLocal(_885966, _885968, _885970)], (6462 ^ _780461) ^ [_886018, _886020, _886022, _886024] : [hAPP(c_Com_Ocom_OBODY, _886018) = c_Com_Ocom_OCall(_886020, _886022, _886024)], (6464 ^ _780461) ^ [_886063] : [hAPP(c_Com_Ocom_OBODY, _886063) = c_Com_Ocom_OSKIP], (6466 ^ _780461) ^ [_886098] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _886098)], (6468 ^ _780461) ^ [_886145, _886147, _886149, _886151, _886153] : [c_Com_Ocom_OWhile(_886145, _886147) = c_Com_Ocom_OCond(_886149, _886151, _886153)], (6470 ^ _780461) ^ [_886204, _886206, _886208, _886210, _886212] : [c_Com_Ocom_OCond(_886204, _886206, _886208) = c_Com_Ocom_OWhile(_886210, _886212)], (6472 ^ _780461) ^ [_886260, _886262, _886264, _886266] : [c_Com_Ocom_OWhile(_886260, _886262) = c_Com_Ocom_OAss(_886264, _886266)], (6474 ^ _780461) ^ [_886313, _886315, _886317, _886319] : [c_Com_Ocom_OAss(_886313, _886315) = c_Com_Ocom_OWhile(_886317, _886319)], (6476 ^ _780461) ^ [_886366, _886368, _886370, _886372] : [c_Com_Ocom_OSemi(_886366, _886368) = c_Com_Ocom_OWhile(_886370, _886372)], (6478 ^ _780461) ^ [_886419, _886421, _886423, _886425] : [c_Com_Ocom_OWhile(_886419, _886421) = c_Com_Ocom_OSemi(_886423, _886425)], (6480 ^ _780461) ^ [_886475, _886477, _886479, _886481, _886483] : [c_Com_Ocom_OLocal(_886475, _886477, _886479) = c_Com_Ocom_OWhile(_886481, _886483)], (6482 ^ _780461) ^ [_886534, _886536, _886538, _886540, _886542] : [c_Com_Ocom_OCall(_886534, _886536, _886538) = c_Com_Ocom_OWhile(_886540, _886542)], (6484 ^ _780461) ^ [_886593, _886595, _886597, _886599, _886601] : [c_Com_Ocom_OWhile(_886593, _886595) = c_Com_Ocom_OLocal(_886597, _886599, _886601)], (6486 ^ _780461) ^ [_886652, _886654, _886656, _886658, _886660] : [c_Com_Ocom_OWhile(_886652, _886654) = c_Com_Ocom_OCall(_886656, _886658, _886660)], (6488 ^ _780461) ^ [_886702, _886704] : [c_Com_Ocom_OWhile(_886702, _886704) = c_Com_Ocom_OSKIP], (6490 ^ _780461) ^ [_886742, _886744] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_886742, _886744)], (6492 ^ _780461) ^ [_886770, _886772, _886774, _886776, _886778, _886780, _886782, _886784, _886786, _886788] : [-(c_Com_Ocom_Ocom__rec(_886770, _886772, _886774, _886776, _886778, _886780, _886782, _886784, _886786, hAPP(c_Com_Ocom_OBODY, _886788)) = hAPP(_886784, _886788))], (6494 ^ _780461) ^ [_886828, _886830, _886832, _886834, _886836, _886838, _886840, _886842, _886844, _886846, _886848] : [-(c_Com_Ocom_Ocom__rec(_886828, _886830, _886832, _886834, _886836, _886838, _886840, _886842, _886844, c_Com_Ocom_OWhile(_886846, _886848)) = hAPP(hAPP(hAPP(_886840, _886846), _886848), c_Com_Ocom_Ocom__rec(_886828, _886830, _886832, _886834, _886836, _886838, _886840, _886842, _886844, _886848)))], (6496 ^ _780461) ^ [_886905, _886907, _886909, _886911, _886913, _886915, _886917, _886919, _886921, _886923] : [-(c_Com_Ocom_Ocom__case(_886905, _886907, _886909, _886911, _886913, _886915, _886917, _886919, _886921, hAPP(c_Com_Ocom_OBODY, _886923)) = hAPP(_886919, _886923))], (6498 ^ _780461) ^ [_886963, _886965, _886967, _886969] : [-(c_Hoare__Mirabelle_Otriple__valid(_886963, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_886963), _886965), hAPP(c_Com_Ocom_OBODY, _886967)), _886969)))], (6500 ^ _780461) ^ [_887031, _887033, _887035, _887037, _887039] : [c_Hoare__Mirabelle_Otriple__valid(_887031, _887033, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_887031), _887035), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _887037))), _887039)), -(c_Hoare__Mirabelle_Otriple__valid(_887031, hAPP(c_Nat_OSuc, _887033), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_887031), _887035), hAPP(c_Com_Ocom_OBODY, _887037)), _887039)))], (6506 ^ _780461) ^ [_887182, _887184, _887186, _887188, _887190] : [c_Hoare__Mirabelle_Otriple__valid(_887182, hAPP(c_Nat_OSuc, _887184), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_887182), _887186), hAPP(c_Com_Ocom_OBODY, _887188)), _887190)), -(c_Hoare__Mirabelle_Otriple__valid(_887182, _887184, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_887182), _887186), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _887188))), _887190)))], (6512 ^ _780461) ^ [_887339, _887341, _887343, _887345, _887347] : [hAPP(_887339, 6513 ^ [_887339, _887341, _887343, _887345, _887347]) = hAPP(c_Nat_Onat_Onat__rec(_887341, _887343, _887345), 6513 ^ [_887339, _887341, _887343, _887345, _887347]), -(hAPP(_887339, hAPP(c_Nat_OSuc, _887347)) = hAPP(hAPP(_887345, _887347), hAPP(_887339, _887347)))], (6519 ^ _780461) ^ [_887531, _887533, _887535, _887537] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_887531, _887533)), _887535), _887537)), -(_887537 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _887535), _887531), hAPP(_887533, _887535)))], (6525 ^ _780461) ^ [_887656, _887658, _887660] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_887656, _887658)), _887660), hAPP(hAPP(hAPP(c_Natural_Oupdate, _887660), _887656), hAPP(_887658, _887660)))))], (6527 ^ _780461) ^ [_887705, _887707, _887709, _887711, _887713] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_887705, _887707), _887709, _887711, _887713), 6532 ^ _780461 : [(6533 ^ _780461) ^ [] : [-(_887713 = _887709)], (6535 ^ _780461) ^ [] : [hBOOL(hAPP(_887705, _887709))]], 6536 ^ _780461 : [(6537 ^ _780461) ^ [] : [-(hBOOL(hAPP(_887705, _887709)))], (6540 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_887707, _887709, _887711, 6538 ^ [_887705, _887707, _887709, _887711, _887713]))], (6542 ^ _780461) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_887705, _887707), 6538 ^ [_887705, _887707, _887709, _887711, _887713], _887711, _887713))]]], (6544 ^ _780461) ^ [_887996, _887998, _888000, _888002] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _887996)), _887998, _888000, _888002), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _887996), _887998, hAPP(c_Nat_OSuc, _888000), _888002))], (6550 ^ _780461) ^ [_888109, _888111, _888113] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_888109, _888111)), _888113), hAPP(hAPP(hAPP(c_Natural_Oupdate, _888113), _888109), hAPP(_888111, _888113)))))], (6552 ^ _780461) ^ [_888158, _888160, _888162, _888164, _888166, _888168] : [c_Natural_Oevaln(_888158, hAPP(hAPP(hAPP(c_Natural_Oupdate, _888160), c_Com_Ovname_OLoc(_888162)), hAPP(_888164, _888160)), _888166, _888168), -(c_Natural_Oevaln(c_Com_Ocom_OLocal(_888162, _888164, _888158), _888160, _888166, hAPP(hAPP(hAPP(c_Natural_Oupdate, _888168), c_Com_Ovname_OLoc(_888162)), hAPP(hAPP(c_Natural_Ogetlocs, _888160), _888162))))], (6558 ^ _780461) ^ [_888342, _888344, _888346, _888348] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _888342), _888344, hAPP(c_Nat_OSuc, _888346), _888348), -(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _888342)), _888344, _888346, _888348))], (6564 ^ _780461) ^ [_888451, _888453, _888455, _888457] : [c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _888451)), _888453, _888455, _888457), -(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _888451), _888453, hAPP(c_Nat_OSuc, _888455), _888457))], (6570 ^ _780461) ^ [_888593, _888595, _888597, _888599, _888601, _888603] : [c_Natural_Oevaln(c_Com_Ocom_OLocal(_888593, _888595, _888597), _888599, _888601, hAPP(hAPP(hAPP(c_Natural_Oupdate, _888603), c_Com_Ovname_OLoc(_888593)), hAPP(hAPP(c_Natural_Ogetlocs, _888599), _888593))), 6574 ^ _780461 : [(6575 ^ _780461) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _888603), c_Com_Ovname_OLoc(_888593)), hAPP(hAPP(c_Natural_Ogetlocs, _888599), _888593)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6573 ^ [_888593, _888595, _888597, _888599, _888601, _888603]), c_Com_Ovname_OLoc(_888593)), hAPP(hAPP(c_Natural_Ogetlocs, _888599), _888593)))], (6577 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_888597, hAPP(hAPP(hAPP(c_Natural_Oupdate, _888599), c_Com_Ovname_OLoc(_888593)), hAPP(_888595, _888599)), _888601, 6573 ^ [_888593, _888595, _888597, _888599, _888601, _888603]))]]], (6579 ^ _780461) ^ [_888881, _888883, _888885, _888887, _888889, _888891] : [-(c_Natural_Oevaln(c_Com_Ocom_OLocal(_888881, _888883, _888885), _888887, _888889, hAPP(hAPP(hAPP(c_Natural_Oupdate, _888891), c_Com_Ovname_OLoc(_888881)), hAPP(hAPP(c_Natural_Ogetlocs, _888887), _888881)))), 6580 ^ _780461 : [(6581 ^ _780461) ^ [_889002] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _888891), c_Com_Ovname_OLoc(_888881)), hAPP(hAPP(c_Natural_Ogetlocs, _888887), _888881)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _889002), c_Com_Ovname_OLoc(_888881)), hAPP(hAPP(c_Natural_Ogetlocs, _888887), _888881)), c_Natural_Oevaln(_888885, hAPP(hAPP(hAPP(c_Natural_Oupdate, _888887), c_Com_Ovname_OLoc(_888881)), hAPP(_888883, _888887)), _888889, _889002)]]], (6589 ^ _780461) ^ [_889237, _889239, _889241] : [-(hBOOL(hAPP(_889237, _889239))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_889237, _889241)), _889239), _889239)))], (6595 ^ _780461) ^ [_889287, _889289, _889291, _889293, _889295] : [hBOOL(hAPP(_889287, _889289)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889291), _889289), _889293)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_889287, _889291)), _889293), _889295)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_889287, _889291)), _889289), _889295)))], (6609 ^ _780461) ^ [_889544, _889546, _889548, _889550, _889552] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_889544, _889546, _889548)), _889550), _889552)), 6614 ^ _780461 : [(6615 ^ _780461) ^ [] : [-(hBOOL(hAPP(_889544, _889550)))], (6617 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889546), _889550), _889552)))]], 6618 ^ _780461 : [(6619 ^ _780461) ^ [] : [hBOOL(hAPP(_889544, _889550))], (6621 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889548), _889550), _889552)))]]], (6623 ^ _780461) ^ [_889812, _889814, _889816, _889818, _889820] : [hBOOL(hAPP(_889812, _889814)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889816), _889814), _889818)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_889812, _889816, _889820)), _889814), _889818)))], (6633 ^ _780461) ^ [_889992, _889994, _889996, _889998, _890000] : [-(hBOOL(hAPP(_889992, _889994))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889996), _889994), _889998)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_889992, _890000, _889996)), _889994), _889998)))], (6643 ^ _780461) ^ [_890169, _890171, _890173, _890175, _890177] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890169), _890171), _890173)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890175), _890173), _890177)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_890169, _890175)), _890171), _890177)))], (6653 ^ _780461) ^ [_890358] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _890358), _890358)))], (6655 ^ _780461) ^ [_890386, _890388] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _890386), _890388)), -(_890388 = _890386)], (6661 ^ _780461) ^ [_890473, _890475, _890477] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _890473)), _890475), _890477)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _890473))), _890475), _890477)))], (6667 ^ _780461) ^ [_890598, _890600, _890602] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _890598))), _890600), _890602)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _890598)), _890600), _890602)))], (6673 ^ _780461) ^ [_890723, _890725, _890727, _890729, _890731] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890723), hAPP(hAPP(hAPP(c_Natural_Oupdate, _890725), c_Com_Ovname_OLoc(_890727)), hAPP(_890729, _890725))), _890731)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_890727, _890729, _890723)), _890725), hAPP(hAPP(hAPP(c_Natural_Oupdate, _890731), c_Com_Ovname_OLoc(_890727)), hAPP(hAPP(c_Natural_Ogetlocs, _890725), _890727)))))], (6679 ^ _780461) ^ [_890919, _890921] : [c_Com_Ovname_OLoc(_890919) = c_Com_Ovname_OLoc(_890921), -(_890919 = _890921)], (6685 ^ _780461) ^ [_891000, _891002] : [_891000 = _891002, -(c_Com_Ovname_OLoc(_891000) = c_Com_Ovname_OLoc(_891002))], (6691 ^ _780461) ^ [_891087, _891089, _891091, _891093] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891087), _891089), _891091)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891087), _891089), _891093)), -(_891093 = _891091)], (6701 ^ _780461) ^ [_891270, _891272, _891274] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _891270)), _891272), _891274)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _891270))), _891272), _891274)))], (6707 ^ _780461) ^ [_891391, _891393, _891395] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _891391))), _891393), _891395)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _891391)), _891393), _891395)))], (6713 ^ _780461) ^ [_891542, _891544, _891546, _891548, _891550] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_891542, _891544, _891546)), _891548), hAPP(hAPP(hAPP(c_Natural_Oupdate, _891550), c_Com_Ovname_OLoc(_891542)), hAPP(hAPP(c_Natural_Ogetlocs, _891548), _891542)))), 6717 ^ _780461 : [(6718 ^ _780461) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _891550), c_Com_Ovname_OLoc(_891542)), hAPP(hAPP(c_Natural_Ogetlocs, _891548), _891542)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6716 ^ [_891542, _891544, _891546, _891548, _891550]), c_Com_Ovname_OLoc(_891542)), hAPP(hAPP(c_Natural_Ogetlocs, _891548), _891542)))], (6720 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891546), hAPP(hAPP(hAPP(c_Natural_Oupdate, _891548), c_Com_Ovname_OLoc(_891542)), hAPP(_891544, _891548))), 6716 ^ [_891542, _891544, _891546, _891548, _891550])))]]], (6722 ^ _780461) ^ [_891844, _891846, _891848, _891850, _891852] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_891844, _891846, _891848)), _891850), hAPP(hAPP(hAPP(c_Natural_Oupdate, _891852), c_Com_Ovname_OLoc(_891844)), hAPP(hAPP(c_Natural_Ogetlocs, _891850), _891844))))), 6723 ^ _780461 : [(6724 ^ _780461) ^ [_891973] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _891852), c_Com_Ovname_OLoc(_891844)), hAPP(hAPP(c_Natural_Ogetlocs, _891850), _891844)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _891973), c_Com_Ovname_OLoc(_891844)), hAPP(hAPP(c_Natural_Ogetlocs, _891850), _891844)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891848), hAPP(hAPP(hAPP(c_Natural_Oupdate, _891850), c_Com_Ovname_OLoc(_891844)), hAPP(_891846, _891850))), _891973))]]], (6732 ^ _780461) ^ [_892234] : [hAPP(c_Nat_OSuc, _892234) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6734 ^ _780461) ^ [_892269] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _892269)], (6736 ^ _780461) ^ [_892304] : [hAPP(c_Nat_OSuc, _892304) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6738 ^ _780461) ^ [_892339] : [hAPP(c_Nat_OSuc, _892339) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6740 ^ _780461) ^ [_892374] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _892374)], (6742 ^ _780461) ^ [_892409] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _892409)], (6744 ^ _780461) ^ [_892453, _892455, _892457] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_892453), _892455), _892457)), -(c_Natural_Oevaln(_892453, _892455, 6747 ^ [_892453, _892455, _892457], _892457))], (6751 ^ _780461) ^ [_892560, _892562, _892564] : [6752 ^ _780461 : [(6753 ^ _780461) ^ [_892610] : [c_Natural_Oevaln(_892560, _892562, _892610, _892564)]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_892560), _892562), _892564)))], (6757 ^ _780461) ^ [_892672, _892674, _892676, _892678] : [c_Natural_Oevaln(_892672, _892674, _892676, _892678), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_892672), _892674), _892678)))], (6763 ^ _780461) ^ [_892789, _892791, _892793] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_892789, _892791)), _892793), _892793)), hBOOL(hAPP(_892789, _892793)), 6771 ^ _780461 : [(6772 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_892791), _892793), 6770 ^ [_892789, _892791, _892793])))], (6774 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_892789, _892791)), 6770 ^ [_892789, _892791, _892793]), _892793)))]]], (6776 ^ _780461) ^ [_893025, _893027, _893029] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893025, _893027)), _893029), _893029))), 6777 ^ _780461 : [(6778 ^ _780461) ^ [] : [-(hBOOL(hAPP(_893025, _893029)))], (6780 ^ _780461) ^ [_893125] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_893027), _893029), _893125)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893025, _893027)), _893125), _893029))]]], (6788 ^ _780461) ^ [_893302, _893304, _893306, _893308] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893302, _893304)), _893306), _893308)), 6793 ^ _780461 : [(6794 ^ _780461) ^ [] : [-(_893308 = _893306)], (6796 ^ _780461) ^ [] : [hBOOL(hAPP(_893302, _893306))]], 6797 ^ _780461 : [(6798 ^ _780461) ^ [] : [-(hBOOL(hAPP(_893302, _893306)))], (6801 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_893304), _893306), 6799 ^ [_893302, _893304, _893306, _893308])))], (6803 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893302, _893304)), 6799 ^ [_893302, _893304, _893306, _893308]), _893308)))]]], (6805 ^ _780461) ^ [_893609, _893611, _893613, _893615] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893609, _893611)), _893613), _893615))), 6806 ^ _780461 : [(6807 ^ _780461) ^ [] : [_893615 = _893613, -(hBOOL(hAPP(_893609, _893613)))], (6813 ^ _780461) ^ [] : [hBOOL(hAPP(_893609, _893613)), 6816 ^ _780461 : [(6817 ^ _780461) ^ [_893828] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_893611), _893613), _893828)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893609, _893611)), _893828), _893615))]]]]], (6825 ^ _780461) ^ [_894014, _894016, _894018, _894020, _894022] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_894014, _894016, _894018)), _894020), _894022)), 6830 ^ _780461 : [(6831 ^ _780461) ^ [] : [-(hBOOL(hAPP(_894014, _894020)))], (6833 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894016), _894020), _894022)))]], 6834 ^ _780461 : [(6835 ^ _780461) ^ [] : [hBOOL(hAPP(_894014, _894020))], (6837 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894018), _894020), _894022)))]]], (6839 ^ _780461) ^ [_894272, _894274, _894276, _894278, _894280] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_894272, _894274, _894276)), _894278), _894280))), 6840 ^ _780461 : [(6841 ^ _780461) ^ [] : [hBOOL(hAPP(_894272, _894278)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894274), _894278), _894280))], (6847 ^ _780461) ^ [] : [-(hBOOL(hAPP(_894272, _894278))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894276), _894278), _894280))]]], (6855 ^ _780461) ^ [_894589, _894591, _894593, _894595, _894597] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_894589, _894591, _894593)), _894595), _894597)), 6860 ^ _780461 : [(6861 ^ _780461) ^ [] : [-(hBOOL(hAPP(_894589, _894595)))], (6863 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894591), _894595), _894597)))]], 6864 ^ _780461 : [(6865 ^ _780461) ^ [] : [hBOOL(hAPP(_894589, _894595))], (6867 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894593), _894595), _894597)))]]], (6869 ^ _780461) ^ [_894847, _894849, _894851, _894853, _894855] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_894847, _894849, _894851)), _894853), _894855))), 6870 ^ _780461 : [(6871 ^ _780461) ^ [] : [hBOOL(hAPP(_894847, _894853)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894849), _894853), _894855))], (6877 ^ _780461) ^ [] : [-(hBOOL(hAPP(_894847, _894853))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894851), _894853), _894855))]]], (6885 ^ _780461) ^ [_895161, _895163, _895165, _895167] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_895161, _895163)), _895165), _895167)), 6889 ^ _780461 : [(6890 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895161), _895165), 6888 ^ [_895161, _895163, _895165, _895167])))], (6892 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895163), 6888 ^ [_895161, _895163, _895165, _895167]), _895167)))]]], (6894 ^ _780461) ^ [_895339, _895341, _895343, _895345] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_895339, _895341)), _895343), _895345))), 6895 ^ _780461 : [(6896 ^ _780461) ^ [_895407] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895339), _895343), _895407)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895341), _895407), _895345))]]], (6904 ^ _780461) ^ [_895557] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _895557), _895557)))], (6906 ^ _780461) ^ [_895585, _895587, _895589] : [-(c_Nat_Onat_Onat__case(_895585, _895587, _895589, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _895587)], (6908 ^ _780461) ^ [_895617, _895619, _895621] : [-(hAPP(c_Nat_Onat_Onat__rec(_895617, _895619, _895621), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _895619)], (6910 ^ _780461) ^ [_895651, _895653, _895655] : [class_Rings_Osemiring__1(_895651), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_895651, _895653, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _895655) = _895655)], (6916 ^ _780461) ^ [_895738, _895740, _895742, _895744, _895746] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_895738, _895740, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_895738), _895742), _895744), _895746)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6918 ^ _780461) ^ [_895784] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(_895784)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6920 ^ _780461) ^ [_895811, _895813, _895815, _895817] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_895811)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_895811), _895813), _895815), _895817)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6922 ^ _780461) ^ [_895858, _895860, _895862, _895864] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _895858), _895860, _895862, _895864), 6926 ^ _780461 : [(6927 ^ _780461) ^ [] : [-(_895862 = hAPP(c_Nat_OSuc, 6925 ^ [_895858, _895860, _895862, _895864]))], (6929 ^ _780461) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _895858)), _895860, 6925 ^ [_895858, _895860, _895862, _895864], _895864))]]], (6931 ^ _780461) ^ [_896028, _896030, _896032, _896034, _896036] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_896028, _896030, _896032)), _896034), _896036)), 6935 ^ _780461 : [(6936 ^ _780461) ^ [] : [-(_896036 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6934 ^ [_896028, _896030, _896032, _896034, _896036]), c_Com_Ovname_OLoc(_896028)), hAPP(hAPP(c_Natural_Ogetlocs, _896034), _896028)))], (6938 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_896032), hAPP(hAPP(hAPP(c_Natural_Oupdate, _896034), c_Com_Ovname_OLoc(_896028)), hAPP(_896030, _896034))), 6934 ^ [_896028, _896030, _896032, _896034, _896036])))]]], (6940 ^ _780461) ^ [_896270, _896272, _896274, _896276, _896278, _896280] : [c_Natural_Oevaln(c_Com_Ocom_OLocal(_896270, _896272, _896274), _896276, _896278, _896280), 6944 ^ _780461 : [(6945 ^ _780461) ^ [] : [-(_896280 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6943 ^ [_896270, _896272, _896274, _896276, _896278, _896280]), c_Com_Ovname_OLoc(_896270)), hAPP(hAPP(c_Natural_Ogetlocs, _896276), _896270)))], (6947 ^ _780461) ^ [] : [-(c_Natural_Oevaln(_896274, hAPP(hAPP(hAPP(c_Natural_Oupdate, _896276), c_Com_Ovname_OLoc(_896270)), hAPP(_896272, _896276)), _896278, 6943 ^ [_896270, _896272, _896274, _896276, _896278, _896280]))]]], (6949 ^ _780461) ^ [_896498] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OLoc(_896498)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6951 ^ _780461) ^ [_896526, _896528, _896530, _896532] : [-(c_Com_Ovname_Ovname__rec(_896526, _896528, _896530, c_Com_Ovname_OLoc(_896532)) = hAPP(_896530, _896532))], (6953 ^ _780461) ^ [_896565, _896567, _896569, _896571] : [-(c_Com_Ovname_Ovname__case(_896565, _896567, _896569, c_Com_Ovname_OLoc(_896571)) = hAPP(_896569, _896571))], (6955 ^ _780461) ^ [_896604, _896606, _896608, _896610] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_896604, _896606)), _896608), _896610)), 6959 ^ _780461 : [(6960 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_896604), _896608), 6958 ^ [_896604, _896606, _896608, _896610])))], (6962 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_896606), 6958 ^ [_896604, _896606, _896608, _896610]), _896610)))]]], (6964 ^ _780461) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6966 ^ _780461) ^ [_896808] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _896808)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6968 ^ _780461) ^ [_896836, _896838] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_896836, _896838)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6970 ^ _780461) ^ [_896866, _896868, _896870] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_896866, _896868, _896870)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6972 ^ _780461) ^ [_896899] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OGlb(_896899)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6974 ^ _780461) ^ [_896927] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(_896927)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6976 ^ _780461) ^ [_896954, _896956] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_896954, _896956)) = 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(_896954)), c_Com_Ocom_Ocom__size(_896956))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6978 ^ _780461) ^ [_897000, _897002, _897004] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_897000, _897002, _897004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_897004)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6980 ^ _780461) ^ [_897041, _897043, _897045] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_897041, _897043, _897045)) = 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(_897043)), c_Com_Ocom_Ocom__size(_897045))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6982 ^ _780461) ^ [_897090, _897092] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_897090, _897092)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_897092)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6984 ^ _780461) ^ [_897128, _897130, _897132, _897134] : [-(c_Com_Ovname_Ovname__case(_897128, _897130, _897132, c_Com_Ovname_OGlb(_897134)) = hAPP(_897130, _897134))], (6986 ^ _780461) ^ [_897167, _897169, _897171, _897173] : [-(c_Com_Ovname_Ovname__rec(_897167, _897169, _897171, c_Com_Ovname_OGlb(_897173)) = hAPP(_897169, _897173))], (6988 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6990 ^ _780461) ^ [_897224, _897226, _897228] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_897224, _897226, _897228)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6992 ^ _780461) ^ [_897258, _897260] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_897258, _897260)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6994 ^ _780461) ^ [_897289, _897291] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897289), _897291) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897291), _897289))], (6996 ^ _780461) ^ [_897326, _897328, _897330] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897326), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897328), _897330)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897328), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897326), _897330)))], (6998 ^ _780461) ^ [_897377, _897379, _897381] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897377), _897379)), _897381) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897379), _897381)))], (7000 ^ _780461) ^ [_897446, _897448, _897450] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897446), _897448) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897446), _897450), -(_897448 = _897450)], (7006 ^ _780461) ^ [_897545, _897547, _897549] : [_897547 = _897549, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897545), _897547) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897545), _897549))], (7012 ^ _780461) ^ [_897668, _897670, _897672] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897668), _897670) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897672), _897670), -(_897668 = _897672)], (7018 ^ _780461) ^ [_897767, _897769, _897771] : [_897767 = _897771, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897767), _897769) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _897771), _897769))], (7024 ^ _780461) ^ [_897887, _897889] : [c_Com_Ovname_OGlb(_897887) = c_Com_Ovname_OGlb(_897889), -(_897887 = _897889)], (7030 ^ _780461) ^ [_897968, _897970] : [_897968 = _897970, -(c_Com_Ovname_OGlb(_897968) = c_Com_Ovname_OGlb(_897970))], (7036 ^ _780461) ^ [_898055] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _898055) = _898055)], (7038 ^ _780461) ^ [_898081] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898081), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _898081)], (7040 ^ _780461) ^ [_898125, _898127] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898125), _898127) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 7043 ^ _780461 : [(7044 ^ _780461) ^ [] : [-(_898125 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7046 ^ _780461) ^ [] : [-(_898127 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7048 ^ _780461) ^ [_898236, _898238] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898236), _898238) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _898236 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _898238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7058 ^ _780461) ^ [_898379, _898381] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898379), _898381) = _898379, -(_898381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7064 ^ _780461) ^ [_898468, _898470] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _898468)), _898470) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898468), hAPP(c_Nat_OSuc, _898470)))], (7066 ^ _780461) ^ [_898511, _898513] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _898511)), _898513) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898511), _898513)))], (7068 ^ _780461) ^ [_898554, _898556] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898554), hAPP(c_Nat_OSuc, _898556)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898554), _898556)))], (7070 ^ _780461) ^ [_898597, _898599] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_898597, _898599)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _898599)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7072 ^ _780461) ^ [_898637, _898639, _898641] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_898637, _898639, _898641)) = 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), _898639)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _898641))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7074 ^ _780461) ^ [_898689, _898691, _898693] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_898689, _898691, _898693)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _898693)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7076 ^ _780461) ^ [_898732, _898734] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_898732, _898734)) = 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), _898732)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _898734))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7078 ^ _780461) ^ [_898796, _898798] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898796), _898798), 7083 ^ _780461 : [(7084 ^ _780461) ^ [] : [-(_898796 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7086 ^ _780461) ^ [] : [-(_898798 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7087 ^ _780461 : [(7088 ^ _780461) ^ [] : [-(_898796 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7090 ^ _780461) ^ [] : [-(_898798 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7092 ^ _780461) ^ [_898980, _898982] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898980), _898982)), 7093 ^ _780461 : [(7094 ^ _780461) ^ [] : [_898980 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _898982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7100 ^ _780461) ^ [] : [_898980 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _898982 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7108 ^ _780461) ^ [_899221, _899223] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899221), _899223) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7113 ^ _780461 : [(7114 ^ _780461) ^ [] : [-(_899221 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7116 ^ _780461) ^ [] : [-(_899223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7117 ^ _780461 : [(7118 ^ _780461) ^ [] : [-(_899221 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7120 ^ _780461) ^ [] : [-(_899223 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7122 ^ _780461) ^ [_899405, _899407] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899405), _899407) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7123 ^ _780461 : [(7124 ^ _780461) ^ [] : [_899405 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _899407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7130 ^ _780461) ^ [] : [_899405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _899407 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7138 ^ _780461) ^ [_899643, _899645] : [c_Com_Ovname_OGlb(_899643) = c_Com_Ovname_OLoc(_899645)], (7140 ^ _780461) ^ [_899684, _899686] : [c_Com_Ovname_OLoc(_899684) = c_Com_Ovname_OGlb(_899686)], (7142 ^ _780461) ^ [_899713] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _899713)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7144 ^ _780461) ^ [_899742, _899744] : [class_Groups_Olinordered__ab__group__add(_899742), 7147 ^ _780461 : [(7148 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899742), _899744), _899744) = c_Groups_Ozero__class_Ozero(_899742), -(_899744 = c_Groups_Ozero__class_Ozero(_899742))], (7154 ^ _780461) ^ [] : [_899744 = c_Groups_Ozero__class_Ozero(_899742), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899742), _899744), _899744) = c_Groups_Ozero__class_Ozero(_899742))]]], (7160 ^ _780461) ^ [_899983, _899985, _899987] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_899983), 7163 ^ _780461 : [(7164 ^ _780461) ^ [] : [_899985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899983), _899985), _899987), -(_899987 = c_Groups_Ozero__class_Ozero(_899983))], (7170 ^ _780461) ^ [] : [_899987 = c_Groups_Ozero__class_Ozero(_899983), -(_899985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899983), _899985), _899987))]]], (7176 ^ _780461) ^ [_900224, _900226] : [class_Groups_Ocomm__monoid__add(_900224), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900224), _900226), c_Groups_Ozero__class_Ozero(_900224)) = _900226)], (7182 ^ _780461) ^ [_900319, _900321] : [class_Rings_Ocomm__semiring__1(_900319), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900319), _900321), c_Groups_Ozero__class_Ozero(_900319)) = _900321)], (7188 ^ _780461) ^ [_900414, _900416] : [class_Groups_Omonoid__add(_900414), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900414), _900416), c_Groups_Ozero__class_Ozero(_900414)) = _900416)], (7194 ^ _780461) ^ [_900509, _900511] : [class_Groups_Olinordered__ab__group__add(_900509), 7197 ^ _780461 : [(7198 ^ _780461) ^ [] : [c_Groups_Ozero__class_Ozero(_900509) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900509), _900511), _900511), -(_900511 = c_Groups_Ozero__class_Ozero(_900509))], (7204 ^ _780461) ^ [] : [_900511 = c_Groups_Ozero__class_Ozero(_900509), -(c_Groups_Ozero__class_Ozero(_900509) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900509), _900511), _900511))]]], (7210 ^ _780461) ^ [_900750, _900752] : [class_Groups_Ocomm__monoid__add(_900750), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900750), c_Groups_Ozero__class_Ozero(_900750)), _900752) = _900752)], (7216 ^ _780461) ^ [_900845, _900847] : [class_Rings_Ocomm__semiring__1(_900845), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900845), c_Groups_Ozero__class_Ozero(_900845)), _900847) = _900847)], (7222 ^ _780461) ^ [_900940, _900942] : [class_Groups_Omonoid__add(_900940), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900940), c_Groups_Ozero__class_Ozero(_900940)), _900942) = _900942)], (7228 ^ _780461) ^ [_901035] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _901035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_901035)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7230 ^ _780461) ^ [_901071] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _901071)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _901071)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7232 ^ _780461) ^ [_901109] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _901109) = _901109)], (7234 ^ _780461) ^ [] : [-(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))], (7236 ^ _780461) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7238 ^ _780461) ^ [_901171, _901173] : [class_Groups_Ozero(_901171), 7241 ^ _780461 : [(7242 ^ _780461) ^ [] : [c_Groups_Ozero__class_Ozero(_901171) = _901173, -(_901173 = c_Groups_Ozero__class_Ozero(_901171))], (7248 ^ _780461) ^ [] : [_901173 = c_Groups_Ozero__class_Ozero(_901171), -(c_Groups_Ozero__class_Ozero(_901171) = _901173)]]], (7254 ^ _780461) ^ [_901388, _901390, _901392] : [class_Rings_Ocomm__semiring__1(_901388), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901388), _901390), _901392) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901388), _901392), _901390))], (7260 ^ _780461) ^ [_901497, _901499, _901501, _901503] : [class_Rings_Ocomm__semiring__1(_901497), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901497), _901499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901497), _901501), _901503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901497), _901501), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901497), _901499), _901503)))], (7266 ^ _780461) ^ [_901640, _901642, _901644, _901646] : [class_Rings_Ocomm__semiring__1(_901640), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901640), _901642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901640), _901644), _901646)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901640), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901640), _901642), _901644)), _901646))], (7272 ^ _780461) ^ [_901783, _901785, _901787, _901789] : [class_Rings_Ocomm__semiring__1(_901783), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901783), _901785), _901787)), _901789) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901783), _901785), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901783), _901787), _901789)))], (7278 ^ _780461) ^ [_901926, _901928, _901930, _901932] : [class_Groups_Oab__semigroup__add(_901926), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901926), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901926), _901928), _901930)), _901932) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901926), _901928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901926), _901930), _901932)))], (7284 ^ _780461) ^ [_902069, _902071, _902073, _902075] : [class_Rings_Ocomm__semiring__1(_902069), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902069), _902071), _902073)), _902075) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902069), _902071), _902075)), _902073))], (7290 ^ _780461) ^ [_902212, _902214, _902216, _902218] : [class_Groups_Ocancel__semigroup__add(_902212), 7293 ^ _780461 : [(7294 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902212), _902214), _902216) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902212), _902214), _902218), -(_902216 = _902218)], (7300 ^ _780461) ^ [] : [_902216 = _902218, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902212), _902214), _902216) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902212), _902214), _902218))]]], (7306 ^ _780461) ^ [_902477, _902479, _902481, _902483] : [class_Groups_Ocancel__semigroup__add(_902477), 7309 ^ _780461 : [(7310 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902477), _902479), _902481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902477), _902483), _902481), -(_902479 = _902483)], (7316 ^ _780461) ^ [] : [_902479 = _902483, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902477), _902479), _902481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902477), _902483), _902481))]]], (7322 ^ _780461) ^ [_902742, _902744, _902746, _902748, _902750] : [class_Rings_Ocomm__semiring__1(_902742), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902742), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902742), _902744), _902746)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902742), _902748), _902750)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902742), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902742), _902744), _902748)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902742), _902746), _902750)))], (7328 ^ _780461) ^ [_902919, _902921, _902923, _902925] : [class_Groups_Ocancel__semigroup__add(_902919), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902919), _902921), _902923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_902919), _902921), _902925), -(_902923 = _902925)], (7338 ^ _780461) ^ [_903086, _903088, _903090, _903092] : [class_Groups_Ocancel__ab__semigroup__add(_903086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903086), _903088), _903090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903086), _903088), _903092), -(_903090 = _903092)], (7348 ^ _780461) ^ [_903253, _903255, _903257, _903259] : [class_Groups_Ocancel__semigroup__add(_903253), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903253), _903255), _903257) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903253), _903259), _903257), -(_903255 = _903259)], (7358 ^ _780461) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7360 ^ _780461) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7362 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7364 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7366 ^ _780461) ^ [_903488] : [-(hAPP(c_Com_Obody, _903488) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _903488))))], (7372 ^ _780461) ^ [_903542] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _903542))), -(hAPP(c_Com_Obody, _903542) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 7375 ^ [_903542]))], (7379 ^ _780461) ^ [_903645] : [7380 ^ _780461 : [(7381 ^ _780461) ^ [_903693] : [hAPP(c_Com_Obody, _903645) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _903693)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _903645))))], (7385 ^ _780461) ^ [_903757, _903759, _903761, _903763, _903765] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _903757)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _903759), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_903761, _903759))), _903763)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_903765, _903757, _903761)), _903759), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _903763), hAPP(c_Natural_Ogetlocs, _903759))), _903765), hAPP(hAPP(c_Natural_Ogetlocs, _903763), c_Com_ORes)))))], (7391 ^ _780461) ^ [_903966, _903968, _903970, _903972, _903974, _903976] : [c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _903966), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _903968), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_903970, _903968)), _903972, _903974), -(c_Natural_Oevaln(c_Com_Ocom_OCall(_903976, _903966, _903970), _903968, _903972, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _903974), hAPP(c_Natural_Ogetlocs, _903968))), _903976), hAPP(hAPP(c_Natural_Ogetlocs, _903974), c_Com_ORes))))], (7397 ^ _780461) ^ [_904157, _904159, _904161, _904163] : [hAPP(_904157, 7398 ^ [_904157, _904159, _904161, _904163]) = hAPP(c_Nat_Onat_Onat__rec(_904159, _904161, _904163), 7398 ^ [_904157, _904159, _904161, _904163]), -(hAPP(_904157, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _904161)], (7404 ^ _780461) ^ [_904341, _904343, _904345, _904347, _904349] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_904341, _904343, _904345)), _904347), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _904349), hAPP(c_Natural_Ogetlocs, _904347))), _904341), hAPP(hAPP(c_Natural_Ogetlocs, _904349), c_Com_ORes)))), 7408 ^ _780461 : [(7409 ^ _780461) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _904349), hAPP(c_Natural_Ogetlocs, _904347))), _904341), hAPP(hAPP(c_Natural_Ogetlocs, _904349), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7407 ^ [_904341, _904343, _904345, _904347, _904349]), hAPP(c_Natural_Ogetlocs, _904347))), _904341), hAPP(hAPP(c_Natural_Ogetlocs, 7407 ^ [_904341, _904343, _904345, _904347, _904349]), c_Com_ORes)))], (7411 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _904343)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _904347), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_904345, _904347))), 7407 ^ [_904341, _904343, _904345, _904347, _904349])))]]], (7413 ^ _780461) ^ [_904712, _904714, _904716, _904718, _904720] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_904712, _904714, _904716)), _904718), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _904720), hAPP(c_Natural_Ogetlocs, _904718))), _904712), hAPP(hAPP(c_Natural_Ogetlocs, _904720), c_Com_ORes))))), 7414 ^ _780461 : [(7415 ^ _780461) ^ [_904869] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _904720), hAPP(c_Natural_Ogetlocs, _904718))), _904712), hAPP(hAPP(c_Natural_Ogetlocs, _904720), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _904869), hAPP(c_Natural_Ogetlocs, _904718))), _904712), hAPP(hAPP(c_Natural_Ogetlocs, _904869), c_Com_ORes)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _904714)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _904718), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_904716, _904718))), _904869))]]], (7423 ^ _780461) ^ [_905197, _905199, _905201, _905203, _905205, _905207] : [c_Natural_Oevaln(c_Com_Ocom_OCall(_905197, _905199, _905201), _905203, _905205, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _905207), hAPP(c_Natural_Ogetlocs, _905203))), _905197), hAPP(hAPP(c_Natural_Ogetlocs, _905207), c_Com_ORes))), 7427 ^ _780461 : [(7428 ^ _780461) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _905207), hAPP(c_Natural_Ogetlocs, _905203))), _905197), hAPP(hAPP(c_Natural_Ogetlocs, _905207), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7426 ^ [_905197, _905199, _905201, _905203, _905205, _905207]), hAPP(c_Natural_Ogetlocs, _905203))), _905197), hAPP(hAPP(c_Natural_Ogetlocs, 7426 ^ [_905197, _905199, _905201, _905203, _905205, _905207]), c_Com_ORes)))], (7430 ^ _780461) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _905199), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _905203), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_905201, _905203)), _905205, 7426 ^ [_905197, _905199, _905201, _905203, _905205, _905207]))]]], (7432 ^ _780461) ^ [_905556, _905558, _905560, _905562, _905564, _905566] : [-(c_Natural_Oevaln(c_Com_Ocom_OCall(_905556, _905558, _905560), _905562, _905564, hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _905566), hAPP(c_Natural_Ogetlocs, _905562))), _905556), hAPP(hAPP(c_Natural_Ogetlocs, _905566), c_Com_ORes)))), 7433 ^ _780461 : [(7434 ^ _780461) ^ [_905705] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _905566), hAPP(c_Natural_Ogetlocs, _905562))), _905556), hAPP(hAPP(c_Natural_Ogetlocs, _905566), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _905705), hAPP(c_Natural_Ogetlocs, _905562))), _905556), hAPP(hAPP(c_Natural_Ogetlocs, _905705), c_Com_ORes)), c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _905558), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _905562), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_905560, _905562)), _905564, _905705)]]], (7442 ^ _780461) ^ [_905993, _905995, _905997, _905999, _906001] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_905993, _905995, _905997)), _905999), _906001)), 7446 ^ _780461 : [(7447 ^ _780461) ^ [] : [-(_906001 = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7445 ^ [_905993, _905995, _905997, _905999, _906001]), hAPP(c_Natural_Ogetlocs, _905999))), _905993), hAPP(hAPP(c_Natural_Ogetlocs, 7445 ^ [_905993, _905995, _905997, _905999, _906001]), c_Com_ORes)))], (7449 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _905995)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _905999), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_905997, _905999))), 7445 ^ [_905993, _905995, _905997, _905999, _906001])))]]], (7451 ^ _780461) ^ [_906276, _906278, _906280, _906282, _906284, _906286] : [c_Natural_Oevaln(c_Com_Ocom_OCall(_906276, _906278, _906280), _906282, _906284, _906286), 7455 ^ _780461 : [(7456 ^ _780461) ^ [] : [-(_906286 = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7454 ^ [_906276, _906278, _906280, _906282, _906284, _906286]), hAPP(c_Natural_Ogetlocs, _906282))), _906276), hAPP(hAPP(c_Natural_Ogetlocs, 7454 ^ [_906276, _906278, _906280, _906282, _906284, _906286]), c_Com_ORes)))], (7458 ^ _780461) ^ [] : [-(c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY, _906278), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _906282), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_906280, _906282)), _906284, 7454 ^ [_906276, _906278, _906280, _906282, _906284, _906286]))]]], (7460 ^ _780461) ^ [_906547, _906549] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _906547) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _906549), -(hBOOL(hAPP(c_Com_OWT, _906549)))], (7470 ^ _780461) ^ [_906686, _906688, _906690] : [-(c_Option_Ooption_Ooption__size(_906686, _906688, hAPP(c_Option_Ooption_OSome(_906686), _906690)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_906688, _906690)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7472 ^ _780461) ^ [_906731, _906733] : [-(c_Option_Ooption_Ooption__size(_906731, _906733, c_Option_Ooption_ONone(_906731)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7474 ^ _780461) ^ [_906762] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _906762))), -(hAPP(c_Com_Obody, _906762) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 7477 ^ [_906762]))], (7481 ^ _780461) ^ [_906873, _906875] : [-(hAPP(c_Option_Othe(_906873), hAPP(c_Option_Ooption_OSome(_906873), _906875)) = _906875)], (7483 ^ _780461) ^ [_906917, _906919] : [-(_906917 = c_Option_Ooption_ONone(_906919)), -(_906917 = hAPP(c_Option_Ooption_OSome(_906919), 7486 ^ [_906917, _906919]))], (7490 ^ _780461) ^ [_906963, _906965] : [7491 ^ _780461 : [(7492 ^ _780461) ^ [_907011] : [_906963 = hAPP(c_Option_Ooption_OSome(_906965), _907011)]], _906963 = c_Option_Ooption_ONone(_906965)], (7496 ^ _780461) ^ [_907079, _907081] : [-(_907079 = hAPP(c_Option_Ooption_OSome(_907081), 7497 ^ [_907079, _907081])), -(_907079 = c_Option_Ooption_ONone(_907081))], (7503 ^ _780461) ^ [_907125, _907127] : [_907125 = c_Option_Ooption_ONone(_907127), 7506 ^ _780461 : [(7507 ^ _780461) ^ [_907197] : [_907125 = hAPP(c_Option_Ooption_OSome(_907127), _907197)]]], (7509 ^ _780461) ^ [_907243, _907245] : [hAPP(c_Option_Ooption_OSome(_907243), _907245) = c_Option_Ooption_ONone(_907243)], (7511 ^ _780461) ^ [_907287, _907289] : [c_Option_Ooption_ONone(_907287) = hAPP(c_Option_Ooption_OSome(_907287), _907289)], (7513 ^ _780461) ^ [_907337, _907339, _907341] : [hAPP(c_Option_Ooption_OSome(_907337), _907339) = hAPP(c_Option_Ooption_OSome(_907337), _907341), -(_907339 = _907341)], (7519 ^ _780461) ^ [_907432, _907434, _907436] : [_907434 = _907436, -(hAPP(c_Option_Ooption_OSome(_907432), _907434) = hAPP(c_Option_Ooption_OSome(_907432), _907436))], (7525 ^ _780461) ^ [_907533, _907535] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_907533)), hAPP(c_Option_Ooption_OSome(_907533), _907535)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7527 ^ _780461) ^ [_907570] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_907570)), c_Option_Ooption_ONone(_907570)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7529 ^ _780461) ^ [_907602, _907604, _907606, _907608, _907610] : [-(c_Option_Ooption_Ooption__rec(_907602, _907604, _907606, _907608, hAPP(c_Option_Ooption_OSome(_907604), _907610)) = hAPP(_907608, _907610))], (7531 ^ _780461) ^ [_907647, _907649, _907651, _907653, _907655] : [-(hAPP(c_Option_Ooption_Ooption__case(_907647, _907649, _907651, _907653), hAPP(c_Option_Ooption_OSome(_907649), _907655)) = hAPP(_907653, _907655))], (7533 ^ _780461) ^ [_907694, _907696, _907698, _907700] : [-(c_Option_Ooption_Ooption__rec(_907694, _907696, _907698, _907700, c_Option_Ooption_ONone(_907696)) = _907698)], (7535 ^ _780461) ^ [_907731, _907733, _907735, _907737] : [-(hAPP(c_Option_Ooption_Ooption__case(_907731, _907733, _907735, _907737), c_Option_Ooption_ONone(_907733)) = _907735)], (7537 ^ _780461) ^ [_907782, _907784] : [c_Option_Ois__none(_907782, hAPP(c_Option_Ooption_OSome(_907782), _907784))], (7539 ^ _780461) ^ [_907812] : [-(c_Option_Ois__none(_907812, c_Option_Ooption_ONone(_907812)))], (7541 ^ _780461) ^ [_907852, _907854] : [c_Option_Ois__none(_907852, _907854), -(_907854 = c_Option_Ooption_ONone(_907852))], (7547 ^ _780461) ^ [_907929, _907931] : [_907931 = c_Option_Ooption_ONone(_907929), -(c_Option_Ois__none(_907929, _907931))], (7553 ^ _780461) ^ [_908012, _908014, _908016, _908018] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_908012, _908014)), _908016), _908018)), 7558 ^ _780461 : [(7559 ^ _780461) ^ [] : [-(_908018 = _908016)], (7561 ^ _780461) ^ [] : [hBOOL(hAPP(_908012, _908016))]], 7562 ^ _780461 : [(7563 ^ _780461) ^ [] : [-(hBOOL(hAPP(_908012, _908016)))], (7566 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_908014), _908016), 7564 ^ [_908012, _908014, _908016, _908018])))], (7568 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_908012, _908014)), 7564 ^ [_908012, _908014, _908016, _908018]), _908018)))]]], (7570 ^ _780461) ^ [_908325, _908327, _908329, _908331, _908333, _908335] : [-(c_Nitpick_Opair__box_Opair__box__size(_908325, _908327, _908329, _908331, c_Nitpick_Opair__box_OPairBox(_908325, _908327, _908333, _908335)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_908329, _908333)), hAPP(_908331, _908335))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7572 ^ _780461) ^ [_908414, _908416, _908418, _908420, _908422, _908424] : [c_Nitpick_Opair__box_OPairBox(_908414, _908416, _908418, _908420) = c_Nitpick_Opair__box_OPairBox(_908414, _908416, _908422, _908424), 7575 ^ _780461 : [(7576 ^ _780461) ^ [] : [-(_908418 = _908422)], (7578 ^ _780461) ^ [] : [-(_908420 = _908424)]]], (7580 ^ _780461) ^ [_908541, _908543, _908545, _908547, _908549, _908551] : [-(c_Nitpick_Opair__box_OPairBox(_908541, _908543, _908545, _908547) = c_Nitpick_Opair__box_OPairBox(_908541, _908543, _908549, _908551)), _908545 = _908549, _908547 = _908551], (7590 ^ _780461) ^ [_908708, _908710, _908712, _908714] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_908708, _908710)), c_Nitpick_Opair__box_OPairBox(_908708, _908710, _908712, _908714)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7592 ^ _780461) ^ [_908750, _908752, _908754, _908756, _908758, _908760] : [-(c_Nitpick_Opair__box_Opair__box__case(_908750, _908752, _908754, _908756, c_Nitpick_Opair__box_OPairBox(_908750, _908752, _908758, _908760)) = hAPP(hAPP(_908756, _908758), _908760))], (7594 ^ _780461) ^ [_908800, _908802, _908804, _908806, _908808, _908810] : [-(c_Nitpick_Opair__box_Opair__box__rec(_908800, _908802, _908804, _908806, c_Nitpick_Opair__box_OPairBox(_908800, _908802, _908808, _908810)) = hAPP(hAPP(_908806, _908808), _908810))], (7596 ^ _780461) ^ [_908850, _908852, _908854] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_908850), _908852), _908854)), -(c_Natural_Oevaln(_908850, _908852, 7599 ^ [_908850, _908852, _908854], _908854))], (7603 ^ _780461) ^ [_908961, _908963, _908965, _908967, _908969] : [-(c_Sum__Type_Osum_Osum__size(_908961, _908963, _908965, _908967, hAPP(c_Sum__Type_OInl(_908961, _908963), _908969)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_908965, _908969)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7605 ^ _780461) ^ [_909013, _909015, _909017, _909019, _909021] : [-(c_Sum__Type_Osum_Osum__size(_909013, _909015, _909017, _909019, hAPP(c_Sum__Type_OInr(_909015, _909013), _909021)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_909019, _909021)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7607 ^ _780461) ^ [_909061, _909063] : [-(_909061 = c_Option_Ooption_ONone(_909063)), -(_909061 = hAPP(c_Option_Ooption_OSome(_909063), 7610 ^ [_909061, _909063]))], (7614 ^ _780461) ^ [_909111] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _909111))))], (7616 ^ _780461) ^ [_909135] : [-(_909135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_909135 = hAPP(c_Nat_OSuc, 7619 ^ [_909135]))], (7623 ^ _780461) ^ [_909177, _909179] : [hBOOL(hAPP(_909177, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7629 ^ _780461 : [(7630 ^ _780461) ^ [] : [-(hBOOL(hAPP(_909177, 7628 ^ [_909177, _909179])))], (7632 ^ _780461) ^ [] : [hBOOL(hAPP(_909177, hAPP(c_Nat_OSuc, 7628 ^ [_909177, _909179])))]], -(hBOOL(hAPP(_909177, _909179)))], (7636 ^ _780461) ^ [_909397, _909399] : [hBOOL(hAPP(_909397, _909399)), 7642 ^ _780461 : [(7643 ^ _780461) ^ [] : [-(hBOOL(hAPP(_909397, hAPP(c_Nat_OSuc, 7641 ^ [_909397, _909399]))))], (7645 ^ _780461) ^ [] : [hBOOL(hAPP(_909397, 7641 ^ [_909397, _909399]))]], -(hBOOL(hAPP(_909397, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7649 ^ _780461) ^ [_909623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909623), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7651 ^ _780461) ^ [_909651] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909651), hAPP(c_Nat_OSuc, _909651))))], (7653 ^ _780461) ^ [_909682, _909684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909682), _909684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909682)), hAPP(c_Nat_OSuc, _909684))))], (7659 ^ _780461) ^ [_909791, _909793, _909795] : [7660 ^ _780461 : [(7661 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909791), _909793)))], (7663 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_909795, _909793), _909791))]], 7666 ^ _780461 : [(7667 ^ _780461) ^ [] : [-(_909791 = _909793)], (7669 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_909795, _909793), _909791))]], 7672 ^ _780461 : [(7673 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _909793), _909791)))], (7675 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_909795, _909793), _909791))]], -(hBOOL(hAPP(hAPP(_909795, _909793), _909791)))], (7679 ^ _780461) ^ [_910137, _910139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910137), _910139)), _910137 = _910139], (7685 ^ _780461) ^ [_910225, _910227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910225), _910227)), _910227 = _910225], (7691 ^ _780461) ^ [_910322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910322), _910322))], (7693 ^ _780461) ^ [_910346, _910348] : [-(_910346 = _910348), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910346), _910348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910348), _910346)))], (7713 ^ _780461) ^ [_910457, _910459] : [7714 ^ _780461 : [(7715 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910457), _910459))], (7717 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910459), _910457))]], _910457 = _910459], (7703 ^ _780461) ^ [_910408, _910410] : [-(_910408 = _910410), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910408), _910410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910410), _910408)))], (7721 ^ _780461) ^ [_910604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910604), _910604))], (7723 ^ _780461) ^ [_910632, _910634, _910636, _910638] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_910632), 7726 ^ _780461 : [(7727 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910632), _910634), _910636)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910632), _910638), _910636))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910632), _910634), _910638)))], (7733 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910632), _910634), _910638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910632), _910634), _910636)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910632), _910638), _910636))))]]], (7739 ^ _780461) ^ [_910939, _910941, _910943, _910945] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_910939), 7742 ^ _780461 : [(7743 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910939), _910941), _910943)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910939), _910941), _910945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910939), _910943), _910945)))], (7749 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910939), _910943), _910945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910939), _910941), _910943)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_910939), _910941), _910945))))]]], (7755 ^ _780461) ^ [_911246, _911248, _911250, _911252] : [class_Groups_Oordered__cancel__ab__semigroup__add(_911246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911246), _911248), _911250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911246), _911248), _911252)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911246), _911250), _911252))))], (7765 ^ _780461) ^ [_911441, _911443, _911445, _911447] : [class_Groups_Oordered__cancel__ab__semigroup__add(_911441), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911441), _911443), _911445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911441), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911441), _911447), _911443)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911441), _911447), _911445))))], (7775 ^ _780461) ^ [_911636, _911638, _911640, _911642, _911644] : [class_Groups_Oordered__cancel__ab__semigroup__add(_911636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911636), _911638), _911640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911636), _911642), _911644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911636), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911636), _911638), _911642)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911636), _911640), _911644))))], (7789 ^ _780461) ^ [_911907, _911909, _911911, _911913] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_911907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911907), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911907), _911909), _911911)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_911907), _911913), _911911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911907), _911909), _911913)))], (7799 ^ _780461) ^ [_912102, _912104, _912106, _912108] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_912102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912102), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_912102), _912104), _912106)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_912102), _912104), _912108))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912102), _912106), _912108)))], (7809 ^ _780461) ^ [_912293] : [-(_912293 = 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)), _912293)))], (7815 ^ _780461) ^ [_912329, _912331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912329), _912331)), _912331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7821 ^ _780461) ^ [_912426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912426), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7823 ^ _780461) ^ [_912460] : [-(_912460 = 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)), _912460)))], (7829 ^ _780461) ^ [_912492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _912492)), _912492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7835 ^ _780461) ^ [_912583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912583), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7837 ^ _780461) ^ [_912620, _912622] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912620), _912622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912622), hAPP(c_Nat_OSuc, _912620))))], (7843 ^ _780461) ^ [_912665, _912667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912667), hAPP(c_Nat_OSuc, _912665))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912665), _912667))], (7859 ^ _780461) ^ [_912898, _912900] : [7860 ^ _780461 : [(7861 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912898), _912900))], (7863 ^ _780461) ^ [] : [_912898 = _912900]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912898), hAPP(c_Nat_OSuc, _912900))))], (7849 ^ _780461) ^ [_912786, _912788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912786), hAPP(c_Nat_OSuc, _912788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _912786), _912788))), -(_912786 = _912788)], (7867 ^ _780461) ^ [_913056, _913058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _913056)), hAPP(c_Nat_OSuc, _913058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913056), _913058)))], (7873 ^ _780461) ^ [_913161, _913163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913161), _913163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _913161)), hAPP(c_Nat_OSuc, _913163))))], (7879 ^ _780461) ^ [_913271, _913273] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913271), _913273))), 7882 ^ _780461 : [(7883 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913271), hAPP(c_Nat_OSuc, _913273))), -(_913271 = _913273)], (7889 ^ _780461) ^ [] : [_913271 = _913273, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913271), hAPP(c_Nat_OSuc, _913273))))]]], (7895 ^ _780461) ^ [_913504, _913506] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913504), _913506))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913504), hAPP(c_Nat_OSuc, _913506))), -(_913506 = _913504)], (7905 ^ _780461) ^ [_913652, _913654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913652), _913654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913652), hAPP(c_Nat_OSuc, _913654))))], (7911 ^ _780461) ^ [_913755, _913757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913755), _913757)), -(hAPP(c_Nat_OSuc, _913755) = _913757), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _913755)), _913757)))], (7921 ^ _780461) ^ [_913879, _913881, _913883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913879), _913881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _913881), _913883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _913879)), _913883)))], (7931 ^ _780461) ^ [_914048, _914050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914048), hAPP(c_Nat_OSuc, _914050))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914048), _914050))), -(_914048 = _914050)], (7941 ^ _780461) ^ [_914166, _914168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _914166)), _914168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914166), _914168)))], (7947 ^ _780461) ^ [_914269, _914271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _914269)), hAPP(c_Nat_OSuc, _914271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914269), _914271)))], (7953 ^ _780461) ^ [_914378, _914380, _914382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914378), _914380)), _914382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914378), _914382)))], (7959 ^ _780461) ^ [_914489, _914491, _914493, _914495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914489), _914491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914493), _914491) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914489), _914495), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914493), _914495)))], (7969 ^ _780461) ^ [_914670, _914672, _914674, _914676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914670), _914672)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914674), _914676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914670), _914674)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914672), _914676))))], (7979 ^ _780461) ^ [_914861, _914863, _914865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914861), _914863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914861), _914865)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914863), _914865))))], (7985 ^ _780461) ^ [_914984, _914986, _914988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914984), _914986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _914984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914988), _914986))))], (7991 ^ _780461) ^ [_915095, _915097, _915099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915095), _915097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915095), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915097), _915099))))], (7997 ^ _780461) ^ [_915224, _915226, _915228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915224), _915226)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915224), _915228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915226), _915228)))], (8003 ^ _780461) ^ [_915343, _915345, _915347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915345), _915347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915343), _915345)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915343), _915347))))], (8009 ^ _780461) ^ [_915480, _915482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915480), _915482)), _915482))], (8011 ^ _780461) ^ [_915528, _915530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915528), _915530)), _915528))], (8013 ^ _780461) ^ [_915564, _915566, _915568] : [class_Groups_Oordered__comm__monoid__add(_915564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915564), _915566), c_Groups_Ozero__class_Ozero(_915564))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915564), _915568), c_Groups_Ozero__class_Ozero(_915564))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915564), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915564), _915566), _915568)), c_Groups_Ozero__class_Ozero(_915564))))], (8027 ^ _780461) ^ [_915819, _915821, _915823] : [class_Groups_Oordered__comm__monoid__add(_915819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915819), c_Groups_Ozero__class_Ozero(_915819)), _915821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915819), c_Groups_Ozero__class_Ozero(_915819)), _915823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915819), c_Groups_Ozero__class_Ozero(_915819)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915819), _915821), _915823))))], (8041 ^ _780461) ^ [_916074, _916076] : [class_Groups_Olinordered__ab__group__add(_916074), 8044 ^ _780461 : [(8045 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916074), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916074), _916076), _916076)), c_Groups_Ozero__class_Ozero(_916074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916074), _916076), c_Groups_Ozero__class_Ozero(_916074))))], (8051 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916074), _916076), c_Groups_Ozero__class_Ozero(_916074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916074), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916074), _916076), _916076)), c_Groups_Ozero__class_Ozero(_916074))))]]], (8057 ^ _780461) ^ [_916357, _916359] : [class_Rings_Olinordered__idom(_916357), 8060 ^ _780461 : [(8061 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916357), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916357), _916359), _916359)), c_Groups_Ozero__class_Ozero(_916357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916357), _916359), c_Groups_Ozero__class_Ozero(_916357))))], (8067 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916357), _916359), c_Groups_Ozero__class_Ozero(_916357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916357), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916357), _916359), _916359)), c_Groups_Ozero__class_Ozero(_916357))))]]], (8073 ^ _780461) ^ [_916640, _916642] : [class_Groups_Olinordered__ab__group__add(_916640), 8076 ^ _780461 : [(8077 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916640), c_Groups_Ozero__class_Ozero(_916640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916640), _916642), _916642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916640), c_Groups_Ozero__class_Ozero(_916640)), _916642)))], (8083 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916640), c_Groups_Ozero__class_Ozero(_916640)), _916642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_916640), c_Groups_Ozero__class_Ozero(_916640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916640), _916642), _916642))))]]], (8089 ^ _780461) ^ [_916938, _916940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916938), hAPP(c_Nat_OSuc, _916940))), -(_916938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8097 ^ _780461 : [(8098 ^ _780461) ^ [] : [-(_916938 = hAPP(c_Nat_OSuc, 8096 ^ [_916938, _916940]))], (8100 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 8096 ^ [_916938, _916940]), _916940)))]]], (8102 ^ _780461) ^ [_917118, _917120] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917118), hAPP(c_Nat_OSuc, _917120)))), 8103 ^ _780461 : [(8104 ^ _780461) ^ [] : [_917118 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8106 ^ _780461) ^ [_917206] : [_917118 = hAPP(c_Nat_OSuc, _917206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917206), _917120))]]], (8114 ^ _780461) ^ [_917352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917352), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_917352 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8120 ^ _780461) ^ [_917433] : [_917433 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917433), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (8126 ^ _780461) ^ [_917532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917532)), -(_917532 = hAPP(c_Nat_OSuc, 8129 ^ [_917532]))], (8133 ^ _780461) ^ [_917623] : [8134 ^ _780461 : [(8135 ^ _780461) ^ [_917665] : [_917623 = hAPP(c_Nat_OSuc, _917665)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917623)))], (8149 ^ _780461) ^ [_917848, _917850] : [8150 ^ _780461 : [(8151 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917848))], (8153 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917850))]], -(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), _917848), _917850))))], (8139 ^ _780461) ^ [_917738, _917740] : [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), _917738), _917740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _917740)))], (8157 ^ _780461) ^ [_918004, _918006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918004), _918006)), -(_918006 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _918004), 8160 ^ [_918004, _918006])))], (8164 ^ _780461) ^ [_918117, _918119] : [8165 ^ _780461 : [(8166 ^ _780461) ^ [_918170] : [_918119 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _918117), _918170))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918117), _918119)))], (8170 ^ _780461) ^ [_918237, _918239] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918237), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _918239), _918237)))))], (8172 ^ _780461) ^ [_918276, _918278] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918276), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _918276), _918278)))))], (8174 ^ _780461) ^ [_918315, _918317, _918319, _918321] : [class_Rings_Olinordered__semidom(_918315), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918315), c_Groups_Ozero__class_Ozero(_918315)), _918317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918315), _918319), _918321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_918315), _918319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918315), _918317), _918321))))], (8188 ^ _780461) ^ [_918586, _918588, _918590, _918592] : [hAPP(c_Sum__Type_OInl(_918586, _918588), _918590) = hAPP(c_Sum__Type_OInr(_918588, _918586), _918592)], (8190 ^ _780461) ^ [_918645, _918647, _918649, _918651] : [hAPP(c_Sum__Type_OInl(_918645, _918647), _918649) = hAPP(c_Sum__Type_OInr(_918647, _918645), _918651)], (8192 ^ _780461) ^ [_918704, _918706, _918708, _918710] : [hAPP(c_Sum__Type_OInr(_918704, _918706), _918708) = hAPP(c_Sum__Type_OInl(_918706, _918704), _918710)], (8194 ^ _780461) ^ [_918763, _918765, _918767, _918769] : [hAPP(c_Sum__Type_OInr(_918763, _918765), _918767) = hAPP(c_Sum__Type_OInl(_918765, _918763), _918769)], (8196 ^ _780461) ^ [_918804, _918806, _918808] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_918804, _918806)), hAPP(c_Sum__Type_OInl(_918804, _918806), _918808)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8198 ^ _780461) ^ [_918845, _918847, _918849] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_918845, _918847)), hAPP(c_Sum__Type_OInr(_918847, _918845), _918849)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8200 ^ _780461) ^ [_918886, _918888, _918890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918886), _918888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _918888), _918890))))], (8206 ^ _780461) ^ [_918997, _918999, _919001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918997), _918999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918997), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919001), _918999))))], (8212 ^ _780461) ^ [_919108, _919110] : [class_Rings_Olinordered__semidom(_919108), 8215 ^ _780461 : [(8216 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919108), c_Groups_Ozero__class_Ozero(_919108)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919108), _919110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919110)))], (8222 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _919110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_919108), c_Groups_Ozero__class_Ozero(_919108)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919108), _919110))))]]], (8228 ^ _780461) ^ [_919361, _919363, _919365] : [class_Nat_Osemiring__char__0(_919361), 8231 ^ _780461 : [(8232 ^ _780461) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919361), _919363) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919361), _919365), -(_919363 = _919365)], (8238 ^ _780461) ^ [] : [_919363 = _919365, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919361), _919363) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_919361), _919365))]]], (8244 ^ _780461) ^ [_919617, _919619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _919617), _919619)), -(_919619 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _919617), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 8247 ^ [_919617, _919619]))))], (8251 ^ _780461) ^ [_919736, _919738] : [8252 ^ _780461 : [(8253 ^ _780461) ^ [_919792] : [_919738 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _919736), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _919792)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _919736), _919738)))], (8257 ^ _780461) ^ [_919877, _919879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _919877)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _919879))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919877), _919879)))], (8263 ^ _780461) ^ [_919982, _919984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919982), _919984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _919982)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _919984))))], (8269 ^ _780461) ^ [_920105] : [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), _920105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _920105)))], (8275 ^ _780461) ^ [_920190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _920190)), -(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), _920190))))], (8281 ^ _780461) ^ [] : [-(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))], (8283 ^ _780461) ^ [_920311] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920311) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_920311 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8289 ^ _780461) ^ [_920388] : [_920388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920388) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8295 ^ _780461) ^ [_920471, _920473] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920471)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920473)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920471), _920473)))], (8297 ^ _780461) ^ [_920517, _920519, _920521] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920517)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _920519)), _920521)) = 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), _920517), _920519))), _920521))], (8299 ^ _780461) ^ [_920577, _920579] : [class_Rings_Olinordered__semidom(_920577), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920577), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920577), _920579)), c_Groups_Ozero__class_Ozero(_920577)))], (8305 ^ _780461) ^ [_920681] : [class_Rings_Osemiring__1(_920681), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920681), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_920681))], (8311 ^ _780461) ^ [_920768, _920770, _920772] : [class_Rings_Olinordered__semidom(_920768), 8314 ^ _780461 : [(8315 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920768), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920768), _920770)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920768), _920772))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920770), _920772)))], (8321 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920770), _920772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920768), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920768), _920770)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_920768), _920772))))]]], (8327 ^ _780461) ^ [_921045, _921047, _921049] : [class_Rings_Olinordered__semidom(_921045), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _921047), _921049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921045), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_921045), _921047)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_921045), _921049))))], (8337 ^ _780461) ^ [_921220, _921222, _921224] : [class_Rings_Olinordered__semidom(_921220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921220), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_921220), _921222)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_921220), _921224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _921222), _921224)))], (8347 ^ _780461) ^ [_921395, _921397, _921399] : [class_Rings_Osemiring__1(_921395), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_921395), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921397), _921399)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921395), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_921395), _921397)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_921395), _921399)))], (8353 ^ _780461) ^ [_921530, _921532, _921534] : [class_Rings_Olinordered__idom(_921530), -(_921532 = _921534), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921530), _921532), _921534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_921530), _921534), _921532)))], (8367 ^ _780461) ^ [_921665, _921667, _921669, _921671] : [hAPP(c_Sum__Type_OInr(_921665, _921667), _921669) = hAPP(c_Sum__Type_OInr(_921665, _921667), _921671), -(_921669 = _921671)], (8373 ^ _780461) ^ [_921791, _921793, _921795, _921797] : [hAPP(c_Sum__Type_OInr(_921791, _921793), _921795) = hAPP(c_Sum__Type_OInr(_921791, _921793), _921797), -(_921795 = _921797)], (8379 ^ _780461) ^ [_921892, _921894, _921896, _921898] : [_921896 = _921898, -(hAPP(c_Sum__Type_OInr(_921892, _921894), _921896) = hAPP(c_Sum__Type_OInr(_921892, _921894), _921898))], (8385 ^ _780461) ^ [_921999, _922001, _922003, _922005] : [hAPP(c_Sum__Type_OInl(_921999, _922001), _922003) = hAPP(c_Sum__Type_OInl(_921999, _922001), _922005), -(_922003 = _922005)], (8391 ^ _780461) ^ [_922125, _922127, _922129, _922131] : [hAPP(c_Sum__Type_OInl(_922125, _922127), _922129) = hAPP(c_Sum__Type_OInl(_922125, _922127), _922131), -(_922129 = _922131)], (8397 ^ _780461) ^ [_922226, _922228, _922230, _922232] : [_922230 = _922232, -(hAPP(c_Sum__Type_OInl(_922226, _922228), _922230) = hAPP(c_Sum__Type_OInl(_922226, _922228), _922232))], (8403 ^ _780461) ^ [_922333, _922335, _922337] : [-(c_Sum__Type_OProjl(_922333, _922335, hAPP(c_Sum__Type_OInl(_922333, _922335), _922337)) = _922337)], (8405 ^ _780461) ^ [_922370, _922372, _922374] : [-(c_Sum__Type_OProjr(_922370, _922372, hAPP(c_Sum__Type_OInr(_922372, _922370), _922374)) = _922374)], (8407 ^ _780461) ^ [_922407, _922409, _922411, _922413, _922415, _922417] : [-(c_Sum__Type_Osum_Osum__rec(_922407, _922409, _922411, _922413, _922415, hAPP(c_Sum__Type_OInl(_922407, _922411), _922417)) = hAPP(_922413, _922417))], (8409 ^ _780461) ^ [_922456, _922458, _922460, _922462, _922464, _922466] : [-(c_Sum__Type_Osum_Osum__rec(_922456, _922458, _922460, _922462, _922464, hAPP(c_Sum__Type_OInr(_922460, _922456), _922466)) = hAPP(_922464, _922466))], (8411 ^ _780461) ^ [_922505, _922507, _922509, _922511, _922513] : [-(hAPP(c_Sum__Type_OSuml(_922505, _922507, _922509, _922511), hAPP(c_Sum__Type_OInl(_922505, _922509), _922513)) = hAPP(_922511, _922513))], (8413 ^ _780461) ^ [_922553, _922555, _922557, _922559, _922561] : [-(hAPP(c_Sum__Type_OSumr(_922553, _922555, _922557, _922559), hAPP(c_Sum__Type_OInr(_922553, _922557), _922561)) = hAPP(_922559, _922561))], (8415 ^ _780461) ^ [_922601, _922603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _922601), _922603)), -(_922603 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922601), 8418 ^ [_922601, _922603])))], (8422 ^ _780461) ^ [_922718, _922720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _922718), _922720)), 8426 ^ _780461 : [(8427 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8425 ^ [_922718, _922720])))], (8429 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922718), 8425 ^ [_922718, _922720]) = _922720)]]], (8431 ^ _780461) ^ [_922866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _922866)), -(_922866 = hAPP(c_Nat_OSuc, 8434 ^ [_922866]))], (8438 ^ _780461) ^ [_922961, _922963, _922965, _922967] : [class_Orderings_Oorder(_922961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922961), hAPP(_922963, 8443 ^ [_922961, _922963, _922965, _922967])), hAPP(_922963, hAPP(c_Nat_OSuc, 8443 ^ [_922961, _922963, _922965, _922967])))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _922965), _922967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_922961), hAPP(_922963, _922965)), hAPP(_922963, _922967))))], (8453 ^ _780461) ^ [_923275, _923277] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923275), _923277))), -(_923275 = _923277), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923277), _923275)))], (8463 ^ _780461) ^ [_923337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923337)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8465 ^ _780461) ^ [_923368, _923370, _923372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _923368), _923370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923368), _923372)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923370), _923372))))], (8471 ^ _780461) ^ [_923506, _923508] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923506) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923508), -(_923506 = _923508)], (8477 ^ _780461) ^ [_923591, _923593] : [_923591 = _923593, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923591) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _923593))], (8483 ^ _780461) ^ [_923682] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923682), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _923682)], (8485 ^ _780461) ^ [_923711] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _923711) = _923711)], (8487 ^ _780461) ^ [_923737, _923739] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923737), _923739) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923739), _923737))], (8489 ^ _780461) ^ [_923774, _923776, _923778] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923774), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923776), _923778)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923774), _923778)))], (8491 ^ _780461) ^ [_923825, _923827, _923829] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923825), _923827)), _923829) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _923827), _923829)))], (8493 ^ _780461) ^ [_923876, _923878, _923880, _923882, _923884] : [c_Sum__Type_OSuml(_923876, _923878, _923880, _923882) = c_Sum__Type_OSuml(_923876, _923878, _923880, _923884), -(_923882 = _923884)], (8499 ^ _780461) ^ [_923979, _923981, _923983, _923985, _923987] : [c_Sum__Type_OSumr(_923979, _923981, _923983, _923985) = c_Sum__Type_OSumr(_923979, _923981, _923983, _923987), -(_923985 = _923987)], (8505 ^ _780461) ^ [_924082, _924084] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924082)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924084)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _924082), _924084)))], (8507 ^ _780461) ^ [_924143, _924145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924143)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _924143), _924145)))], (8513 ^ _780461) ^ [_924248, _924250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _924248), _924250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924248)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _924250))))], (8519 ^ _780461) ^ [] : [-(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)))], (8521 ^ _780461) ^ [_924377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _924377)), 8525 ^ _780461 : [(8526 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8524 ^ [_924377])))], (8528 ^ _780461) ^ [] : [-(_924377 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8524 ^ [_924377]))]]], (8530 ^ _780461) ^ [_924507, _924509] : [class_Rings_Olinordered__idom(_924507), 8533 ^ _780461 : [(8534 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924507), c_Groups_Ozero__class_Ozero(_924507)), hAPP(c_Int_Oring__1__class_Oof__int(_924507), _924509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _924509)))], (8540 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _924509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924507), c_Groups_Ozero__class_Ozero(_924507)), hAPP(c_Int_Oring__1__class_Oof__int(_924507), _924509))))]]], (8546 ^ _780461) ^ [_924760, _924762] : [class_Rings_Olinordered__idom(_924760), 8549 ^ _780461 : [(8550 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924760), hAPP(c_Int_Oring__1__class_Oof__int(_924760), _924762)), c_Groups_Ozero__class_Ozero(_924760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _924762), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8556 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _924762), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924760), hAPP(c_Int_Oring__1__class_Oof__int(_924760), _924762)), c_Groups_Ozero__class_Ozero(_924760))))]]], (8562 ^ _780461) ^ [_925022, _925024, _925026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _925022), _925024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _925026)), -(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), _925026)), _925022)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _925026)), _925024))))], (8572 ^ _780461) ^ [_925215] : [-(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, _925215)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8590 ^ _780461) ^ [_925530, _925532] : [-(hBOOL(hAPP(_925530, hAPP(c_Int_Onat, _925532)))), 8594 ^ _780461 : [(8595 ^ _780461) ^ [] : [-(_925532 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 8593 ^ [_925530, _925532]))], (8597 ^ _780461) ^ [] : [hBOOL(hAPP(_925530, 8593 ^ [_925530, _925532]))]], 8598 ^ _780461 : [(8599 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _925532), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8601 ^ _780461) ^ [] : [hBOOL(hAPP(_925530, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8574 ^ _780461) ^ [_925267, _925269] : [hBOOL(hAPP(_925267, hAPP(c_Int_Onat, _925269))), 8577 ^ _780461 : [(8578 ^ _780461) ^ [_925367] : [_925269 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _925367), -(hBOOL(hAPP(_925267, _925367)))], (8584 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _925269), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_925267, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (8605 ^ _780461) ^ [_925805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _925805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _925805)))], (8611 ^ _780461) ^ [_925890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _925890)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _925890))))], (8617 ^ _780461) ^ [_925981, _925983] : [-(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, _925981)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _925983))))], (8619 ^ _780461) ^ [_926023, _926025] : [class_Groups_Ogroup__add(_926023), -(hAPP(c_Groups_Ouminus__class_Ouminus(_926023), hAPP(c_Groups_Ouminus__class_Ouminus(_926023), _926025)) = _926025)], (8625 ^ _780461) ^ [_926118] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _926118)) = _926118)], (8627 ^ _780461) ^ [_926147, _926149] : [class_Rings_Oring__1(_926147), -(hAPP(c_Int_Oring__1__class_Oof__int(_926147), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _926149)) = hAPP(c_Groups_Ouminus__class_Ouminus(_926147), hAPP(c_Int_Oring__1__class_Oof__int(_926147), _926149)))], (8633 ^ _780461) ^ [_926258, _926260, _926262] : [class_Rings_Oring__1(_926258), -(hAPP(c_Int_Oring__1__class_Oof__int(_926258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _926260), _926262)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926258), hAPP(c_Int_Oring__1__class_Oof__int(_926258), _926260)), hAPP(c_Int_Oring__1__class_Oof__int(_926258), _926262)))], (8639 ^ _780461) ^ [_926393, _926395, _926397] : [class_Rings_Ocomm__semiring__1(_926393), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926393), _926395), _926397) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926393), _926397), _926395))], (8645 ^ _780461) ^ [_926502, _926504] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _926502), _926504) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _926504), _926502))], (8647 ^ _780461) ^ [_926539, _926541, _926543] : [class_Groups_Ogroup__add(_926539), 8650 ^ _780461 : [(8651 ^ _780461) ^ [] : [_926541 = hAPP(c_Groups_Ouminus__class_Ouminus(_926539), _926543), -(_926543 = hAPP(c_Groups_Ouminus__class_Ouminus(_926539), _926541))], (8657 ^ _780461) ^ [] : [_926543 = hAPP(c_Groups_Ouminus__class_Ouminus(_926539), _926541), -(_926541 = hAPP(c_Groups_Ouminus__class_Ouminus(_926539), _926543))]]], (8663 ^ _780461) ^ [_926780, _926782, _926784, _926786] : [class_Rings_Ocomm__semiring__1(_926780), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926780), _926782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926780), _926784), _926786)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926780), _926784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926780), _926782), _926786)))], (8669 ^ _780461) ^ [_926923, _926925, _926927, _926929] : [class_Rings_Ocomm__semiring__1(_926923), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926923), _926925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926923), _926927), _926929)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_926923), _926925), _926927)), _926929))], (8675 ^ _780461) ^ [_927066, _927068] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _927066)), _927068) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _927066), _927068)))], (8677 ^ _780461) ^ [_927109, _927111, _927113] : [class_Groups_Ogroup__add(_927109), 8680 ^ _780461 : [(8681 ^ _780461) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_927109), _927111) = _927113, -(hAPP(c_Groups_Ouminus__class_Ouminus(_927109), _927113) = _927111)], (8687 ^ _780461) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_927109), _927113) = _927111, -(hAPP(c_Groups_Ouminus__class_Ouminus(_927109), _927111) = _927113)]]], (8693 ^ _780461) ^ [_927350, _927352, _927354] : [class_Int_Oring__char__0(_927350), 8696 ^ _780461 : [(8697 ^ _780461) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_927350), _927352) = hAPP(c_Int_Oring__1__class_Oof__int(_927350), _927354), -(_927352 = _927354)], (8703 ^ _780461) ^ [] : [_927352 = _927354, -(hAPP(c_Int_Oring__1__class_Oof__int(_927350), _927352) = hAPP(c_Int_Oring__1__class_Oof__int(_927350), _927354))]]], (8709 ^ _780461) ^ [_927591, _927593, _927595] : [class_Groups_Ogroup__add(_927591), 8712 ^ _780461 : [(8713 ^ _780461) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_927591), _927593) = hAPP(c_Groups_Ouminus__class_Ouminus(_927591), _927595), -(_927593 = _927595)], (8719 ^ _780461) ^ [] : [_927593 = _927595, -(hAPP(c_Groups_Ouminus__class_Ouminus(_927591), _927593) = hAPP(c_Groups_Ouminus__class_Ouminus(_927591), _927595))]]], (8725 ^ _780461) ^ [_927832, _927834, _927836, _927838] : [class_Groups_Oab__semigroup__mult(_927832), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927832), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927832), _927834), _927836)), _927838) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927832), _927834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927832), _927836), _927838)))], (8731 ^ _780461) ^ [_927975, _927977, _927979, _927981] : [class_Rings_Ocomm__semiring__1(_927975), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927975), _927977), _927979)), _927981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927975), _927977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_927975), _927979), _927981)))], (8737 ^ _780461) ^ [_928118, _928120, _928122] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _928118), _928120)), _928122) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _928118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _928120), _928122)))], (8739 ^ _780461) ^ [_928169, _928171, _928173, _928175] : [class_Rings_Ocomm__semiring__1(_928169), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928169), _928171), _928173)), _928175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928169), _928171), _928175)), _928173))], (8745 ^ _780461) ^ [_928312, _928314, _928316, _928318, _928320] : [class_Rings_Ocomm__semiring__1(_928312), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928312), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928312), _928314), _928316)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928312), _928318), _928320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928312), _928314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928312), _928316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928312), _928318), _928320))))], (8751 ^ _780461) ^ [_928489, _928491, _928493, _928495, _928497] : [class_Rings_Ocomm__semiring__1(_928489), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928489), _928491), _928493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928489), _928495), _928497)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928489), _928495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928489), _928491), _928493)), _928497)))], (8757 ^ _780461) ^ [_928666, _928668, _928670, _928672, _928674] : [class_Rings_Ocomm__semiring__1(_928666), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928666), _928668), _928670)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928666), _928672), _928674)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928666), _928668), _928672)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928666), _928670), _928674)))], (8763 ^ _780461) ^ [_928843, _928845, _928847] : [class_Rings_Oring(_928843), -(hAPP(c_Groups_Ouminus__class_Ouminus(_928843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928843), _928845), _928847)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928843), _928845), hAPP(c_Groups_Ouminus__class_Ouminus(_928843), _928847)))], (8769 ^ _780461) ^ [_928972, _928974, _928976] : [class_Rings_Oring(_928972), -(hAPP(c_Groups_Ouminus__class_Ouminus(_928972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928972), _928974), _928976)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_928972), hAPP(c_Groups_Ouminus__class_Ouminus(_928972), _928974)), _928976))], (8775 ^ _780461) ^ [_929101, _929103, _929105] : [class_Rings_Oring(_929101), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929101), hAPP(c_Groups_Ouminus__class_Ouminus(_929101), _929103)), _929105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929101), _929103), hAPP(c_Groups_Ouminus__class_Ouminus(_929101), _929105)))], (8781 ^ _780461) ^ [_929230, _929232, _929234] : [class_Rings_Oring(_929230), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929230), hAPP(c_Groups_Ouminus__class_Ouminus(_929230), _929232)), hAPP(c_Groups_Ouminus__class_Ouminus(_929230), _929234)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929230), _929232), _929234))], (8787 ^ _780461) ^ [_929359, _929361, _929363] : [class_Rings_Oidom(_929359), 8790 ^ _780461 : [(8801 ^ _780461) ^ [] : [8802 ^ _780461 : [(8803 ^ _780461) ^ [] : [_929361 = _929363], (8805 ^ _780461) ^ [] : [_929361 = hAPP(c_Groups_Ouminus__class_Ouminus(_929359), _929363)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929359), _929361), _929361) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929359), _929363), _929363))], (8791 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929359), _929361), _929361) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929359), _929363), _929363), -(_929361 = _929363), -(_929361 = hAPP(c_Groups_Ouminus__class_Ouminus(_929359), _929363))]]], (8809 ^ _780461) ^ [_929678, _929680, _929682] : [class_Rings_Osemiring__1(_929678), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _929680), _929682)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_929678), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929678), _929680)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929678), _929682)))], (8815 ^ _780461) ^ [_929813, _929815] : [class_Rings_Oring__1(_929813), 8818 ^ _780461 : [(8819 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _929815), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_929813), _929815) = hAPP(c_Groups_Ouminus__class_Ouminus(_929813), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929813), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _929815)))))], (8825 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _929815), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_929813), _929815) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_929813), hAPP(c_Int_Onat, _929815)))]]], (8831 ^ _780461) ^ [_930075] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _930075))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8833 ^ _780461) ^ [_930107, _930109] : [class_Groups_Olinordered__ab__group__add(_930107), 8836 ^ _780461 : [(8837 ^ _780461) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_930107), _930109) = _930109, -(_930109 = c_Groups_Ozero__class_Ozero(_930107))], (8843 ^ _780461) ^ [] : [_930109 = c_Groups_Ozero__class_Ozero(_930107), -(hAPP(c_Groups_Ouminus__class_Ouminus(_930107), _930109) = _930109)]]], (8849 ^ _780461) ^ [_930333, _930335] : [class_Groups_Ogroup__add(_930333), 8852 ^ _780461 : [(8853 ^ _780461) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_930333), _930335) = c_Groups_Ozero__class_Ozero(_930333), -(_930335 = c_Groups_Ozero__class_Ozero(_930333))], (8859 ^ _780461) ^ [] : [_930335 = c_Groups_Ozero__class_Ozero(_930333), -(hAPP(c_Groups_Ouminus__class_Ouminus(_930333), _930335) = c_Groups_Ozero__class_Ozero(_930333))]]], (8865 ^ _780461) ^ [_930565, _930567] : [class_Groups_Olinordered__ab__group__add(_930565), 8868 ^ _780461 : [(8869 ^ _780461) ^ [] : [_930567 = hAPP(c_Groups_Ouminus__class_Ouminus(_930565), _930567), -(_930567 = c_Groups_Ozero__class_Ozero(_930565))], (8875 ^ _780461) ^ [] : [_930567 = c_Groups_Ozero__class_Ozero(_930565), -(_930567 = hAPP(c_Groups_Ouminus__class_Ouminus(_930565), _930567))]]], (8881 ^ _780461) ^ [_930791, _930793] : [class_Groups_Ogroup__add(_930791), 8884 ^ _780461 : [(8885 ^ _780461) ^ [] : [c_Groups_Ozero__class_Ozero(_930791) = hAPP(c_Groups_Ouminus__class_Ouminus(_930791), _930793), -(c_Groups_Ozero__class_Ozero(_930791) = _930793)], (8891 ^ _780461) ^ [] : [c_Groups_Ozero__class_Ozero(_930791) = _930793, -(c_Groups_Ozero__class_Ozero(_930791) = hAPP(c_Groups_Ouminus__class_Ouminus(_930791), _930793))]]], (8897 ^ _780461) ^ [_931023] : [class_Groups_Ogroup__add(_931023), -(hAPP(c_Groups_Ouminus__class_Ouminus(_931023), c_Groups_Ozero__class_Ozero(_931023)) = c_Groups_Ozero__class_Ozero(_931023))], (8903 ^ _780461) ^ [_931114, _931116, _931118] : [class_Groups_Oordered__ab__group__add(_931114), 8906 ^ _780461 : [(8907 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931114), _931116), hAPP(c_Groups_Ouminus__class_Ouminus(_931114), _931118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931114), _931118), hAPP(c_Groups_Ouminus__class_Ouminus(_931114), _931116))))], (8913 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931114), _931118), hAPP(c_Groups_Ouminus__class_Ouminus(_931114), _931116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931114), _931116), hAPP(c_Groups_Ouminus__class_Ouminus(_931114), _931118))))]]], (8919 ^ _780461) ^ [_931397, _931399, _931401] : [class_Groups_Oordered__ab__group__add(_931397), 8922 ^ _780461 : [(8923 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931397), hAPP(c_Groups_Ouminus__class_Ouminus(_931397), _931399)), _931401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931397), hAPP(c_Groups_Ouminus__class_Ouminus(_931397), _931401)), _931399)))], (8929 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931397), hAPP(c_Groups_Ouminus__class_Ouminus(_931397), _931401)), _931399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931397), hAPP(c_Groups_Ouminus__class_Ouminus(_931397), _931399)), _931401)))]]], (8935 ^ _780461) ^ [_931680, _931682, _931684] : [class_Groups_Oordered__ab__group__add(_931680), 8938 ^ _780461 : [(8939 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931680), hAPP(c_Groups_Ouminus__class_Ouminus(_931680), _931682)), hAPP(c_Groups_Ouminus__class_Ouminus(_931680), _931684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931680), _931684), _931682)))], (8945 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931680), _931684), _931682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931680), hAPP(c_Groups_Ouminus__class_Ouminus(_931680), _931682)), hAPP(c_Groups_Ouminus__class_Ouminus(_931680), _931684))))]]], (8951 ^ _780461) ^ [_931963, _931965, _931967] : [class_Groups_Ogroup__add(_931963), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931963), hAPP(c_Groups_Ouminus__class_Ouminus(_931963), _931965)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931963), _931965), _931967)) = _931967)], (8957 ^ _780461) ^ [_932082, _932084, _932086] : [class_Groups_Ogroup__add(_932082), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932082), _932084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932082), hAPP(c_Groups_Ouminus__class_Ouminus(_932082), _932084)), _932086)) = _932086)], (8963 ^ _780461) ^ [_932201, _932203, _932205] : [class_Groups_Ogroup__add(_932201), -(hAPP(c_Groups_Ouminus__class_Ouminus(_932201), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932201), _932203), _932205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932201), hAPP(c_Groups_Ouminus__class_Ouminus(_932201), _932205)), hAPP(c_Groups_Ouminus__class_Ouminus(_932201), _932203)))], (8969 ^ _780461) ^ [_932340, _932342, _932344] : [class_Groups_Oab__group__add(_932340), -(hAPP(c_Groups_Ouminus__class_Ouminus(_932340), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932340), _932342), _932344)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932340), hAPP(c_Groups_Ouminus__class_Ouminus(_932340), _932342)), hAPP(c_Groups_Ouminus__class_Ouminus(_932340), _932344)))], (8975 ^ _780461) ^ [_932479, _932481, _932483] : [class_Rings_Ono__zero__divisors(_932479), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932479), _932481), _932483) = c_Groups_Ozero__class_Ozero(_932479), -(_932481 = c_Groups_Ozero__class_Ozero(_932479)), -(_932483 = c_Groups_Ozero__class_Ozero(_932479))], (8989 ^ _780461) ^ [_932651, _932653, _932655] : [class_Rings_Ono__zero__divisors(_932651), -(_932653 = c_Groups_Ozero__class_Ozero(_932651)), -(_932655 = c_Groups_Ozero__class_Ozero(_932651)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932651), _932653), _932655) = c_Groups_Ozero__class_Ozero(_932651)], (9003 ^ _780461) ^ [_932871, _932873, _932875] : [class_Rings_Oring__no__zero__divisors(_932871), 9006 ^ _780461 : [(9017 ^ _780461) ^ [] : [9018 ^ _780461 : [(9019 ^ _780461) ^ [] : [_932873 = c_Groups_Ozero__class_Ozero(_932871)], (9021 ^ _780461) ^ [] : [_932875 = c_Groups_Ozero__class_Ozero(_932871)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932871), _932873), _932875) = c_Groups_Ozero__class_Ozero(_932871))], (9007 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932871), _932873), _932875) = c_Groups_Ozero__class_Ozero(_932871), -(_932873 = c_Groups_Ozero__class_Ozero(_932871)), -(_932875 = c_Groups_Ozero__class_Ozero(_932871))]]], (9025 ^ _780461) ^ [_933169, _933171] : [class_Rings_Omult__zero(_933169), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933169), _933171), c_Groups_Ozero__class_Ozero(_933169)) = c_Groups_Ozero__class_Ozero(_933169))], (9031 ^ _780461) ^ [_933268, _933270] : [class_Rings_Omult__zero(_933268), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933268), c_Groups_Ozero__class_Ozero(_933268)), _933270) = c_Groups_Ozero__class_Ozero(_933268))], (9037 ^ _780461) ^ [_933367, _933369] : [class_Rings_Ocomm__semiring__1(_933367), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933367), _933369), c_Groups_Ozero__class_Ozero(_933367)) = c_Groups_Ozero__class_Ozero(_933367))], (9043 ^ _780461) ^ [_933466, _933468] : [class_Rings_Ocomm__semiring__1(_933466), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933466), c_Groups_Ozero__class_Ozero(_933466)), _933468) = c_Groups_Ozero__class_Ozero(_933466))], (9049 ^ _780461) ^ [] : [-(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))], (9051 ^ _780461) ^ [_933583] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _933583)) = _933583)], (9053 ^ _780461) ^ [_933612, _933614, _933616, _933618, _933620] : [class_Rings_Osemiring(_933612), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933612), _933614), _933616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933612), _933618), _933616)), _933620)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933612), _933614), _933618)), _933616)), _933620))], (9059 ^ _780461) ^ [_933805, _933807, _933809, _933811] : [class_Rings_Ocomm__semiring(_933805), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933805), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933805), _933807), _933809)), _933811) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933805), _933807), _933811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933805), _933809), _933811)))], (9065 ^ _780461) ^ [_933964, _933966, _933968, _933970, _933972] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_933964), 9068 ^ _780461 : [(9079 ^ _780461) ^ [] : [9080 ^ _780461 : [(9081 ^ _780461) ^ [] : [_933966 = _933970], (9083 ^ _780461) ^ [] : [_933968 = _933972]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933964), _933966), _933968)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933964), _933970), _933972)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933964), _933966), _933972)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933964), _933970), _933968)))], (9069 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933964), _933966), _933968)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933964), _933970), _933972)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933964), _933966), _933972)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933964), _933970), _933968)), -(_933966 = _933970), -(_933968 = _933972)]]], (9087 ^ _780461) ^ [_934376, _934378, _934380, _934382] : [class_Rings_Ocomm__semiring__1(_934376), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934376), _934378), _934380)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934376), _934382), _934380)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934376), _934378), _934382)), _934380))], (9093 ^ _780461) ^ [_934535, _934537, _934539, _934541] : [class_Rings_Ocomm__semiring__1(_934535), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934535), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934535), _934537), _934539)), _934541) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934535), _934537), _934541)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934535), _934539), _934541)))], (9099 ^ _780461) ^ [_934694, _934696, _934698, _934700, _934702] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_934694), 9102 ^ _780461 : [(9113 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934694), _934696), _934700)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934694), _934698), _934702)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934694), _934696), _934702)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934694), _934698), _934700))), 9116 ^ _780461 : [(9117 ^ _780461) ^ [] : [_934696 = _934698], (9119 ^ _780461) ^ [] : [_934700 = _934702]]], (9103 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934694), _934696), _934700)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934694), _934698), _934702)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934694), _934696), _934702)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_934694), _934698), _934700)), -(_934696 = _934698), -(_934700 = _934702)]]], (9121 ^ _780461) ^ [_935112, _935114, _935116, _935118] : [class_Rings_Ocomm__semiring__1(_935112), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935112), _935114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935112), _935116), _935118)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935112), _935114), _935116)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_935112), _935114), _935118)))], (9127 ^ _780461) ^ [_935271, _935273] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _935271), _935273)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _935271)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _935273)))], (9129 ^ _780461) ^ [_935317, _935319, _935321] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _935317), _935319)), _935321) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935317), _935321)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935319), _935321)))], (9131 ^ _780461) ^ [_935374, _935376, _935378] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _935376), _935378)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935374), _935376)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _935374), _935378)))], (9133 ^ _780461) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9135 ^ _780461) ^ [_935449] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _935449)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _935449))], (9137 ^ _780461) ^ [_935481, _935483] : [class_Rings_Olinordered__idom(_935481), 9140 ^ _780461 : [(9141 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935481), _935483), hAPP(c_Groups_Ouminus__class_Ouminus(_935481), _935483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935481), _935483), c_Groups_Ozero__class_Ozero(_935481))))], (9147 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935481), _935483), c_Groups_Ozero__class_Ozero(_935481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935481), _935483), hAPP(c_Groups_Ouminus__class_Ouminus(_935481), _935483))))]]], (9153 ^ _780461) ^ [_935749, _935751] : [class_Groups_Olinordered__ab__group__add(_935749), 9156 ^ _780461 : [(9157 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935749), hAPP(c_Groups_Ouminus__class_Ouminus(_935749), _935751)), _935751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935749), c_Groups_Ozero__class_Ozero(_935749)), _935751)))], (9163 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935749), c_Groups_Ozero__class_Ozero(_935749)), _935751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935749), hAPP(c_Groups_Ouminus__class_Ouminus(_935749), _935751)), _935751)))]]], (9169 ^ _780461) ^ [_936017, _936019] : [class_Groups_Oordered__ab__group__add(_936017), 9172 ^ _780461 : [(9173 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936017), hAPP(c_Groups_Ouminus__class_Ouminus(_936017), _936019)), c_Groups_Ozero__class_Ozero(_936017))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936017), c_Groups_Ozero__class_Ozero(_936017)), _936019)))], (9179 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936017), c_Groups_Ozero__class_Ozero(_936017)), _936019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936017), hAPP(c_Groups_Ouminus__class_Ouminus(_936017), _936019)), c_Groups_Ozero__class_Ozero(_936017))))]]], (9185 ^ _780461) ^ [_936291, _936293] : [class_Groups_Oordered__ab__group__add(_936291), 9188 ^ _780461 : [(9189 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936291), c_Groups_Ozero__class_Ozero(_936291)), hAPP(c_Groups_Ouminus__class_Ouminus(_936291), _936293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936291), _936293), c_Groups_Ozero__class_Ozero(_936291))))], (9195 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936291), _936293), c_Groups_Ozero__class_Ozero(_936291))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936291), c_Groups_Ozero__class_Ozero(_936291)), hAPP(c_Groups_Ouminus__class_Ouminus(_936291), _936293))))]]], (9201 ^ _780461) ^ [_936565, _936567] : [class_Groups_Ogroup__add(_936565), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936565), _936567), hAPP(c_Groups_Ouminus__class_Ouminus(_936565), _936567)) = c_Groups_Ozero__class_Ozero(_936565))], (9207 ^ _780461) ^ [_936670, _936672, _936674] : [class_Groups_Ogroup__add(_936670), 9210 ^ _780461 : [(9211 ^ _780461) ^ [] : [_936672 = hAPP(c_Groups_Ouminus__class_Ouminus(_936670), _936674), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936670), _936672), _936674) = c_Groups_Ozero__class_Ozero(_936670))], (9217 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936670), _936672), _936674) = c_Groups_Ozero__class_Ozero(_936670), -(_936672 = hAPP(c_Groups_Ouminus__class_Ouminus(_936670), _936674))]]], (9223 ^ _780461) ^ [_936926, _936928] : [class_Groups_Ogroup__add(_936926), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936926), hAPP(c_Groups_Ouminus__class_Ouminus(_936926), _936928)), _936928) = c_Groups_Ozero__class_Ozero(_936926))], (9229 ^ _780461) ^ [_937031, _937033] : [class_Groups_Oab__group__add(_937031), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937031), hAPP(c_Groups_Ouminus__class_Ouminus(_937031), _937033)), _937033) = c_Groups_Ozero__class_Ozero(_937031))], (9235 ^ _780461) ^ [_937136, _937138, _937140] : [class_Groups_Ogroup__add(_937136), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937136), _937138), _937140) = c_Groups_Ozero__class_Ozero(_937136), -(hAPP(c_Groups_Ouminus__class_Ouminus(_937136), _937138) = _937140)], (9245 ^ _780461) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9247 ^ _780461) ^ [_937315, _937317, _937319, _937321] : [class_Rings_Olinordered__ring__strict(_937315), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937315), _937317), _937319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937315), _937321), c_Groups_Ozero__class_Ozero(_937315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937315), _937321), _937319)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937315), _937321), _937317))))], (9261 ^ _780461) ^ [_937584, _937586, _937588, _937590] : [class_Rings_Olinordered__ring__strict(_937584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937584), _937586), _937588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937584), _937590), c_Groups_Ozero__class_Ozero(_937584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937584), _937588), _937590)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937584), _937586), _937590))))], (9275 ^ _780461) ^ [_937853, _937855, _937857, _937859] : [class_Rings_Olinordered__comm__semiring__strict(_937853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937853), _937855), _937857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937853), c_Groups_Ozero__class_Ozero(_937853)), _937859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937853), _937859), _937855)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_937853), _937859), _937857))))], (9289 ^ _780461) ^ [_938122, _938124, _938126, _938128] : [class_Rings_Olinordered__semiring__strict(_938122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938122), _938124), _938126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938122), c_Groups_Ozero__class_Ozero(_938122)), _938128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938122), _938128), _938124)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938122), _938128), _938126))))], (9303 ^ _780461) ^ [_938391, _938393, _938395, _938397] : [class_Rings_Olinordered__semiring__strict(_938391), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938391), _938393), _938395)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938391), c_Groups_Ozero__class_Ozero(_938391)), _938397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938391), _938393), _938397)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938391), _938395), _938397))))], (9317 ^ _780461) ^ [_938660, _938662, _938664] : [class_Rings_Olinordered__ring__strict(_938660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938660), _938662), c_Groups_Ozero__class_Ozero(_938660))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938660), _938664), c_Groups_Ozero__class_Ozero(_938660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938660), c_Groups_Ozero__class_Ozero(_938660)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938660), _938662), _938664))))], (9331 ^ _780461) ^ [_938915, _938917, _938919] : [class_Rings_Olinordered__semiring__strict(_938915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938915), _938917), c_Groups_Ozero__class_Ozero(_938915))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938915), c_Groups_Ozero__class_Ozero(_938915)), _938919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_938915), _938917), _938919)), c_Groups_Ozero__class_Ozero(_938915))))], (9345 ^ _780461) ^ [_939170, _939172, _939174, _939176] : [class_Rings_Olinordered__ring__strict(_939170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939170), _939172), c_Groups_Ozero__class_Ozero(_939170))), 9352 ^ _780461 : [(9353 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939170), _939172), _939174)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939170), _939172), _939176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939170), _939176), _939174)))], (9359 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939170), _939176), _939174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939170), _939172), _939174)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939170), _939172), _939176))))]]], (9365 ^ _780461) ^ [_939551, _939553, _939555] : [class_Rings_Olinordered__semiring__strict(_939551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939551), c_Groups_Ozero__class_Ozero(_939551)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939551), _939553), _939555))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939551), c_Groups_Ozero__class_Ozero(_939551)), _939555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939551), c_Groups_Ozero__class_Ozero(_939551)), _939553)))], (9379 ^ _780461) ^ [_939806, _939808, _939810] : [class_Rings_Olinordered__semiring__strict(_939806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939806), c_Groups_Ozero__class_Ozero(_939806)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_939806), _939808), _939810))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939806), c_Groups_Ozero__class_Ozero(_939806)), _939808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939806), c_Groups_Ozero__class_Ozero(_939806)), _939810)))], (9393 ^ _780461) ^ [_940061, _940063, _940065] : [class_Rings_Olinordered__semiring__strict(_940061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940061), c_Groups_Ozero__class_Ozero(_940061)), _940063)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940061), _940065), c_Groups_Ozero__class_Ozero(_940061))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940061), _940065), _940063)), c_Groups_Ozero__class_Ozero(_940061))))], (9407 ^ _780461) ^ [_940316, _940318, _940320] : [class_Rings_Olinordered__semiring__strict(_940316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940316), c_Groups_Ozero__class_Ozero(_940316)), _940318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940316), _940320), c_Groups_Ozero__class_Ozero(_940316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940316), _940318), _940320)), c_Groups_Ozero__class_Ozero(_940316))))], (9421 ^ _780461) ^ [_940571, _940573, _940575] : [class_Rings_Olinordered__semiring__strict(_940571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940571), c_Groups_Ozero__class_Ozero(_940571)), _940573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940571), c_Groups_Ozero__class_Ozero(_940571)), _940575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940571), c_Groups_Ozero__class_Ozero(_940571)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940571), _940573), _940575))))], (9435 ^ _780461) ^ [_940826, _940828, _940830, _940832] : [class_Rings_Olinordered__ring__strict(_940826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940826), c_Groups_Ozero__class_Ozero(_940826)), _940828)), 9442 ^ _780461 : [(9443 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940826), _940828), _940830)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940826), _940828), _940832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940826), _940830), _940832)))], (9449 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940826), _940830), _940832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940826), _940828), _940830)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_940826), _940828), _940832))))]]], (9455 ^ _780461) ^ [_941207, _941209, _941211, _941213] : [class_Rings_Olinordered__ring__strict(_941207), 9458 ^ _780461 : [(9459 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941207), _941209), _941211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941207), _941209), _941213))), 9464 ^ _780461 : [(9465 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), c_Groups_Ozero__class_Ozero(_941207)), _941209)))], (9467 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), _941211), _941213)))]], 9468 ^ _780461 : [(9469 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), _941209), c_Groups_Ozero__class_Ozero(_941207))))], (9471 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), _941213), _941211)))]]], (9473 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941207), _941209), _941211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941207), _941209), _941213)))), 9474 ^ _780461 : [(9475 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), c_Groups_Ozero__class_Ozero(_941207)), _941209)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), _941211), _941213))], (9481 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), _941209), c_Groups_Ozero__class_Ozero(_941207))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941207), _941213), _941211))]]]]], (9489 ^ _780461) ^ [_941813, _941815, _941817, _941819] : [class_Rings_Olinordered__ring__strict(_941813), 9492 ^ _780461 : [(9493 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941813), _941815), _941817)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941813), _941819), _941817))), 9498 ^ _780461 : [(9499 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), c_Groups_Ozero__class_Ozero(_941813)), _941817)))], (9501 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), _941815), _941819)))]], 9502 ^ _780461 : [(9503 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), _941817), c_Groups_Ozero__class_Ozero(_941813))))], (9505 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), _941819), _941815)))]]], (9507 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941813), _941815), _941817)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941813), _941819), _941817)))), 9508 ^ _780461 : [(9509 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), c_Groups_Ozero__class_Ozero(_941813)), _941817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), _941815), _941819))], (9515 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), _941817), c_Groups_Ozero__class_Ozero(_941813))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941813), _941819), _941815))]]]]], (9523 ^ _780461) ^ [_942419, _942421] : [class_Rings_Olinordered__ring(_942419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942419), _942421), _942421)), c_Groups_Ozero__class_Ozero(_942419)))], (9529 ^ _780461) ^ [_942529, _942531, _942533] : [class_Rings_Olinordered__ring__strict(_942529), 9532 ^ _780461 : [(9533 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942529), _942531), _942531)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942529), _942533), _942533)) = c_Groups_Ozero__class_Ozero(_942529), 9536 ^ _780461 : [(9537 ^ _780461) ^ [] : [-(_942531 = c_Groups_Ozero__class_Ozero(_942529))], (9539 ^ _780461) ^ [] : [-(_942533 = c_Groups_Ozero__class_Ozero(_942529))]]], (9541 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942529), _942531), _942531)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942529), _942533), _942533)) = c_Groups_Ozero__class_Ozero(_942529)), _942531 = c_Groups_Ozero__class_Ozero(_942529), _942533 = c_Groups_Ozero__class_Ozero(_942529)]]], (9551 ^ _780461) ^ [_942904, _942906, _942908, _942910, _942912, _942914] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_942904), -(_942906 = c_Groups_Ozero__class_Ozero(_942904)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942904), _942908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942904), _942906), _942912)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942904), _942910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942904), _942906), _942914)), _942908 = _942910, -(_942912 = _942914)], (9569 ^ _780461) ^ [_943242] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _943242)), _943242) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9571 ^ _780461) ^ [_943289, _943291] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943289)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943291), 9574 ^ _780461 : [(9575 ^ _780461) ^ [] : [-(_943289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9577 ^ _780461) ^ [] : [-(_943291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9579 ^ _780461) ^ [_943406, _943408] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943406)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943408)), _943406 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _943408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9589 ^ _780461) ^ [_943567, _943569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943567)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _943569))))], (9591 ^ _780461) ^ [_943606, _943608, _943610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _943606), _943608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _943610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _943610), _943606)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _943610), _943608))))], (9601 ^ _780461) ^ [_943787, _943789] : [class_Int_Oring__char__0(_943787), 9604 ^ _780461 : [(9605 ^ _780461) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_943787), _943789) = c_Groups_Ozero__class_Ozero(_943787), -(_943789 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9611 ^ _780461) ^ [] : [_943789 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_943787), _943789) = c_Groups_Ozero__class_Ozero(_943787))]]], (9617 ^ _780461) ^ [_944013, _944015] : [class_Int_Oring__char__0(_944013), 9620 ^ _780461 : [(9621 ^ _780461) ^ [] : [c_Groups_Ozero__class_Ozero(_944013) = hAPP(c_Int_Oring__1__class_Oof__int(_944013), _944015), -(_944015 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9627 ^ _780461) ^ [] : [_944015 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_944013) = hAPP(c_Int_Oring__1__class_Oof__int(_944013), _944015))]]], (9633 ^ _780461) ^ [_944239] : [class_Rings_Oring__1(_944239), -(hAPP(c_Int_Oring__1__class_Oof__int(_944239), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_944239))], (9639 ^ _780461) ^ [_944326, _944328, _944330] : [class_Rings_Olinordered__idom(_944326), 9642 ^ _780461 : [(9643 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944326), hAPP(c_Int_Oring__1__class_Oof__int(_944326), _944328)), hAPP(c_Int_Oring__1__class_Oof__int(_944326), _944330))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _944328), _944330)))], (9649 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _944328), _944330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944326), hAPP(c_Int_Oring__1__class_Oof__int(_944326), _944328)), hAPP(c_Int_Oring__1__class_Oof__int(_944326), _944330))))]]], (9655 ^ _780461) ^ [_944603, _944605, _944607] : [class_Rings_Oring__1(_944603), -(hAPP(c_Int_Oring__1__class_Oof__int(_944603), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _944605), _944607)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944603), hAPP(c_Int_Oring__1__class_Oof__int(_944603), _944605)), hAPP(c_Int_Oring__1__class_Oof__int(_944603), _944607)))], (9661 ^ _780461) ^ [_944738, _944740] : [class_Rings_Oring__1(_944738), -(hAPP(c_Int_Oring__1__class_Oof__int(_944738), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _944740)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_944738), _944740))], (9667 ^ _780461) ^ [_944839, _944841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _944839)), 9670 ^ _780461 : [(9671 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _944841)), hAPP(c_Int_Onat, _944839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _944841), _944839)))], (9677 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _944841), _944839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _944841)), hAPP(c_Int_Onat, _944839))))]]], (9683 ^ _780461) ^ [_945113, _945115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _945113)), hAPP(c_Int_Onat, _945115))), 9686 ^ _780461 : [(9687 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _945115)))], (9689 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _945113), _945115)))]]], (9691 ^ _780461) ^ [_945248, _945250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _945248)), hAPP(c_Int_Onat, _945250)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _945250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _945248), _945250))], (9701 ^ _780461) ^ [_945430, _945432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945430), hAPP(c_Int_Onat, _945432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945430)), _945432)))], (9707 ^ _780461) ^ [_945535, _945537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _945535)), _945537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945535), hAPP(c_Int_Onat, _945537))))], (9713 ^ _780461) ^ [_945646, _945648, _945650] : [class_Rings_Olinordered__ring__strict(_945646), 9716 ^ _780461 : [(9727 ^ _780461) ^ [] : [9728 ^ _780461 : [(9729 ^ _780461) ^ [] : [-(_945648 = c_Groups_Ozero__class_Ozero(_945646))], (9731 ^ _780461) ^ [] : [-(_945650 = c_Groups_Ozero__class_Ozero(_945646))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945646), c_Groups_Ozero__class_Ozero(_945646)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945646), _945648), _945648)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945646), _945650), _945650)))))], (9717 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945646), c_Groups_Ozero__class_Ozero(_945646)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_945646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945646), _945648), _945648)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945646), _945650), _945650)))), _945648 = c_Groups_Ozero__class_Ozero(_945646), _945650 = c_Groups_Ozero__class_Ozero(_945646)]]], (9735 ^ _780461) ^ [_946021, _946023, _946025] : [class_Rings_Olinordered__ring(_946021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946021), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946021), _946023), _946023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946021), _946025), _946025))), c_Groups_Ozero__class_Ozero(_946021)))], (9741 ^ _780461) ^ [_946180, _946182] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _946180) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _946182), -(_946180 = _946182)], (9747 ^ _780461) ^ [_946265, _946267] : [_946265 = _946267, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _946265) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _946267))], (9753 ^ _780461) ^ [_946356, _946358] : [-(c_Int_Onat__aux(_946356, _946358) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _946356)), _946358))], (9755 ^ _780461) ^ [_946393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _946393), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_946393 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 9758 ^ [_946393]))))], (9762 ^ _780461) ^ [_946506, _946508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _946506)), 9765 ^ _780461 : [(9766 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _946506)), _946508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _946506), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _946508))))], (9772 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _946506), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _946508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _946506)), _946508)))]]], (9778 ^ _780461) ^ [_946777] : [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, _946777))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _946777)))], (9784 ^ _780461) ^ [_946862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _946862)), -(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, _946862))))], (9790 ^ _780461) ^ [_946953, _946955] : [class_Rings_Oring__1(_946953), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _946955)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_946953), hAPP(c_Int_Onat, _946955)) = hAPP(c_Int_Oring__1__class_Oof__int(_946953), _946955))], (9800 ^ _780461) ^ [_947119] : [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, _947119)))))], (9802 ^ _780461) ^ [_947153, _947155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947155)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _947153)), hAPP(c_Int_Onat, _947155)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _947153), _947155)))], (9812 ^ _780461) ^ [_947332, _947334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947334)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _947332), _947334)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _947332)), hAPP(c_Int_Onat, _947334)))], (9838 ^ _780461) ^ [_947718, _947720] : [-(_947718 = hAPP(c_Int_Onat, _947720)), 9841 ^ _780461 : [(9842 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947720)))], (9844 ^ _780461) ^ [] : [_947720 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _947718)]], 9845 ^ _780461 : [(9846 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947720))], (9848 ^ _780461) ^ [] : [_947718 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (9822 ^ _780461) ^ [_947526, _947528] : [_947526 = hAPP(c_Int_Onat, _947528), 9825 ^ _780461 : [(9826 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947528)), -(_947528 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _947526))], (9832 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947528))), -(_947526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9868 ^ _780461) ^ [_948149, _948151] : [-(hAPP(c_Int_Onat, _948149) = _948151), 9871 ^ _780461 : [(9872 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948149)))], (9874 ^ _780461) ^ [] : [_948149 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948151)]], 9875 ^ _780461 : [(9876 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _948149))], (9878 ^ _780461) ^ [] : [_948151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (9852 ^ _780461) ^ [_947957, _947959] : [hAPP(c_Int_Onat, _947957) = _947959, 9855 ^ _780461 : [(9856 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947957)), -(_947957 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _947959))], (9862 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _947957))), -(_947959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9882 ^ _780461) ^ [_948373, _948375] : [-(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), _948373))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _948375))))], (9884 ^ _780461) ^ [] : [-(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))))], (9886 ^ _780461) ^ [_948430, _948432] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948430), _948432) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948432), _948430))], (9888 ^ _780461) ^ [_948467, _948469, _948471] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948467), _948469)), _948471) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _948469), _948471)))], (9890 ^ _780461) ^ [_948518, _948520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948518), _948520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948520), _948518)), -(_948518 = _948520)], (9900 ^ _780461) ^ [_948667, _948669, _948671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948667), _948669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948669), _948671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948667), _948671)))], (9910 ^ _780461) ^ [_948826, _948828] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948826), _948828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _948828), _948826)))], (9916 ^ _780461) ^ [_948872, _948874] : [class_Groups_Oone(_948872), 9919 ^ _780461 : [(9920 ^ _780461) ^ [] : [c_Groups_Oone__class_Oone(_948872) = _948874, -(_948874 = c_Groups_Oone__class_Oone(_948872))], (9926 ^ _780461) ^ [] : [_948874 = c_Groups_Oone__class_Oone(_948872), -(c_Groups_Oone__class_Oone(_948872) = _948874)]]], (9932 ^ _780461) ^ [_949089] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _949089), _949089)))], (9934 ^ _780461) ^ [_949117] : [class_Rings_Olinordered__semidom(_949117), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949117), c_Groups_Oone__class_Oone(_949117)), c_Groups_Ozero__class_Ozero(_949117)))], (9940 ^ _780461) ^ [_949213] : [class_Rings_Olinordered__semidom(_949213), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949213), c_Groups_Ozero__class_Ozero(_949213)), c_Groups_Oone__class_Oone(_949213))))], (9946 ^ _780461) ^ [_949308] : [class_Rings_Osemiring__1(_949308), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_949308), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_949308))], (9952 ^ _780461) ^ [_949395, _949397, _949399] : [class_Rings_Olinordered__semidom(_949395), 9955 ^ _780461 : [(9956 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949395), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_949395), _949397)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_949395), _949399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949397), _949399)))], (9962 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949397), _949399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949395), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_949395), _949397)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_949395), _949399))))]]], (9968 ^ _780461) ^ [_949672, _949674, _949676] : [class_Rings_Olinordered__idom(_949672), 9971 ^ _780461 : [(9972 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949672), hAPP(c_Int_Oring__1__class_Oof__int(_949672), _949674)), hAPP(c_Int_Oring__1__class_Oof__int(_949672), _949676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _949674), _949676)))], (9978 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _949674), _949676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949672), hAPP(c_Int_Oring__1__class_Oof__int(_949672), _949674)), hAPP(c_Int_Oring__1__class_Oof__int(_949672), _949676))))]]], (9984 ^ _780461) ^ [_949949] : [class_Rings_Oring__1(_949949), -(hAPP(c_Int_Oring__1__class_Oof__int(_949949), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_949949))], (9990 ^ _780461) ^ [_950036, _950038, _950040] : [class_Rings_Olinordered__idom(_950036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950036), c_Groups_Ozero__class_Ozero(_950036)), _950038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950036), c_Groups_Ozero__class_Ozero(_950036)), _950040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950036), _950040), c_Groups_Oone__class_Oone(_950036))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950036), _950038), _950040)), _950038)))], (10008 ^ _780461) ^ [_950359, _950361, _950363] : [class_Rings_Olinordered__idom(_950359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950359), c_Groups_Ozero__class_Ozero(_950359)), _950361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950359), c_Groups_Ozero__class_Ozero(_950359)), _950363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950359), _950363), c_Groups_Oone__class_Oone(_950359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950359), _950363), _950361)), _950361)))], (10026 ^ _780461) ^ [_950694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _950694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950694)))], (10032 ^ _780461) ^ [_950773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _950773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _950773)))], (10038 ^ _780461) ^ [_950873, _950875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _950873), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _950875), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _950873), _950875)))], (10044 ^ _780461) ^ [_950978, _950980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _950978), _950980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _950978), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _950980), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (10050 ^ _780461) ^ [_951104, _951106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _951104), c_Groups_Oone__class_Oone(tc_Int_Oint))), _951106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _951104), _951106)))], (10056 ^ _780461) ^ [_951209, _951211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _951209), _951211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _951209), c_Groups_Oone__class_Oone(tc_Int_Oint))), _951211)))], (10062 ^ _780461) ^ [_951320, _951322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _951320), _951322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _951320), c_Groups_Oone__class_Oone(tc_Int_Oint))), _951322)))], (10068 ^ _780461) ^ [_951429] : [class_Rings_Ozero__neq__one(_951429), c_Groups_Oone__class_Oone(_951429) = c_Groups_Ozero__class_Ozero(_951429)], (10074 ^ _780461) ^ [_951511] : [class_Rings_Ozero__neq__one(_951511), c_Groups_Ozero__class_Ozero(_951511) = c_Groups_Oone__class_Oone(_951511)], (10080 ^ _780461) ^ [_951593, _951595] : [class_Groups_Ocomm__monoid__mult(_951593), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951593), _951595), c_Groups_Oone__class_Oone(_951593)) = _951595)], (10086 ^ _780461) ^ [_951688, _951690] : [class_Rings_Ocomm__semiring__1(_951688), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951688), _951690), c_Groups_Oone__class_Oone(_951688)) = _951690)], (10092 ^ _780461) ^ [_951783, _951785] : [class_Groups_Omonoid__mult(_951783), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951783), _951785), c_Groups_Oone__class_Oone(_951783)) = _951785)], (10098 ^ _780461) ^ [_951878, _951880] : [class_Groups_Ocomm__monoid__mult(_951878), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951878), c_Groups_Oone__class_Oone(_951878)), _951880) = _951880)], (10104 ^ _780461) ^ [_951973, _951975] : [class_Rings_Ocomm__semiring__1(_951973), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951973), c_Groups_Oone__class_Oone(_951973)), _951975) = _951975)], (10110 ^ _780461) ^ [_952068, _952070] : [class_Groups_Omonoid__mult(_952068), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952068), c_Groups_Oone__class_Oone(_952068)), _952070) = _952070)], (10116 ^ _780461) ^ [_952163, _952165, _952167, _952169] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_952163), 10119 ^ _780461 : [(10120 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952163), _952165), _952167)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952163), _952169), _952167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952163), _952165), _952169)))], (10126 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952163), _952165), _952169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952163), _952165), _952167)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952163), _952169), _952167))))]]], (10132 ^ _780461) ^ [_952470, _952472, _952474, _952476] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_952470), 10135 ^ _780461 : [(10136 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952470), _952472), _952474)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952470), _952472), _952476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952470), _952474), _952476)))], (10142 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952470), _952474), _952476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952470), _952472), _952474)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952470), _952472), _952476))))]]], (10148 ^ _780461) ^ [_952777, _952779, _952781, _952783] : [class_Groups_Oordered__ab__semigroup__add(_952777), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952777), _952779), _952781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952777), _952779), _952783)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952777), _952781), _952783))))], (10158 ^ _780461) ^ [_952972, _952974, _952976, _952978] : [class_Groups_Oordered__ab__semigroup__add(_952972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952972), _952974), _952976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952972), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952972), _952978), _952974)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952972), _952978), _952976))))], (10168 ^ _780461) ^ [_953167, _953169, _953171, _953173, _953175] : [class_Groups_Oordered__ab__semigroup__add(_953167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953167), _953169), _953171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953167), _953173), _953175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953167), _953169), _953173)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953167), _953171), _953175))))], (10182 ^ _780461) ^ [_953438, _953440, _953442, _953444] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_953438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953438), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953438), _953440), _953442)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953438), _953444), _953442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953438), _953440), _953444)))], (10192 ^ _780461) ^ [_953633, _953635, _953637, _953639] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_953633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953633), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953633), _953635), _953637)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953633), _953635), _953639))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953633), _953637), _953639)))], (10212 ^ _780461) ^ [_953958, _953960, _953962] : [10213 ^ _780461 : [(10214 ^ _780461) ^ [] : [_953958 = _953962], (10216 ^ _780461) ^ [] : [_953960 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953958), _953960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953962), _953960))], (10202 ^ _780461) ^ [_953846, _953848, _953850] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953846), _953848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953850), _953848), -(_953846 = _953850), -(_953848 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10230 ^ _780461) ^ [_954231, _954233, _954235] : [10231 ^ _780461 : [(10232 ^ _780461) ^ [] : [_954233 = _954235], (10234 ^ _780461) ^ [] : [_954231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954231), _954233) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954231), _954235))], (10220 ^ _780461) ^ [_954119, _954121, _954123] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954119), _954121) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954119), _954123), -(_954121 = _954123), -(_954119 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10248 ^ _780461) ^ [_954487, _954489] : [10249 ^ _780461 : [(10250 ^ _780461) ^ [] : [_954487 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10252 ^ _780461) ^ [] : [_954489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954487), _954489) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10238 ^ _780461) ^ [_954389, _954391] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954389), _954391) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_954389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_954391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10256 ^ _780461) ^ [_954616] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954616), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10258 ^ _780461) ^ [_954645] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _954645) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10260 ^ _780461) ^ [_954689, _954691, _954693] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954689)), _954691) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954689)), _954693), -(_954691 = _954693)], (10266 ^ _780461) ^ [_954800, _954802, _954804] : [_954802 = _954804, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954800)), _954802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954800)), _954804))], (10272 ^ _780461) ^ [_954917, _954919, _954921] : [class_Groups_Oordered__ab__group__add(_954917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954917), _954919), _954921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954917), hAPP(c_Groups_Ouminus__class_Ouminus(_954917), _954921)), hAPP(c_Groups_Ouminus__class_Ouminus(_954917), _954919))))], (10282 ^ _780461) ^ [_955096, _955098, _955100] : [class_Groups_Oordered__ab__group__add(_955096), 10285 ^ _780461 : [(10286 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955096), hAPP(c_Groups_Ouminus__class_Ouminus(_955096), _955098)), hAPP(c_Groups_Ouminus__class_Ouminus(_955096), _955100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955096), _955100), _955098)))], (10292 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955096), _955100), _955098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955096), hAPP(c_Groups_Ouminus__class_Ouminus(_955096), _955098)), hAPP(c_Groups_Ouminus__class_Ouminus(_955096), _955100))))]]], (10298 ^ _780461) ^ [_955379, _955381, _955383] : [class_Groups_Oordered__ab__group__add(_955379), 10301 ^ _780461 : [(10302 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955379), hAPP(c_Groups_Ouminus__class_Ouminus(_955379), _955381)), _955383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955379), hAPP(c_Groups_Ouminus__class_Ouminus(_955379), _955383)), _955381)))], (10308 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955379), hAPP(c_Groups_Ouminus__class_Ouminus(_955379), _955383)), _955381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955379), hAPP(c_Groups_Ouminus__class_Ouminus(_955379), _955381)), _955383)))]]], (10314 ^ _780461) ^ [_955662, _955664, _955666] : [class_Groups_Oordered__ab__group__add(_955662), 10317 ^ _780461 : [(10318 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955662), _955664), hAPP(c_Groups_Ouminus__class_Ouminus(_955662), _955666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955662), _955666), hAPP(c_Groups_Ouminus__class_Ouminus(_955662), _955664))))], (10324 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955662), _955666), hAPP(c_Groups_Ouminus__class_Ouminus(_955662), _955664))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955662), _955664), hAPP(c_Groups_Ouminus__class_Ouminus(_955662), _955666))))]]], (10330 ^ _780461) ^ [_955945, _955947, _955949] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _955945), _955947)), _955949) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955945), _955949)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _955947), _955949)))], (10332 ^ _780461) ^ [_956002, _956004, _956006] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956004), _956006)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956002), _956004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956002), _956006)))], (10334 ^ _780461) ^ [] : [-(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))))], (10336 ^ _780461) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (10338 ^ _780461) ^ [_956116, _956118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _956116), _956118)), 10341 ^ _780461 : [(10342 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _956116), _956118)))], (10344 ^ _780461) ^ [] : [_956116 = _956118]]], (10346 ^ _780461) ^ [_956243, _956245] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _956243), _956245))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _956243), _956245)), -(_956243 = _956245)], (10356 ^ _780461) ^ [_956397, _956399, _956401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _956397), _956399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _956401), _956397)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _956401), _956399))))], (10362 ^ _780461) ^ [_956520] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _956520), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _956520)], (10364 ^ _780461) ^ [_956549] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _956549) = _956549)], (10366 ^ _780461) ^ [_956575, _956577, _956579, _956581, _956583, _956585] : [class_Rings_Olinordered__semiring__1(_956575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956575), _956577), _956579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956575), _956581), _956579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956575), c_Groups_Ozero__class_Ozero(_956575)), _956583)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956575), c_Groups_Ozero__class_Ozero(_956575)), _956585)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956575), _956583), _956585) = c_Groups_Oone__class_Oone(_956575), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956575), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956575), _956583), _956577)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956575), _956585), _956581))), _956579)))], (10392 ^ _780461) ^ [_957104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _957104)), -(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)), _957104))))], (10398 ^ _780461) ^ [_957193, _957195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _957193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _957195)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _957193)), hAPP(c_Int_Onat, _957195)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _957193), _957195)))], (10408 ^ _780461) ^ [_957372, _957374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _957372)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _957372), _957374)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _957372)), hAPP(c_Int_Onat, _957374)))], (10414 ^ _780461) ^ [_957495, _957497] : [class_Rings_Olinordered__idom(_957495), 10417 ^ _780461 : [(10418 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957495), c_Groups_Ozero__class_Ozero(_957495)), hAPP(c_Int_Oring__1__class_Oof__int(_957495), _957497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _957497)))], (10424 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _957497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957495), c_Groups_Ozero__class_Ozero(_957495)), hAPP(c_Int_Oring__1__class_Oof__int(_957495), _957497))))]]], (10430 ^ _780461) ^ [_957748, _957750] : [class_Rings_Olinordered__idom(_957748), 10433 ^ _780461 : [(10434 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957748), hAPP(c_Int_Oring__1__class_Oof__int(_957748), _957750)), c_Groups_Ozero__class_Ozero(_957748))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _957750), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10440 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _957750), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957748), hAPP(c_Int_Oring__1__class_Oof__int(_957748), _957750)), c_Groups_Ozero__class_Ozero(_957748))))]]], (10446 ^ _780461) ^ [_958010, _958012, _958014, _958016, _958018, _958020] : [class_Rings_Olinordered__semiring__1__strict(_958010), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958010), _958012), _958014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958010), _958016), _958014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958010), c_Groups_Ozero__class_Ozero(_958010)), _958018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958010), c_Groups_Ozero__class_Ozero(_958010)), _958020)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958010), _958018), _958020) = c_Groups_Oone__class_Oone(_958010), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958010), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958010), _958018), _958012)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958010), _958020), _958016))), _958014)))], (10472 ^ _780461) ^ [_958539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _958539)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _958539)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _958539)))], (10478 ^ _780461) ^ [_958642] : [class_Rings_Olinordered__semidom(_958642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958642), c_Groups_Oone__class_Oone(_958642)), c_Groups_Ozero__class_Ozero(_958642)))], (10484 ^ _780461) ^ [_958738] : [class_Rings_Olinordered__semidom(_958738), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958738), c_Groups_Ozero__class_Ozero(_958738)), c_Groups_Oone__class_Oone(_958738))))], (10490 ^ _780461) ^ [_958833, _958835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _958833), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _958833), _958835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _958833))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _958835))))], (10496 ^ _780461) ^ [_958974, _958976] : [class_Rings_Olinordered__semidom(_958974), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958974), _958976), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958974), _958976), c_Groups_Oone__class_Oone(_958974)))))], (10502 ^ _780461) ^ [_959083, _959085, _959087] : [class_Rings_Olinordered__semidom(_959083), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959083), c_Groups_Oone__class_Oone(_959083)), _959085)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959083), c_Groups_Oone__class_Oone(_959083)), _959087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959083), c_Groups_Oone__class_Oone(_959083)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959083), _959085), _959087))))], (10516 ^ _780461) ^ [_959338, _959340, _959342] : [class_Rings_Ocomm__semiring__1(_959338), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959338), _959340), _959342)), _959342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959338), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959338), _959340), c_Groups_Oone__class_Oone(_959338))), _959342))], (10522 ^ _780461) ^ [_959483, _959485, _959487] : [class_Rings_Ocomm__semiring__1(_959483), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959483), _959485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959483), _959487), _959485)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959483), _959487), c_Groups_Oone__class_Oone(_959483))), _959485))], (10528 ^ _780461) ^ [_959628, _959630] : [class_Rings_Ocomm__semiring__1(_959628), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959628), _959630), _959630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959628), c_Groups_Oone__class_Oone(_959628)), c_Groups_Oone__class_Oone(_959628))), _959630))], (10534 ^ _780461) ^ [_959759, _959761, _959763] : [class_Groups_Oordered__comm__monoid__add(_959759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959759), _959761), c_Groups_Ozero__class_Ozero(_959759))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959759), _959763), c_Groups_Ozero__class_Ozero(_959759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959759), _959761), _959763)), c_Groups_Ozero__class_Ozero(_959759))))], (10548 ^ _780461) ^ [_960014, _960016, _960018, _960020] : [class_Groups_Oordered__comm__monoid__add(_960014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960014), c_Groups_Ozero__class_Ozero(_960014)), _960016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960014), _960018), _960020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960014), _960018), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960014), _960020), _960016))))], (10562 ^ _780461) ^ [_960267, _960269, _960271, _960273] : [class_Groups_Oordered__comm__monoid__add(_960267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960267), c_Groups_Ozero__class_Ozero(_960267)), _960269)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960267), _960271), _960273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960267), _960271), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960267), _960269), _960273))))], (10576 ^ _780461) ^ [_960520, _960522, _960524] : [class_Groups_Oordered__comm__monoid__add(_960520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960520), c_Groups_Ozero__class_Ozero(_960520)), _960522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960520), c_Groups_Ozero__class_Ozero(_960520)), _960524)), 10587 ^ _780461 : [(10588 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960520), _960522), _960524) = c_Groups_Ozero__class_Ozero(_960520), 10591 ^ _780461 : [(10592 ^ _780461) ^ [] : [-(_960522 = c_Groups_Ozero__class_Ozero(_960520))], (10594 ^ _780461) ^ [] : [-(_960524 = c_Groups_Ozero__class_Ozero(_960520))]]], (10596 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960520), _960522), _960524) = c_Groups_Ozero__class_Ozero(_960520)), _960522 = c_Groups_Ozero__class_Ozero(_960520), _960524 = c_Groups_Ozero__class_Ozero(_960520)]]], (10606 ^ _780461) ^ [_960991, _960993, _960995] : [class_Groups_Oordered__comm__monoid__add(_960991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960991), c_Groups_Ozero__class_Ozero(_960991)), _960993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960991), c_Groups_Ozero__class_Ozero(_960991)), _960995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960991), c_Groups_Ozero__class_Ozero(_960991)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960991), _960993), _960995))))], (10620 ^ _780461) ^ [_961246, _961248] : [class_Groups_Olinordered__ab__group__add(_961246), 10623 ^ _780461 : [(10624 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961246), _961248), _961248)), c_Groups_Ozero__class_Ozero(_961246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961246), _961248), c_Groups_Ozero__class_Ozero(_961246))))], (10630 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961246), _961248), c_Groups_Ozero__class_Ozero(_961246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961246), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961246), _961248), _961248)), c_Groups_Ozero__class_Ozero(_961246))))]]], (10636 ^ _780461) ^ [_961529, _961531] : [class_Groups_Olinordered__ab__group__add(_961529), 10639 ^ _780461 : [(10640 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961529), c_Groups_Ozero__class_Ozero(_961529)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961529), _961531), _961531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961529), c_Groups_Ozero__class_Ozero(_961529)), _961531)))], (10646 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961529), c_Groups_Ozero__class_Ozero(_961529)), _961531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961529), c_Groups_Ozero__class_Ozero(_961529)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961529), _961531), _961531))))]]], (10652 ^ _780461) ^ [_961812, _961814] : [class_Rings_Olinordered__ring(_961812), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961812), c_Groups_Ozero__class_Ozero(_961812)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961812), _961814), _961814))))], (10658 ^ _780461) ^ [_961921, _961923, _961925] : [class_Rings_Olinordered__ring__strict(_961921), 10661 ^ _780461 : [(10662 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), c_Groups_Ozero__class_Ozero(_961921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961921), _961923), _961925))), 10667 ^ _780461 : [(10668 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), c_Groups_Ozero__class_Ozero(_961921)), _961923)))], (10670 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), c_Groups_Ozero__class_Ozero(_961921)), _961925)))]], 10671 ^ _780461 : [(10672 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), _961923), c_Groups_Ozero__class_Ozero(_961921))))], (10674 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), _961925), c_Groups_Ozero__class_Ozero(_961921))))]]], (10676 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), c_Groups_Ozero__class_Ozero(_961921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961921), _961923), _961925)))), 10677 ^ _780461 : [(10678 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), c_Groups_Ozero__class_Ozero(_961921)), _961923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), c_Groups_Ozero__class_Ozero(_961921)), _961925))], (10684 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), _961923), c_Groups_Ozero__class_Ozero(_961921))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961921), _961925), c_Groups_Ozero__class_Ozero(_961921)))]]]]], (10692 ^ _780461) ^ [_962511, _962513, _962515] : [class_Rings_Olinordered__ring__strict(_962511), 10695 ^ _780461 : [(10696 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962511), _962513), _962515)), c_Groups_Ozero__class_Ozero(_962511))), 10701 ^ _780461 : [(10702 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), c_Groups_Ozero__class_Ozero(_962511)), _962513)))], (10704 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), _962515), c_Groups_Ozero__class_Ozero(_962511))))]], 10705 ^ _780461 : [(10706 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), _962513), c_Groups_Ozero__class_Ozero(_962511))))], (10708 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), c_Groups_Ozero__class_Ozero(_962511)), _962515)))]]], (10710 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962511), _962513), _962515)), c_Groups_Ozero__class_Ozero(_962511)))), 10711 ^ _780461 : [(10712 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), c_Groups_Ozero__class_Ozero(_962511)), _962513)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), _962515), c_Groups_Ozero__class_Ozero(_962511)))], (10718 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), _962513), c_Groups_Ozero__class_Ozero(_962511))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962511), c_Groups_Ozero__class_Ozero(_962511)), _962515))]]]]], (10726 ^ _780461) ^ [_963101, _963103, _963105] : [class_Rings_Oordered__cancel__semiring(_963101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963101), c_Groups_Ozero__class_Ozero(_963101)), _963103)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963101), c_Groups_Ozero__class_Ozero(_963101)), _963105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963101), c_Groups_Ozero__class_Ozero(_963101)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963101), _963103), _963105))))], (10740 ^ _780461) ^ [_963356, _963358, _963360] : [class_Rings_Oordered__cancel__semiring(_963356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963356), c_Groups_Ozero__class_Ozero(_963356)), _963358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963356), _963360), c_Groups_Ozero__class_Ozero(_963356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963356), _963358), _963360)), c_Groups_Ozero__class_Ozero(_963356))))], (10754 ^ _780461) ^ [_963611, _963613, _963615] : [class_Rings_Oordered__cancel__semiring(_963611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963611), c_Groups_Ozero__class_Ozero(_963611)), _963613)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963611), _963615), c_Groups_Ozero__class_Ozero(_963611))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963611), _963615), _963613)), c_Groups_Ozero__class_Ozero(_963611))))], (10768 ^ _780461) ^ [_963866, _963868, _963870] : [class_Rings_Oordered__cancel__semiring(_963866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963866), _963868), c_Groups_Ozero__class_Ozero(_963866))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963866), c_Groups_Ozero__class_Ozero(_963866)), _963870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963866), _963868), _963870)), c_Groups_Ozero__class_Ozero(_963866))))], (10782 ^ _780461) ^ [_964121, _964123, _964125] : [class_Rings_Oordered__ring(_964121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964121), _964123), c_Groups_Ozero__class_Ozero(_964121))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964121), _964125), c_Groups_Ozero__class_Ozero(_964121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964121), c_Groups_Ozero__class_Ozero(_964121)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964121), _964123), _964125))))], (10796 ^ _780461) ^ [_964376, _964378, _964380, _964382] : [class_Rings_Oordered__semiring(_964376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964376), _964378), _964380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964376), c_Groups_Ozero__class_Ozero(_964376)), _964382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964376), _964378), _964382)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964376), _964380), _964382))))], (10810 ^ _780461) ^ [_964645, _964647, _964649, _964651] : [class_Rings_Oordered__semiring(_964645), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964645), _964647), _964649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964645), c_Groups_Ozero__class_Ozero(_964645)), _964651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964645), _964651), _964647)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964645), _964651), _964649))))], (10824 ^ _780461) ^ [_964914, _964916, _964918, _964920] : [class_Rings_Oordered__comm__semiring(_964914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964914), _964916), _964918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964914), c_Groups_Ozero__class_Ozero(_964914)), _964920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964914), _964920), _964916)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964914), _964920), _964918))))], (10838 ^ _780461) ^ [_965183, _965185, _965187, _965189] : [class_Rings_Oordered__ring(_965183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965183), _965185), _965187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965183), _965189), c_Groups_Ozero__class_Ozero(_965183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965183), _965187), _965189)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965183), _965185), _965189))))], (10852 ^ _780461) ^ [_965452, _965454, _965456, _965458] : [class_Rings_Oordered__ring(_965452), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965452), _965454), _965456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965452), _965458), c_Groups_Ozero__class_Ozero(_965452))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965452), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965452), _965458), _965456)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965452), _965458), _965454))))], (10866 ^ _780461) ^ [_965721, _965723, _965725, _965727, _965729] : [class_Rings_Oordered__semiring(_965721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965721), _965723), _965725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965721), _965727), _965729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965721), c_Groups_Ozero__class_Ozero(_965721)), _965723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965721), c_Groups_Ozero__class_Ozero(_965721)), _965727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965721), _965723), _965727)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_965721), _965725), _965729))))], (10888 ^ _780461) ^ [_966144, _966146, _966148, _966150, _966152] : [class_Rings_Oordered__semiring(_966144), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966144), _966146), _966148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966144), _966150), _966152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966144), c_Groups_Ozero__class_Ozero(_966144)), _966148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966144), c_Groups_Ozero__class_Ozero(_966144)), _966150)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966144), _966146), _966150)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966144), _966148), _966152))))], (10910 ^ _780461) ^ [_966567, _966569, _966571] : [class_Rings_Oordered__ring(_966567), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966567), c_Groups_Ozero__class_Ozero(_966567)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966567), _966569), _966571)))), 10915 ^ _780461 : [(10916 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966567), c_Groups_Ozero__class_Ozero(_966567)), _966569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966567), c_Groups_Ozero__class_Ozero(_966567)), _966571))], (10922 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966567), _966569), c_Groups_Ozero__class_Ozero(_966567))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966567), _966571), c_Groups_Ozero__class_Ozero(_966567)))]]], (10930 ^ _780461) ^ [_966943, _966945, _966947] : [class_Rings_Oordered__cancel__semiring(_966943), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966943), _966945), _966947)), c_Groups_Ozero__class_Ozero(_966943)))), 10935 ^ _780461 : [(10936 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966943), c_Groups_Ozero__class_Ozero(_966943)), _966945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966943), _966947), c_Groups_Ozero__class_Ozero(_966943)))], (10942 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966943), _966945), c_Groups_Ozero__class_Ozero(_966943))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966943), c_Groups_Ozero__class_Ozero(_966943)), _966947))]]], (10950 ^ _780461) ^ [_967319, _967321, _967323, _967325, _967327] : [class_Groups_Oordered__cancel__ab__semigroup__add(_967319), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967319), _967321), _967323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967319), _967325), _967327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967319), _967321), _967325)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967319), _967323), _967327))))], (10964 ^ _780461) ^ [_967590, _967592, _967594, _967596, _967598] : [class_Groups_Oordered__cancel__ab__semigroup__add(_967590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967590), _967592), _967594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967590), _967596), _967598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967590), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967590), _967592), _967596)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967590), _967594), _967598))))], (10978 ^ _780461) ^ [_967861, _967863] : [class_Rings_Oring__1__no__zero__divisors(_967861), 10981 ^ _780461 : [(10992 ^ _780461) ^ [] : [10993 ^ _780461 : [(10994 ^ _780461) ^ [] : [_967863 = c_Groups_Oone__class_Oone(_967861)], (10996 ^ _780461) ^ [] : [_967863 = hAPP(c_Groups_Ouminus__class_Ouminus(_967861), c_Groups_Oone__class_Oone(_967861))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967861), _967863), _967863) = c_Groups_Oone__class_Oone(_967861))], (10982 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967861), _967863), _967863) = c_Groups_Oone__class_Oone(_967861), -(_967863 = c_Groups_Oone__class_Oone(_967861)), -(_967863 = hAPP(c_Groups_Ouminus__class_Ouminus(_967861), c_Groups_Oone__class_Oone(_967861)))]]], (11000 ^ _780461) ^ [_968168, _968170] : [class_Rings_Ocomm__ring__1(_968168), -(hAPP(c_Groups_Ouminus__class_Ouminus(_968168), _968170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_968168), hAPP(c_Groups_Ouminus__class_Ouminus(_968168), c_Groups_Oone__class_Oone(_968168))), _968170))], (11006 ^ _780461) ^ [_968283, _968285] : [class_Groups_Olinordered__ab__group__add(_968283), 11009 ^ _780461 : [(11010 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968283), hAPP(c_Groups_Ouminus__class_Ouminus(_968283), _968285)), _968285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968283), c_Groups_Ozero__class_Ozero(_968283)), _968285)))], (11016 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968283), c_Groups_Ozero__class_Ozero(_968283)), _968285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968283), hAPP(c_Groups_Ouminus__class_Ouminus(_968283), _968285)), _968285)))]]], (11022 ^ _780461) ^ [_968551, _968553] : [class_Groups_Oordered__ab__group__add(_968551), 11025 ^ _780461 : [(11026 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968551), hAPP(c_Groups_Ouminus__class_Ouminus(_968551), _968553)), c_Groups_Ozero__class_Ozero(_968551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968551), c_Groups_Ozero__class_Ozero(_968551)), _968553)))], (11032 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968551), c_Groups_Ozero__class_Ozero(_968551)), _968553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968551), hAPP(c_Groups_Ouminus__class_Ouminus(_968551), _968553)), c_Groups_Ozero__class_Ozero(_968551))))]]], (11038 ^ _780461) ^ [_968825, _968827] : [class_Groups_Olinordered__ab__group__add(_968825), 11041 ^ _780461 : [(11042 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968825), _968827), hAPP(c_Groups_Ouminus__class_Ouminus(_968825), _968827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968825), _968827), c_Groups_Ozero__class_Ozero(_968825))))], (11048 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968825), _968827), c_Groups_Ozero__class_Ozero(_968825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968825), _968827), hAPP(c_Groups_Ouminus__class_Ouminus(_968825), _968827))))]]], (11054 ^ _780461) ^ [_969093, _969095] : [class_Groups_Oordered__ab__group__add(_969093), 11057 ^ _780461 : [(11058 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969093), c_Groups_Ozero__class_Ozero(_969093)), hAPP(c_Groups_Ouminus__class_Ouminus(_969093), _969095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969093), _969095), c_Groups_Ozero__class_Ozero(_969093))))], (11064 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969093), _969095), c_Groups_Ozero__class_Ozero(_969093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969093), c_Groups_Ozero__class_Ozero(_969093)), hAPP(c_Groups_Ouminus__class_Ouminus(_969093), _969095))))]]], (11070 ^ _780461) ^ [_969382, _969384] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969382), _969384) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11073 ^ _780461 : [(11074 ^ _780461) ^ [] : [-(_969382 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11076 ^ _780461) ^ [] : [-(_969384 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (11078 ^ _780461) ^ [_969493, _969495] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969493), _969495) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _969493 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969495 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11088 ^ _780461) ^ [_969636, _969638] : [class_Rings_Olinordered__semidom(_969636), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969636), c_Groups_Ozero__class_Ozero(_969636)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_969636), _969638))))], (11094 ^ _780461) ^ [_969739, _969741] : [class_Rings_Olinordered__semidom(_969739), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969739), c_Groups_Ozero__class_Ozero(_969739)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_969739), _969741))))], (11100 ^ _780461) ^ [_969842, _969844, _969846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _969842), _969844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969846), _969842)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969846), _969844))))], (11110 ^ _780461) ^ [_970023, _970025, _970027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970023), _970025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970023), _970027)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970025), _970027))))], (11120 ^ _780461) ^ [_970222, _970224, _970226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970222), _970224)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970226), _970224))), 11123 ^ _780461 : [(11124 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970224)))], (11126 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970222), _970226)))]]], (11128 ^ _780461) ^ [_970371, _970373, _970375] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970371), _970373)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970375), _970373)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970371), _970375))], (11138 ^ _780461) ^ [_970572, _970574, _970576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970572), _970574)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970572), _970576))), 11141 ^ _780461 : [(11142 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970572)))], (11144 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970574), _970576)))]]], (11146 ^ _780461) ^ [_970721, _970723, _970725] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970721), _970723)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970721), _970725)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970721)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970723), _970725))], (11156 ^ _780461) ^ [_970919, _970921] : [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), _970919), _970921))), 11159 ^ _780461 : [(11160 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970919)))], (11162 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970921)))]]], (11164 ^ _780461) ^ [_971042, _971044] : [-(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), _971042), _971044)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971044))], (11174 ^ _780461) ^ [_971215, _971217, _971219] : [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, _971215)), _971217)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _971215)), _971219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971217), _971219)))], (11180 ^ _780461) ^ [_971346, _971348, _971350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _971348), _971350)), -(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, _971346)), _971348)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _971346)), _971350))))], (11186 ^ _780461) ^ [_971483, _971485] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _971483)), _971485) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _971485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971483), _971485)))], (11188 ^ _780461) ^ [_971529, _971531] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971529), hAPP(c_Nat_OSuc, _971531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _971529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _971529), _971531)))], (11190 ^ _780461) ^ [_971575, _971577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _971575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _971577)), -(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), _971575), _971577))))], (11200 ^ _780461) ^ [] : [-(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))))], (11202 ^ _780461) ^ [_971746] : [-(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), _971746))))], (11204 ^ _780461) ^ [_971786] : [11206 ^ _780461 : [(11207 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11205 ^ [_971786])))], (11209 ^ _780461) ^ [] : [hBOOL(hAPP(_971786, 11205 ^ [_971786]))]], 11210 ^ _780461 : [(11211 ^ _780461) ^ [_971913] : [-(hBOOL(hAPP(_971786, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _971913))))]]], (11213 ^ _780461) ^ [_971943] : [hBOOL(hAPP(_971943, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 11214 ^ [_971943]))), 11217 ^ _780461 : [(11218 ^ _780461) ^ [_972043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _972043)), -(hBOOL(hAPP(_971943, _972043)))]]], (11235 ^ _780461) ^ [_972316] : [11236 ^ _780461 : [(11237 ^ _780461) ^ [_972373] : [hBOOL(hAPP(_972316, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _972373)))]], 11239 ^ _780461 : [(11240 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11238 ^ [_972316])))], (11242 ^ _780461) ^ [] : [-(hBOOL(hAPP(_972316, 11238 ^ [_972316])))]]], (11224 ^ _780461) ^ [_972146] : [-(hBOOL(hAPP(_972146, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 11231 ^ [_972146])))), 11225 ^ _780461 : [(11226 ^ _780461) ^ [_972198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _972198)), hBOOL(hAPP(_972146, _972198))]]], (11244 ^ _780461) ^ [_972465] : [-(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), _972465))))], (11246 ^ _780461) ^ [_972493, _972495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _972493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _972495)), 11253 ^ _780461 : [(11254 ^ _780461) ^ [] : [hAPP(c_Int_Onat, _972493) = hAPP(c_Int_Onat, _972495), -(_972493 = _972495)], (11260 ^ _780461) ^ [] : [_972493 = _972495, -(hAPP(c_Int_Onat, _972493) = hAPP(c_Int_Onat, _972495))]]], (11266 ^ _780461) ^ [_972778, _972780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _972778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _972780)), 11273 ^ _780461 : [(11274 ^ _780461) ^ [] : [hAPP(c_Int_Onat, _972778) = hAPP(c_Int_Onat, _972780), -(_972778 = _972780)], (11280 ^ _780461) ^ [] : [_972778 = _972780, -(hAPP(c_Int_Onat, _972778) = hAPP(c_Int_Onat, _972780))]]], (11297 ^ _780461) ^ [_973260] : [11299 ^ _780461 : [(11300 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11298 ^ [_973260])))], (11302 ^ _780461) ^ [] : [hBOOL(hAPP(_973260, hAPP(c_Int_Onat, 11298 ^ [_973260])))]], 11303 ^ _780461 : [(11304 ^ _780461) ^ [_973393] : [-(hBOOL(hAPP(_973260, _973393)))]]], (11286 ^ _780461) ^ [_973075] : [hBOOL(hAPP(_973075, 11287 ^ [_973075])), 11290 ^ _780461 : [(11291 ^ _780461) ^ [_973169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _973169)), -(hBOOL(hAPP(_973075, hAPP(c_Int_Onat, _973169))))]]], (11306 ^ _780461) ^ [_973438] : [11307 ^ _780461 : [(11308 ^ _780461) ^ [_973495] : [hBOOL(hAPP(_973438, _973495))]], 11310 ^ _780461 : [(11311 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11309 ^ [_973438])))], (11313 ^ _780461) ^ [] : [-(hBOOL(hAPP(_973438, hAPP(c_Int_Onat, 11309 ^ [_973438]))))]]], (11315 ^ _780461) ^ [_973581] : [-(hBOOL(hAPP(_973581, 11322 ^ [_973581]))), 11316 ^ _780461 : [(11317 ^ _780461) ^ [_973633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _973633)), hBOOL(hAPP(_973581, hAPP(c_Int_Onat, _973633)))]]], (11326 ^ _780461) ^ [_973760, _973762, _973764, _973766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _973760), _973762)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _973764), _973766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _973760), _973764)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _973762), _973766))))], (11336 ^ _780461) ^ [_973951, _973953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _973951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _973953)), -(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), _973951), _973953))))], (11346 ^ _780461) ^ [_974113] : [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)), _974113)), _974113) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (11348 ^ _780461) ^ [_974145, _974147] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974145), _974147)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974145)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974147)))], (11350 ^ _780461) ^ [_974191, _974193] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974191)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974193)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974191), _974193)))], (11352 ^ _780461) ^ [_974237, _974239] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974237)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974239)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974237), _974239)))], (11364 ^ _780461) ^ [_974416, _974418] : [11365 ^ _780461 : [(11366 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _974416), _974418))], (11368 ^ _780461) ^ [] : [_974416 = _974418]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _974416), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _974418), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (11354 ^ _780461) ^ [_974298, _974300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _974298), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _974300), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _974298), _974300))), -(_974298 = _974300)], (11372 ^ _780461) ^ [_974580, _974582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _974580), _974582)), -(_974582 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _974580), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 11375 ^ [_974580, _974582])))], (11379 ^ _780461) ^ [_974693, _974695] : [11380 ^ _780461 : [(11381 ^ _780461) ^ [_974746] : [_974695 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _974693), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _974746))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _974693), _974695)))], (11385 ^ _780461) ^ [_974813] : [class_Rings_Olinordered__semidom(_974813), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974813), c_Groups_Ozero__class_Ozero(_974813)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974813), c_Groups_Oone__class_Oone(_974813)), c_Groups_Oone__class_Oone(_974813)))))], (11391 ^ _780461) ^ [_974928, _974930, _974932] : [class_Groups_Oordered__comm__monoid__add(_974928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974928), _974930), c_Groups_Ozero__class_Ozero(_974928))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974928), _974932), c_Groups_Ozero__class_Ozero(_974928))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974928), _974930), _974932)), c_Groups_Ozero__class_Ozero(_974928))))], (11405 ^ _780461) ^ [_975183, _975185, _975187] : [class_Groups_Oordered__comm__monoid__add(_975183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975183), _975185), c_Groups_Ozero__class_Ozero(_975183))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975183), _975187), c_Groups_Ozero__class_Ozero(_975183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975183), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975183), _975185), _975187)), c_Groups_Ozero__class_Ozero(_975183))))], (11419 ^ _780461) ^ [_975438, _975440, _975442, _975444] : [class_Groups_Oordered__comm__monoid__add(_975438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975438), c_Groups_Ozero__class_Ozero(_975438)), _975440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975438), _975442), _975444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975438), _975442), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975438), _975440), _975444))))], (11433 ^ _780461) ^ [_975691, _975693, _975695, _975697] : [class_Groups_Oordered__comm__monoid__add(_975691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975691), c_Groups_Ozero__class_Ozero(_975691)), _975693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975691), _975695), _975697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975691), _975695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975691), _975693), _975697))))], (11447 ^ _780461) ^ [_975944, _975946, _975948] : [class_Groups_Oordered__comm__monoid__add(_975944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975944), c_Groups_Ozero__class_Ozero(_975944)), _975946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975944), c_Groups_Ozero__class_Ozero(_975944)), _975948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_975944), c_Groups_Ozero__class_Ozero(_975944)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975944), _975946), _975948))))], (11461 ^ _780461) ^ [_976199, _976201, _976203] : [class_Groups_Oordered__comm__monoid__add(_976199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976199), c_Groups_Ozero__class_Ozero(_976199)), _976201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976199), c_Groups_Ozero__class_Ozero(_976199)), _976203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976199), c_Groups_Ozero__class_Ozero(_976199)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976199), _976201), _976203))))], (11475 ^ _780461) ^ [_976454, _976456, _976458, _976460] : [class_Rings_Olinordered__ring__strict(_976454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976454), c_Groups_Ozero__class_Ozero(_976454)), _976456)), 11482 ^ _780461 : [(11483 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976454), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976454), _976456), _976458)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976454), _976456), _976460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976454), _976458), _976460)))], (11489 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976454), _976458), _976460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976454), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976454), _976456), _976458)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976454), _976456), _976460))))]]], (11495 ^ _780461) ^ [_976835, _976837, _976839, _976841] : [class_Rings_Olinordered__ring__strict(_976835), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976835), _976837), c_Groups_Ozero__class_Ozero(_976835))), 11502 ^ _780461 : [(11503 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976835), _976837), _976839)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976835), _976837), _976841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976835), _976841), _976839)))], (11509 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976835), _976841), _976839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976835), _976837), _976839)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976835), _976837), _976841))))]]], (11515 ^ _780461) ^ [_977216, _977218, _977220, _977222, _977224] : [class_Rings_Olinordered__semiring__strict(_977216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977216), _977218), _977220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977216), _977222), _977224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977216), c_Groups_Ozero__class_Ozero(_977216)), _977220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977216), c_Groups_Ozero__class_Ozero(_977216)), _977222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977216), _977218), _977222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977216), _977220), _977224))))], (11537 ^ _780461) ^ [_977639, _977641, _977643, _977645, _977647] : [class_Rings_Olinordered__semiring__strict(_977639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977639), _977641), _977643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977639), _977645), _977647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977639), c_Groups_Ozero__class_Ozero(_977639)), _977641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977639), c_Groups_Ozero__class_Ozero(_977639)), _977645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977639), _977641), _977645)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977639), _977643), _977647))))], (11559 ^ _780461) ^ [_978062, _978064, _978066, _978068, _978070] : [class_Rings_Olinordered__semiring__strict(_978062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978062), _978064), _978066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978062), _978068), _978070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978062), c_Groups_Ozero__class_Ozero(_978062)), _978064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978062), c_Groups_Ozero__class_Ozero(_978062)), _978068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978062), _978064), _978068)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978062), _978066), _978070))))], (11581 ^ _780461) ^ [_978485, _978487, _978489, _978491, _978493] : [class_Rings_Olinordered__semiring__strict(_978485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978485), _978487), _978489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978485), _978491), _978493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978485), c_Groups_Ozero__class_Ozero(_978485)), _978487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978485), c_Groups_Ozero__class_Ozero(_978485)), _978491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978485), _978487), _978491)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978485), _978489), _978493))))], (11603 ^ _780461) ^ [_978908, _978910, _978912, _978914] : [class_Rings_Olinordered__semiring(_978908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978908), _978910), _978912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978908), _978914), _978912))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978908), c_Groups_Ozero__class_Ozero(_978908)), _978912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978908), _978910), _978914)))], (11617 ^ _780461) ^ [_979177, _979179, _979181, _979183] : [class_Rings_Olinordered__semiring__strict(_979177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979177), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979177), _979179), _979181)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979177), _979183), _979181))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979177), c_Groups_Ozero__class_Ozero(_979177)), _979181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979177), _979179), _979183)))], (11631 ^ _780461) ^ [_979446, _979448, _979450, _979452] : [class_Rings_Olinordered__semiring(_979446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979446), _979448), _979450)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979446), _979448), _979452))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979446), c_Groups_Ozero__class_Ozero(_979446)), _979448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979446), _979450), _979452)))], (11645 ^ _780461) ^ [_979715, _979717, _979719, _979721] : [class_Rings_Olinordered__semiring__strict(_979715), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979715), _979717), _979719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979715), _979717), _979721))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979715), c_Groups_Ozero__class_Ozero(_979715)), _979717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979715), _979719), _979721)))], (11659 ^ _780461) ^ [_979984, _979986, _979988, _979990] : [class_Rings_Olinordered__semiring__strict(_979984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979984), _979986), _979988)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979984), _979990), _979988))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979984), c_Groups_Ozero__class_Ozero(_979984)), _979988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979984), _979986), _979990)))], (11673 ^ _780461) ^ [_980253, _980255, _980257, _980259] : [class_Rings_Olinordered__semiring__strict(_980253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980253), _980255), _980257)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980253), _980255), _980259))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980253), c_Groups_Ozero__class_Ozero(_980253)), _980255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980253), _980257), _980259)))], (11687 ^ _780461) ^ [_980522, _980524, _980526] : [class_Rings_Olinordered__ring(_980522), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980522), c_Groups_Ozero__class_Ozero(_980522)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980522), _980524), _980524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980522), _980526), _980526)))))], (11693 ^ _780461) ^ [_980665, _980667, _980669] : [class_Rings_Olinordered__ring__strict(_980665), 11696 ^ _780461 : [(11697 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980665), _980667), _980667)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980665), _980669), _980669))), c_Groups_Ozero__class_Ozero(_980665))), 11700 ^ _780461 : [(11701 ^ _780461) ^ [] : [-(_980667 = c_Groups_Ozero__class_Ozero(_980665))], (11703 ^ _780461) ^ [] : [-(_980669 = c_Groups_Ozero__class_Ozero(_980665))]]], (11705 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980665), _980667), _980667)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980665), _980669), _980669))), c_Groups_Ozero__class_Ozero(_980665)))), _980667 = c_Groups_Ozero__class_Ozero(_980665), _980669 = c_Groups_Ozero__class_Ozero(_980665)]]], (11715 ^ _780461) ^ [_981061, _981063] : [class_Rings_Osemiring__1(_981061), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_981061), hAPP(c_Nat_OSuc, _981063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981061), c_Groups_Oone__class_Oone(_981061)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_981061), _981063)))], (11721 ^ _780461) ^ [_981182, _981184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _981182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _981184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _981184), _981182))))], (11731 ^ _780461) ^ [_981341, _981343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _981341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _981343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _981341), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _981341), _981343))))], (11741 ^ _780461) ^ [_981500, _981502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _981500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _981502)), -(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), _981502), _981500))))], (11751 ^ _780461) ^ [_981665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _981665)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_981665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11757 ^ _780461) ^ [_981752] : [_981752 = 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), _981752)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11763 ^ _780461) ^ [_981857] : [hAPP(c_Int_Onat, _981857) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981857), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11769 ^ _780461) ^ [_981944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _981944), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _981944) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11775 ^ _780461) ^ [_982037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _982037), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _982037) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11781 ^ _780461) ^ [] : [-(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))], (11783 ^ _780461) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11785 ^ _780461) ^ [_982176] : [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)), _982176)), _982176)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _982176), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11791 ^ _780461) ^ [_982285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _982285), 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)), _982285)), _982285)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11797 ^ _780461) ^ [_982400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982400)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _982400)) = _982400)], (11803 ^ _780461) ^ [_982506, _982508] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982506) = _982508, 11806 ^ _780461 : [(11807 ^ _780461) ^ [] : [-(_982506 = hAPP(c_Int_Onat, _982508))], (11809 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982508)))]]], (11811 ^ _780461) ^ [_982621, _982623] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _982621) = _982623), _982621 = hAPP(c_Int_Onat, _982623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982623))], (11821 ^ _780461) ^ [_982774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982774)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _982774)) = _982774)], (11827 ^ _780461) ^ [_982859] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982859))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _982859)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11833 ^ _780461) ^ [_982903, _982905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _982903)), 11836 ^ _780461 : [(11837 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _982903), _982905) = c_Groups_Oone__class_Oone(tc_Int_Oint), 11840 ^ _780461 : [(11841 ^ _780461) ^ [] : [-(_982903 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (11843 ^ _780461) ^ [] : [-(_982905 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (11845 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _982903), _982905) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _982903 = c_Groups_Oone__class_Oone(tc_Int_Oint), _982905 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (11855 ^ _780461) ^ [_983204] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _983204)) = 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), _983204)))], (11857 ^ _780461) ^ [_983254, _983256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _983254)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _983256)))), 11860 ^ _780461 : [(11861 ^ _780461) ^ [] : [-(_983254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11863 ^ _780461) ^ [] : [-(_983256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11865 ^ _780461) ^ [_983381, _983383] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _983381)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _983383))))), _983381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _983383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11875 ^ _780461) ^ [_983540] : [-(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), _983540))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11877 ^ _780461) ^ [_983574, _983576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983574)), 11880 ^ _780461 : [(11881 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _983574)), hAPP(c_Int_Onat, _983576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _983574), _983576)))], (11887 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _983574), _983576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _983574)), hAPP(c_Int_Onat, _983576))))]]], (11893 ^ _780461) ^ [_983833, _983835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _983835)), 11900 ^ _780461 : [(11901 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _983833)), hAPP(c_Int_Onat, _983835))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _983833), _983835)))], (11907 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _983833), _983835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _983833)), hAPP(c_Int_Onat, _983835))))]]], (11913 ^ _780461) ^ [_984148, _984150, _984152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _984148)), _984148 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _984150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _984148), _984152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984150), _984148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _984152)))], (11927 ^ _780461) ^ [_984377, _984379, _984381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _984377)), _984377 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _984379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _984377), _984381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _984379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _984381), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (11941 ^ _780461) ^ [_984606, _984608, _984610, _984612, _984614, _984616] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _984606), _984608)), _984610) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _984612), _984614)), _984616), 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), _984612), _984614)), _984616)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _984610), _984606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _984616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _984612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _984612), _984606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _984614), _984608)))], (11967 ^ _780461) ^ [_985111, _985113, _985115, _985117, _985119] : [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), _985111), _985113)), _985115)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _985111), _985117)), _985119))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _985119), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985111), _985119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985111), _985115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _985117), _985113)))], (11985 ^ _780461) ^ [_985466, _985468, _985470, _985472, _985474, _985476] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _985466), _985468)), _985470) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _985472), _985474)), _985476), 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), _985472), _985474)), _985476))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985476), _985472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _985472), _985466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _985468), _985474)))], (12011 ^ _780461) ^ [_985965, _985967, _985969, _985971, _985973] : [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), _985965), _985967)), _985969)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _985965), _985971)), _985973))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _985969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985969), _985965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _985973), _985965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _985967), _985971)))], (12029 ^ _780461) ^ [_986314, _986316, _986318] : [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), _986314), _986316)), _986318)), 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)), _986318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _986316), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12043 ^ _780461) ^ [_986553, _986555, _986557] : [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), _986553), _986555)), _986557))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _986557), _986553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _986555)))], (12057 ^ _780461) ^ [_986786, _986788, _986790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _986786)), 12060 ^ _780461 : [(12061 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986786), _986788) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986786), _986790), -(_986788 = _986790)], (12067 ^ _780461) ^ [] : [_986788 = _986790, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986786), _986788) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986786), _986790))]]], (12073 ^ _780461) ^ [_987039] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987039)))], (12075 ^ _780461) ^ [_987064, _987066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987064), _987066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987066), _987064)), -(_987064 = _987066)], (12085 ^ _780461) ^ [_987213, _987215, _987217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987213), _987215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987215), _987217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987213), _987217)))], (12095 ^ _780461) ^ [_987376, _987378] : [_987376 = _987378, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987376), _987378)))], (12101 ^ _780461) ^ [_987459, _987461] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987459), _987461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987461), _987459)))], (12107 ^ _780461) ^ [_987505] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987505), _987505)))], (12109 ^ _780461) ^ [_987533] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _987533)))], (12111 ^ _780461) ^ [_987570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987570), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_987570 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12117 ^ _780461) ^ [_987651] : [_987651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987651), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12123 ^ _780461) ^ [_987738, _987740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _987738)), _987740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987738), _987740)))], (12129 ^ _780461) ^ [_987841, _987843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987841), hAPP(c_Nat_OSuc, _987843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987841), _987843))), -(_987841 = hAPP(c_Nat_OSuc, _987843))], (12139 ^ _780461) ^ [_987965, _987967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987965), _987967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _987965), hAPP(c_Nat_OSuc, _987967))))], (12145 ^ _780461) ^ [_988083, _988085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988083)), hAPP(c_Nat_OSuc, _988085))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988083), _988085)))], (12151 ^ _780461) ^ [_988188, _988190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988188), _988190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988188)), hAPP(c_Nat_OSuc, _988190))))], (12167 ^ _780461) ^ [_988432, _988434] : [12168 ^ _780461 : [(12169 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988432), _988434))], (12171 ^ _780461) ^ [] : [_988432 = hAPP(c_Nat_OSuc, _988434)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988432), hAPP(c_Nat_OSuc, _988434))))], (12157 ^ _780461) ^ [_988314, _988316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988314), hAPP(c_Nat_OSuc, _988316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988314), _988316))), -(_988314 = hAPP(c_Nat_OSuc, _988316))], (12175 ^ _780461) ^ [_988590, _988592] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988590), _988592))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988592)), _988590)))], (12181 ^ _780461) ^ [_988635, _988637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988637)), _988635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988635), _988637))], (12187 ^ _780461) ^ [_988750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _988750)), _988750))], (12189 ^ _780461) ^ [_988781, _988783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988781), _988783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988781), _988783)))], (12195 ^ _780461) ^ [_988893, _988895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _988893), _988895)), 12198 ^ _780461 : [(12199 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _988893), _988895)))], (12201 ^ _780461) ^ [] : [_988893 = _988895]]], (12203 ^ _780461) ^ [_989020, _989022] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989020), _989022))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989020), _989022)), -(_989020 = _989022)], (12223 ^ _780461) ^ [_989295, _989297] : [12224 ^ _780461 : [(12225 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989295), _989297))], (12227 ^ _780461) ^ [] : [_989295 = _989297]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989295), _989297)))], (12213 ^ _780461) ^ [_989189, _989191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989189), _989191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989189), _989191))), -(_989189 = _989191)], (12231 ^ _780461) ^ [_989432, _989434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989432), _989434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989432), _989434)))], (12237 ^ _780461) ^ [_989529, _989531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989529), _989531)), -(_989529 = _989531), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989529), _989531)))], (12247 ^ _780461) ^ [_989641, _989643] : [12248 ^ _780461 : [(12249 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989641), _989643))], (12251 ^ _780461) ^ [] : [_989641 = _989643]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989641), _989643)))], (12255 ^ _780461) ^ [_989776, _989778, _989780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989776), _989778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989780), _989778))))], (12261 ^ _780461) ^ [_989887, _989889, _989891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989887), _989889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989887), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989889), _989891))))], (12267 ^ _780461) ^ [_989998, _990000] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _989998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990000), _989998))))], (12269 ^ _780461) ^ [_990034, _990036] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990034), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990034), _990036))))], (12271 ^ _780461) ^ [_990085, _990087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990085), _990087)), -(_990087 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990085), 12274 ^ [_990085, _990087]))], (12278 ^ _780461) ^ [_990192, _990194] : [12279 ^ _780461 : [(12280 ^ _780461) ^ [_990242] : [_990194 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990192), _990242)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990192), _990194)))], (12284 ^ _780461) ^ [_990324, _990326, _990328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990324), _990326)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990324), _990328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990326), _990328)))], (12290 ^ _780461) ^ [_990443, _990445, _990447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990445), _990447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990443), _990445)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990443), _990447))))], (12296 ^ _780461) ^ [_990568, _990570, _990572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990568), _990570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990570), _990572))))], (12302 ^ _780461) ^ [_990679, _990681, _990683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990679), _990681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990683), _990681))))], (12308 ^ _780461) ^ [_990790, _990792, _990794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990790), _990792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990790), _990794)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990792), _990794))))], (12314 ^ _780461) ^ [_990913, _990915, _990917, _990919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990913), _990915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990917), _990919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990913), _990917)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990915), _990919))))], (12324 ^ _780461) ^ [_991104, _991106, _991108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _991104), _991106)), _991108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991106), _991108)))], (12330 ^ _780461) ^ [_991215, _991217, _991219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _991215), _991217)), _991219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991215), _991219)))], (12336 ^ _780461) ^ [_991326, _991328, _991330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _991326), _991328)), _991330)), 12339 ^ _780461 : [(12340 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991326), _991330)))], (12342 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991328), _991330)))]]], (12344 ^ _780461) ^ [_991477, _991479, _991481, _991483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991477), _991479)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991481), _991483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991477), _991481)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991479), _991483))))], (12354 ^ _780461) ^ [_991668, _991670, _991672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991668), _991670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991672), _991668)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991672), _991670))))], (12360 ^ _780461) ^ [_991791, _991793, _991795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991791), _991793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991791), _991795)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991793), _991795))))], (12366 ^ _780461) ^ [_991914] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991914), _991914)))))], (12368 ^ _780461) ^ [_991954] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991954), _991954))))], (12370 ^ _780461) ^ [_992003, _992005] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992003), _992005) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12373 ^ _780461 : [(12374 ^ _780461) ^ [] : [-(_992003 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12376 ^ _780461) ^ [] : [-(_992005 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12378 ^ _780461) ^ [_992114, _992116] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992114), _992116) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _992114 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _992116 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12388 ^ _780461) ^ [_992257] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992257), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _992257)], (12390 ^ _780461) ^ [_992301, _992303] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992301), _992303), 12393 ^ _780461 : [(12394 ^ _780461) ^ [] : [-(_992301 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12396 ^ _780461) ^ [] : [-(_992303 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12398 ^ _780461) ^ [_992412, _992414] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992412), _992414)), _992412 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _992414 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12408 ^ _780461) ^ [_992555] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _992555) = _992555)], (12410 ^ _780461) ^ [_992581, _992583, _992585, _992587, _992589] : [c_Natural_Oevaln(_992581, _992583, _992585, _992587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992585), _992589)), -(c_Natural_Oevaln(_992581, _992583, _992589, _992587))], (12420 ^ _780461) ^ [_992740, _992742, _992744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992740)), 12423 ^ _780461 : [(12424 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992740), _992742)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992740), _992744))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992742), _992744)))], (12430 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992742), _992744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992740), _992742)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992740), _992744))))]]], (12436 ^ _780461) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12438 ^ _780461) ^ [_993056, _993058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993056), _993058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993056)), _993058)))], (12444 ^ _780461) ^ [_993155, _993157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993155)), _993157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993155), _993157)))], (12450 ^ _780461) ^ [_993275, _993277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993275), hAPP(c_Nat_OSuc, _993277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993275), _993277)))], (12456 ^ _780461) ^ [_993374, _993376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993374), _993376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993374), hAPP(c_Nat_OSuc, _993376))))], (12462 ^ _780461) ^ [_993494, _993496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993494)), _993496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993494), _993496)))], (12468 ^ _780461) ^ [_993593, _993595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993593), _993595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993593)), _993595)))], (12474 ^ _780461) ^ [_993698, _993700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993698), _993700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993698), hAPP(c_Nat_OSuc, _993700))))], (12480 ^ _780461) ^ [_993801, _993803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993801), _993803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993801)), _993803)))], (12486 ^ _780461) ^ [_993904, _993906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993904), _993906)), 12489 ^ _780461 : [(12490 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993906), hAPP(c_Nat_OSuc, _993904))), -(_993906 = _993904)], (12496 ^ _780461) ^ [] : [_993906 = _993904, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993906), hAPP(c_Nat_OSuc, _993904))))]]], (12502 ^ _780461) ^ [_994145, _994147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _994145)), _994147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994145), _994147)))], (12508 ^ _780461) ^ [_994248] : [-(hAPP(c_Nat_OSuc, _994248) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _994248))], (12510 ^ _780461) ^ [_994277] : [-(hAPP(c_Nat_OSuc, _994277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994277), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12512 ^ _780461) ^ [_994309, _994311] : [_994309 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994309), _994311), -(_994311 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_994309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12522 ^ _780461) ^ [_994429, _994431, _994433] : [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, _994429)), _994431)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _994429)), _994433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994431), _994433)))], (12528 ^ _780461) ^ [_994560, _994562, _994564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994562), _994564)), -(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, _994560)), _994562)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _994560)), _994564))))], (12534 ^ _780461) ^ [_994712, _994714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994712)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994714))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994712), _994714)))], (12540 ^ _780461) ^ [_994817, _994819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994817), _994819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994817)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994819))))], (12546 ^ _780461) ^ [_994943, _994945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994943)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _994945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994943), _994945)))], (12552 ^ _780461) ^ [_995048, _995050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995048), _995050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _995048)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _995050))))], (12558 ^ _780461) ^ [] : [-(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)))], (12560 ^ _780461) ^ [] : [-(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))], (12562 ^ _780461) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (12564 ^ _780461) ^ [_995228, _995230] : [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), _995228), _995230))), 12567 ^ _780461 : [(12568 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _995228)))], (12570 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _995230)))]]], (12572 ^ _780461) ^ [_995351, _995353] : [-(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), _995351), _995353)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _995351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _995353))], (12592 ^ _780461) ^ [_995701, _995703, _995705] : [12593 ^ _780461 : [(12594 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _995701)))], (12596 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995703), _995705))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995701), _995703)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995701), _995705))))], (12582 ^ _780461) ^ [_995524, _995526, _995528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995524), _995526)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995524), _995528))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _995524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995526), _995528)))], (12610 ^ _780461) ^ [_996058, _996060, _996062] : [12611 ^ _780461 : [(12612 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _996060)))], (12614 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996058), _996062))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996058), _996060)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996062), _996060))))], (12600 ^ _780461) ^ [_995881, _995883, _995885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995881), _995883)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995885), _995883))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _995883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995881), _995885)))], (12618 ^ _780461) ^ [_996220, _996222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996222)), 12625 ^ _780461 : [(12626 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _996220)), hAPP(c_Int_Onat, _996222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996220), _996222)))], (12632 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996220), _996222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _996220)), hAPP(c_Int_Onat, _996222))))]]], (12638 ^ _780461) ^ [_996535, _996537] : [12639 ^ _780461 : [(12640 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996535))], (12642 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _996537))]], 12643 ^ _780461 : [(12644 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _996535)), hAPP(c_Int_Onat, _996537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996535), _996537)))], (12650 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _996535), _996537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _996535)), hAPP(c_Int_Onat, _996537))))]]], (12666 ^ _780461) ^ [_996966, _996968, _996970] : [12667 ^ _780461 : [(12668 ^ _780461) ^ [] : [_996966 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12670 ^ _780461) ^ [] : [_996968 = _996970]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996966), _996968) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996966), _996970))], (12656 ^ _780461) ^ [_996854, _996856, _996858] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996854), _996856) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996854), _996858), -(_996854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_996856 = _996858)], (12674 ^ _780461) ^ [_997109, _997111, _997113, _997115] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _997109), _997111)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _997113), _997111)), _997115)) = 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), _997109), _997113)), _997111)), _997115))], (12676 ^ _780461) ^ [_997180, _997182, _997184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _997180)), 12679 ^ _780461 : [(12680 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _997180), _997182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _997180), _997184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _997182), _997184)))], (12686 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _997182), _997184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _997180), _997182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _997180), _997184))))]]], (12692 ^ _780461) ^ [] : [-(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))))], (12694 ^ _780461) ^ [_997481, _997483] : [class_Orderings_Opreorder(_997481), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997481), _997483), _997483)))], (12700 ^ _780461) ^ [_997570, _997572, _997574] : [class_Lattices_Oboolean__algebra(_997570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997570), _997572), _997574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997570), hAPP(c_Groups_Ouminus__class_Ouminus(_997570), _997574)), hAPP(c_Groups_Ouminus__class_Ouminus(_997570), _997572))))], (12710 ^ _780461) ^ [_997749, _997751, _997753] : [class_Lattices_Oboolean__algebra(_997749), 12713 ^ _780461 : [(12714 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997749), hAPP(c_Groups_Ouminus__class_Ouminus(_997749), _997751)), hAPP(c_Groups_Ouminus__class_Ouminus(_997749), _997753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997749), _997753), _997751)))], (12720 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997749), _997753), _997751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997749), hAPP(c_Groups_Ouminus__class_Ouminus(_997749), _997751)), hAPP(c_Groups_Ouminus__class_Ouminus(_997749), _997753))))]]], (12726 ^ _780461) ^ [_998032, _998034, _998036, _998038] : [class_Orderings_Oorder(_998032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998032), _998034), _998036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998032), _998038), _998034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998032), _998038), _998036)))], (12740 ^ _780461) ^ [_998265, _998267, _998269, _998271] : [class_Orderings_Opreorder(_998265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998265), _998267), _998269)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998265), _998269), _998271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998265), _998267), _998271)))], (12754 ^ _780461) ^ [_998498, _998500, _998502, _998504] : [class_Orderings_Oorder(_998498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998498), _998500), _998502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998498), _998504), _998500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998498), _998504), _998502)))], (12768 ^ _780461) ^ [_998731, _998733, _998735, _998737] : [class_Orderings_Opreorder(_998731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998731), _998733), _998735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998731), _998735), _998737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998731), _998733), _998737)))], (12782 ^ _780461) ^ [_998964, _998966, _998968] : [class_Orderings_Oorder(_998964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998964), _998966), _998968)), -(_998968 = _998966), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998964), _998966), _998968)))], (12796 ^ _780461) ^ [_999138, _999140, _999142, _999144] : [class_Orderings_Oord(_999138), 12799 ^ _780461 : [(12800 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999140, _999138)), _999142), _999144)), 12803 ^ _780461 : [(12804 ^ _780461) ^ [_999295] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999138), hAPP(_999142, _999295)), hAPP(_999144, _999295))))]]], (12806 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999138), hAPP(_999142, 12807 ^ [_999138, _999140, _999142, _999144])), hAPP(_999144, 12807 ^ [_999138, _999140, _999142, _999144]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999140, _999138)), _999142), _999144)))]]], (12813 ^ _780461) ^ [_999484, _999486, _999488] : [class_Orderings_Olinorder(_999484), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999484), _999486), _999488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999484), _999488), _999486)))], (12823 ^ _780461) ^ [_999602, _999604, _999606] : [class_Orderings_Oorder(_999602), 12826 ^ _780461 : [(12827 ^ _780461) ^ [] : [_999604 = _999606, 12830 ^ _780461 : [(12831 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999602), _999604), _999606)))], (12833 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999602), _999606), _999604)))]]], (12835 ^ _780461) ^ [] : [-(_999604 = _999606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999602), _999604), _999606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999602), _999606), _999604))]]], (12845 ^ _780461) ^ [_999929, _999931, _999933] : [class_Orderings_Opreorder(_999929), _999931 = _999933, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999929), _999931), _999933)))], (12855 ^ _780461) ^ [_1000074, _1000076, _1000078, _1000080, _1000082] : [class_Orderings_Oord(_1000074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000076, _1000074)), _1000078), _1000080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000074), hAPP(_1000078, _1000082)), hAPP(_1000080, _1000082))))], (12865 ^ _780461) ^ [_1000259, _1000261, _1000263] : [class_Orderings_Oorder(_1000259), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000259), _1000261), _1000263)), 12872 ^ _780461 : [(12873 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000259), _1000263), _1000261)), -(_1000263 = _1000261)], (12879 ^ _780461) ^ [] : [_1000263 = _1000261, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000259), _1000263), _1000261)))]]], (12885 ^ _780461) ^ [_1000559, _1000561, _1000563, _1000565] : [class_Orderings_Oord(_1000559), _1000561 = _1000563, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000559), _1000563), _1000565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000559), _1000561), _1000565)))], (12899 ^ _780461) ^ [_1000778, _1000780, _1000782, _1000784] : [class_Orderings_Oorder(_1000778), _1000780 = _1000782, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000778), _1000784), _1000782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000778), _1000784), _1000780)))], (12913 ^ _780461) ^ [_1000997, _1000999, _1001001, _1001003] : [class_Orderings_Oord(_1000997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000997), _1000999), _1001001)), _1001001 = _1001003, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000997), _1000999), _1001003)))], (12927 ^ _780461) ^ [_1001216, _1001218, _1001220, _1001222] : [class_Orderings_Oorder(_1001216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001216), _1001218), _1001220)), _1001218 = _1001222, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001216), _1001222), _1001220)))], (12941 ^ _780461) ^ [_1001435, _1001437, _1001439] : [class_Orderings_Oorder(_1001435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001435), _1001437), _1001439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001435), _1001439), _1001437)), -(_1001437 = _1001439)], (12955 ^ _780461) ^ [_1001648, _1001650, _1001652, _1001654] : [class_Orderings_Opreorder(_1001648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001648), _1001650), _1001652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001648), _1001652), _1001654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001648), _1001650), _1001654)))], (12969 ^ _780461) ^ [_1001881, _1001883, _1001885] : [class_Orderings_Oorder(_1001881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001881), _1001883), _1001885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001881), _1001885), _1001883)), -(_1001885 = _1001883)], (12983 ^ _780461) ^ [_1002094, _1002096, _1002098, _1002100] : [class_Orderings_Oorder(_1002094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002094), _1002096), _1002098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002094), _1002100), _1002096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002094), _1002100), _1002098)))], (12997 ^ _780461) ^ [_1002327, _1002329, _1002331, _1002333, _1002335] : [class_Orderings_Oord(_1002327), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002329, _1002327)), _1002331), _1002333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002327), hAPP(_1002331, _1002335)), hAPP(_1002333, _1002335))))], (13007 ^ _780461) ^ [_1002512, _1002514, _1002516] : [class_Orderings_Olinorder(_1002512), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002512), _1002514), _1002516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002512), _1002516), _1002514)))], (13017 ^ _780461) ^ [_1002632, _1002634] : [class_Orderings_Opreorder(_1002632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002632), _1002634), _1002634))], (13023 ^ _780461) ^ [_1002722, _1002724, _1002726] : [class_Orderings_Olinorder(_1002722), 13026 ^ _780461 : [(13037 ^ _780461) ^ [] : [13038 ^ _780461 : [(13039 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002722), _1002724), _1002726))], (13041 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002722), _1002726), _1002724))]], _1002724 = _1002726], (13027 ^ _780461) ^ [] : [-(_1002724 = _1002726), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002722), _1002724), _1002726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002722), _1002726), _1002724)))]]], (13045 ^ _780461) ^ [_1002976, _1002978, _1002980] : [class_Orderings_Olinorder(_1002976), 13048 ^ _780461 : [(13059 ^ _780461) ^ [] : [13060 ^ _780461 : [(13061 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002976), _1002980), _1002978))], (13063 ^ _780461) ^ [] : [_1002978 = _1002980]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002976), _1002978), _1002980))], (13049 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002976), _1002978), _1002980))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002976), _1002980), _1002978))), -(_1002978 = _1002980)]]], (13067 ^ _780461) ^ [_1003230, _1003232, _1003234] : [class_Orderings_Olinorder(_1003230), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003230), _1003232), _1003234))), -(_1003232 = _1003234), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003230), _1003234), _1003232)))], (13081 ^ _780461) ^ [_1003361, _1003363, _1003365] : [class_Orderings_Olinorder(_1003361), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003361), _1003363), _1003365))), 13088 ^ _780461 : [(13089 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003361), _1003365), _1003363))), -(_1003365 = _1003363)], (13095 ^ _780461) ^ [] : [_1003365 = _1003363, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003361), _1003365), _1003363))]]], (13101 ^ _780461) ^ [_1003620, _1003622, _1003624] : [class_Orderings_Olinorder(_1003620), -(_1003622 = _1003624), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003620), _1003622), _1003624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003620), _1003624), _1003622)))], (13115 ^ _780461) ^ [_1003755, _1003757, _1003759] : [class_Orderings_Oorder(_1003755), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003755), _1003757), _1003759)), _1003757 = _1003759], (13125 ^ _780461) ^ [_1003901, _1003903, _1003905] : [class_Orderings_Opreorder(_1003901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003901), _1003903), _1003905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003901), _1003905), _1003903))], (13135 ^ _780461) ^ [_1004061, _1004063, _1004065] : [class_Orderings_Opreorder(_1004061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004061), _1004063), _1004065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004061), _1004065), _1004063))], (13145 ^ _780461) ^ [_1004221, _1004223, _1004225] : [class_Orderings_Oorder(_1004221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004221), _1004223), _1004225)), _1004223 = _1004225], (13155 ^ _780461) ^ [_1004367, _1004369, _1004371] : [class_Orderings_Oorder(_1004367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004367), _1004369), _1004371)), _1004371 = _1004369], (13165 ^ _780461) ^ [_1004513, _1004515, _1004517] : [class_Orderings_Opreorder(_1004513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004513), _1004515), _1004517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004513), _1004517), _1004515))], (13175 ^ _780461) ^ [_1004673, _1004675, _1004677] : [class_Orderings_Oorder(_1004673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004673), _1004675), _1004677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004673), _1004677), _1004675))], (13185 ^ _780461) ^ [_1004833, _1004835, _1004837, _1004839] : [class_Orderings_Oord(_1004833), _1004835 = _1004837, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004833), _1004837), _1004839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004833), _1004835), _1004839)))], (13199 ^ _780461) ^ [_1005052, _1005054, _1005056, _1005058] : [class_Orderings_Oorder(_1005052), _1005054 = _1005056, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005052), _1005058), _1005056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005052), _1005058), _1005054)))], (13213 ^ _780461) ^ [_1005271, _1005273, _1005275, _1005277] : [class_Orderings_Oord(_1005271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005271), _1005273), _1005275)), _1005275 = _1005277, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005271), _1005273), _1005277)))], (13227 ^ _780461) ^ [_1005490, _1005492, _1005494, _1005496] : [class_Orderings_Oorder(_1005490), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005490), _1005492), _1005494)), _1005492 = _1005496, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005490), _1005496), _1005494)))], (13241 ^ _780461) ^ [_1005709, _1005711, _1005713, _1005715] : [class_Orderings_Opreorder(_1005709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005709), _1005711), _1005713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005709), _1005713), _1005715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005709), _1005711), _1005715)))], (13255 ^ _780461) ^ [_1005942, _1005944, _1005946, _1005948] : [class_Orderings_Oorder(_1005942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005942), _1005944), _1005946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005942), _1005948), _1005944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005942), _1005948), _1005946)))], (13269 ^ _780461) ^ [_1006175, _1006177, _1006179] : [class_Orderings_Opreorder(_1006175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006175), _1006177), _1006179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006175), _1006179), _1006177))], (13279 ^ _780461) ^ [_1006335, _1006337, _1006339] : [class_Orderings_Olinorder(_1006335), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006335), _1006337), _1006339))), -(_1006337 = _1006339), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006335), _1006339), _1006337)))], (13293 ^ _780461) ^ [_1006470, _1006472] : [class_Lattices_Oab__semigroup__idem__mult(_1006470), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006470), _1006472), _1006472) = _1006472)], (13299 ^ _780461) ^ [_1006561, _1006563] : [class_Lattices_Oab__semigroup__idem__mult(_1006561), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006561), _1006563), _1006563) = _1006563)], (13305 ^ _780461) ^ [_1006652, _1006654, _1006656] : [class_Lattices_Oab__semigroup__idem__mult(_1006652), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006652), _1006654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006652), _1006654), _1006656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006652), _1006654), _1006656))], (13311 ^ _780461) ^ [_1006777, _1006779] : [class_Lattices_Oboolean__algebra(_1006777), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1006777), hAPP(c_Groups_Ouminus__class_Ouminus(_1006777), _1006779)) = _1006779)], (13317 ^ _780461) ^ [_1006872, _1006874, _1006876, _1006878] : [class_Groups_Ouminus(_1006872), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006874, _1006872)), _1006876), _1006878) = hAPP(c_Groups_Ouminus__class_Ouminus(_1006872), hAPP(_1006876, _1006878)))], (13323 ^ _780461) ^ [_1006989, _1006991, _1006993] : [class_Lattices_Oboolean__algebra(_1006989), 13326 ^ _780461 : [(13327 ^ _780461) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1006989), _1006991) = hAPP(c_Groups_Ouminus__class_Ouminus(_1006989), _1006993), -(_1006991 = _1006993)], (13333 ^ _780461) ^ [] : [_1006991 = _1006993, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1006989), _1006991) = hAPP(c_Groups_Ouminus__class_Ouminus(_1006989), _1006993))]]], (13339 ^ _780461) ^ [_1007230, _1007232, _1007234] : [class_Orderings_Olinorder(_1007230), 13342 ^ _780461 : [(13343 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007230), _1007232), _1007234))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007230), _1007234), _1007232)))], (13349 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007230), _1007234), _1007232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007230), _1007232), _1007234))]]], (13355 ^ _780461) ^ [_1007439, _1007441, _1007443] : [class_Orderings_Olinorder(_1007439), 13358 ^ _780461 : [(13359 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007439), _1007441), _1007443))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007439), _1007443), _1007441)))], (13365 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007439), _1007443), _1007441)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007439), _1007441), _1007443))]]], (13371 ^ _780461) ^ [_1007648, _1007650, _1007652] : [class_Orderings_Olinorder(_1007648), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007648), _1007650), _1007652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007648), _1007652), _1007650)))], (13381 ^ _780461) ^ [_1007766, _1007768, _1007770] : [class_Orderings_Oorder(_1007766), 13384 ^ _780461 : [(13385 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007766), _1007768), _1007770)), 13388 ^ _780461 : [(13389 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007766), _1007768), _1007770)))], (13391 ^ _780461) ^ [] : [_1007768 = _1007770]]], (13393 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007766), _1007768), _1007770))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007766), _1007768), _1007770)), -(_1007768 = _1007770)]]], (13403 ^ _780461) ^ [_1008102, _1008104, _1008106] : [class_Orderings_Opreorder(_1008102), 13406 ^ _780461 : [(13407 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008102), _1008104), _1008106)), 13410 ^ _780461 : [(13411 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008102), _1008104), _1008106)))], (13413 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008102), _1008106), _1008104))]]], (13415 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008102), _1008104), _1008106))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008102), _1008104), _1008106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008102), _1008106), _1008104)))]]], (13425 ^ _780461) ^ [_1008459, _1008461, _1008463] : [class_Orderings_Oorder(_1008459), 13428 ^ _780461 : [(13439 ^ _780461) ^ [] : [13440 ^ _780461 : [(13441 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008459), _1008461), _1008463))], (13443 ^ _780461) ^ [] : [_1008461 = _1008463]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008459), _1008461), _1008463)))], (13429 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008459), _1008461), _1008463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008459), _1008461), _1008463))), -(_1008461 = _1008463)]]], (13447 ^ _780461) ^ [_1008757, _1008759, _1008761] : [class_Orderings_Olinorder(_1008757), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008757), _1008759), _1008761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008757), _1008761), _1008759)))], (13457 ^ _780461) ^ [_1008877, _1008879, _1008881] : [class_Orderings_Olinorder(_1008877), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008877), _1008879), _1008881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008877), _1008881), _1008879)))], (13467 ^ _780461) ^ [_1008997, _1008999, _1009001] : [class_Orderings_Olinorder(_1008997), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008997), _1008999), _1009001))), 13474 ^ _780461 : [(13475 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008997), _1008999), _1009001)), -(_1008999 = _1009001)], (13481 ^ _780461) ^ [] : [_1008999 = _1009001, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008997), _1008999), _1009001)))]]], (13487 ^ _780461) ^ [_1009300, _1009302, _1009304] : [class_Orderings_Oorder(_1009300), -(_1009302 = _1009304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009300), _1009302), _1009304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009300), _1009302), _1009304)))], (13501 ^ _780461) ^ [_1009516, _1009518, _1009520] : [class_Orderings_Oorder(_1009516), -(_1009518 = _1009520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009516), _1009520), _1009518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009516), _1009520), _1009518)))], (13515 ^ _780461) ^ [_1009732, _1009734, _1009736] : [class_Orderings_Olinorder(_1009732), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009732), _1009734), _1009736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009732), _1009736), _1009734))], (13525 ^ _780461) ^ [_1009892, _1009894, _1009896] : [class_Orderings_Opreorder(_1009892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009892), _1009894), _1009896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009892), _1009894), _1009896)))], (13535 ^ _780461) ^ [_1010051, _1010053, _1010055] : [class_Orderings_Olinorder(_1010051), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010051), _1010053), _1010055)), 13542 ^ _780461 : [(13543 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010051), _1010053), _1010055))), -(_1010053 = _1010055)], (13549 ^ _780461) ^ [] : [_1010053 = _1010055, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010051), _1010053), _1010055))]]], (13555 ^ _780461) ^ [_1010307, _1010309, _1010311] : [class_Orderings_Oorder(_1010307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010307), _1010309), _1010311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010307), _1010309), _1010311))), -(_1010309 = _1010311)], (13569 ^ _780461) ^ [_1010479, _1010481, _1010483] : [class_Orderings_Oorder(_1010479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010479), _1010481), _1010483)), -(_1010481 = _1010483), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010479), _1010481), _1010483)))], (13583 ^ _780461) ^ [_1010652, _1010654] : [-(hBOOL(hAPP(_1010652, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1010652, _1010654)), 13591 ^ _780461 : [(13592 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13590 ^ [_1010652, _1010654]), _1010654)))], (13600 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1010652, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 13590 ^ [_1010652, _1010654]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (13594 ^ _780461) ^ [_1010890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1010890), 13590 ^ [_1010652, _1010654])), hBOOL(hAPP(_1010652, _1010890))]]], (13602 ^ _780461) ^ [_1011042, _1011044] : [class_Groups_Osgn__if(_1011042), 13605 ^ _780461 : [(13606 ^ _780461) ^ [] : [_1011044 = c_Groups_Ozero__class_Ozero(_1011042), -(c_Groups_Osgn__class_Osgn(_1011042, _1011044) = c_Groups_Ozero__class_Ozero(_1011042))], (13612 ^ _780461) ^ [] : [-(_1011044 = c_Groups_Ozero__class_Ozero(_1011042)), 13615 ^ _780461 : [(13616 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011042), c_Groups_Ozero__class_Ozero(_1011042)), _1011044)), -(c_Groups_Osgn__class_Osgn(_1011042, _1011044) = c_Groups_Oone__class_Oone(_1011042))], (13622 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011042), c_Groups_Ozero__class_Ozero(_1011042)), _1011044))), -(c_Groups_Osgn__class_Osgn(_1011042, _1011044) = hAPP(c_Groups_Ouminus__class_Ouminus(_1011042), c_Groups_Oone__class_Oone(_1011042)))]]]]], (13628 ^ _780461) ^ [_1011439, _1011441] : [class_Rings_Olinordered__idom(_1011439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011439), _1011441), c_Groups_Ozero__class_Ozero(_1011439))), -(c_Groups_Osgn__class_Osgn(_1011439, _1011441) = hAPP(c_Groups_Ouminus__class_Ouminus(_1011439), c_Groups_Oone__class_Oone(_1011439)))], (13638 ^ _780461) ^ [_1011604, _1011606] : [class_Rings_Olinordered__idom(_1011604), 13641 ^ _780461 : [(13642 ^ _780461) ^ [] : [c_Groups_Osgn__class_Osgn(_1011604, _1011606) = hAPP(c_Groups_Ouminus__class_Ouminus(_1011604), c_Groups_Oone__class_Oone(_1011604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011604), _1011606), c_Groups_Ozero__class_Ozero(_1011604))))], (13648 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011604), _1011606), c_Groups_Ozero__class_Ozero(_1011604))), -(c_Groups_Osgn__class_Osgn(_1011604, _1011606) = hAPP(c_Groups_Ouminus__class_Ouminus(_1011604), c_Groups_Oone__class_Oone(_1011604)))]]], (13654 ^ _780461) ^ [_1011872] : [_1011872 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1011872) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13660 ^ _780461) ^ [_1011948] : [-(_1011948 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 13663 ^ _780461 : [(13664 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011948)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1011948) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (13670 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1011948))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1011948) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (13676 ^ _780461) ^ [_1012140, _1012142, _1012144, _1012146] : [_1012140 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012142), _1012144)), _1012146), -(_1012142 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012140, _1012142) = _1012146), 13683 ^ _780461 : [(13684 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012142)))], (13686 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012146), _1012142))]], 13691 ^ _780461 : [(13692 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012142))], (13694 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012142), _1012146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1012146), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (13706 ^ _780461) ^ [_1012605, _1012607, _1012609, _1012611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012605)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012607), _1012609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1012609), 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), _1012607), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012611, _1012605))), _1012609)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13720 ^ _780461) ^ [_1012864, _1012866, _1012868, _1012870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1012864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1012866), _1012868)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1012868), 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), _1012866), _1012864)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1012866), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1012870, _1012864))), _1012868))))], (13734 ^ _780461) ^ [_1013135, _1013137, _1013139, _1013141] : [class_Orderings_Oord(_1013135), 13737 ^ _780461 : [(13738 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013137, _1013135)), _1013139), _1013141)), 13741 ^ _780461 : [(13742 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013137, _1013135)), _1013139), _1013141)))], (13744 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013137, _1013135)), _1013141), _1013139))]]], (13746 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013137, _1013135)), _1013139), _1013141))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013137, _1013135)), _1013139), _1013141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013137, _1013135)), _1013141), _1013139)))]]], (13756 ^ _780461) ^ [_1013527, _1013529] : [class_Rings_Olinordered__idom(_1013527), -(c_Groups_Osgn__class_Osgn(_1013527, c_Groups_Osgn__class_Osgn(_1013527, _1013529)) = c_Groups_Osgn__class_Osgn(_1013527, _1013529))], (13762 ^ _780461) ^ [_1013620, _1013622, _1013624] : [class_Divides_Osemiring__div(_1013620), -(c_Divides_Odiv__class_Omod(_1013620, c_Divides_Odiv__class_Omod(_1013620, _1013622, _1013624), _1013624) = c_Divides_Odiv__class_Omod(_1013620, _1013622, _1013624))], (13768 ^ _780461) ^ [_1013721, _1013723] : [class_Divides_Osemiring__div(_1013721), -(c_Divides_Odiv__class_Omod(_1013721, c_Groups_Ozero__class_Ozero(_1013721), _1013723) = c_Groups_Ozero__class_Ozero(_1013721))], (13774 ^ _780461) ^ [_1013812, _1013814] : [class_Divides_Osemiring__div(_1013812), -(c_Divides_Odiv__class_Omod(_1013812, _1013814, c_Groups_Ozero__class_Ozero(_1013812)) = _1013814)], (13780 ^ _780461) ^ [_1013899, _1013901] : [class_Divides_Osemiring__div(_1013899), -(c_Divides_Odiv__class_Omod(_1013899, _1013901, _1013901) = c_Groups_Ozero__class_Ozero(_1013899))], (13786 ^ _780461) ^ [_1013986, _1013988, _1013990] : [class_Divides_Osemiring__div(_1013986), -(c_Divides_Odiv__class_Omod(_1013986, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013986), _1013988), _1013990), _1013990) = c_Divides_Odiv__class_Omod(_1013986, _1013988, _1013990))], (13792 ^ _780461) ^ [_1014095, _1014097, _1014099] : [class_Divides_Osemiring__div(_1014095), -(c_Divides_Odiv__class_Omod(_1014095, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014095), _1014097), _1014099), _1014097) = c_Divides_Odiv__class_Omod(_1014095, _1014099, _1014097))], (13798 ^ _780461) ^ [_1014204, _1014206, _1014208, _1014210] : [class_Divides_Osemiring__div(_1014204), -(c_Divides_Odiv__class_Omod(_1014204, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014204), _1014206), _1014208), _1014210) = c_Divides_Odiv__class_Omod(_1014204, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014204), _1014206), c_Divides_Odiv__class_Omod(_1014204, _1014208, _1014210)), _1014210))], (13804 ^ _780461) ^ [_1014339, _1014341, _1014343, _1014345] : [class_Divides_Osemiring__div(_1014339), -(c_Divides_Odiv__class_Omod(_1014339, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014339), _1014341), _1014343), _1014345) = c_Divides_Odiv__class_Omod(_1014339, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014339), c_Divides_Odiv__class_Omod(_1014339, _1014341, _1014345)), _1014343), _1014345))], (13810 ^ _780461) ^ [_1014474, _1014476, _1014478, _1014480] : [class_Divides_Osemiring__div(_1014474), -(c_Divides_Odiv__class_Omod(_1014474, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014474), _1014476), _1014478), _1014480) = c_Divides_Odiv__class_Omod(_1014474, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014474), c_Divides_Odiv__class_Omod(_1014474, _1014476, _1014480)), c_Divides_Odiv__class_Omod(_1014474, _1014478, _1014480)), _1014480))], (13816 ^ _780461) ^ [_1014617, _1014619, _1014621, _1014623] : [class_Divides_Osemiring__div(_1014617), -(c_Divides_Odiv__class_Omod(_1014617, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014617), _1014619), c_Divides_Odiv__class_Omod(_1014617, _1014621, _1014623)), _1014623) = c_Divides_Odiv__class_Omod(_1014617, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014617), _1014619), _1014621), _1014623))], (13822 ^ _780461) ^ [_1014752, _1014754, _1014756, _1014758] : [class_Divides_Osemiring__div(_1014752), -(c_Divides_Odiv__class_Omod(_1014752, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014752), c_Divides_Odiv__class_Omod(_1014752, _1014754, _1014756)), _1014758), _1014756) = c_Divides_Odiv__class_Omod(_1014752, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014752), _1014754), _1014758), _1014756))], (13828 ^ _780461) ^ [_1014887, _1014889, _1014891, _1014893, _1014895, _1014897] : [class_Divides_Osemiring__div(_1014887), c_Divides_Odiv__class_Omod(_1014887, _1014889, _1014891) = c_Divides_Odiv__class_Omod(_1014887, _1014893, _1014891), c_Divides_Odiv__class_Omod(_1014887, _1014895, _1014891) = c_Divides_Odiv__class_Omod(_1014887, _1014897, _1014891), -(c_Divides_Odiv__class_Omod(_1014887, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014887), _1014889), _1014895), _1014891) = c_Divides_Odiv__class_Omod(_1014887, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014887), _1014893), _1014897), _1014891))], (13842 ^ _780461) ^ [_1015170, _1015172, _1015174, _1015176] : [class_Divides_Osemiring__div(_1015170), -(c_Divides_Odiv__class_Omod(_1015170, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015170), _1015172), _1015174), _1015176) = c_Divides_Odiv__class_Omod(_1015170, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015170), _1015172), c_Divides_Odiv__class_Omod(_1015170, _1015174, _1015176)), _1015176))], (13848 ^ _780461) ^ [_1015305, _1015307, _1015309, _1015311] : [class_Divides_Osemiring__div(_1015305), -(c_Divides_Odiv__class_Omod(_1015305, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015305), _1015307), _1015309), _1015311) = c_Divides_Odiv__class_Omod(_1015305, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015305), c_Divides_Odiv__class_Omod(_1015305, _1015307, _1015311)), _1015309), _1015311))], (13854 ^ _780461) ^ [_1015440, _1015442, _1015444, _1015446] : [class_Divides_Osemiring__div(_1015440), -(c_Divides_Odiv__class_Omod(_1015440, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015440), _1015442), _1015444), _1015446) = c_Divides_Odiv__class_Omod(_1015440, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015440), c_Divides_Odiv__class_Omod(_1015440, _1015442, _1015446)), c_Divides_Odiv__class_Omod(_1015440, _1015444, _1015446)), _1015446))], (13860 ^ _780461) ^ [_1015583, _1015585, _1015587, _1015589] : [class_Divides_Osemiring__div(_1015583), -(c_Divides_Odiv__class_Omod(_1015583, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015583), _1015585), _1015587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015583), _1015585), _1015589)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015583), _1015585), c_Divides_Odiv__class_Omod(_1015583, _1015587, _1015589)))], (13866 ^ _780461) ^ [_1015726, _1015728, _1015730, _1015732] : [class_Divides_Osemiring__div(_1015726), -(c_Divides_Odiv__class_Omod(_1015726, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015726), _1015728), _1015730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015726), _1015732), _1015730)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015726), c_Divides_Odiv__class_Omod(_1015726, _1015728, _1015732)), _1015730))], (13872 ^ _780461) ^ [_1015869, _1015871, _1015873, _1015875] : [class_Divides_Osemiring__div(_1015869), -(c_Divides_Odiv__class_Omod(_1015869, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015869), c_Divides_Odiv__class_Omod(_1015869, _1015871, _1015873)), _1015875), _1015873) = c_Divides_Odiv__class_Omod(_1015869, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015869), _1015871), _1015875), _1015873))], (13878 ^ _780461) ^ [_1016004, _1016006, _1016008, _1016010, _1016012, _1016014] : [class_Divides_Osemiring__div(_1016004), c_Divides_Odiv__class_Omod(_1016004, _1016006, _1016008) = c_Divides_Odiv__class_Omod(_1016004, _1016010, _1016008), c_Divides_Odiv__class_Omod(_1016004, _1016012, _1016008) = c_Divides_Odiv__class_Omod(_1016004, _1016014, _1016008), -(c_Divides_Odiv__class_Omod(_1016004, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016004), _1016006), _1016012), _1016008) = c_Divides_Odiv__class_Omod(_1016004, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016004), _1016010), _1016014), _1016008))], (13892 ^ _780461) ^ [_1016287, _1016289, _1016291] : [class_Divides_Oring__div(_1016287), -(c_Divides_Odiv__class_Omod(_1016287, hAPP(c_Groups_Ouminus__class_Ouminus(_1016287), _1016289), _1016291) = c_Divides_Odiv__class_Omod(_1016287, hAPP(c_Groups_Ouminus__class_Ouminus(_1016287), c_Divides_Odiv__class_Omod(_1016287, _1016289, _1016291)), _1016291))], (13898 ^ _780461) ^ [_1016408, _1016410, _1016412, _1016414] : [class_Divides_Oring__div(_1016408), c_Divides_Odiv__class_Omod(_1016408, _1016410, _1016412) = c_Divides_Odiv__class_Omod(_1016408, _1016414, _1016412), -(c_Divides_Odiv__class_Omod(_1016408, hAPP(c_Groups_Ouminus__class_Ouminus(_1016408), _1016410), _1016412) = c_Divides_Odiv__class_Omod(_1016408, hAPP(c_Groups_Ouminus__class_Ouminus(_1016408), _1016414), _1016412))], (13908 ^ _780461) ^ [_1016595] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016595, _1016595) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13910 ^ _780461) ^ [_1016622] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1016622) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13912 ^ _780461) ^ [_1016649, _1016651, _1016653] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016649), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016651, _1016653)), _1016653) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016649), _1016651), _1016653))], (13914 ^ _780461) ^ [_1016700, _1016702, _1016704] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016700), _1016702), _1016704) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016700), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016702, _1016704)), _1016704))], (13916 ^ _780461) ^ [_1016751, _1016753] : [-(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, _1016751, _1016753)), _1016753) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016751), _1016753))], (13918 ^ _780461) ^ [_1016794, _1016796] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016794), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016796)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016794, _1016796)))], (13920 ^ _780461) ^ [_1016836, _1016838] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1016836, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1016838)) = 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), _1016836), _1016838)))], (13922 ^ _780461) ^ [_1016878, _1016880] : [class_Rings_Olinordered__idom(_1016878), 13925 ^ _780461 : [(13926 ^ _780461) ^ [] : [c_Groups_Osgn__class_Osgn(_1016878, _1016880) = c_Groups_Ozero__class_Ozero(_1016878), -(_1016880 = c_Groups_Ozero__class_Ozero(_1016878))], (13932 ^ _780461) ^ [] : [_1016880 = c_Groups_Ozero__class_Ozero(_1016878), -(c_Groups_Osgn__class_Osgn(_1016878, _1016880) = c_Groups_Ozero__class_Ozero(_1016878))]]], (13938 ^ _780461) ^ [_1017104] : [class_Groups_Osgn__if(_1017104), -(c_Groups_Osgn__class_Osgn(_1017104, c_Groups_Ozero__class_Ozero(_1017104)) = c_Groups_Ozero__class_Ozero(_1017104))], (13944 ^ _780461) ^ [_1017191, _1017193, _1017195] : [class_Rings_Olinordered__idom(_1017191), -(c_Groups_Osgn__class_Osgn(_1017191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017191), _1017193), _1017195)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017191), c_Groups_Osgn__class_Osgn(_1017191, _1017193)), c_Groups_Osgn__class_Osgn(_1017191, _1017195)))], (13950 ^ _780461) ^ [_1017318, _1017320, _1017322] : [class_Divides_Osemiring__div(_1017318), -(c_Divides_Odiv__class_Omod(_1017318, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017318), _1017320), _1017322), _1017322) = c_Groups_Ozero__class_Ozero(_1017318))], (13956 ^ _780461) ^ [_1017423, _1017425, _1017427] : [class_Divides_Osemiring__div(_1017423), -(c_Divides_Odiv__class_Omod(_1017423, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017423), _1017425), _1017427), _1017425) = c_Groups_Ozero__class_Ozero(_1017423))], (13962 ^ _780461) ^ [_1017528, _1017530, _1017532, _1017534] : [class_Divides_Osemiring__div(_1017528), -(c_Divides_Odiv__class_Omod(_1017528, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017528), _1017530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017528), _1017532), _1017534)), _1017532) = c_Divides_Odiv__class_Omod(_1017528, _1017530, _1017532))], (13968 ^ _780461) ^ [_1017655, _1017657, _1017659, _1017661] : [class_Divides_Osemiring__div(_1017655), -(c_Divides_Odiv__class_Omod(_1017655, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1017655), _1017657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017655), _1017659), _1017661)), _1017661) = c_Divides_Odiv__class_Omod(_1017655, _1017657, _1017661))], (13974 ^ _780461) ^ [_1017782, _1017784] : [class_Divides_Osemiring__div(_1017782), -(c_Divides_Odiv__class_Omod(_1017782, _1017784, c_Groups_Oone__class_Oone(_1017782)) = c_Groups_Ozero__class_Ozero(_1017782))], (13980 ^ _780461) ^ [_1017873, _1017875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1017873, _1017875)), _1017873)))], (13986 ^ _780461) ^ [_1017972, _1017974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017974)), -(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, _1017972, _1017974))))], (13996 ^ _780461) ^ [_1018121, _1018123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018121), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018121), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018123, _1018121))))], (14002 ^ _780461) ^ [_1018226, _1018228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1018226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018228, _1018226)), _1018226)))], (14008 ^ _780461) ^ [_1018340, _1018342] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018340, _1018342) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1018340 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018342), 14011 ^ [_1018340, _1018342]))], (14015 ^ _780461) ^ [_1018445, _1018447] : [14016 ^ _780461 : [(14017 ^ _780461) ^ [_1018494] : [_1018445 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018447), _1018494)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018445, _1018447) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14021 ^ _780461) ^ [_1018556, _1018558] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018556, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1018558)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018556, _1018558) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (14027 ^ _780461) ^ [_1018646, _1018648] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1018646), _1018648) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018646, _1018648) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (14033 ^ _780461) ^ [_1018737, _1018739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018737), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018739), _1018737)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018737, _1018739) = _1018737)], (14043 ^ _780461) ^ [_1018894, _1018896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018894), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14046 ^ _780461 : [(14047 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018896, _1018894)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14049 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1018894), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1018896, _1018894))))]]], (14051 ^ _780461) ^ [_1019043, _1019045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019043), 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, _1019045, _1019043)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14057 ^ _780461) ^ [_1019148, _1019150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019148), _1019150)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019148, _1019150) = _1019148)], (14067 ^ _780461) ^ [_1019299, _1019301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019299)), 14070 ^ _780461 : [(14071 ^ _780461) ^ [] : [-(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, _1019301, _1019299))))], (14073 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1019301, _1019299)), _1019299)))]]], (14075 ^ _780461) ^ [_1019436, _1019438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019436)), -(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, _1019438, _1019436))))], (14081 ^ _780461) ^ [_1019529, _1019531] : [class_Rings_Olinordered__idom(_1019529), 14084 ^ _780461 : [(14085 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019529), c_Groups_Osgn__class_Osgn(_1019529, _1019531)), c_Groups_Ozero__class_Ozero(_1019529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019529), _1019531), c_Groups_Ozero__class_Ozero(_1019529))))], (14091 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019529), _1019531), c_Groups_Ozero__class_Ozero(_1019529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019529), c_Groups_Osgn__class_Osgn(_1019529, _1019531)), c_Groups_Ozero__class_Ozero(_1019529))))]]], (14097 ^ _780461) ^ [_1019797, _1019799] : [class_Rings_Olinordered__idom(_1019797), 14100 ^ _780461 : [(14101 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019797), c_Groups_Ozero__class_Ozero(_1019797)), c_Groups_Osgn__class_Osgn(_1019797, _1019799))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019797), c_Groups_Ozero__class_Ozero(_1019797)), _1019799)))], (14107 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019797), c_Groups_Ozero__class_Ozero(_1019797)), _1019799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019797), c_Groups_Ozero__class_Ozero(_1019797)), c_Groups_Osgn__class_Osgn(_1019797, _1019799))))]]], (14113 ^ _780461) ^ [_1020065, _1020067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020065), _1020067)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1020065, _1020067) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020065), _1020067))], (14123 ^ _780461) ^ [_1020240, _1020242] : [class_Rings_Olinordered__idom(_1020240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020240), c_Groups_Ozero__class_Ozero(_1020240)), _1020242)), -(c_Groups_Osgn__class_Osgn(_1020240, _1020242) = c_Groups_Oone__class_Oone(_1020240))], (14133 ^ _780461) ^ [_1020395, _1020397] : [class_Rings_Olinordered__idom(_1020395), 14136 ^ _780461 : [(14137 ^ _780461) ^ [] : [c_Groups_Osgn__class_Osgn(_1020395, _1020397) = c_Groups_Oone__class_Oone(_1020395), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020395), c_Groups_Ozero__class_Ozero(_1020395)), _1020397)))], (14143 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020395), c_Groups_Ozero__class_Ozero(_1020395)), _1020397)), -(c_Groups_Osgn__class_Osgn(_1020395, _1020397) = c_Groups_Oone__class_Oone(_1020395))]]], (14195 ^ _780461) ^ [_1021537, _1021539, _1021541] : [-(hBOOL(hAPP(_1021537, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1021539, _1021541)))), 14198 ^ _780461 : [(14199 ^ _780461) ^ [] : [-(_1021541 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14201 ^ _780461) ^ [] : [hBOOL(hAPP(_1021537, _1021539))]], 14204 ^ _780461 : [(14205 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021541)))], (14209 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14207 ^ [_1021537, _1021539, _1021541])))], (14211 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14207 ^ [_1021537, _1021539, _1021541]), _1021541)))], (14213 ^ _780461) ^ [] : [-(_1021539 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1021541), 14206 ^ [_1021537, _1021539, _1021541])), 14207 ^ [_1021537, _1021539, _1021541]))], (14215 ^ _780461) ^ [] : [hBOOL(hAPP(_1021537, 14207 ^ [_1021537, _1021539, _1021541]))]], 14216 ^ _780461 : [(14217 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021541), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14221 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021541), 14219 ^ [_1021537, _1021539, _1021541])))], (14223 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14219 ^ [_1021537, _1021539, _1021541]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14225 ^ _780461) ^ [] : [-(_1021539 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1021541), 14218 ^ [_1021537, _1021539, _1021541])), 14219 ^ [_1021537, _1021539, _1021541]))], (14227 ^ _780461) ^ [] : [hBOOL(hAPP(_1021537, 14219 ^ [_1021537, _1021539, _1021541]))]]], (14149 ^ _780461) ^ [_1020660, _1020662, _1020664] : [hBOOL(hAPP(_1020660, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1020662, _1020664))), 14152 ^ _780461 : [(14153 ^ _780461) ^ [] : [_1020664 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1020660, _1020662)))], (14159 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020664)), 14162 ^ _780461 : [(14163 ^ _780461) ^ [_1020990, _1020992] : [-(hBOOL(hAPP(_1020660, _1020990))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020990), _1020664)), _1020662 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1020664), _1020992)), _1020990)]]], (14177 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020664), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14180 ^ _780461 : [(14181 ^ _780461) ^ [_1021282, _1021284] : [-(hBOOL(hAPP(_1020660, _1021282))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020664), _1021282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021282), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1020662 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1020664), _1021284)), _1021282)]]]]], (14231 ^ _780461) ^ [_1022249, _1022251, _1022253, _1022255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022249)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022251), _1022253)), -(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), _1022253), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1022255, _1022249))), _1022251))))], (14245 ^ _780461) ^ [_1022496, _1022498, _1022500, _1022502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022498), _1022500)), -(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), _1022500), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1022502, _1022496))), _1022498)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022500), _1022496))))], (14259 ^ _780461) ^ [_1022770, _1022772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022770)), -(c_SMT_Oz3mod(_1022772, _1022770) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1022772, _1022770))], (14265 ^ _780461) ^ [_1022859, _1022861] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022859))), -(c_SMT_Oz3mod(_1022861, _1022859) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1022861, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1022859)))], (14271 ^ _780461) ^ [_1022909, _1022911, _1022913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022909), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14274 ^ _780461 : [(14293 ^ _780461) ^ [] : [14296 ^ _780461 : [(14297 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022909), 14295 ^ [_1022909, _1022911, _1022913])))], (14299 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14295 ^ [_1022909, _1022911, _1022913]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14301 ^ _780461) ^ [] : [-(_1022913 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022909), 14294 ^ [_1022909, _1022911, _1022913])), 14295 ^ [_1022909, _1022911, _1022913]))], (14303 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1022911, 14294 ^ [_1022909, _1022911, _1022913]), 14295 ^ [_1022909, _1022911, _1022913]))]], -(hBOOL(hAPP(hAPP(_1022911, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022913), _1022909)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1022913, _1022909))))], (14275 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1022911, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1022913), _1022909)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1022913, _1022909))), 14278 ^ _780461 : [(14279 ^ _780461) ^ [_1023119, _1023121] : [-(hBOOL(hAPP(hAPP(_1022911, _1023121), _1023119))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022909), _1023119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023119), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1022913 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022909), _1023121)), _1023119)]]]]], (14307 ^ _780461) ^ [_1023642, _1023644, _1023646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023642)), 14310 ^ _780461 : [(14329 ^ _780461) ^ [] : [14332 ^ _780461 : [(14333 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14331 ^ [_1023642, _1023644, _1023646])))], (14335 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14331 ^ [_1023642, _1023644, _1023646]), _1023642)))], (14337 ^ _780461) ^ [] : [-(_1023646 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023642), 14330 ^ [_1023642, _1023644, _1023646])), 14331 ^ [_1023642, _1023644, _1023646]))], (14339 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1023644, 14330 ^ [_1023642, _1023644, _1023646]), 14331 ^ [_1023642, _1023644, _1023646]))]], -(hBOOL(hAPP(hAPP(_1023644, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023646), _1023642)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1023646, _1023642))))], (14311 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1023644, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1023646), _1023642)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1023646, _1023642))), 14314 ^ _780461 : [(14315 ^ _780461) ^ [_1023843, _1023845] : [-(hBOOL(hAPP(hAPP(_1023644, _1023845), _1023843))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023843), _1023642)), _1023646 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023642), _1023845)), _1023843)]]]]], (14343 ^ _780461) ^ [_1024357, _1024359, _1024361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024357)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024359, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024361), _1024357)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024361), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024359), _1024361), _1024357))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1024359, _1024361)))], (14349 ^ _780461) ^ [_1024512, _1024514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1024512, _1024514))))], (14405 ^ _780461) ^ [_1025637, _1025639, _1025641] : [-(hBOOL(hAPP(_1025637, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1025639), _1025641)))), 14408 ^ _780461 : [(14409 ^ _780461) ^ [] : [-(_1025641 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14411 ^ _780461) ^ [] : [hBOOL(hAPP(_1025637, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 14414 ^ _780461 : [(14415 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025641)))], (14419 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14417 ^ [_1025637, _1025639, _1025641])))], (14421 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 14417 ^ [_1025637, _1025639, _1025641]), _1025641)))], (14423 ^ _780461) ^ [] : [-(_1025639 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025641), 14416 ^ [_1025637, _1025639, _1025641])), 14417 ^ [_1025637, _1025639, _1025641]))], (14425 ^ _780461) ^ [] : [hBOOL(hAPP(_1025637, 14416 ^ [_1025637, _1025639, _1025641]))]], 14426 ^ _780461 : [(14427 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025641), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14431 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025641), 14429 ^ [_1025637, _1025639, _1025641])))], (14433 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 14429 ^ [_1025637, _1025639, _1025641]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14435 ^ _780461) ^ [] : [-(_1025639 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025641), 14428 ^ [_1025637, _1025639, _1025641])), 14429 ^ [_1025637, _1025639, _1025641]))], (14437 ^ _780461) ^ [] : [hBOOL(hAPP(_1025637, 14428 ^ [_1025637, _1025639, _1025641]))]]], (14359 ^ _780461) ^ [_1024677, _1024679, _1024681] : [hBOOL(hAPP(_1024677, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1024679), _1024681))), 14362 ^ _780461 : [(14363 ^ _780461) ^ [] : [_1024681 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1024677, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14369 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024681)), 14372 ^ _780461 : [(14373 ^ _780461) ^ [_1025011] : [-(hBOOL(hAPP(_1024677, _1025011))), 14374 ^ _780461 : [(14375 ^ _780461) ^ [_1025082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025082), _1024681)), _1024679 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024681), _1025011)), _1025082)]]]]], (14387 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024681), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14390 ^ _780461 : [(14391 ^ _780461) ^ [_1025341] : [-(hBOOL(hAPP(_1024677, _1025341))), 14392 ^ _780461 : [(14393 ^ _780461) ^ [_1025415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024681), _1025415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1025415), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1024679 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024681), _1025341)), _1025415)]]]]]]], (14441 ^ _780461) ^ [_1026351, _1026353, _1026355, _1026357] : [_1026351 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1026353), _1026355)), _1026357), -(_1026353 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1026351), _1026353) = _1026355), 14448 ^ _780461 : [(14449 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026353)))], (14451 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026357), _1026353))]], 14456 ^ _780461 : [(14457 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026353))], (14459 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1026353), _1026357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1026357), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (14471 ^ _780461) ^ [_1026838, _1026840, _1026842] : [hBOOL(hAPP(_1026838, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1026840), _1026842))), 14476 ^ _780461 : [(14477 ^ _780461) ^ [] : [-(_1026842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14479 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1026838, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 14481 ^ _780461 : [(14482 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026842), 14480 ^ [_1026838, _1026840, _1026842])), _1026840)))], (14484 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1026840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1026842), hAPP(c_Nat_OSuc, 14480 ^ [_1026838, _1026840, _1026842])))))], (14486 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1026838, 14480 ^ [_1026838, _1026840, _1026842])))]]], (14488 ^ _780461) ^ [_1027142, _1027144, _1027146] : [-(hBOOL(hAPP(_1027142, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027144), _1027146)))), 14489 ^ _780461 : [(14490 ^ _780461) ^ [] : [_1027146 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1027142, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14496 ^ _780461) ^ [_1027310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027146), _1027310)), _1027144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027146), hAPP(c_Nat_OSuc, _1027310)))), hBOOL(hAPP(_1027142, _1027310))]]], (14508 ^ _780461) ^ [_1027540, _1027542, _1027544] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027540), _1027542)), _1027544) = 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), _1027540), _1027544)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027542), _1027544))), 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, _1027540, _1027544)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027542, _1027544))), _1027544)))], (14510 ^ _780461) ^ [_1027623, _1027625] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027623)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027625)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027623), _1027625)))], (14512 ^ _780461) ^ [_1027669, _1027671] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027669), _1027671)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027669)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027671)))], (14514 ^ _780461) ^ [_1027715, _1027717, _1027719] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027717), _1027719)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027717), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027715), _1027717), _1027719))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027715, _1027717)))], (14516 ^ _780461) ^ [_1027778, _1027780, _1027782] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027778), _1027780)), _1027782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027778), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027780), _1027782))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027778), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1027780, _1027782))), _1027782)))], (14518 ^ _780461) ^ [_1027851, _1027853, _1027855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027851), _1027853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027851), _1027855)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027853), _1027855))))], (14524 ^ _780461) ^ [_1027974, _1027976] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1027974), _1027976)), _1027974)))], (14526 ^ _780461) ^ [_1028010] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028010) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14528 ^ _780461) ^ [_1028036, _1028038] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1028036), _1028038) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028036, _1028038)), _1028038))], (14530 ^ _780461) ^ [_1028079, _1028081, _1028083] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028081), _1028083)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1028079), _1028081)), _1028083))], (14532 ^ _780461) ^ [_1028130, _1028132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028130), _1028132)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028130, _1028132) = _1028130)], (14538 ^ _780461) ^ [_1028225, _1028227] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028225, _1028227)), _1028225)))], (14540 ^ _780461) ^ [_1028259, _1028261, _1028263] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028259, _1028261)), _1028263) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028259), _1028263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028261), _1028263)))], (14542 ^ _780461) ^ [_1028312, _1028314, _1028316] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028312), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1028314, _1028316)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028312), _1028314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028312), _1028316)))], (14544 ^ _780461) ^ [_1028365, _1028367] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028365), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1028367)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1028365)), _1028367))], (14546 ^ _780461) ^ [_1028408, _1028410] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1028408)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1028410)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028408), _1028410))], (14548 ^ _780461) ^ [_1028451, _1028453] : [class_Divides_Osemiring__div(_1028451), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028451), c_Groups_Ozero__class_Ozero(_1028451)), _1028453) = c_Groups_Ozero__class_Ozero(_1028451))], (14554 ^ _780461) ^ [_1028550, _1028552] : [class_Divides_Osemiring__div(_1028550), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028550), _1028552), c_Groups_Ozero__class_Ozero(_1028550)) = c_Groups_Ozero__class_Ozero(_1028550))], (14560 ^ _780461) ^ [_1028649, _1028651] : [class_Divides_Osemiring__div(_1028649), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1028649), _1028651), c_Groups_Oone__class_Oone(_1028649)) = _1028651)], (14566 ^ _780461) ^ [_1028744, _1028746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028744)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028744), _1028746)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1028744)), hAPP(c_Int_Onat, _1028746)))], (14572 ^ _780461) ^ [_1028867, _1028869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1028869)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1028867)), hAPP(c_Int_Onat, _1028869)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1028867), _1028869)))], (14582 ^ _780461) ^ [_1029046] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029046), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1029046)], (14584 ^ _780461) ^ [_1029075, _1029077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029075), _1029077)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029075), _1029077) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14590 ^ _780461) ^ [_1029186, _1029188, _1029190] : [_1029186 = 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), _1029186), _1029188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029186), _1029190)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14596 ^ _780461) ^ [_1029295, _1029297, _1029299] : [-(_1029295 = 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), _1029295), _1029297)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029295), _1029299)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1029297), _1029299))], (14602 ^ _780461) ^ [_1029368, _1029370] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029368, _1029370)) = _1029370, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1029368), _1029370) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14608 ^ _780461) ^ [_1029467, _1029469] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029467, _1029469)) = _1029469), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1029467), _1029469) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029467, _1029469)))], (14614 ^ _780461) ^ [_1029526] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029526, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14616 ^ _780461) ^ [_1029553, _1029555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029555)), -(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), _1029553), _1029555))))], (14626 ^ _780461) ^ [_1029706, _1029708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1029708, _1029706)), _1029706)))], (14632 ^ _780461) ^ [_1029805, _1029807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029805)), 14635 ^ _780461 : [(14636 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1029807), _1029805)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1029807), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14642 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1029807), 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), _1029807), _1029805)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (14648 ^ _780461) ^ [_1030064, _1030066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030064), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14651 ^ _780461 : [(14652 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030066), _1030064)), 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)), _1030066)))], (14658 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030066), _1030064)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (14664 ^ _780461) ^ [_1030320, _1030322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030320), 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)), _1030322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030320), _1030322)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14674 ^ _780461) ^ [_1030481] : [-(_1030481 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030481), _1030481) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (14680 ^ _780461) ^ [_1030536, _1030538] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1030536, _1030538) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1030536 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030538), 14683 ^ [_1030536, _1030538]))], (14687 ^ _780461) ^ [_1030641, _1030643] : [14688 ^ _780461 : [(14689 ^ _780461) ^ [_1030690] : [_1030641 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030643), _1030690)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1030641, _1030643) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14693 ^ _780461) ^ [_1030751] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030751), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14695 ^ _780461) ^ [_1030777] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1030777, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1030777)], (14697 ^ _780461) ^ [_1030806, _1030808] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1030806, _1030808)), _1030808) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14699 ^ _780461) ^ [_1030841, _1030843, _1030845] : [-(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), _1030841), _1030843)), _1030845), _1030843) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1030845, _1030843))], (14701 ^ _780461) ^ [_1030888, _1030890, _1030892] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1030888), _1030890)), _1030892) = 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), _1030888), _1030892)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1030890), _1030892))), 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, _1030888, _1030892)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1030890, _1030892))), _1030892)))], (14703 ^ _780461) ^ [_1030971, _1030973] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1030971), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1030973)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1030971, _1030973)))], (14705 ^ _780461) ^ [_1031013, _1031015] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1031013, _1031015)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031013), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031015)))], (14707 ^ _780461) ^ [_1031055, _1031057, _1031059, _1031061] : [class_Divides_Osemiring__div(_1031055), -(_1031057 = c_Groups_Ozero__class_Ozero(_1031055)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031055), _1031057), _1031059)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031055), _1031057), _1031061)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031055), _1031059), _1031061))], (14717 ^ _780461) ^ [_1031217, _1031219, _1031221, _1031223] : [class_Divides_Osemiring__div(_1031217), -(_1031219 = c_Groups_Ozero__class_Ozero(_1031217)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031217), _1031221), _1031219)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031217), _1031223), _1031219)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031217), _1031221), _1031223))], (14727 ^ _780461) ^ [_1031379, _1031381, _1031383] : [class_Divides_Osemiring__div(_1031379), -(_1031381 = c_Groups_Ozero__class_Ozero(_1031379)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031379), _1031381), _1031383)), _1031381) = _1031383)], (14737 ^ _780461) ^ [_1031507, _1031509, _1031511] : [class_Divides_Osemiring__div(_1031507), -(_1031509 = c_Groups_Ozero__class_Ozero(_1031507)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031507), _1031511), _1031509)), _1031509) = _1031511)], (14747 ^ _780461) ^ [_1031635, _1031637, _1031639, _1031641] : [class_Divides_Osemiring__div(_1031635), 14750 ^ _780461 : [(14751 ^ _780461) ^ [] : [_1031637 = c_Groups_Ozero__class_Ozero(_1031635), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031635), _1031637), _1031639)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031635), _1031637), _1031641)) = c_Groups_Ozero__class_Ozero(_1031635))], (14757 ^ _780461) ^ [] : [-(_1031637 = c_Groups_Ozero__class_Ozero(_1031635)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031635), _1031637), _1031639)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031635), _1031637), _1031641)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031635), _1031639), _1031641))]]], (14763 ^ _780461) ^ [_1031941, _1031943] : [class_Divides_Osemiring__div(_1031941), -(_1031943 = c_Groups_Ozero__class_Ozero(_1031941)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1031941), _1031943), _1031943) = c_Groups_Oone__class_Oone(_1031941))], (14773 ^ _780461) ^ [_1032055, _1032057, _1032059] : [class_Divides_Osemiring__div(_1032055), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1032055), c_Divides_Odiv__class_Omod(_1032055, _1032057, _1032059)), _1032059) = c_Groups_Ozero__class_Ozero(_1032055))], (14779 ^ _780461) ^ [_1032160, _1032162, _1032164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032160), _1032162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1032164), _1032162)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1032164), _1032160))))], (14789 ^ _780461) ^ [_1032341, _1032343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032341)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032343), _1032341)), _1032341) = _1032343)], (14795 ^ _780461) ^ [_1032446, _1032448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032446)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032446), _1032448)), _1032446) = _1032448)], (14801 ^ _780461) ^ [_1032551, _1032553, _1032555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032551)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032551), _1032553)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032551), _1032555)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1032553), _1032555))], (14807 ^ _780461) ^ [_1032682, _1032684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1032682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1032684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1032684), _1032682)), _1032684)))], (14817 ^ _780461) ^ [_1032856, _1032858] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1032856), _1032858) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1032858 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14826 ^ _780461 : [(14827 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1032856)))], (14829 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032856), _1032858)))]], 14830 ^ _780461 : [(14831 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1032856), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14833 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1032858), _1032856)))]]], (14835 ^ _780461) ^ [_1033087, _1033089] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1033087), _1033089) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14836 ^ _780461 : [(14837 ^ _780461) ^ [] : [_1033089 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (14839 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033087), _1033089))], (14845 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033087), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033089), _1033087))]]], (14853 ^ _780461) ^ [_1033382, _1033384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033382)), 14856 ^ _780461 : [(14857 ^ _780461) ^ [] : [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), _1033384), _1033382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033384)))], (14863 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033384)), -(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), _1033384), _1033382))))]]], (14869 ^ _780461) ^ [_1033623, _1033625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033623)), 14872 ^ _780461 : [(14873 ^ _780461) ^ [] : [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), _1033625), _1033623))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033623), _1033625)))], (14879 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033623), _1033625)), -(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), _1033625), _1033623))))]]], (14885 ^ _780461) ^ [_1033873, _1033875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033873)), 14888 ^ _780461 : [(14889 ^ _780461) ^ [] : [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), _1033873), _1033875))), 14892 ^ _780461 : [(14893 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033875), _1033873)))], (14895 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033875)))]]], (14897 ^ _780461) ^ [] : [-(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), _1033873), _1033875)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033875), _1033873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1033875))]]], (14907 ^ _780461) ^ [_1034201, _1034203, _1034205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1034203), _1034205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034201), _1034205)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034201), _1034203))))], (14921 ^ _780461) ^ [_1034440, _1034442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034442), 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), _1034440), _1034442)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14931 ^ _780461) ^ [_1034605, _1034607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1034605)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034605), _1034607)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1034605), _1034607) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14941 ^ _780461) ^ [_1034760, _1034762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1034760), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 14944 ^ _780461 : [(14945 ^ _780461) ^ [] : [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), _1034762), _1034760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1034762), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14951 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1034762), 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), _1034762), _1034760))))]]], (14957 ^ _780461) ^ [_1035016, _1035018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1035016), 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)), _1035018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035016), _1035018)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14967 ^ _780461) ^ [_1035181, _1035183, _1035185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1035181), 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)), _1035183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1035183), _1035185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035181), _1035183)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035181), _1035185))))], (14981 ^ _780461) ^ [_1035426, _1035428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1035426), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1035428), _1035426)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035426), _1035428) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14991 ^ _780461) ^ [_1035587, _1035589, _1035591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1035587), _1035589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1035591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035587), _1035591)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035589), _1035591))))], (15001 ^ _780461) ^ [_1035768, _1035770, _1035772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1035768), _1035770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1035772), 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), _1035770), _1035772)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1035768), _1035772))))], (15011 ^ _780461) ^ [_1035955, _1035957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1035955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1035957, _1035955)), _1035955)))], (15017 ^ _780461) ^ [_1036054, _1036056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1036054)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1036056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1036054), _1036056)), _1036054)))], (15027 ^ _780461) ^ [_1036213, _1036215, _1036217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1036213)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1036215), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1036217), _1036213)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1036215), _1036217)), _1036213))], (15033 ^ _780461) ^ [_1036344, _1036346, _1036348] : [-(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), _1036344), _1036346)), _1036348)), _1036346) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1036348), _1036346))], (15035 ^ _780461) ^ [_1036397, _1036399, _1036401] : [-(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), _1036397), _1036399)), _1036399)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1036397, _1036399))), _1036401) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1036397), _1036401))], (15037 ^ _780461) ^ [_1036458, _1036460, _1036462] : [-(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), _1036458), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1036460), _1036458))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1036460, _1036458))), _1036462) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1036460), _1036462))], (15039 ^ _780461) ^ [_1036519, _1036521, _1036523] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1036519), _1036521)), _1036523) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1036519), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1036521), _1036523))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1036519), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1036521, _1036523))), _1036523)))], (15041 ^ _780461) ^ [_1036592, _1036594] : [-(_1036592 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1036594), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1036592), _1036594))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1036592, _1036594)))], (15043 ^ _780461) ^ [_1036639, _1036641, _1036643, _1036645] : [class_Divides_Osemiring__div(_1036639), -(_1036641 = c_Groups_Ozero__class_Ozero(_1036639)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1036639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036639), _1036643), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036639), _1036645), _1036641))), _1036641) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036639), _1036645), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1036639), _1036643), _1036641)))], (15053 ^ _780461) ^ [_1036817, _1036819, _1036821, _1036823] : [class_Divides_Osemiring__div(_1036817), -(_1036819 = c_Groups_Ozero__class_Ozero(_1036817)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1036817), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036817), _1036821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036817), _1036819), _1036823))), _1036819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036817), _1036823), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1036817), _1036821), _1036819)))], (15063 ^ _780461) ^ [_1036995, _1036997, _1036999] : [class_Divides_Osemiring__div(_1036995), -(_1036997 = c_Groups_Ozero__class_Ozero(_1036995)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1036995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036995), _1036997), _1036999)), _1036997) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036995), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1036995), _1036999), _1036997)), c_Groups_Oone__class_Oone(_1036995)))], (15073 ^ _780461) ^ [_1037159, _1037161, _1037163] : [class_Divides_Osemiring__div(_1037159), -(_1037161 = c_Groups_Ozero__class_Ozero(_1037159)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1037159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037159), _1037163), _1037161)), _1037161) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037159), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1037159), _1037163), _1037161)), c_Groups_Oone__class_Oone(_1037159)))], (15083 ^ _780461) ^ [_1037323, _1037325, _1037327, _1037329] : [class_Divides_Osemiring__div(_1037323), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037323), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037323), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1037323), _1037325), _1037327)), _1037327)), c_Divides_Odiv__class_Omod(_1037323, _1037325, _1037327))), _1037329) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037323), _1037325), _1037329))], (15089 ^ _780461) ^ [_1037490, _1037492, _1037494, _1037496] : [class_Divides_Osemiring__div(_1037490), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037490), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037490), _1037492), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1037490), _1037494), _1037492))), c_Divides_Odiv__class_Omod(_1037490, _1037494, _1037492))), _1037496) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037490), _1037494), _1037496))], (15095 ^ _780461) ^ [_1037657, _1037659, _1037661] : [class_Divides_Osemiring__div(_1037657), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037657), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1037657), _1037659), _1037661)), _1037661)), c_Divides_Odiv__class_Omod(_1037657, _1037659, _1037661)) = _1037659)], (15101 ^ _780461) ^ [_1037790, _1037792, _1037794] : [class_Divides_Osemiring__div(_1037790), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037790), _1037792), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1037790), _1037794), _1037792))), c_Divides_Odiv__class_Omod(_1037790, _1037794, _1037792)) = _1037794)], (15107 ^ _780461) ^ [_1037923, _1037925, _1037927] : [class_Divides_Osemiring__div(_1037923), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037923), c_Divides_Odiv__class_Omod(_1037923, _1037925, _1037927)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037923), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1037923), _1037925), _1037927)), _1037927)) = _1037925)], (15137 ^ _780461) ^ [_1038511, _1038513, _1038515] : [-(hBOOL(hAPP(_1038511, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1038513), _1038515)))), 15140 ^ _780461 : [(15141 ^ _780461) ^ [] : [-(_1038515 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15143 ^ _780461) ^ [] : [hBOOL(hAPP(_1038511, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 15144 ^ _780461 : [(15145 ^ _780461) ^ [] : [_1038515 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15149 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15147 ^ [_1038511, _1038513, _1038515]), _1038515)))], (15151 ^ _780461) ^ [] : [-(_1038513 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1038515), 15146 ^ [_1038511, _1038513, _1038515])), 15147 ^ [_1038511, _1038513, _1038515]))], (15153 ^ _780461) ^ [] : [hBOOL(hAPP(_1038511, 15146 ^ [_1038511, _1038513, _1038515]))]]], (15113 ^ _780461) ^ [_1038074, _1038076, _1038078] : [hBOOL(hAPP(_1038074, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1038076), _1038078))), 15116 ^ _780461 : [(15117 ^ _780461) ^ [] : [_1038078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1038074, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15123 ^ _780461) ^ [] : [-(_1038078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15126 ^ _780461 : [(15127 ^ _780461) ^ [_1038326, _1038328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038326), _1038078)), _1038076 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1038078), _1038328)), _1038326), -(hBOOL(hAPP(_1038074, _1038328)))]]]]], (15157 ^ _780461) ^ [_1038933, _1038935, _1038937, _1038939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1038933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038935), _1038937)), -(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), _1038937), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1038939, _1038933))), _1038935)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1038937), _1038933))))], (15191 ^ _780461) ^ [_1039589, _1039591, _1039593] : [-(hBOOL(hAPP(_1039589, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1039591, _1039593)))), 15194 ^ _780461 : [(15195 ^ _780461) ^ [] : [-(_1039593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15197 ^ _780461) ^ [] : [hBOOL(hAPP(_1039589, _1039591))]], 15198 ^ _780461 : [(15199 ^ _780461) ^ [] : [_1039593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15203 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 15201 ^ [_1039589, _1039591, _1039593]), _1039593)))], (15205 ^ _780461) ^ [] : [-(_1039591 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039593), 15200 ^ [_1039589, _1039591, _1039593])), 15201 ^ [_1039589, _1039591, _1039593]))], (15207 ^ _780461) ^ [] : [hBOOL(hAPP(_1039589, 15201 ^ [_1039589, _1039591, _1039593]))]]], (15167 ^ _780461) ^ [_1039156, _1039158, _1039160] : [hBOOL(hAPP(_1039156, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1039158, _1039160))), 15170 ^ _780461 : [(15171 ^ _780461) ^ [] : [_1039160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1039156, _1039158)))], (15177 ^ _780461) ^ [] : [-(_1039160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15180 ^ _780461 : [(15181 ^ _780461) ^ [_1039404, _1039406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1039404), _1039160)), _1039158 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039160), _1039406)), _1039404), -(hBOOL(hAPP(_1039156, _1039404)))]]]]], (15211 ^ _780461) ^ [_1039998, _1040000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1039998)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039998), _1040000)), _1039998) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15217 ^ _780461) ^ [_1040105, _1040107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1040105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1040107)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040105, _1040107)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1040105), hAPP(c_Int_Onat, _1040107)))], (15227 ^ _780461) ^ [_1040276, _1040278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1040276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1040278)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1040276), hAPP(c_Int_Onat, _1040278)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040276, _1040278)))], (15237 ^ _780461) ^ [_1040447, _1040449, _1040451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1040447)), 15240 ^ _780461 : [(15251 ^ _780461) ^ [] : [_1040449 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040451), _1040447), 15254 ^ _780461 : [(15255 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040447), _1040449)), _1040451)))], (15257 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040447), hAPP(c_Nat_OSuc, _1040449)))))]]], (15241 ^ _780461) ^ [] : [-(_1040449 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1040451), _1040447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040447), _1040449)), _1040451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1040451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1040447), hAPP(c_Nat_OSuc, _1040449))))]]], (15259 ^ _780461) ^ [_1040840, _1040842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1040840)), -(c_SMT_Oz3div(_1040842, _1040840) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1040842), _1040840))], (15265 ^ _780461) ^ [_1040933, _1040935] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1040933))), -(c_SMT_Oz3div(_1040935, _1040933) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1040935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1040933))))], (15271 ^ _780461) ^ [_1040987, _1040989] : [-(_1040987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15274 ^ _780461 : [(15275 ^ _780461) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040989, _1040987) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1040989), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1040987)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1040989), _1040987)))], (15281 ^ _780461) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1040989, _1040987) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1040989), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1040987)) = 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), _1040989), _1040987))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (15287 ^ _780461) ^ [_1041260, _1041262] : [-(_1041260 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15290 ^ _780461 : [(15291 ^ _780461) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1041262, _1041260) = 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), _1041262)), _1041260) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1041262), _1041260)))], (15297 ^ _780461) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1041262, _1041260) = 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), _1041262)), _1041260) = 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), _1041262), _1041260))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (15303 ^ _780461) ^ [_1041534, _1041536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1041534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041534), _1041536)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1041536), _1041534) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041536), _1041534)), _1041534)))], (15313 ^ _780461) ^ [_1041719, _1041721, _1041723] : [class_Divides_Osemiring__div(_1041719), -(_1041721 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041719), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1041719), _1041721), _1041723)), _1041723)), c_Divides_Odiv__class_Omod(_1041719, _1041721, _1041723)))], (15319 ^ _780461) ^ [_1041852, _1041854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1041852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1041854)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1041852)), hAPP(c_Int_Onat, _1041854)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1041852, _1041854)))], (15329 ^ _780461) ^ [_1042025, _1042027, _1042029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042025)), 15335 ^ _780461 : [(15336 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1042027, 15334 ^ [_1042025, _1042027, _1042029])))], (15338 ^ _780461) ^ [] : [hBOOL(hAPP(_1042027, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 15334 ^ [_1042025, _1042027, _1042029]), _1042025)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042029)), 15343 ^ _780461 : [(15344 ^ _780461) ^ [_1042314] : [hBOOL(hAPP(_1042027, _1042314)), -(hBOOL(hAPP(_1042027, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1042314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1042029), _1042025)))))]]], (15350 ^ _780461) ^ [_1042437, _1042439, _1042441] : [class_Fields_Olinordered__field__inverse__zero(_1042437), 15356 ^ _780461 : [(15357 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042437), c_Groups_Ozero__class_Ozero(_1042437)), 15355 ^ [_1042437, _1042439, _1042441])))], (15359 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042437), 15355 ^ [_1042437, _1042439, _1042441]), c_Groups_Oone__class_Oone(_1042437))))], (15361 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042437), 15355 ^ [_1042437, _1042439, _1042441]), _1042439)), _1042441))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1042437), _1042439), _1042441)))], (15365 ^ _780461) ^ [_1042786, _1042788, _1042790, _1042792, _1042794] : [class_Groups_Ominus(_1042786), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042788, _1042786)), _1042790), _1042792), _1042794) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042786), hAPP(_1042790, _1042794)), hAPP(_1042792, _1042794)))], (15371 ^ _780461) ^ [_1042923, _1042925, _1042927] : [class_Rings_Oring__1(_1042923), -(hAPP(c_Int_Oring__1__class_Oof__int(_1042923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042925), _1042927)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042923), hAPP(c_Int_Oring__1__class_Oof__int(_1042923), _1042925)), hAPP(c_Int_Oring__1__class_Oof__int(_1042923), _1042927)))], (15377 ^ _780461) ^ [_1043058, _1043060, _1043062, _1043064, _1043066] : [class_Groups_Oab__group__add(_1043058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043058), _1043060), _1043062) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043058), _1043064), _1043066), 15384 ^ _780461 : [(15385 ^ _780461) ^ [] : [_1043060 = _1043062, -(_1043064 = _1043066)], (15391 ^ _780461) ^ [] : [_1043064 = _1043066, -(_1043060 = _1043062)]]], (15397 ^ _780461) ^ [_1043371, _1043373, _1043375] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043371), _1043373)), _1043375) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043371), _1043375)), _1043373))], (15399 ^ _780461) ^ [_1043422, _1043424, _1043426] : [class_Rings_Oring__1(_1043422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043424), _1043426)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1043422), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043426), _1043424)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043422), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1043422), _1043426)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1043422), _1043424)))], (15409 ^ _780461) ^ [_1043621, _1043623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043621), _1043623)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1043623)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1043621)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043623), _1043621)))], (15415 ^ _780461) ^ [_1043750, _1043752, _1043754, _1043756, _1043758] : [class_Groups_Oordered__ab__group__add(_1043750), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043750), _1043752), _1043754) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1043750), _1043756), _1043758), 15422 ^ _780461 : [(15423 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043750), _1043752), _1043754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043750), _1043756), _1043758)))], (15429 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043750), _1043756), _1043758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043750), _1043752), _1043754)))]]], (15435 ^ _780461) ^ [_1044105, _1044107, _1044109] : [class_Groups_Ogroup__add(_1044105), 15438 ^ _780461 : [(15439 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044105), _1044107), _1044109) = c_Groups_Ozero__class_Ozero(_1044105), -(_1044107 = _1044109)], (15445 ^ _780461) ^ [] : [_1044107 = _1044109, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044105), _1044107), _1044109) = c_Groups_Ozero__class_Ozero(_1044105))]]], (15451 ^ _780461) ^ [_1044346, _1044348, _1044350] : [class_Groups_Oab__group__add(_1044346), 15454 ^ _780461 : [(15455 ^ _780461) ^ [] : [_1044348 = _1044350, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044346), _1044348), _1044350) = c_Groups_Ozero__class_Ozero(_1044346))], (15461 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044346), _1044348), _1044350) = c_Groups_Ozero__class_Ozero(_1044346), -(_1044348 = _1044350)]]], (15467 ^ _780461) ^ [_1044587, _1044589] : [class_Groups_Ogroup__add(_1044587), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044587), _1044589), _1044589) = c_Groups_Ozero__class_Ozero(_1044587))], (15473 ^ _780461) ^ [_1044682, _1044684] : [class_Groups_Ogroup__add(_1044682), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044682), _1044684), c_Groups_Ozero__class_Ozero(_1044682)) = _1044684)], (15479 ^ _780461) ^ [_1044777, _1044779, _1044781, _1044783, _1044785] : [class_Groups_Oordered__ab__group__add(_1044777), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044777), _1044779), _1044781) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1044777), _1044783), _1044785), 15486 ^ _780461 : [(15487 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044777), _1044779), _1044781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044777), _1044783), _1044785)))], (15493 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044777), _1044783), _1044785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044777), _1044779), _1044781)))]]], (15499 ^ _780461) ^ [_1045132, _1045134, _1045136] : [class_Groups_Ogroup__add(_1045132), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045132), _1045134), _1045136)), _1045136) = _1045134)], (15505 ^ _780461) ^ [_1045241, _1045243, _1045245] : [class_Groups_Ogroup__add(_1045241), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1045241), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045241), _1045243), _1045245)), _1045245) = _1045243)], (15511 ^ _780461) ^ [_1045350, _1045352, _1045354] : [class_Groups_Oab__group__add(_1045350), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1045350), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045350), _1045352), _1045354)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045350), _1045354), _1045352))], (15517 ^ _780461) ^ [_1045469, _1045471, _1045473, _1045475] : [class_Divides_Oring__div(_1045469), -(c_Divides_Odiv__class_Omod(_1045469, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045469), _1045471), _1045473), _1045475) = c_Divides_Odiv__class_Omod(_1045469, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045469), _1045471), c_Divides_Odiv__class_Omod(_1045469, _1045473, _1045475)), _1045475))], (15523 ^ _780461) ^ [_1045604, _1045606, _1045608, _1045610] : [class_Divides_Oring__div(_1045604), -(c_Divides_Odiv__class_Omod(_1045604, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045604), _1045606), _1045608), _1045610) = c_Divides_Odiv__class_Omod(_1045604, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045604), c_Divides_Odiv__class_Omod(_1045604, _1045606, _1045610)), _1045608), _1045610))], (15529 ^ _780461) ^ [_1045739, _1045741, _1045743, _1045745] : [class_Divides_Oring__div(_1045739), -(c_Divides_Odiv__class_Omod(_1045739, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045739), _1045741), _1045743), _1045745) = c_Divides_Odiv__class_Omod(_1045739, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045739), c_Divides_Odiv__class_Omod(_1045739, _1045741, _1045745)), c_Divides_Odiv__class_Omod(_1045739, _1045743, _1045745)), _1045745))], (15535 ^ _780461) ^ [_1045882, _1045884, _1045886, _1045888, _1045890, _1045892] : [class_Divides_Oring__div(_1045882), c_Divides_Odiv__class_Omod(_1045882, _1045884, _1045886) = c_Divides_Odiv__class_Omod(_1045882, _1045888, _1045886), c_Divides_Odiv__class_Omod(_1045882, _1045890, _1045886) = c_Divides_Odiv__class_Omod(_1045882, _1045892, _1045886), -(c_Divides_Odiv__class_Omod(_1045882, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045882), _1045884), _1045890), _1045886) = c_Divides_Odiv__class_Omod(_1045882, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1045882), _1045888), _1045892), _1045886))], (15549 ^ _780461) ^ [_1046165] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1046165) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15551 ^ _780461) ^ [_1046191] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046191), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1046191)], (15553 ^ _780461) ^ [_1046220] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046220), _1046220) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15555 ^ _780461) ^ [_1046249, _1046251] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046249), _1046251) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046251), _1046249) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1046249 = _1046251)], (15565 ^ _780461) ^ [_1046402, _1046404, _1046406] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1046402)), _1046404)), hAPP(c_Nat_OSuc, _1046406)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046402), _1046404)), _1046406))], (15567 ^ _780461) ^ [_1046459, _1046461] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1046459)), hAPP(c_Nat_OSuc, _1046461)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046459), _1046461))], (15569 ^ _780461) ^ [_1046502, _1046504, _1046506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046502), _1046504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046502), _1046506)), _1046504)))], (15575 ^ _780461) ^ [_1046613, _1046615, _1046617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046613), _1046615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046613), _1046617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046617), _1046615)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046617), _1046613))))], (15585 ^ _780461) ^ [_1046809, _1046811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046809), _1046811)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1046809, _1046811) = _1046809)], (15591 ^ _780461) ^ [_1046898, _1046900] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046898), _1046900))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1046898, _1046900) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046898), _1046900), _1046900))], (15597 ^ _780461) ^ [_1046951, _1046953] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046951), _1046953))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1046951, _1046953) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1046951), _1046953), _1046953))], (15603 ^ _780461) ^ [_1047006, _1047008] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047006), _1047008)), _1047008) = _1047006)], (15605 ^ _780461) ^ [_1047043, _1047045] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047043), _1047045)), _1047043) = _1047045)], (15607 ^ _780461) ^ [_1047080, _1047082, _1047084] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047080), _1047082)), _1047084) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047080), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047082), _1047084)))], (15609 ^ _780461) ^ [_1047131, _1047133, _1047135] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047131), _1047133)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047131), _1047135)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047133), _1047135))], (15611 ^ _780461) ^ [_1047182, _1047184, _1047186] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047182), _1047184)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1047186), _1047184)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047182), _1047186))], (15613 ^ _780461) ^ [_1047233, _1047235, _1047237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047233), _1047235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047233), _1047237)), 15620 ^ _780461 : [(15621 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047235), _1047233)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047237), _1047233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047235), _1047237)))], (15627 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047235), _1047237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047235), _1047233)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047237), _1047233))))]]], (15633 ^ _780461) ^ [_1047586, _1047588, _1047590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047586), _1047588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047586), _1047590)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047588), _1047586)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047590), _1047586)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047588), _1047590))], (15643 ^ _780461) ^ [_1047787, _1047789, _1047791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047787), _1047789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047787), _1047791)), 15650 ^ _780461 : [(15651 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047789), _1047787) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047791), _1047787), -(_1047789 = _1047791)], (15657 ^ _780461) ^ [] : [_1047789 = _1047791, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047789), _1047787) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047791), _1047787))]]], (15663 ^ _780461) ^ [_1048110, _1048112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048110), _1048112)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048112), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048112), _1048110)) = _1048110)], (15669 ^ _780461) ^ [_1048221, _1048223, _1048225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048221), _1048223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048221), _1048225)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048223), _1048225))))], (15675 ^ _780461) ^ [_1048344, _1048346, _1048348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048344), _1048346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048348), _1048346)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048348), _1048344))))], (15681 ^ _780461) ^ [_1048467, _1048469] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048467), _1048469)), _1048467)))], (15683 ^ _780461) ^ [_1048503, _1048505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1048503), _1048505)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1048505, _1048503) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048505), _1048503), _1048503))], (15689 ^ _780461) ^ [_1048618, _1048620, _1048622] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048618), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1048620), _1048622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048618), _1048620)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048618), _1048622)))], (15691 ^ _780461) ^ [_1048675, _1048677, _1048679] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1048675), _1048677)), _1048679) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048675), _1048679)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1048677), _1048679)))], (15693 ^ _780461) ^ [_1048732, _1048734, _1048736] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048732), _1048734)), _1048736) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048732), _1048736)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048734), _1048736)))], (15695 ^ _780461) ^ [_1048789, _1048791, _1048793] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048789), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048791), _1048793)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048789), _1048791)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048789), _1048793)))], (15697 ^ _780461) ^ [_1048846, _1048848, _1048850] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1048846), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1048848, _1048850)), _1048850) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1048846), _1048848), _1048850))], (15699 ^ _780461) ^ [_1048897, _1048899, _1048901] : [-(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, _1048897, _1048899)), _1048901), _1048899) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1048897), _1048901), _1048899))], (15701 ^ _780461) ^ [_1048948, _1048950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1048948), _1048950)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1048950), _1048948)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1048950)), hAPP(c_Int_Onat, _1048948)))], (15727 ^ _780461) ^ [_1049440, _1049442, _1049444] : [-(hBOOL(hAPP(_1049440, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049442), _1049444))))), 15730 ^ _780461 : [(15731 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049444), _1049442)))], (15733 ^ _780461) ^ [] : [hBOOL(hAPP(_1049440, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049442)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049444))))]], 15734 ^ _780461 : [(15735 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049442), _1049444)))], (15737 ^ _780461) ^ [] : [hBOOL(hAPP(_1049440, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (15711 ^ _780461) ^ [_1049151, _1049153, _1049155] : [hBOOL(hAPP(_1049151, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1049153), _1049155)))), 15714 ^ _780461 : [(15715 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1049155), _1049153)), -(hBOOL(hAPP(_1049151, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049153)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049155)))))], (15721 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049153), _1049155)), -(hBOOL(hAPP(_1049151, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (15741 ^ _780461) ^ [_1049715, _1049717, _1049719] : [class_Groups_Oordered__ab__group__add(_1049715), 15744 ^ _780461 : [(15745 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049715), _1049717), _1049719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049715), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049715), _1049717), _1049719)), c_Groups_Ozero__class_Ozero(_1049715))))], (15751 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049715), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049715), _1049717), _1049719)), c_Groups_Ozero__class_Ozero(_1049715))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049715), _1049717), _1049719)))]]], (15757 ^ _780461) ^ [_1049998, _1050000, _1050002] : [class_Groups_Oordered__ab__group__add(_1049998), 15760 ^ _780461 : [(15761 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049998), _1050000), _1050002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049998), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049998), _1050000), _1050002)), c_Groups_Ozero__class_Ozero(_1049998))))], (15767 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049998), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1049998), _1050000), _1050002)), c_Groups_Ozero__class_Ozero(_1049998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1049998), _1050000), _1050002)))]]], (15773 ^ _780461) ^ [_1050281, _1050283, _1050285, _1050287, _1050289, _1050291] : [class_Rings_Oring(_1050281), 15776 ^ _780461 : [(15777 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050281), _1050283), _1050285)), _1050287) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050281), _1050289), _1050285)), _1050291), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050281), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050281), _1050283), _1050289)), _1050285)), _1050287) = _1050291)], (15783 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050281), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050281), _1050283), _1050289)), _1050285)), _1050287) = _1050291, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050281), _1050283), _1050285)), _1050287) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050281), _1050289), _1050285)), _1050291))]]], (15789 ^ _780461) ^ [_1050678, _1050680, _1050682, _1050684, _1050686, _1050688] : [class_Rings_Oring(_1050678), 15792 ^ _780461 : [(15793 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050678), _1050680), _1050682)), _1050684) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050678), _1050686), _1050682)), _1050688), -(_1050684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050678), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050678), _1050686), _1050680)), _1050682)), _1050688))], (15799 ^ _780461) ^ [] : [_1050684 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050678), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050678), _1050686), _1050680)), _1050682)), _1050688), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050678), _1050680), _1050682)), _1050684) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050678), _1050686), _1050682)), _1050688))]]], (15805 ^ _780461) ^ [_1051075, _1051077] : [class_Groups_Ogroup__add(_1051075), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1051075), c_Groups_Ozero__class_Ozero(_1051075)), _1051077) = hAPP(c_Groups_Ouminus__class_Ouminus(_1051075), _1051077))], (15811 ^ _780461) ^ [_1051180, _1051182, _1051184] : [class_Groups_Ogroup__add(_1051180), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1051180), _1051182), _1051184) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051180), _1051182), hAPP(c_Groups_Ouminus__class_Ouminus(_1051180), _1051184)))], (15817 ^ _780461) ^ [_1051299, _1051301, _1051303] : [class_Groups_Oab__group__add(_1051299), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1051299), _1051301), _1051303) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051299), _1051301), hAPP(c_Groups_Ouminus__class_Ouminus(_1051299), _1051303)))], (15823 ^ _780461) ^ [_1051418, _1051420, _1051422] : [class_Rings_Ocomm__ring__1(_1051418), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1051418), _1051420), _1051422) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051418), _1051420), hAPP(c_Groups_Ouminus__class_Ouminus(_1051418), _1051422)))], (15829 ^ _780461) ^ [_1051537, _1051539, _1051541] : [class_Groups_Ogroup__add(_1051537), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1051537), _1051539), hAPP(c_Groups_Ouminus__class_Ouminus(_1051537), _1051541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051537), _1051539), _1051541))], (15835 ^ _780461) ^ [_1051671, _1051673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051671), _1051673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1051671), _1051673)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15841 ^ _780461) ^ [_1051776, _1051778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1051776), _1051778)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051776), _1051778)))], (15847 ^ _780461) ^ [_1051902, _1051904] : [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), _1051902), _1051904))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051904), _1051902)))], (15853 ^ _780461) ^ [_1052001, _1052003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052003), _1052001)), -(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), _1052001), _1052003))))], (15859 ^ _780461) ^ [_1052106, _1052108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1052108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052108), _1052106)), _1052108)))], (15869 ^ _780461) ^ [_1052265, _1052267] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052265), _1052267)), hAPP(c_Nat_OSuc, _1052265))))], (15871 ^ _780461) ^ [_1052304, _1052306] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052304), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052304), _1052306)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15873 ^ _780461) ^ [_1052341, _1052343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052341), _1052343)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052341), _1052343) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15879 ^ _780461) ^ [_1052455, _1052457] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052455), _1052457) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052455), _1052457)))], (15885 ^ _780461) ^ [_1052550, _1052552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052550), _1052552)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052550), _1052552) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15891 ^ _780461) ^ [_1052669, _1052671, _1052673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052671), _1052673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052669), _1052673)), _1052671)))], (15897 ^ _780461) ^ [_1052788, _1052790, _1052792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052788), _1052792)), _1052790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052788), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052790), _1052792))))], (15903 ^ _780461) ^ [_1052909, _1052911] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052909), _1052911))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052911), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052909), _1052911)) = _1052909)], (15909 ^ _780461) ^ [_1052962, _1052964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052962), _1052964)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1052964)), _1052962) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1052964), _1052962)))], (15915 ^ _780461) ^ [_1053085, _1053087, _1053089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053085), _1053087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053085), _1053089)), 15922 ^ _780461 : [(15923 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053087), _1053085)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053089), _1053085))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1053087), _1053089)))], (15929 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1053087), _1053089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053087), _1053085)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053089), _1053085))))]]], (15935 ^ _780461) ^ [_1053438, _1053440, _1053442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1053438), _1053440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053442), _1053438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053438), _1053442)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053440), _1053442))))], (15945 ^ _780461) ^ [_1053625, _1053627, _1053629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053625), _1053627)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053629), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053627), _1053625)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053629), _1053625)), _1053627))], (15951 ^ _780461) ^ [_1053780, _1053782, _1053784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053780), _1053782)), _1053784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053784), _1053782))))], (15957 ^ _780461) ^ [_1053899, _1053901, _1053903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1053899), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053903), _1053901))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053899), _1053901)), _1053903)))], (15963 ^ _780461) ^ [_1054024, _1054026, _1054028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054024), _1054026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054028), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054026), _1054028)), _1054024))))], (15969 ^ _780461) ^ [_1054147, _1054149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054147), _1054149)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054147), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054149), _1054147)) = _1054149)], (15975 ^ _780461) ^ [_1054258, _1054260, _1054262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054258), _1054260)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054262), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054260), _1054258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054262), _1054260)), _1054258))], (15981 ^ _780461) ^ [_1054395, _1054397, _1054399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054395), _1054397)), 15984 ^ _780461 : [(15985 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054397), _1054395))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054399), _1054395)), _1054397)))], (15991 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054399), _1054395)), _1054397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054397), _1054395))))]]], (15997 ^ _780461) ^ [_1054684, _1054686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054684), _1054686)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054686), _1054684)), _1054684) = _1054686)], (16003 ^ _780461) ^ [_1054795, _1054797, _1054799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1054795), _1054797)), 16006 ^ _780461 : [(16007 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054797), _1054795) = _1054799, -(_1054797 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054799), _1054795))], (16013 ^ _780461) ^ [] : [_1054797 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1054799), _1054795), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1054797), _1054795) = _1054799)]]], (16019 ^ _780461) ^ [_1055054, _1055056, _1055058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055054), _1055056)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1055058), _1055056)), _1055054) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1055058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055056), _1055054)))], (16025 ^ _780461) ^ [_1055191, _1055193, _1055195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055191), _1055193)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055193), _1055191)), _1055195) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1055193), _1055195)), _1055191))], (16031 ^ _780461) ^ [_1055328, _1055330, _1055332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055328), _1055330)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1055330), _1055332)), _1055328) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055330), _1055328)), _1055332))], (16037 ^ _780461) ^ [_1055465, _1055467] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1055465), _1055467) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1055465), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1055467)))], (16039 ^ _780461) ^ [_1055505, _1055507] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1055505), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1055507)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1055505), _1055507))], (16041 ^ _780461) ^ [_1055545, _1055547] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055545), hAPP(c_Nat_OSuc, _1055547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055545), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1055547))], (16043 ^ _780461) ^ [_1055591] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1055591)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1055591)], (16045 ^ _780461) ^ [_1055623, _1055625] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1055623), _1055625)), _1055625) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055623), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1055623, _1055625)))], (16047 ^ _780461) ^ [_1055670, _1055672] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1055670), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1055672), _1055670)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055672), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1055672, _1055670)))], (16049 ^ _780461) ^ [_1055717, _1055719] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1055717, _1055719) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1055717), _1055719)), _1055719)))], (16051 ^ _780461) ^ [_1055764, _1055766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055764), _1055766)), -(c_Nat__Transfer_Otsub(_1055766, _1055764) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1055766), _1055764))], (16057 ^ _780461) ^ [_1055869, _1055871] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055869), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055871)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055869), _1055871)))], (16059 ^ _780461) ^ [_1055912, _1055914, _1055916, _1055918, _1055920, _1055922] : [class_Rings_Oordered__ring(_1055912), 16062 ^ _780461 : [(16063 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055912), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055912), _1055914), _1055916)), _1055918)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055912), _1055920), _1055916)), _1055922))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055912), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055912), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055912), _1055914), _1055920)), _1055916)), _1055918)), _1055922)))], (16069 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055912), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055912), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1055912), _1055914), _1055920)), _1055916)), _1055918)), _1055922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055912), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055912), _1055914), _1055916)), _1055918)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055912), _1055920), _1055916)), _1055922))))]]], (16075 ^ _780461) ^ [_1056351, _1056353, _1056355, _1056357, _1056359, _1056361] : [class_Rings_Oordered__ring(_1056351), 16078 ^ _780461 : [(16079 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056351), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056351), _1056353), _1056355)), _1056357)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056351), _1056359), _1056355)), _1056361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056351), _1056357), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056351), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056351), _1056359), _1056353)), _1056355)), _1056361))))], (16085 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056351), _1056357), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056351), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056351), _1056359), _1056353)), _1056355)), _1056361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056351), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056351), _1056353), _1056355)), _1056357)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056351), _1056359), _1056355)), _1056361))))]]], (16091 ^ _780461) ^ [_1056790, _1056792, _1056794, _1056796, _1056798, _1056800] : [class_Rings_Oordered__ring(_1056790), 16094 ^ _780461 : [(16095 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056790), _1056792), _1056794)), _1056796)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056790), _1056798), _1056794)), _1056800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056790), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056790), _1056792), _1056798)), _1056794)), _1056796)), _1056800)))], (16101 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056790), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056790), _1056792), _1056798)), _1056794)), _1056796)), _1056800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056790), _1056792), _1056794)), _1056796)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056790), _1056798), _1056794)), _1056800))))]]], (16107 ^ _780461) ^ [_1057229, _1057231, _1057233, _1057235, _1057237, _1057239] : [class_Rings_Oordered__ring(_1057229), 16110 ^ _780461 : [(16111 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057229), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057229), _1057231), _1057233)), _1057235)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057229), _1057237), _1057233)), _1057239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057229), _1057235), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057229), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057229), _1057237), _1057231)), _1057233)), _1057239))))], (16117 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057229), _1057235), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057229), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057229), _1057237), _1057231)), _1057233)), _1057239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057229), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057229), _1057231), _1057233)), _1057235)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057229), _1057237), _1057233)), _1057239))))]]], (16123 ^ _780461) ^ [_1057668, _1057670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1057668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057668), hAPP(c_Nat_OSuc, _1057670))), _1057668)))], (16129 ^ _780461) ^ [_1057777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1057777)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057777), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1057777)], (16151 ^ _780461) ^ [_1058176, _1058178, _1058180] : [-(hBOOL(hAPP(_1058176, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1058178), _1058180)))), 16154 ^ _780461 : [(16155 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058178), _1058180)))], (16157 ^ _780461) ^ [] : [hBOOL(hAPP(_1058176, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 16159 ^ _780461 : [(16160 ^ _780461) ^ [] : [-(_1058178 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058180), 16158 ^ [_1058176, _1058178, _1058180]))], (16162 ^ _780461) ^ [] : [hBOOL(hAPP(_1058176, 16158 ^ [_1058176, _1058178, _1058180]))]]], (16135 ^ _780461) ^ [_1057892, _1057894, _1057896] : [hBOOL(hAPP(_1057892, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1057894), _1057896))), 16138 ^ _780461 : [(16139 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1057894), _1057896)), -(hBOOL(hAPP(_1057892, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16145 ^ _780461) ^ [_1058077] : [_1057894 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1057896), _1058077), -(hBOOL(hAPP(_1057892, _1058077)))]]], (16182 ^ _780461) ^ [_1058771, _1058773, _1058775] : [-(hBOOL(hAPP(_1058771, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1058773), _1058775)))), 16185 ^ _780461 : [(16186 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058773), _1058775)))], (16188 ^ _780461) ^ [] : [hBOOL(hAPP(_1058771, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 16190 ^ _780461 : [(16191 ^ _780461) ^ [] : [-(_1058773 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058775), 16189 ^ [_1058771, _1058773, _1058775]))], (16193 ^ _780461) ^ [] : [hBOOL(hAPP(_1058771, 16189 ^ [_1058771, _1058773, _1058775]))]]], (16166 ^ _780461) ^ [_1058479, _1058481, _1058483] : [hBOOL(hAPP(_1058479, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1058481), _1058483))), 16169 ^ _780461 : [(16170 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1058481), _1058483)), -(hBOOL(hAPP(_1058479, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16176 ^ _780461) ^ [_1058670] : [_1058481 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058483), _1058670), -(hBOOL(hAPP(_1058479, _1058670)))]]], (16197 ^ _780461) ^ [_1059079, _1059081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059079), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1059081), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059079), _1059081)))], (16203 ^ _780461) ^ [_1059184, _1059186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059184), _1059186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1059184), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1059186), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (16209 ^ _780461) ^ [_1059295, _1059297, _1059299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059295), _1059297)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059297), _1059295))), _1059299) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1059297)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1059295), _1059299)))], (16215 ^ _780461) ^ [_1059444, _1059446, _1059448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059444), _1059446)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059448), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059446), _1059444))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1059448), _1059444)), hAPP(c_Nat_OSuc, _1059446)))], (16221 ^ _780461) ^ [_1059593, _1059595, _1059597, _1059599, _1059601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059593), _1059595)), 16224 ^ _780461 : [(16225 ^ _780461) ^ [] : [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), _1059595), _1059597)), _1059599)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059593), _1059597)), _1059601))), -(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), _1059595), _1059593)), _1059597)), _1059599)), _1059601)))], (16231 ^ _780461) ^ [] : [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), _1059595), _1059593)), _1059597)), _1059599)), _1059601)), -(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), _1059595), _1059597)), _1059599)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059593), _1059597)), _1059601))))]]], (16237 ^ _780461) ^ [_1059984, _1059986, _1059988, _1059990, _1059992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059984), _1059986)), -(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), _1059986), _1059988)), _1059990)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1059984), _1059988)), _1059992)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059986), _1059984)), _1059988)), _1059990)), _1059992))], (16243 ^ _780461) ^ [_1060185, _1060187, _1060189, _1060191, _1060193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060185), _1060187)), 16246 ^ _780461 : [(16247 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060187), _1060189)), _1060191) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060185), _1060189)), _1060193), -(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), _1060187), _1060185)), _1060189)), _1060191) = _1060193)], (16253 ^ _780461) ^ [] : [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), _1060187), _1060185)), _1060189)), _1060191) = _1060193, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060187), _1060189)), _1060191) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060185), _1060189)), _1060193))]]], (16259 ^ _780461) ^ [_1060546, _1060548, _1060550, _1060552, _1060554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060546), _1060548)), 16262 ^ _780461 : [(16263 ^ _780461) ^ [] : [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), _1060546), _1060550)), _1060552)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060548), _1060550)), _1060554))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060552), 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), _1060548), _1060546)), _1060550)), _1060554))))], (16269 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060552), 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), _1060548), _1060546)), _1060550)), _1060554))), -(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), _1060546), _1060550)), _1060552)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060548), _1060550)), _1060554))))]]], (16275 ^ _780461) ^ [_1060937, _1060939, _1060941, _1060943, _1060945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1060937), _1060939)), -(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), _1060937), _1060941)), _1060943)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1060939), _1060941)), _1060945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060943), 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), _1060939), _1060937)), _1060941)), _1060945)))], (16281 ^ _780461) ^ [_1061138, _1061140, _1061142, _1061144, _1061146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061138), _1061140)), 16284 ^ _780461 : [(16285 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061138), _1061142)), _1061144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061140), _1061142)), _1061146), -(_1061144 = 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), _1061140), _1061138)), _1061142)), _1061146))], (16291 ^ _780461) ^ [] : [_1061144 = 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), _1061140), _1061138)), _1061142)), _1061146), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061138), _1061142)), _1061144) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061140), _1061142)), _1061146))]]], (16297 ^ _780461) ^ [_1061508, _1061510] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061508, _1061510) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061508, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1061510)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16303 ^ _780461) ^ [_1061601, _1061603] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061601, _1061603) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061601, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1061603)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061601, _1061603)), _1061603))], (16309 ^ _780461) ^ [_1061669, _1061671] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061669, _1061671) = 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), _1061669), _1061671) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16315 ^ _780461) ^ [_1061762, _1061764] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061762, _1061764) = 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), _1061762), _1061764) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1061764), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061762, _1061764)))], (16321 ^ _780461) ^ [_1061821, _1061823] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061821, _1061823) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1061821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1061821), _1061823)), _1061823)))], (16323 ^ _780461) ^ [_1061868, _1061870] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1061868), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1061870), _1061868)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1061870), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1061870, _1061868)))], (16325 ^ _780461) ^ [_1061924, _1061926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1061924), _1061926)), -(c_Nat__Transfer_Otsub(_1061926, _1061924) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1061926), _1061924))], (16331 ^ _780461) ^ [_1062023, _1062025] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1062023), _1062025))), -(c_Nat__Transfer_Otsub(_1062025, _1062023) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16337 ^ _780461) ^ [_1062069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062069)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1062069), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1062069)], (16343 ^ _780461) ^ [_1062166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1062166)), -(_1062166 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1062166), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (16349 ^ _780461) ^ [_1062263, _1062265, _1062267, _1062269, _1062271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062263), _1062265)), 16352 ^ _780461 : [(16353 ^ _780461) ^ [] : [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), _1062265), _1062267)), _1062269)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062263), _1062267)), _1062271))), -(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), _1062265), _1062263)), _1062267)), _1062269)), _1062271)))], (16359 ^ _780461) ^ [] : [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), _1062265), _1062263)), _1062267)), _1062269)), _1062271)), -(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), _1062265), _1062267)), _1062269)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062263), _1062267)), _1062271))))]]], (16365 ^ _780461) ^ [_1062654, _1062656, _1062658, _1062660, _1062662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062654), _1062656)), 16368 ^ _780461 : [(16369 ^ _780461) ^ [] : [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), _1062654), _1062658)), _1062660)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062656), _1062658)), _1062662))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062660), 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), _1062656), _1062654)), _1062658)), _1062662))))], (16375 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1062660), 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), _1062656), _1062654)), _1062658)), _1062662))), -(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), _1062654), _1062658)), _1062660)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062656), _1062658)), _1062662))))]]], (16381 ^ _780461) ^ [_1063054, _1063056] : [_1063054 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063054), _1063056) = _1063056)], (16387 ^ _780461) ^ [_1063137, _1063139] : [-(_1063137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063137), _1063139) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063137), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1063139)))], (16393 ^ _780461) ^ [_1063196, _1063198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063196)), 16396 ^ _780461 : [(16397 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063198), _1063196)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1063198), _1063196) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16403 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063198), _1063196))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1063198), _1063196) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063198), _1063196)), _1063196)))]]], (16409 ^ _780461) ^ [_1063450, _1063452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063452), _1063450))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1063452), _1063450) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063452), _1063450)), _1063450)))], (16419 ^ _780461) ^ [_1063607, _1063609] : [_1063607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063607), _1063609) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16425 ^ _780461) ^ [_1063690, _1063692] : [-(_1063690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063690), _1063692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063692), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063690), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1063692)))], (16431 ^ _780461) ^ [_1063752, _1063754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1063752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1063754)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1063754), _1063752)), _1063754) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1063754), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063752), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (16441 ^ _780461) ^ [_1063937, _1063939, _1063941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1063937)), 16447 ^ _780461 : [(16448 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1063939, 16446 ^ [_1063937, _1063939, _1063941])))], (16450 ^ _780461) ^ [] : [hBOOL(hAPP(_1063939, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 16446 ^ [_1063937, _1063939, _1063941]), _1063937)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1063941)), 16455 ^ _780461 : [(16456 ^ _780461) ^ [_1064226] : [hBOOL(hAPP(_1063939, _1064226)), -(hBOOL(hAPP(_1063939, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1064226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1063941), _1063937)))))]]], (16462 ^ _780461) ^ [_1064349, _1064351, _1064353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1064349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1064351), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1064353), 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), _1064353), _1064351))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1064349)))))], (16468 ^ _780461) ^ [_1064496, _1064498, _1064500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1064496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1064498), 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), _1064498), _1064500))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1064496))), _1064500)))], (16474 ^ _780461) ^ [_1064643, _1064645, _1064647] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1064643, _1064645) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1064647, _1064645), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1064647), _1064643)), -(_1064643 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064645), 16481 ^ [_1064643, _1064645, _1064647])))], (16485 ^ _780461) ^ [_1064840, _1064842, _1064844] : [16487 ^ _780461 : [(16488 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16486 ^ [_1064840, _1064842, _1064844]), _1064840)))], (16490 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1064842, 16486 ^ [_1064840, _1064842, _1064844])))], (16492 ^ _780461) ^ [] : [hBOOL(hAPP(_1064842, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 16486 ^ [_1064840, _1064842, _1064844]), _1064840)))]], hBOOL(hAPP(_1064842, _1064844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1064844), _1064840)), -(hBOOL(hAPP(_1064842, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16504 ^ _780461) ^ [_1065202] : [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), _1065202))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1065202) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1065202)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (16510 ^ _780461) ^ [_1065317, _1065319, _1065321] : [class_Int_Onumber__ring(_1065317), class_Int_Oring__char__0(_1065317), 16517 ^ _780461 : [(16518 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1065317), _1065319) = hAPP(c_Int_Onumber__class_Onumber__of(_1065317), _1065321), -(_1065319 = _1065321)], (16524 ^ _780461) ^ [] : [_1065319 = _1065321, -(hAPP(c_Int_Onumber__class_Onumber__of(_1065317), _1065319) = hAPP(c_Int_Onumber__class_Onumber__of(_1065317), _1065321))]]], (16530 ^ _780461) ^ [_1065612, _1065614, _1065616] : [class_Int_Onumber(_1065612), 16533 ^ _780461 : [(16534 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1065612), _1065614) = _1065616, -(_1065616 = hAPP(c_Int_Onumber__class_Onumber__of(_1065612), _1065614))], (16540 ^ _780461) ^ [] : [_1065616 = hAPP(c_Int_Onumber__class_Onumber__of(_1065612), _1065614), -(hAPP(c_Int_Onumber__class_Onumber__of(_1065612), _1065614) = _1065616)]]], (16546 ^ _780461) ^ [_1065853, _1065855] : [class_Groups_Oordered__ab__group__add__abs(_1065853), -(hAPP(c_Groups_Oabs__class_Oabs(_1065853), hAPP(c_Groups_Oabs__class_Oabs(_1065853), _1065855)) = hAPP(c_Groups_Oabs__class_Oabs(_1065853), _1065855))], (16552 ^ _780461) ^ [_1065958, _1065960] : [class_Int_Onumber__ring(_1065958), -(hAPP(c_Int_Oring__1__class_Oof__int(_1065958), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1065960)) = hAPP(c_Int_Onumber__class_Onumber__of(_1065958), _1065960))], (16558 ^ _780461) ^ [_1066059, _1066061, _1066063] : [class_Rings_Oring__1(_1066059), -(hAPP(c_Int_Oring__1__class_Oof__int(_1066059), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1066061), _1066063)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1066059), hAPP(c_Int_Oring__1__class_Oof__int(_1066059), _1066061)), _1066063))], (16564 ^ _780461) ^ [_1066184, _1066186] : [-(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), _1066184)), _1066186))))], (16566 ^ _780461) ^ [_1066220, _1066222, _1066224] : [class_Groups_Oordered__ab__group__add__abs(_1066220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066220), hAPP(c_Groups_Oabs__class_Oabs(_1066220), _1066222)), _1066224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066220), _1066222), _1066224)))], (16576 ^ _780461) ^ [_1066389, _1066391] : [class_Groups_Oordered__ab__group__add__abs(_1066389), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066389), _1066391), hAPP(c_Groups_Oabs__class_Oabs(_1066389), _1066391))))], (16582 ^ _780461) ^ [_1066488] : [class_Groups_Oordered__ab__group__add__abs(_1066488), -(hAPP(c_Groups_Oabs__class_Oabs(_1066488), c_Groups_Ozero__class_Ozero(_1066488)) = c_Groups_Ozero__class_Ozero(_1066488))], (16588 ^ _780461) ^ [_1066579, _1066581] : [class_Groups_Oordered__ab__group__add__abs(_1066579), 16591 ^ _780461 : [(16592 ^ _780461) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1066579), _1066581) = c_Groups_Ozero__class_Ozero(_1066579), -(_1066581 = c_Groups_Ozero__class_Ozero(_1066579))], (16598 ^ _780461) ^ [] : [_1066581 = c_Groups_Ozero__class_Ozero(_1066579), -(hAPP(c_Groups_Oabs__class_Oabs(_1066579), _1066581) = c_Groups_Ozero__class_Ozero(_1066579))]]], (16604 ^ _780461) ^ [_1066811, _1066813, _1066815] : [class_Groups_Oordered__ab__group__add__abs(_1066811), -(hAPP(c_Groups_Oabs__class_Oabs(_1066811), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066811), hAPP(c_Groups_Oabs__class_Oabs(_1066811), _1066813)), hAPP(c_Groups_Oabs__class_Oabs(_1066811), _1066815))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066811), hAPP(c_Groups_Oabs__class_Oabs(_1066811), _1066813)), hAPP(c_Groups_Oabs__class_Oabs(_1066811), _1066815)))], (16610 ^ _780461) ^ [_1066970, _1066972] : [class_Rings_Olinordered__idom(_1066970), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066970), hAPP(c_Groups_Oabs__class_Oabs(_1066970), _1066972)), hAPP(c_Groups_Oabs__class_Oabs(_1066970), _1066972)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066970), _1066972), _1066972))], (16616 ^ _780461) ^ [_1067097, _1067099, _1067101] : [class_Rings_Olinordered__idom(_1067097), -(hAPP(c_Groups_Oabs__class_Oabs(_1067097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067097), _1067099), _1067101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067097), hAPP(c_Groups_Oabs__class_Oabs(_1067097), _1067099)), hAPP(c_Groups_Oabs__class_Oabs(_1067097), _1067101)))], (16622 ^ _780461) ^ [_1067236, _1067238, _1067240] : [class_Groups_Oordered__ab__group__add__abs(_1067236), -(hAPP(c_Groups_Oabs__class_Oabs(_1067236), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067236), _1067238), _1067240)) = hAPP(c_Groups_Oabs__class_Oabs(_1067236), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1067236), _1067240), _1067238)))], (16628 ^ _780461) ^ [_1067365] : [class_Rings_Olinordered__idom(_1067365), -(hAPP(c_Groups_Oabs__class_Oabs(_1067365), c_Groups_Oone__class_Oone(_1067365)) = c_Groups_Oone__class_Oone(_1067365))], (16634 ^ _780461) ^ [_1067456, _1067458] : [class_Groups_Oordered__ab__group__add__abs(_1067456), -(hAPP(c_Groups_Oabs__class_Oabs(_1067456), hAPP(c_Groups_Ouminus__class_Ouminus(_1067456), _1067458)) = hAPP(c_Groups_Oabs__class_Oabs(_1067456), _1067458))], (16640 ^ _780461) ^ [_1067561, _1067563, _1067565, _1067567] : [class_Rings_Ocomm__semiring__1(_1067561), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1067561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067561), _1067563), _1067565)), _1067567) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067561), hAPP(hAPP(c_Power_Opower__class_Opower(_1067561), _1067563), _1067567)), hAPP(hAPP(c_Power_Opower__class_Opower(_1067561), _1067565), _1067567)))], (16646 ^ _780461) ^ [_1067720, _1067722] : [class_Rings_Olinordered__idom(_1067720), -(hAPP(c_Groups_Oabs__class_Oabs(_1067720), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1067720), _1067722)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1067720), _1067722))], (16652 ^ _780461) ^ [_1067825] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1067825)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1067825))], (16654 ^ _780461) ^ [_1067857, _1067859, _1067861, _1067863] : [class_Rings_Ocomm__semiring__1(_1067857), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1067857), hAPP(hAPP(c_Power_Opower__class_Opower(_1067857), _1067859), _1067861)), _1067863) = hAPP(hAPP(c_Power_Opower__class_Opower(_1067857), _1067859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1067861), _1067863)))], (16660 ^ _780461) ^ [_1067996, _1067998, _1068000] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1067996), _1067998)), _1068000) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1067996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1067998), _1068000)))], (16662 ^ _780461) ^ [_1068047, _1068049] : [class_Rings_Ocomm__semiring__1(_1068047), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1068047), _1068049), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1068049)], (16668 ^ _780461) ^ [_1068138, _1068140, _1068142] : [-(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, _1068138, _1068140)), _1068142), _1068140) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1068138), _1068142), _1068140))], (16670 ^ _780461) ^ [_1068189, _1068191] : [class_Int_Onumber__ring(_1068189), 16673 ^ _780461 : [(16674 ^ _780461) ^ [] : [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), _1068191))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1068189), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068191)) = hAPP(c_Int_Onumber__class_Onumber__of(_1068189), _1068191))], (16680 ^ _780461) ^ [] : [-(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), _1068191)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1068189), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1068191)) = c_Groups_Ozero__class_Ozero(_1068189))]]], (16686 ^ _780461) ^ [_1068429, _1068431] : [class_Int_Onumber__ring(_1068429), -(hAPP(c_Int_Onumber__class_Onumber__of(_1068429), _1068431) = hAPP(c_Int_Oring__1__class_Oof__int(_1068429), _1068431))], (16692 ^ _780461) ^ [_1068524, _1068526] : [class_Int_Onumber__ring(_1068524), class_Rings_Olinordered__idom(_1068524), 16699 ^ _780461 : [(16700 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068524), hAPP(c_Int_Onumber__class_Onumber__of(_1068524), _1068526)), c_Groups_Ozero__class_Ozero(_1068524))), -(hAPP(c_Groups_Oabs__class_Oabs(_1068524), hAPP(c_Int_Onumber__class_Onumber__of(_1068524), _1068526)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1068524), hAPP(c_Int_Onumber__class_Onumber__of(_1068524), _1068526)))], (16706 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068524), hAPP(c_Int_Onumber__class_Onumber__of(_1068524), _1068526)), c_Groups_Ozero__class_Ozero(_1068524)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1068524), hAPP(c_Int_Onumber__class_Onumber__of(_1068524), _1068526)) = hAPP(c_Int_Onumber__class_Onumber__of(_1068524), _1068526))]]], (16722 ^ _780461) ^ [_1069040, _1069042] : [16723 ^ _780461 : [(16724 ^ _780461) ^ [] : [-(_1069040 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16726 ^ _780461) ^ [] : [_1069042 = 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), _1069040)), _1069042))))], (16712 ^ _780461) ^ [_1068891, _1068893] : [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), _1068891)), _1068893))), _1068891 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1068893 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16730 ^ _780461) ^ [_1069176, _1069178] : [class_Groups_Oordered__ab__group__add__abs(_1069176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069176), c_Groups_Ozero__class_Ozero(_1069176)), _1069178)), -(hAPP(c_Groups_Oabs__class_Oabs(_1069176), _1069178) = _1069178)], (16740 ^ _780461) ^ [_1069331, _1069333] : [class_Groups_Oordered__ab__group__add__abs(_1069331), 16743 ^ _780461 : [(16744 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069331), hAPP(c_Groups_Oabs__class_Oabs(_1069331), _1069333)), c_Groups_Ozero__class_Ozero(_1069331))), -(_1069333 = c_Groups_Ozero__class_Ozero(_1069331))], (16750 ^ _780461) ^ [] : [_1069333 = c_Groups_Ozero__class_Ozero(_1069331), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069331), hAPP(c_Groups_Oabs__class_Oabs(_1069331), _1069333)), c_Groups_Ozero__class_Ozero(_1069331))))]]], (16756 ^ _780461) ^ [_1069584, _1069586] : [class_Groups_Oordered__ab__group__add__abs(_1069584), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069584), c_Groups_Ozero__class_Ozero(_1069584)), hAPP(c_Groups_Oabs__class_Oabs(_1069584), _1069586))))], (16762 ^ _780461) ^ [_1069687, _1069689] : [class_Groups_Oordered__ab__group__add__abs(_1069687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069687), hAPP(c_Groups_Oabs__class_Oabs(_1069687), _1069689)), c_Groups_Ozero__class_Ozero(_1069687)))], (16768 ^ _780461) ^ [_1069791, _1069793] : [class_Groups_Oordered__ab__group__add__abs(_1069791), 16771 ^ _780461 : [(16772 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069791), c_Groups_Ozero__class_Ozero(_1069791)), hAPP(c_Groups_Oabs__class_Oabs(_1069791), _1069793))), _1069793 = c_Groups_Ozero__class_Ozero(_1069791)], (16778 ^ _780461) ^ [] : [-(_1069793 = c_Groups_Ozero__class_Ozero(_1069791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069791), c_Groups_Ozero__class_Ozero(_1069791)), hAPP(c_Groups_Oabs__class_Oabs(_1069791), _1069793))))]]], (16784 ^ _780461) ^ [_1070006, _1070008] : [class_Groups_Oordered__ab__group__add__abs(_1070006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070006), c_Groups_Ozero__class_Ozero(_1070006)), _1070008)), -(hAPP(c_Groups_Oabs__class_Oabs(_1070006), _1070008) = _1070008)], (16794 ^ _780461) ^ [_1070161, _1070163, _1070165] : [class_Groups_Oordered__ab__group__add__abs(_1070161), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070161), hAPP(c_Groups_Oabs__class_Oabs(_1070161), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070161), _1070163), _1070165))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1070161), hAPP(c_Groups_Oabs__class_Oabs(_1070161), _1070163)), hAPP(c_Groups_Oabs__class_Oabs(_1070161), _1070165)))))], (16800 ^ _780461) ^ [_1070314, _1070316, _1070318, _1070320, _1070322] : [class_Rings_Olinordered__idom(_1070314), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070314), hAPP(c_Groups_Oabs__class_Oabs(_1070314), _1070316)), _1070318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070314), hAPP(c_Groups_Oabs__class_Oabs(_1070314), _1070320)), _1070322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070314), hAPP(c_Groups_Oabs__class_Oabs(_1070314), _1070316)), hAPP(c_Groups_Oabs__class_Oabs(_1070314), _1070320))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070314), _1070318), _1070322))))], (16814 ^ _780461) ^ [_1070625, _1070627, _1070629] : [class_Groups_Oordered__ab__group__add__abs(_1070625), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070625), hAPP(c_Groups_Oabs__class_Oabs(_1070625), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070625), hAPP(c_Groups_Oabs__class_Oabs(_1070625), _1070627)), hAPP(c_Groups_Oabs__class_Oabs(_1070625), _1070629)))), hAPP(c_Groups_Oabs__class_Oabs(_1070625), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070625), _1070627), _1070629)))))], (16820 ^ _780461) ^ [_1070788, _1070790, _1070792] : [class_Groups_Oordered__ab__group__add__abs(_1070788), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070788), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070788), hAPP(c_Groups_Oabs__class_Oabs(_1070788), _1070790)), hAPP(c_Groups_Oabs__class_Oabs(_1070788), _1070792))), hAPP(c_Groups_Oabs__class_Oabs(_1070788), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070788), _1070790), _1070792)))))], (16826 ^ _780461) ^ [_1070941, _1070943, _1070945] : [class_Groups_Oordered__ab__group__add__abs(_1070941), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070941), hAPP(c_Groups_Oabs__class_Oabs(_1070941), _1070943)), hAPP(c_Groups_Oabs__class_Oabs(_1070941), _1070945))), hAPP(c_Groups_Oabs__class_Oabs(_1070941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1070941), _1070945), _1070943)))))], (16832 ^ _780461) ^ [_1071094, _1071096] : [class_Groups_Oordered__ab__group__add__abs(_1071094), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071094), hAPP(c_Groups_Ouminus__class_Ouminus(_1071094), _1071096)), hAPP(c_Groups_Oabs__class_Oabs(_1071094), _1071096))))], (16838 ^ _780461) ^ [_1071203, _1071205, _1071207] : [class_Groups_Oordered__ab__group__add__abs(_1071203), 16841 ^ _780461 : [(16842 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071203), hAPP(c_Groups_Oabs__class_Oabs(_1071203), _1071205)), _1071207)), 16845 ^ _780461 : [(16846 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071203), _1071205), _1071207)))], (16848 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071203), hAPP(c_Groups_Ouminus__class_Ouminus(_1071203), _1071205)), _1071207)))]]], (16850 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071203), hAPP(c_Groups_Oabs__class_Oabs(_1071203), _1071205)), _1071207))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071203), _1071205), _1071207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071203), hAPP(c_Groups_Ouminus__class_Ouminus(_1071203), _1071205)), _1071207))]]], (16860 ^ _780461) ^ [_1071581, _1071583, _1071585] : [class_Groups_Oordered__ab__group__add__abs(_1071581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071581), _1071583), _1071585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071581), hAPP(c_Groups_Ouminus__class_Ouminus(_1071581), _1071583)), _1071585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071581), hAPP(c_Groups_Oabs__class_Oabs(_1071581), _1071583)), _1071585)))], (16874 ^ _780461) ^ [_1071828, _1071830, _1071832] : [class_Groups_Oordered__ab__group__add__abs(_1071828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071828), hAPP(c_Groups_Oabs__class_Oabs(_1071828), _1071830)), _1071832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071828), hAPP(c_Groups_Ouminus__class_Ouminus(_1071828), _1071830)), _1071832)))], (16884 ^ _780461) ^ [_1072007, _1072009, _1072011] : [class_Rings_Olinordered__idom(_1072007), 16887 ^ _780461 : [(16888 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072007), hAPP(c_Groups_Oabs__class_Oabs(_1072007), _1072009)), _1072011)), 16891 ^ _780461 : [(16892 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072007), _1072009), _1072011)))], (16894 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072007), hAPP(c_Groups_Ouminus__class_Ouminus(_1072007), _1072009)), _1072011)))]]], (16896 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072007), hAPP(c_Groups_Oabs__class_Oabs(_1072007), _1072009)), _1072011))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072007), _1072009), _1072011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072007), hAPP(c_Groups_Ouminus__class_Ouminus(_1072007), _1072009)), _1072011))]]], (16906 ^ _780461) ^ [_1072385, _1072387, _1072389] : [class_Int_Onumber(_1072385), class_Orderings_Olinorder(_1072385), 16913 ^ _780461 : [(16914 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072385), hAPP(c_Int_Onumber__class_Onumber__of(_1072385), _1072387)), hAPP(c_Int_Onumber__class_Onumber__of(_1072385), _1072389))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072385), hAPP(c_Int_Onumber__class_Onumber__of(_1072385), _1072389)), hAPP(c_Int_Onumber__class_Onumber__of(_1072385), _1072387)))], (16920 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072385), hAPP(c_Int_Onumber__class_Onumber__of(_1072385), _1072389)), hAPP(c_Int_Onumber__class_Onumber__of(_1072385), _1072387)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072385), hAPP(c_Int_Onumber__class_Onumber__of(_1072385), _1072387)), hAPP(c_Int_Onumber__class_Onumber__of(_1072385), _1072389))))]]], (16926 ^ _780461) ^ [_1072712, _1072714, _1072716, _1072718] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072712), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072712), _1072714), _1072716)), hAPP(c_Int_Onumber__class_Onumber__of(_1072712), _1072718)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072712), _1072714), hAPP(c_Int_Onumber__class_Onumber__of(_1072712), _1072718))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072712), _1072716), hAPP(c_Int_Onumber__class_Onumber__of(_1072712), _1072718)))), class_Int_Onumber(_1072712), class_Rings_Osemiring(_1072712)], (16936 ^ _780461) ^ [_1072955, _1072957, _1072959, _1072961] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072955), hAPP(c_Int_Onumber__class_Onumber__of(_1072955), _1072957)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072955), _1072959), _1072961)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072955), hAPP(c_Int_Onumber__class_Onumber__of(_1072955), _1072957)), _1072959)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072955), hAPP(c_Int_Onumber__class_Onumber__of(_1072955), _1072957)), _1072961))), class_Int_Onumber(_1072955), class_Rings_Osemiring(_1072955)], (16946 ^ _780461) ^ [_1073198, _1073200, _1073202] : [class_Rings_Ocomm__semiring__1(_1073198), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1073198), _1073200), hAPP(c_Nat_OSuc, _1073202)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073198), _1073200), hAPP(hAPP(c_Power_Opower__class_Opower(_1073198), _1073200), _1073202)))], (16952 ^ _780461) ^ [_1073329, _1073331, _1073333] : [class_Rings_Ocomm__semiring__1(_1073329), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073329), _1073331), hAPP(hAPP(c_Power_Opower__class_Opower(_1073329), _1073331), _1073333)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1073329), _1073331), hAPP(c_Nat_OSuc, _1073333)))], (16958 ^ _780461) ^ [_1073460, _1073462, _1073464] : [class_Rings_Ocomm__semiring__1(_1073460), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073460), hAPP(hAPP(c_Power_Opower__class_Opower(_1073460), _1073462), _1073464)), _1073462) = hAPP(hAPP(c_Power_Opower__class_Opower(_1073460), _1073462), hAPP(c_Nat_OSuc, _1073464)))], (16964 ^ _780461) ^ [_1073591, _1073593, _1073595, _1073597] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073591), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1073591), _1073593), _1073595)), hAPP(c_Int_Onumber__class_Onumber__of(_1073591), _1073597)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1073591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073591), _1073593), hAPP(c_Int_Onumber__class_Onumber__of(_1073591), _1073597))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073591), _1073595), hAPP(c_Int_Onumber__class_Onumber__of(_1073591), _1073597)))), class_Int_Onumber(_1073591), class_Rings_Oring(_1073591)], (16974 ^ _780461) ^ [_1073834, _1073836, _1073838, _1073840] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073834), hAPP(c_Int_Onumber__class_Onumber__of(_1073834), _1073836)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1073834), _1073838), _1073840)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1073834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073834), hAPP(c_Int_Onumber__class_Onumber__of(_1073834), _1073836)), _1073838)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073834), hAPP(c_Int_Onumber__class_Onumber__of(_1073834), _1073836)), _1073840))), class_Int_Onumber(_1073834), class_Rings_Oring(_1073834)], (16984 ^ _780461) ^ [_1074077, _1074079, _1074081] : [class_Int_Onumber__ring(_1074077), class_Rings_Olinordered__idom(_1074077), 16991 ^ _780461 : [(16992 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074077), hAPP(c_Int_Onumber__class_Onumber__of(_1074077), _1074079)), hAPP(c_Int_Onumber__class_Onumber__of(_1074077), _1074081))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1074079), _1074081)))], (16998 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1074079), _1074081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074077), hAPP(c_Int_Onumber__class_Onumber__of(_1074077), _1074079)), hAPP(c_Int_Onumber__class_Onumber__of(_1074077), _1074081))))]]], (17004 ^ _780461) ^ [_1074408, _1074410] : [class_Rings_Ocomm__semiring__1(_1074408), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1074408), _1074410), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1074408))], (17010 ^ _780461) ^ [_1074503, _1074505, _1074507, _1074509] : [class_Rings_Ocomm__semiring__1(_1074503), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074503), hAPP(hAPP(c_Power_Opower__class_Opower(_1074503), _1074505), _1074507)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074503), _1074505), _1074509)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1074503), _1074505), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074507), _1074509)))], (17016 ^ _780461) ^ [_1074658, _1074660, _1074662] : [class_Int_Onumber__ring(_1074658), class_Rings_Olinordered__idom(_1074658), 17023 ^ _780461 : [(17024 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074658), hAPP(c_Int_Onumber__class_Onumber__of(_1074658), _1074660)), hAPP(c_Int_Onumber__class_Onumber__of(_1074658), _1074662))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1074660), _1074662)))], (17030 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1074660), _1074662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074658), hAPP(c_Int_Onumber__class_Onumber__of(_1074658), _1074660)), hAPP(c_Int_Onumber__class_Onumber__of(_1074658), _1074662))))]]], (17036 ^ _780461) ^ [_1074989, _1074991, _1074993] : [class_Int_Onumber__ring(_1074989), -(hAPP(c_Int_Onumber__class_Onumber__of(_1074989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1074991), _1074993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074989), hAPP(c_Int_Onumber__class_Onumber__of(_1074989), _1074991)), hAPP(c_Int_Onumber__class_Onumber__of(_1074989), _1074993)))], (17042 ^ _780461) ^ [_1075124, _1075126, _1075128] : [class_Int_Onumber__ring(_1075124), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075124), hAPP(c_Int_Onumber__class_Onumber__of(_1075124), _1075126)), hAPP(c_Int_Onumber__class_Onumber__of(_1075124), _1075128)) = hAPP(c_Int_Onumber__class_Onumber__of(_1075124), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1075126), _1075128)))], (17048 ^ _780461) ^ [_1075259, _1075261, _1075263, _1075265] : [class_Int_Onumber__ring(_1075259), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075259), hAPP(c_Int_Onumber__class_Onumber__of(_1075259), _1075261)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075259), hAPP(c_Int_Onumber__class_Onumber__of(_1075259), _1075263)), _1075265)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075259), hAPP(c_Int_Onumber__class_Onumber__of(_1075259), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1075261), _1075263))), _1075265))], (17054 ^ _780461) ^ [_1075428, _1075430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1075428)), -(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), _1075428), _1075430))))], (17060 ^ _780461) ^ [_1075525, _1075527, _1075529, _1075531] : [class_Int_Onumber__ring(_1075525), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075525), hAPP(c_Int_Onumber__class_Onumber__of(_1075525), _1075527)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075525), hAPP(c_Int_Onumber__class_Onumber__of(_1075525), _1075529)), _1075531)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075525), hAPP(c_Int_Onumber__class_Onumber__of(_1075525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1075527), _1075529))), _1075531))], (17066 ^ _780461) ^ [_1075694, _1075696, _1075698] : [class_Int_Onumber__ring(_1075694), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075694), hAPP(c_Int_Onumber__class_Onumber__of(_1075694), _1075696)), hAPP(c_Int_Onumber__class_Onumber__of(_1075694), _1075698)) = hAPP(c_Int_Onumber__class_Onumber__of(_1075694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1075696), _1075698)))], (17072 ^ _780461) ^ [_1075829, _1075831, _1075833] : [class_Int_Onumber__ring(_1075829), -(hAPP(c_Int_Onumber__class_Onumber__of(_1075829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1075831), _1075833)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075829), hAPP(c_Int_Onumber__class_Onumber__of(_1075829), _1075831)), hAPP(c_Int_Onumber__class_Onumber__of(_1075829), _1075833)))], (17078 ^ _780461) ^ [_1075964, _1075966] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1075964), _1075966)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1075964) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (17084 ^ _780461) ^ [_1076065, _1076067, _1076069] : [class_Int_Onumber__ring(_1076065), -(hAPP(c_Int_Onumber__class_Onumber__of(_1076065), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1076067), _1076069)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1076065), hAPP(c_Int_Onumber__class_Onumber__of(_1076065), _1076067)), hAPP(c_Int_Onumber__class_Onumber__of(_1076065), _1076069)))], (17090 ^ _780461) ^ [_1076200, _1076202, _1076204] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076202), _1076204)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076200), _1076202)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076200), _1076204)))], (17092 ^ _780461) ^ [_1076257, _1076259] : [class_Int_Onumber__ring(_1076257), -(hAPP(c_Int_Onumber__class_Onumber__of(_1076257), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1076259)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1076257), hAPP(c_Int_Onumber__class_Onumber__of(_1076257), _1076259)))], (17098 ^ _780461) ^ [_1076368, _1076370] : [class_Int_Onumber__ring(_1076368), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1076368), hAPP(c_Int_Onumber__class_Onumber__of(_1076368), _1076370)) = hAPP(c_Int_Onumber__class_Onumber__of(_1076368), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1076370)))], (17104 ^ _780461) ^ [_1076479, _1076481] : [class_Rings_Olinordered__idom(_1076479), -(hAPP(c_Groups_Oabs__class_Oabs(_1076479), _1076481) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076479), _1076481), c_Groups_Osgn__class_Osgn(_1076479, _1076481)))], (17110 ^ _780461) ^ [_1076586, _1076588] : [class_Rings_Olinordered__idom(_1076586), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076586), c_Groups_Osgn__class_Osgn(_1076586, _1076588)), hAPP(c_Groups_Oabs__class_Oabs(_1076586), _1076588)) = _1076588)], (17116 ^ _780461) ^ [_1076693, _1076695, _1076697] : [class_Rings_Olinordered__idom(_1076693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076693), c_Groups_Ozero__class_Ozero(_1076693)), _1076695)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076693), hAPP(c_Groups_Oabs__class_Oabs(_1076693), _1076697)), _1076695) = hAPP(c_Groups_Oabs__class_Oabs(_1076693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076693), _1076697), _1076695)))], (17126 ^ _780461) ^ [_1076894, _1076896, _1076898] : [class_Rings_Oordered__ring__abs(_1076894), -(hAPP(c_Groups_Oabs__class_Oabs(_1076894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076894), _1076896), _1076898)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076894), hAPP(c_Groups_Oabs__class_Oabs(_1076894), _1076896)), hAPP(c_Groups_Oabs__class_Oabs(_1076894), _1076898))), 17133 ^ _780461 : [(17134 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076894), c_Groups_Ozero__class_Ozero(_1076894)), _1076896))], (17136 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076894), _1076896), c_Groups_Ozero__class_Ozero(_1076894)))]], 17137 ^ _780461 : [(17138 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076894), c_Groups_Ozero__class_Ozero(_1076894)), _1076898))], (17140 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076894), _1076898), c_Groups_Ozero__class_Ozero(_1076894)))]]], (17144 ^ _780461) ^ [_1077289, _1077291, _1077293, _1077295, _1077297] : [class_Groups_Oordered__ab__group__add__abs(_1077289), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077289), hAPP(c_Groups_Oabs__class_Oabs(_1077289), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077289), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077289), _1077291), _1077293)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077289), _1077295), _1077297)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077289), hAPP(c_Groups_Oabs__class_Oabs(_1077289), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077289), _1077291), _1077295))), hAPP(c_Groups_Oabs__class_Oabs(_1077289), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077289), _1077293), _1077297))))))], (17150 ^ _780461) ^ [_1077510, _1077512, _1077514] : [class_Groups_Oordered__ab__group__add__abs(_1077510), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077510), hAPP(c_Groups_Oabs__class_Oabs(_1077510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1077510), _1077512), _1077514))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077510), hAPP(c_Groups_Oabs__class_Oabs(_1077510), _1077512)), hAPP(c_Groups_Oabs__class_Oabs(_1077510), _1077514)))))], (17156 ^ _780461) ^ [_1077663, _1077665] : [class_Groups_Oordered__ab__group__add__abs(_1077663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077663), _1077665), c_Groups_Ozero__class_Ozero(_1077663))), -(hAPP(c_Groups_Oabs__class_Oabs(_1077663), _1077665) = hAPP(c_Groups_Ouminus__class_Ouminus(_1077663), _1077665))], (17166 ^ _780461) ^ [_1077828, _1077830] : [class_Groups_Oordered__ab__group__add__abs(_1077828), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077828), hAPP(c_Groups_Ouminus__class_Ouminus(_1077828), hAPP(c_Groups_Oabs__class_Oabs(_1077828), _1077830))), c_Groups_Ozero__class_Ozero(_1077828))))], (17172 ^ _780461) ^ [_1077941, _1077943] : [class_Groups_Oabs__if(_1077941), 17175 ^ _780461 : [(17176 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077941), _1077943), c_Groups_Ozero__class_Ozero(_1077941))), -(hAPP(c_Groups_Oabs__class_Oabs(_1077941), _1077943) = hAPP(c_Groups_Ouminus__class_Ouminus(_1077941), _1077943))], (17182 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077941), _1077943), c_Groups_Ozero__class_Ozero(_1077941)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1077941), _1077943) = _1077943)]]], (17188 ^ _780461) ^ [_1078181, _1078183] : [class_Groups_Oordered__ab__group__add__abs(_1078181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1078181), _1078183), c_Groups_Ozero__class_Ozero(_1078181))), -(hAPP(c_Groups_Oabs__class_Oabs(_1078181), _1078183) = hAPP(c_Groups_Ouminus__class_Ouminus(_1078181), _1078183))], (17198 ^ _780461) ^ [_1078358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1078358)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1078358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17204 ^ _780461) ^ [_1078445] : [_1078445 = 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), _1078445)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (17210 ^ _780461) ^ [_1078538, _1078540, _1078542, _1078544] : [class_Int_Onumber__ring(_1078538), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078538), hAPP(c_Int_Onumber__class_Onumber__of(_1078538), _1078540)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1078538), hAPP(c_Int_Onumber__class_Onumber__of(_1078538), _1078542)), _1078544)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1078538), hAPP(c_Int_Onumber__class_Onumber__of(_1078538), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1078540), _1078542))), _1078544))], (17216 ^ _780461) ^ [_1078713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078713), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1078713) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1078713))], (17222 ^ _780461) ^ [_1078804] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078804), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1078804) = _1078804)], (17228 ^ _780461) ^ [_1078848, _1078850, _1078852] : [class_Int_Onumber__ring(_1078848), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078848), hAPP(c_Groups_Ouminus__class_Ouminus(_1078848), hAPP(c_Int_Onumber__class_Onumber__of(_1078848), _1078850))), _1078852) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078848), hAPP(c_Int_Onumber__class_Onumber__of(_1078848), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1078850))), _1078852))], (17234 ^ _780461) ^ [_1078993, _1078995] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1078993), _1078995))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1078993))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1078995))))], (17236 ^ _780461) ^ [_1079048, _1079050, _1079052] : [class_Int_Onumber__ring(_1079048), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1079048), hAPP(c_Int_Onumber__class_Onumber__of(_1079048), _1079050)), hAPP(c_Int_Onumber__class_Onumber__of(_1079048), _1079052)) = hAPP(c_Int_Onumber__class_Onumber__of(_1079048), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1079050), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1079052))))], (17242 ^ _780461) ^ [_1079189, _1079191, _1079193, _1079195] : [class_Int_Onumber__ring(_1079189), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079189), hAPP(c_Int_Onumber__class_Onumber__of(_1079189), _1079191)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1079189), _1079193), hAPP(c_Int_Onumber__class_Onumber__of(_1079189), _1079195))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079189), hAPP(c_Int_Onumber__class_Onumber__of(_1079189), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1079191), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1079195)))), _1079193))], (17248 ^ _780461) ^ [_1079364, _1079366, _1079368, _1079370] : [class_Rings_Olinordered__semidom(_1079364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079364), _1079366), _1079368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079364), c_Groups_Ozero__class_Ozero(_1079364)), _1079366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1079370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079364), hAPP(hAPP(c_Power_Opower__class_Opower(_1079364), _1079366), _1079370)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079364), _1079368), _1079370))))], (17266 ^ _780461) ^ [_1079693, _1079695, _1079697] : [class_Rings_Olinordered__semidom(_1079693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079693), c_Groups_Oone__class_Oone(_1079693)), _1079695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1079697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079693), c_Groups_Oone__class_Oone(_1079693)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079693), _1079695), _1079697))))], (17280 ^ _780461) ^ [_1079934, _1079936, _1079938, _1079940] : [class_Rings_Olinordered__semidom(_1079934), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1079934), c_Groups_Oone__class_Oone(_1079934)), _1079936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079934), hAPP(hAPP(c_Power_Opower__class_Opower(_1079934), _1079936), _1079938)), hAPP(hAPP(c_Power_Opower__class_Opower(_1079934), _1079936), _1079940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1079938), _1079940)))], (17294 ^ _780461) ^ [_1080199, _1080201, _1080203, _1080205] : [class_Rings_Olinordered__semidom(_1080199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080199), c_Groups_Oone__class_Oone(_1080199)), _1080201)), 17301 ^ _780461 : [(17302 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080199), hAPP(hAPP(c_Power_Opower__class_Opower(_1080199), _1080201), _1080203)), hAPP(hAPP(c_Power_Opower__class_Opower(_1080199), _1080201), _1080205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1080203), _1080205)))], (17308 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1080203), _1080205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080199), hAPP(hAPP(c_Power_Opower__class_Opower(_1080199), _1080201), _1080203)), hAPP(hAPP(c_Power_Opower__class_Opower(_1080199), _1080201), _1080205))))]]], (17314 ^ _780461) ^ [_1080574, _1080576, _1080578, _1080580] : [class_Rings_Olinordered__semidom(_1080574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1080576), _1080578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080574), c_Groups_Ozero__class_Ozero(_1080574)), _1080580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080574), _1080580), c_Groups_Oone__class_Oone(_1080574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080574), hAPP(hAPP(c_Power_Opower__class_Opower(_1080574), _1080580), _1080578)), hAPP(hAPP(c_Power_Opower__class_Opower(_1080574), _1080580), _1080576))))], (17332 ^ _780461) ^ [_1080913, _1080915, _1080917, _1080919] : [class_Rings_Olinordered__semidom(_1080913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1080915), _1080917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080913), c_Groups_Ozero__class_Ozero(_1080913)), _1080919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080913), _1080919), c_Groups_Oone__class_Oone(_1080913))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080913), hAPP(hAPP(c_Power_Opower__class_Opower(_1080913), _1080919), _1080917)), hAPP(hAPP(c_Power_Opower__class_Opower(_1080913), _1080919), _1080915))))], (17350 ^ _780461) ^ [_1081252, _1081254, _1081256] : [class_Rings_Olinordered__semidom(_1081252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081252), c_Groups_Ozero__class_Ozero(_1081252)), _1081254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081252), _1081254), c_Groups_Oone__class_Oone(_1081252))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081252), hAPP(hAPP(c_Power_Opower__class_Opower(_1081252), _1081254), hAPP(c_Nat_OSuc, _1081256))), c_Groups_Oone__class_Oone(_1081252))))], (17364 ^ _780461) ^ [_1081513] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081513) = _1081513)], (17366 ^ _780461) ^ [_1081554, _1081556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081554)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1081554), _1081556)))], (17372 ^ _780461) ^ [_1081659, _1081661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1081659), _1081661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081659)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081661))))], (17378 ^ _780461) ^ [_1081785, _1081787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081785)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081787))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1081785), _1081787)))], (17384 ^ _780461) ^ [_1081890, _1081892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1081890), _1081892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081890)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081892))))], (17390 ^ _780461) ^ [_1082001, _1082003] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082001)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082003)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1082001), _1082003)))], (17392 ^ _780461) ^ [_1082047, _1082049] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082047)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082049)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1082047), _1082049)))], (17394 ^ _780461) ^ [_1082093] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082093)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1082093)))], (17396 ^ _780461) ^ [_1082128] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1082128) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17408 ^ _780461) ^ [_1082267, _1082269] : [17409 ^ _780461 : [(17410 ^ _780461) ^ [] : [_1082269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17412 ^ _780461) ^ [] : [_1082267 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1082267), _1082269) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17398 ^ _780461) ^ [_1082169, _1082171] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1082169), _1082171) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1082171 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1082169 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17416 ^ _780461) ^ [_1082396, _1082398, _1082400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1082396), _1082398)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1082396), _1082400))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1082398), _1082400)))], (17436 ^ _780461) ^ [_1082698, _1082700] : [17437 ^ _780461 : [(17438 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082698))], (17440 ^ _780461) ^ [] : [_1082700 = 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), _1082698), _1082700))))], (17426 ^ _780461) ^ [_1082592, _1082594] : [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), _1082592), _1082594))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1082592))), -(_1082594 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17444 ^ _780461) ^ [_1082835] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082835) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1082835))], (17446 ^ _780461) ^ [_1082864, _1082866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1082864)), -(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), _1082864), _1082866))))], (17452 ^ _780461) ^ [_1082961] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082961)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082961))], (17454 ^ _780461) ^ [_1082993] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082993) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082993)))], (17456 ^ _780461) ^ [_1083025, _1083027] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1083025), _1083027)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1083025)), _1083027))], (17458 ^ _780461) ^ [_1083068, _1083070] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1083068)), _1083070) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1083068), _1083070)))], (17460 ^ _780461) ^ [_1083111, _1083113] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1083111)), _1083113) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1083111), _1083113)))], (17462 ^ _780461) ^ [_1083154, _1083156] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083154)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083156)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1083154), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1083156))))], (17464 ^ _780461) ^ [_1083212, _1083214] : [_1083212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1083214), _1083212) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17470 ^ _780461) ^ [_1083295, _1083297] : [-(_1083295 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1083297), _1083295) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1083297), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1083297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1083295), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (17476 ^ _780461) ^ [_1083372, _1083374] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1083372) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083374), 17479 ^ _780461 : [(17480 ^ _780461) ^ [] : [-(_1083372 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083374)))], (17482 ^ _780461) ^ [] : [-(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), _1083374))))]]], (17484 ^ _780461) ^ [_1083505, _1083507] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1083505) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083507)), _1083505 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083507)), 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), _1083507)))], (17494 ^ _780461) ^ [_1083670, _1083672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083670)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1083670), _1083672)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1083670)), _1083672))], (17500 ^ _780461) ^ [_1083787, _1083789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083787)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1083787)), _1083789) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1083787), _1083789)))], (17506 ^ _780461) ^ [_1083904, _1083906, _1083908] : [class_Rings_Oring__1__no__zero__divisors(_1083904), -(_1083906 = c_Groups_Ozero__class_Ozero(_1083904)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083904), _1083906), _1083908) = c_Groups_Ozero__class_Ozero(_1083904)], (17516 ^ _780461) ^ [_1084063, _1084065, _1084067] : [class_Groups_Omonoid__mult(_1084063), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084063), hAPP(hAPP(c_Power_Opower__class_Opower(_1084063), _1084065), _1084067)), _1084065) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084063), _1084065), hAPP(hAPP(c_Power_Opower__class_Opower(_1084063), _1084065), _1084067)))], (17522 ^ _780461) ^ [_1084204, _1084206, _1084208, _1084210] : [class_Groups_Ocomm__monoid__mult(_1084204), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084204), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084204), _1084206), _1084208)), _1084210) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084204), hAPP(hAPP(c_Power_Opower__class_Opower(_1084204), _1084206), _1084210)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084204), _1084208), _1084210)))], (17528 ^ _780461) ^ [_1084363, _1084365] : [class_Groups_Omonoid__mult(_1084363), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084363), c_Groups_Oone__class_Oone(_1084363)), _1084365) = c_Groups_Oone__class_Oone(_1084363))], (17534 ^ _780461) ^ [_1084462, _1084464, _1084466] : [class_Rings_Osemiring__1(_1084462), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1084462), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1084464), _1084466)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084462), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1084462), _1084464)), _1084466))], (17540 ^ _780461) ^ [_1084587, _1084589, _1084591, _1084593] : [class_Groups_Omonoid__mult(_1084587), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084587), _1084589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1084591), _1084593)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084587), hAPP(hAPP(c_Power_Opower__class_Opower(_1084587), _1084589), _1084591)), _1084593))], (17546 ^ _780461) ^ [_1084726] : [-(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), _1084726)) = 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), _1084726))))], (17548 ^ _780461) ^ [_1084764, _1084766, _1084768] : [class_Rings_Olinordered__idom(_1084764), -(hAPP(c_Groups_Oabs__class_Oabs(_1084764), hAPP(hAPP(c_Power_Opower__class_Opower(_1084764), _1084766), _1084768)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1084764), hAPP(c_Groups_Oabs__class_Oabs(_1084764), _1084766)), _1084768))], (17554 ^ _780461) ^ [_1084893, _1084895] : [class_Groups_Omonoid__mult(_1084893), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1084893), _1084895), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1084895)], (17560 ^ _780461) ^ [_1084984, _1084986, _1084988] : [class_Rings_Olinordered__semidom(_1084984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084984), c_Groups_Ozero__class_Ozero(_1084984)), _1084986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084984), c_Groups_Ozero__class_Ozero(_1084984)), hAPP(hAPP(c_Power_Opower__class_Opower(_1084984), _1084986), _1084988))))], (17570 ^ _780461) ^ [_1085167, _1085169, _1085171, _1085173] : [class_Rings_Olinordered__semidom(_1085167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085167), _1085169), _1085171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085167), c_Groups_Ozero__class_Ozero(_1085167)), _1085169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085167), hAPP(hAPP(c_Power_Opower__class_Opower(_1085167), _1085169), _1085173)), hAPP(hAPP(c_Power_Opower__class_Opower(_1085167), _1085171), _1085173))))], (17584 ^ _780461) ^ [_1085436, _1085438, _1085440] : [class_Rings_Olinordered__semidom(_1085436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085436), c_Groups_Ozero__class_Ozero(_1085436)), _1085438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1085436), c_Groups_Ozero__class_Ozero(_1085436)), hAPP(hAPP(c_Power_Opower__class_Opower(_1085436), _1085438), _1085440))))], (17594 ^ _780461) ^ [_1085619, _1085621, _1085623] : [class_Power_Opower(_1085619), class_Rings_Omult__zero(_1085619), class_Rings_Ono__zero__divisors(_1085619), class_Rings_Ozero__neq__one(_1085619), 17609 ^ _780461 : [(17610 ^ _780461) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1085619), _1085621), _1085623) = c_Groups_Ozero__class_Ozero(_1085619), 17613 ^ _780461 : [(17614 ^ _780461) ^ [] : [-(_1085621 = c_Groups_Ozero__class_Ozero(_1085619))], (17616 ^ _780461) ^ [] : [_1085623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (17618 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1085619), _1085621), _1085623) = c_Groups_Ozero__class_Ozero(_1085619)), _1085621 = c_Groups_Ozero__class_Ozero(_1085619), -(_1085623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (17628 ^ _780461) ^ [_1086111, _1086113, _1086115] : [class_Rings_Olinordered__semidom(_1086111), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086111), c_Groups_Oone__class_Oone(_1086111)), _1086113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086111), c_Groups_Oone__class_Oone(_1086111)), hAPP(hAPP(c_Power_Opower__class_Opower(_1086111), _1086113), _1086115))))], (17638 ^ _780461) ^ [_1086294, _1086296] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1086294), c_Groups_Ozero__class_Ozero(_1086294)), hAPP(c_Nat_OSuc, _1086296)) = c_Groups_Ozero__class_Ozero(_1086294)), class_Power_Opower(_1086294), class_Rings_Osemiring__0(_1086294)], (17648 ^ _780461) ^ [_1086449, _1086451, _1086453, _1086455] : [class_Rings_Olinordered__semidom(_1086449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086449), c_Groups_Oone__class_Oone(_1086449)), _1086451)), 17655 ^ _780461 : [(17656 ^ _780461) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1086449), _1086451), _1086453) = hAPP(hAPP(c_Power_Opower__class_Opower(_1086449), _1086451), _1086455), -(_1086453 = _1086455)], (17662 ^ _780461) ^ [] : [_1086453 = _1086455, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1086449), _1086451), _1086453) = hAPP(hAPP(c_Power_Opower__class_Opower(_1086449), _1086451), _1086455))]]], (17668 ^ _780461) ^ [_1086788, _1086790, _1086792] : [class_Power_Opower(_1086788), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1086788), _1086790), hAPP(c_Nat_OSuc, _1086792)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086788), _1086790), hAPP(hAPP(c_Power_Opower__class_Opower(_1086788), _1086790), _1086792)))], (17674 ^ _780461) ^ [_1086919, _1086921, _1086923] : [class_Groups_Omonoid__mult(_1086919), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1086919), _1086921), hAPP(c_Nat_OSuc, _1086923)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086919), hAPP(hAPP(c_Power_Opower__class_Opower(_1086919), _1086921), _1086923)), _1086921))], (17680 ^ _780461) ^ [_1087050, _1087052] : [class_Power_Opower(_1087050), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1087050), _1087052), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1087050))], (17686 ^ _780461) ^ [_1087145, _1087147, _1087149, _1087151] : [class_Groups_Omonoid__mult(_1087145), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1087145), _1087147), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1087149), _1087151)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087145), hAPP(hAPP(c_Power_Opower__class_Opower(_1087145), _1087147), _1087149)), hAPP(hAPP(c_Power_Opower__class_Opower(_1087145), _1087147), _1087151)))], (17692 ^ _780461) ^ [_1087300, _1087302, _1087304] : [class_Rings_Olinordered__idom(_1087300), -(hAPP(c_Groups_Oabs__class_Oabs(_1087300), hAPP(hAPP(c_Power_Opower__class_Opower(_1087300), hAPP(c_Groups_Ouminus__class_Ouminus(_1087300), _1087302)), _1087304)) = hAPP(c_Groups_Oabs__class_Oabs(_1087300), hAPP(hAPP(c_Power_Opower__class_Opower(_1087300), _1087302), _1087304)))], (17698 ^ _780461) ^ [_1087439, _1087441, _1087443, _1087445] : [class_Rings_Olinordered__semidom(_1087439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087439), hAPP(hAPP(c_Power_Opower__class_Opower(_1087439), _1087441), _1087443)), hAPP(hAPP(c_Power_Opower__class_Opower(_1087439), _1087445), _1087443))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087439), c_Groups_Ozero__class_Ozero(_1087439)), _1087445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087439), _1087441), _1087445)))], (17712 ^ _780461) ^ [_1087708, _1087710, _1087712, _1087714] : [class_Rings_Olinordered__semidom(_1087708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087708), hAPP(hAPP(c_Power_Opower__class_Opower(_1087708), _1087710), hAPP(c_Nat_OSuc, _1087712))), hAPP(hAPP(c_Power_Opower__class_Opower(_1087708), _1087714), hAPP(c_Nat_OSuc, _1087712)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087708), c_Groups_Ozero__class_Ozero(_1087708)), _1087714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087708), _1087710), _1087714)))], (17726 ^ _780461) ^ [_1087989, _1087991, _1087993, _1087995] : [class_Rings_Olinordered__semidom(_1087989), hAPP(hAPP(c_Power_Opower__class_Opower(_1087989), _1087991), hAPP(c_Nat_OSuc, _1087993)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1087989), _1087995), hAPP(c_Nat_OSuc, _1087993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087989), c_Groups_Ozero__class_Ozero(_1087989)), _1087991)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087989), c_Groups_Ozero__class_Ozero(_1087989)), _1087995)), -(_1087991 = _1087995)], (17744 ^ _780461) ^ [_1088316, _1088318, _1088320] : [class_Rings_Olinordered__semidom(_1088316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088316), c_Groups_Oone__class_Oone(_1088316)), _1088318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088316), c_Groups_Oone__class_Oone(_1088316)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088316), _1088318), hAPP(hAPP(c_Power_Opower__class_Opower(_1088316), _1088318), _1088320)))))], (17754 ^ _780461) ^ [_1088515, _1088517, _1088519] : [class_Rings_Olinordered__semidom(_1088515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088515), c_Groups_Oone__class_Oone(_1088515)), _1088517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088515), hAPP(hAPP(c_Power_Opower__class_Opower(_1088515), _1088517), _1088519)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088515), _1088517), hAPP(hAPP(c_Power_Opower__class_Opower(_1088515), _1088517), _1088519)))))], (17764 ^ _780461) ^ [_1088726, _1088728] : [class_Power_Opower(_1088726), class_Rings_Osemiring__0(_1088726), 17771 ^ _780461 : [(17772 ^ _780461) ^ [] : [_1088728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1088726), c_Groups_Ozero__class_Ozero(_1088726)), _1088728) = c_Groups_Oone__class_Oone(_1088726))], (17778 ^ _780461) ^ [] : [-(_1088728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1088726), c_Groups_Ozero__class_Ozero(_1088726)), _1088728) = c_Groups_Ozero__class_Ozero(_1088726))]]], (17784 ^ _780461) ^ [_1089000, _1089002, _1089004] : [class_Rings_Olinordered__semidom(_1089000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089000), c_Groups_Oone__class_Oone(_1089000)), _1089002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089000), c_Groups_Oone__class_Oone(_1089000)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089000), _1089002), hAPP(c_Nat_OSuc, _1089004)))))], (17794 ^ _780461) ^ [_1089189, _1089191, _1089193, _1089195] : [class_Rings_Olinordered__semidom(_1089189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1089191), _1089193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089189), c_Groups_Oone__class_Oone(_1089189)), _1089195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089189), hAPP(hAPP(c_Power_Opower__class_Opower(_1089189), _1089195), _1089191)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089189), _1089195), _1089193))))], (17808 ^ _780461) ^ [_1089454, _1089456, _1089458, _1089460] : [class_Rings_Olinordered__semidom(_1089454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089454), c_Groups_Oone__class_Oone(_1089454)), _1089456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089454), hAPP(hAPP(c_Power_Opower__class_Opower(_1089454), _1089456), _1089458)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089454), _1089456), _1089460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1089458), _1089460)))], (17822 ^ _780461) ^ [_1089719, _1089721, _1089723, _1089725] : [class_Rings_Olinordered__semidom(_1089719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089719), c_Groups_Oone__class_Oone(_1089719)), _1089721)), 17829 ^ _780461 : [(17830 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089719), hAPP(hAPP(c_Power_Opower__class_Opower(_1089719), _1089721), _1089723)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089719), _1089721), _1089725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1089723), _1089725)))], (17836 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1089723), _1089725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089719), hAPP(hAPP(c_Power_Opower__class_Opower(_1089719), _1089721), _1089723)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089719), _1089721), _1089725))))]]], (17842 ^ _780461) ^ [_1090094, _1090096, _1090098] : [class_Rings_Olinordered__idom(_1090094), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090094), c_Groups_Ozero__class_Ozero(_1090094)), hAPP(hAPP(c_Power_Opower__class_Opower(_1090094), hAPP(c_Groups_Oabs__class_Oabs(_1090094), _1090096)), _1090098))))], (17848 ^ _780461) ^ [_1090215, _1090217, _1090219, _1090221] : [class_Rings_Olinordered__semidom(_1090215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1090217), _1090219)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090215), c_Groups_Oone__class_Oone(_1090215)), _1090221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090215), hAPP(hAPP(c_Power_Opower__class_Opower(_1090215), _1090221), _1090217)), hAPP(hAPP(c_Power_Opower__class_Opower(_1090215), _1090221), _1090219))))], (17862 ^ _780461) ^ [_1090480, _1090482, _1090484] : [class_Rings_Oring__1(_1090480), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1090480), hAPP(c_Groups_Ouminus__class_Ouminus(_1090480), _1090482)), _1090484) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090480), hAPP(hAPP(c_Power_Opower__class_Opower(_1090480), hAPP(c_Groups_Ouminus__class_Ouminus(_1090480), c_Groups_Oone__class_Oone(_1090480))), _1090484)), hAPP(hAPP(c_Power_Opower__class_Opower(_1090480), _1090482), _1090484)))], (17868 ^ _780461) ^ [_1090645, _1090647, _1090649] : [class_Rings_Olinordered__semidom(_1090645), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090645), c_Groups_Ozero__class_Ozero(_1090645)), _1090647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090645), _1090647), c_Groups_Oone__class_Oone(_1090645))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090645), _1090647), hAPP(hAPP(c_Power_Opower__class_Opower(_1090645), _1090647), _1090649))), hAPP(hAPP(c_Power_Opower__class_Opower(_1090645), _1090647), _1090649))))], (17882 ^ _780461) ^ [_1090928, _1090930, _1090932, _1090934] : [class_Rings_Olinordered__semidom(_1090928), hAPP(hAPP(c_Power_Opower__class_Opower(_1090928), _1090930), _1090932) = hAPP(hAPP(c_Power_Opower__class_Opower(_1090928), _1090934), _1090932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090928), c_Groups_Ozero__class_Ozero(_1090928)), _1090930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090928), c_Groups_Ozero__class_Ozero(_1090928)), _1090934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1090932)), -(_1090930 = _1090934)], (17904 ^ _780461) ^ [_1091309] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091309))), -(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), _1091309)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17910 ^ _780461) ^ [_1091402] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091402)))), -(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), _1091402)) = 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), _1091402))))], (17916 ^ _780461) ^ [_1091460] : [class_Power_Opower(_1091460), -(c_Power_Opower__class_Opower(_1091460) = c_Power_Opower_Opower(_1091460, c_Groups_Oone__class_Oone(_1091460), c_Groups_Otimes__class_Otimes(_1091460)))], (17922 ^ _780461) ^ [_1091562, _1091564] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091562))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091562)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091564)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17928 ^ _780461) ^ [_1091667, _1091669] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091667)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091667)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091669)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091667)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091669))))], (17934 ^ _780461) ^ [_1091746, _1091748] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091746))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091746), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091748)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17940 ^ _780461) ^ [_1091848, _1091850] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091848)))), 17943 ^ _780461 : [(17944 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091850))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091848), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091850)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091848))], (17950 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091850)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091848), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1091850)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091848), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1091850))))]]], (17956 ^ _780461) ^ [_1092121, _1092123] : [-(c_Nitpick_Oint__lcm(_1092121, _1092123) = 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), _1092121)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1092123)))))], (17958 ^ _780461) ^ [_1092176, _1092178] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092176))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092176)), _1092178) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1092178))], (17964 ^ _780461) ^ [_1092281, _1092283] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092281)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092281)), _1092283) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092281)), _1092283)))], (17970 ^ _780461) ^ [_1092354, _1092356] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092354))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092354)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092356)) = 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), _1092356)))], (17976 ^ _780461) ^ [_1092471, _1092473] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092471)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092471)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092473)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1092471)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1092473))))], (17982 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17984 ^ _780461) ^ [_1092574] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092574)))], (17986 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (17988 ^ _780461) ^ [_1092632] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1092632))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092632)))], (17994 ^ _780461) ^ [_1092666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1092666)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1092666))], (18000 ^ _780461) ^ [_1092764] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1092764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092764), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18006 ^ _780461) ^ [_1092849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092849), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1092849)))], (18012 ^ _780461) ^ [_1092940] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1092940)), -(hAPP(c_Int_Onat, _1092940) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18018 ^ _780461) ^ [_1093021] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1093021))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1093021)) = _1093021)], (18024 ^ _780461) ^ [_1093063, _1093065, _1093067, _1093069] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1093063, _1093065, _1093067), _1093069), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1093065)], (18026 ^ _780461) ^ [_1093102, _1093104, _1093106, _1093108, _1093110] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1093102, _1093104, _1093106), _1093108), hAPP(c_Nat_OSuc, _1093110)) = hAPP(hAPP(_1093106, _1093108), hAPP(hAPP(c_Power_Opower_Opower(_1093102, _1093104, _1093106), _1093108), _1093110)))], (18028 ^ _780461) ^ [_1093162] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093162))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18034 ^ _780461) ^ [_1093253] : [-(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, _1093253))))))], (18062 ^ _780461) ^ [_1093687, _1093689] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093687) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093689)), 18065 ^ _780461 : [(18066 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093687))))], (18068 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093689)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 18069 ^ _780461 : [(18070 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093687)))], (18072 ^ _780461) ^ [] : [18073 ^ _780461 : [(18074 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093689))))], (18076 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093687) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 18077 ^ _780461 : [(18078 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093689)))], (18080 ^ _780461) ^ [] : [_1093687 = _1093689]]]]], (18036 ^ _780461) ^ [_1093302, _1093304] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093302) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1093304), 18039 ^ _780461 : [(18040 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093302))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093304)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18046 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093302)))), 18049 ^ _780461 : [(18050 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093304))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093302) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18056 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093304)))), -(_1093302 = _1093304)]]]]], (18084 ^ _780461) ^ [_1094100, _1094102, _1094104] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094100))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094100)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094102)), _1094104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094102)), _1094104))], (18090 ^ _780461) ^ [_1094238, _1094240, _1094242] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094238)))), 18093 ^ _780461 : [(18094 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094240))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094238)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094240)), _1094242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094238)), _1094242))], (18100 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094240)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094238)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094240)), _1094242)) = 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), _1094238), _1094240))), _1094242))]]], (18106 ^ _780461) ^ [_1094569] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094569))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094569)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18112 ^ _780461) ^ [_1094660] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094660)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094660)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094660))], (18118 ^ _780461) ^ [_1094710, _1094712] : [class_Int_Onumber__ring(_1094710), 18121 ^ _780461 : [(18122 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094712))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1094710), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094712)) = c_Groups_Ozero__class_Ozero(_1094710))], (18128 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094712)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1094710), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094712)) = hAPP(c_Int_Onumber__class_Onumber__of(_1094710), _1094712))]]], (18134 ^ _780461) ^ [_1094959, _1094961] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094959))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1094959)), _1094961)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1094961))], (18140 ^ _780461) ^ [_1095070, _1095072] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095070)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095070)), _1095072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1095070))), _1095072))], (18146 ^ _780461) ^ [_1095136, _1095138] : [-(c_Nitpick_Onat__lcm(_1095136, _1095138) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1095136), _1095138)), c_Nitpick_Onat__gcd(_1095136, _1095138)))], (18148 ^ _780461) ^ [_1095185] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095185))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095185)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18154 ^ _780461) ^ [_1095276] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1095276)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1095276)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1095276)))], (18160 ^ _780461) ^ [_1095328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095328)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1095328) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1095328), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18166 ^ _780461) ^ [_1095427, _1095429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1095427), _1095429)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1095427), _1095429) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18176 ^ _780461) ^ [_1095594, _1095596, _1095598] : [18178 ^ _780461 : [(18179 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18177 ^ [_1095594, _1095596, _1095598]), _1095594)))], (18181 ^ _780461) ^ [] : [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(_1095596, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18177 ^ [_1095594, _1095596, _1095598]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1095596, 18177 ^ [_1095594, _1095596, _1095598])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1095596, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1095598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095598), hAPP(_1095596, _1095594))), 18191 ^ _780461 : [(18192 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18190 ^ [_1095594, _1095596, _1095598]), _1095594)))], (18194 ^ _780461) ^ [] : [-(hAPP(_1095596, 18190 ^ [_1095594, _1095596, _1095598]) = _1095598)]]], (18196 ^ _780461) ^ [_1096044, _1096046, _1096048] : [18198 ^ _780461 : [(18199 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 18197 ^ [_1096044, _1096046, _1096048]), _1096044)))], (18201 ^ _780461) ^ [] : [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(_1096046, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 18197 ^ [_1096044, _1096046, _1096048]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1096046, 18197 ^ [_1096044, _1096046, _1096048])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1096046, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1096048)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096048), hAPP(_1096046, _1096044))), 18211 ^ _780461 : [(18212 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 18210 ^ [_1096044, _1096046, _1096048]), _1096044)))], (18214 ^ _780461) ^ [] : [-(hAPP(_1096046, 18210 ^ [_1096044, _1096046, _1096048]) = _1096048)]]], (18216 ^ _780461) ^ [_1096494] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1096494), c_Int_OMin) = c_Int_Osucc(_1096494))], (18218 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (18220 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (18222 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18224 ^ _780461) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18226 ^ _780461) ^ [_1096603] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1096603) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1096603))], (18228 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (18230 ^ _780461) ^ [_1096650, _1096652] : [class_Int_Onumber__ring(_1096650), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096650), _1096652), hAPP(c_Int_Onumber__class_Onumber__of(_1096650), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1096650), _1096652))], (18236 ^ _780461) ^ [_1096761, _1096763] : [class_Int_Onumber__ring(_1096761), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096761), hAPP(c_Int_Onumber__class_Onumber__of(_1096761), c_Int_OMin)), _1096763) = hAPP(c_Groups_Ouminus__class_Ouminus(_1096761), _1096763))], (18242 ^ _780461) ^ [_1096872] : [class_Int_Onumber__ring(_1096872), -(hAPP(c_Int_Onumber__class_Onumber__of(_1096872), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1096872), c_Groups_Oone__class_Oone(_1096872)))], (18248 ^ _780461) ^ [_1096969] : [class_Int_Onumber__ring(_1096969), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1096969), c_Groups_Oone__class_Oone(_1096969)) = hAPP(c_Int_Onumber__class_Onumber__of(_1096969), c_Int_OMin))], (18254 ^ _780461) ^ [_1097066] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1097066), hAPP(c_Int_Onumber__class_Onumber__of(_1097066), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1097066)), class_Int_Onumber__ring(_1097066), class_Rings_Olinordered__idom(_1097066)], (18264 ^ _780461) ^ [_1097211] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1097211, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18266 ^ _780461) ^ [_1097238, _1097240] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1097238), _1097240) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1097238 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1097238 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18276 ^ _780461) ^ [_1097355, _1097357] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1097355), _1097357) = c_Groups_Oone__class_Oone(tc_Int_Oint), 18281 ^ _780461 : [(18282 ^ _780461) ^ [] : [-(_1097355 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18284 ^ _780461) ^ [] : [-(_1097357 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 18285 ^ _780461 : [(18286 ^ _780461) ^ [] : [-(_1097355 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18288 ^ _780461) ^ [] : [-(_1097357 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (18290 ^ _780461) ^ [_1097539, _1097541] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1097539), _1097541) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 18291 ^ _780461 : [(18292 ^ _780461) ^ [] : [_1097539 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1097541 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (18298 ^ _780461) ^ [] : [_1097539 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1097541 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (18306 ^ _780461) ^ [_1097765] : [class_Int_Onumber__ring(_1097765), -(hAPP(c_Int_Oring__1__class_Oof__int(_1097765), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1097765), c_Int_OMin))], (18312 ^ _780461) ^ [_1097858] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1097858), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1097858))], (18314 ^ _780461) ^ [_1097890] : [-(c_Int_Osucc(_1097890) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1097890), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18316 ^ _780461) ^ [_1097921, _1097923] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1097921), hAPP(hAPP(c_Power_Opower__class_Opower(_1097921), hAPP(c_Int_Onumber__class_Onumber__of(_1097921), c_Int_OMin)), _1097923)) = c_Groups_Oone__class_Oone(_1097921)), class_Int_Onumber__ring(_1097921), class_Rings_Olinordered__idom(_1097921)], (18326 ^ _780461) ^ [_1098086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1098086)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1098086) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18332 ^ _780461) ^ [_1098171, _1098173] : [class_Int_Onumber__ring(_1098171), -(hAPP(c_Int_Onumber__class_Onumber__of(_1098171), c_Int_Osucc(_1098173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098171), c_Groups_Oone__class_Oone(_1098171)), hAPP(c_Int_Onumber__class_Onumber__of(_1098171), _1098173)))], (18338 ^ _780461) ^ [_1098299, _1098301] : [_1098299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1098301, _1098299) = _1098301)], (18344 ^ _780461) ^ [_1098376, _1098378] : [-(_1098376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1098378, _1098376) = c_Nitpick_Onat__gcd(_1098376, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1098378, _1098376)))], (18350 ^ _780461) ^ [_1098424, _1098426] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1098424), _1098426) = 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), _1098424)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1098426)))))], (18352 ^ _780461) ^ [_1098479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098479), 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), _1098479)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18358 ^ _780461) ^ [_1098570] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098570), 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), _1098570)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1098570)))], (18364 ^ _780461) ^ [_1098628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098628), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098628)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18370 ^ _780461) ^ [_1098725] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098725), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098725)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1098725)))], (18376 ^ _780461) ^ [_1098780, _1098782, _1098784] : [class_Int_Onumber__ring(_1098780), 18379 ^ _780461 : [(18380 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1098780), _1098782) = hAPP(c_Int_Onumber__class_Onumber__of(_1098780), _1098784), -(c_Int_Oiszero(_1098780, hAPP(c_Int_Onumber__class_Onumber__of(_1098780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1098782), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098784)))))], (18386 ^ _780461) ^ [] : [c_Int_Oiszero(_1098780, hAPP(c_Int_Onumber__class_Onumber__of(_1098780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1098782), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1098784)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1098780), _1098782) = hAPP(c_Int_Onumber__class_Onumber__of(_1098780), _1098784))]]], (18392 ^ _780461) ^ [_1099075] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1099075)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099075) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18398 ^ _780461) ^ [_1099166] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099166) = 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(_1099166)))))], (18404 ^ _780461) ^ [_1099275, _1099277, _1099279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099275), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099275)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099277)), _1099279)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18410 ^ _780461) ^ [_1099394, _1099396, _1099398] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099394), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099394)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099396)), _1099398)) = 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), _1099394), _1099396))), _1099398))], (18416 ^ _780461) ^ [_1099481, _1099483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099481), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099481)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099483)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18422 ^ _780461) ^ [_1099586, _1099588] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1099586), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099586)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1099588)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1099586), _1099588)))], (18428 ^ _780461) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (18430 ^ _780461) ^ [_1099668] : [class_Int_Onumber__ring(_1099668), -(c_Int_Oiszero(_1099668, hAPP(c_Int_Onumber__class_Onumber__of(_1099668), c_Int_OPls)))], (18436 ^ _780461) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18438 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (18440 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (18442 ^ _780461) ^ [_1099811] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1099811) = _1099811)], (18444 ^ _780461) ^ [_1099837] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1099837), c_Int_OPls) = _1099837)], (18446 ^ _780461) ^ [_1099866] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1099866) = c_Int_OPls)], (18448 ^ _780461) ^ [_1099892] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1099892), c_Int_OPls) = _1099892)], (18450 ^ _780461) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (18452 ^ _780461) ^ [] : [c_Int_OPls = c_Int_OMin], (18454 ^ _780461) ^ [] : [c_Int_OMin = c_Int_OPls], (18456 ^ _780461) ^ [_1099987] : [-(c_Int_Osucc(c_Int_Opred(_1099987)) = _1099987)], (18458 ^ _780461) ^ [_1100014] : [class_Rings_Osemiring__1(_1100014), -(c_Int_Oiszero(_1100014, c_Groups_Ozero__class_Ozero(_1100014)))], (18464 ^ _780461) ^ [_1100091, _1100093] : [class_Rings_Osemiring__1(_1100091), 18467 ^ _780461 : [(18468 ^ _780461) ^ [] : [c_Int_Oiszero(_1100091, _1100093), -(_1100093 = c_Groups_Ozero__class_Ozero(_1100091))], (18474 ^ _780461) ^ [] : [_1100093 = c_Groups_Ozero__class_Ozero(_1100091), -(c_Int_Oiszero(_1100091, _1100093))]]], (18480 ^ _780461) ^ [_1100302] : [class_Rings_Osemiring__1(_1100302), c_Int_Oiszero(_1100302, c_Groups_Oone__class_Oone(_1100302))], (18486 ^ _780461) ^ [_1100380] : [class_Int_Onumber__ring(_1100380), -(hAPP(c_Int_Onumber__class_Onumber__of(_1100380), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1100380))], (18492 ^ _780461) ^ [_1100467] : [class_Int_Onumber__ring(_1100467), -(c_Groups_Ozero__class_Ozero(_1100467) = hAPP(c_Int_Onumber__class_Onumber__of(_1100467), c_Int_OPls))], (18498 ^ _780461) ^ [_1100554, _1100556] : [class_Int_Onumber__ring(_1100554), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100554), hAPP(c_Int_Onumber__class_Onumber__of(_1100554), c_Int_OPls)), _1100556) = _1100556)], (18504 ^ _780461) ^ [_1100655, _1100657] : [class_Int_Onumber__ring(_1100655), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100655), _1100657), hAPP(c_Int_Onumber__class_Onumber__of(_1100655), c_Int_OPls)) = _1100657)], (18510 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18512 ^ _780461) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18514 ^ _780461) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (18516 ^ _780461) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (18518 ^ _780461) ^ [_1100834, _1100836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1100834)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1100836)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100834)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1100836), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1100834))))], (18524 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (18526 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (18528 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (18530 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (18532 ^ _780461) ^ [] : [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)], (18534 ^ _780461) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (18536 ^ _780461) ^ [_1101093, _1101095] : [class_Int_Onumber__ring(_1101093), 18539 ^ _780461 : [(18540 ^ _780461) ^ [] : [c_Groups_Ozero__class_Ozero(_1101093) = hAPP(c_Int_Onumber__class_Onumber__of(_1101093), _1101095), -(c_Int_Oiszero(_1101093, hAPP(c_Int_Onumber__class_Onumber__of(_1101093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1101095)))))], (18546 ^ _780461) ^ [] : [c_Int_Oiszero(_1101093, hAPP(c_Int_Onumber__class_Onumber__of(_1101093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1101095)))), -(c_Groups_Ozero__class_Ozero(_1101093) = hAPP(c_Int_Onumber__class_Onumber__of(_1101093), _1101095))]]], (18552 ^ _780461) ^ [_1101352, _1101354] : [class_Int_Onumber__ring(_1101352), 18555 ^ _780461 : [(18556 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1101352), _1101354) = c_Groups_Ozero__class_Ozero(_1101352), -(c_Int_Oiszero(_1101352, hAPP(c_Int_Onumber__class_Onumber__of(_1101352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1101354), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (18562 ^ _780461) ^ [] : [c_Int_Oiszero(_1101352, hAPP(c_Int_Onumber__class_Onumber__of(_1101352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1101354), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1101352), _1101354) = c_Groups_Ozero__class_Ozero(_1101352))]]], (18568 ^ _780461) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (18570 ^ _780461) ^ [_1101644, _1101646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1101644), _1101646)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1101644)), _1101646)))], (18576 ^ _780461) ^ [_1101741, _1101743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1101741)), _1101743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1101741), _1101743)))], (18582 ^ _780461) ^ [_1101844] : [-(c_Int_Opred(_1101844) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1101844), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18584 ^ _780461) ^ [_1101875] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1101875), c_Int_OMin) = c_Int_Opred(_1101875))], (18586 ^ _780461) ^ [_1101906] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1101906) = c_Int_Opred(_1101906))], (18588 ^ _780461) ^ [_1101940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1101940), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1101940)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18594 ^ _780461) ^ [_1102037] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102037), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102037)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1102037)))], (18600 ^ _780461) ^ [_1102104] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102104), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102104), c_Int_OPls)))], (18606 ^ _780461) ^ [_1102191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102191), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102191))], (18612 ^ _780461) ^ [_1102296] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102296) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102296), c_Int_OPls)))], (18618 ^ _780461) ^ [_1102383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102383), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102383) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18624 ^ _780461) ^ [] : [-(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))))], (18626 ^ _780461) ^ [_1102509, _1102511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102509)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102511))), 18629 ^ _780461 : [(18636 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102509), _1102511)))], (18630 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102509), _1102511)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1102511)))]]], (18638 ^ _780461) ^ [_1102712, _1102714] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102712)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102714)))), 18641 ^ _780461 : [(18642 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102712), _1102714)))], (18644 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1102714))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1102712), _1102714))], (18660 ^ _780461) ^ [_1103067, _1103069] : [18661 ^ _780461 : [(18662 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103067), _1103069))], (18664 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103067), 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), _1103067)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1103069))))], (18650 ^ _780461) ^ [_1102937, _1102939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102937)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1102939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102937), _1102939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102937), c_Int_OPls)))], (18668 ^ _780461) ^ [_1103228] : [class_Int_Onumber__ring(_1103228), c_Int_Oiszero(_1103228, hAPP(c_Int_Onumber__class_Onumber__of(_1103228), c_Int_OMin))], (18674 ^ _780461) ^ [_1103312, _1103314] : [class_Int_Onumber__ring(_1103312), class_Rings_Olinordered__idom(_1103312), 18681 ^ _780461 : [(18682 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103312), hAPP(c_Int_Onumber__class_Onumber__of(_1103312), _1103314)), c_Groups_Ozero__class_Ozero(_1103312))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103314), c_Int_OPls)))], (18688 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103314), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103312), hAPP(c_Int_Onumber__class_Onumber__of(_1103312), _1103314)), c_Groups_Ozero__class_Ozero(_1103312))))]]], (18694 ^ _780461) ^ [_1103626, _1103628] : [class_Int_Onumber__ring(_1103626), class_Rings_Olinordered__idom(_1103626), 18701 ^ _780461 : [(18702 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103626), c_Groups_Ozero__class_Ozero(_1103626)), hAPP(c_Int_Onumber__class_Onumber__of(_1103626), _1103628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1103628)))], (18708 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1103628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103626), c_Groups_Ozero__class_Ozero(_1103626)), hAPP(c_Int_Onumber__class_Onumber__of(_1103626), _1103628))))]]], (18714 ^ _780461) ^ [_1103931, _1103933] : [class_Int_Onumber__ring(_1103931), class_Rings_Olinordered__idom(_1103931), 18721 ^ _780461 : [(18722 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103931), c_Groups_Ozero__class_Ozero(_1103931)), hAPP(c_Int_Onumber__class_Onumber__of(_1103931), _1103933))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1103933)))], (18728 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1103933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103931), c_Groups_Ozero__class_Ozero(_1103931)), hAPP(c_Int_Onumber__class_Onumber__of(_1103931), _1103933))))]]], (18734 ^ _780461) ^ [_1104236, _1104238] : [class_Int_Onumber__ring(_1104236), class_Rings_Olinordered__idom(_1104236), 18741 ^ _780461 : [(18742 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104236), hAPP(c_Int_Onumber__class_Onumber__of(_1104236), _1104238)), c_Groups_Ozero__class_Ozero(_1104236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104238), c_Int_OPls)))], (18748 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104238), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104236), hAPP(c_Int_Onumber__class_Onumber__of(_1104236), _1104238)), c_Groups_Ozero__class_Ozero(_1104236))))]]], (18754 ^ _780461) ^ [_1104562] : [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), _1104562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1104562)))], (18760 ^ _780461) ^ [_1104647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1104647)), -(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), _1104647))))], (18766 ^ _780461) ^ [_1104747, _1104749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104747), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104747)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104749)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104749))], (18772 ^ _780461) ^ [_1104859, _1104861] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104859), c_Int_OPls))), 18775 ^ _780461 : [(18776 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104861), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104859)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104861)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104859))], (18782 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104861), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104859)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1104861)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1104859), _1104861)))]]], (18788 ^ _780461) ^ [_1105132, _1105134] : [class_Int_Onumber__ring(_1105132), -(hAPP(c_Int_Onumber__class_Onumber__of(_1105132), c_Int_Opred(_1105134)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105132), hAPP(c_Groups_Ouminus__class_Ouminus(_1105132), c_Groups_Oone__class_Oone(_1105132))), hAPP(c_Int_Onumber__class_Onumber__of(_1105132), _1105134)))], (18794 ^ _780461) ^ [_1105261, _1105263] : [class_Int_Onumber__ring(_1105261), 18797 ^ _780461 : [(18798 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1105261), _1105263) = c_Groups_Oone__class_Oone(_1105261), -(c_Int_Oiszero(_1105261, hAPP(c_Int_Onumber__class_Onumber__of(_1105261), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105263), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (18804 ^ _780461) ^ [] : [c_Int_Oiszero(_1105261, hAPP(c_Int_Onumber__class_Onumber__of(_1105261), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105263), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1105261), _1105263) = c_Groups_Oone__class_Oone(_1105261))]]], (18810 ^ _780461) ^ [_1105520, _1105522] : [class_Int_Onumber__ring(_1105520), 18813 ^ _780461 : [(18814 ^ _780461) ^ [] : [c_Groups_Oone__class_Oone(_1105520) = hAPP(c_Int_Onumber__class_Onumber__of(_1105520), _1105522), -(c_Int_Oiszero(_1105520, hAPP(c_Int_Onumber__class_Onumber__of(_1105520), 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), _1105522)))))], (18820 ^ _780461) ^ [] : [c_Int_Oiszero(_1105520, hAPP(c_Int_Onumber__class_Onumber__of(_1105520), 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), _1105522)))), -(c_Groups_Oone__class_Oone(_1105520) = hAPP(c_Int_Onumber__class_Onumber__of(_1105520), _1105522))]]], (18826 ^ _780461) ^ [_1105779, _1105781] : [class_Int_Onumber__ring(_1105779), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1105779), c_Groups_Oone__class_Oone(_1105779)), hAPP(c_Int_Onumber__class_Onumber__of(_1105779), _1105781)) = hAPP(c_Int_Onumber__class_Onumber__of(_1105779), 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), _1105781))))], (18832 ^ _780461) ^ [_1105906, _1105908] : [class_Int_Onumber__ring(_1105906), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1105906), hAPP(c_Int_Onumber__class_Onumber__of(_1105906), _1105908)), c_Groups_Oone__class_Oone(_1105906)) = hAPP(c_Int_Onumber__class_Onumber__of(_1105906), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105908), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (18838 ^ _780461) ^ [_1106033, _1106035] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1106033)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106035)) = 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)))), _1106033)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106035)))], (18840 ^ _780461) ^ [_1106088, _1106090] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1106088)))), _1106090) = 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)))), _1106088)), _1106090))], (18842 ^ _780461) ^ [_1106152, _1106154] : [c_Int_OBit1(_1106152) = c_Int_OBit1(_1106154), -(_1106152 = _1106154)], (18848 ^ _780461) ^ [_1106233, _1106235] : [_1106233 = _1106235, -(c_Int_OBit1(_1106233) = c_Int_OBit1(_1106235))], (18854 ^ _780461) ^ [_1106335, _1106337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1106335)), c_Int_OBit1(_1106337))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106335), _1106337)))], (18860 ^ _780461) ^ [_1106436, _1106438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106436), _1106438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1106436)), c_Int_OBit1(_1106438))))], (18866 ^ _780461) ^ [_1106558, _1106560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1106558)), c_Int_OBit1(_1106560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106558), _1106560)))], (18872 ^ _780461) ^ [_1106659, _1106661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106659), _1106661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1106659)), c_Int_OBit1(_1106661))))], (18878 ^ _780461) ^ [_1106781, _1106783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1106781)), c_Int_OBit1(_1106783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106781), _1106783)))], (18884 ^ _780461) ^ [_1106882, _1106884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106882), _1106884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1106882)), c_Int_OBit1(_1106884))))], (18890 ^ _780461) ^ [_1107004, _1107006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1107004)), c_Int_OBit1(_1107006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107004), _1107006)))], (18896 ^ _780461) ^ [_1107105, _1107107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107105), _1107107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1107105)), c_Int_OBit1(_1107107))))], (18902 ^ _780461) ^ [_1107221] : [c_Int_OPls = c_Int_OBit1(_1107221)], (18904 ^ _780461) ^ [_1107255] : [c_Int_OBit1(_1107255) = c_Int_OPls], (18906 ^ _780461) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (18908 ^ _780461) ^ [_1107310] : [c_Int_OMin = c_Int_OBit1(_1107310), -(c_Int_OMin = _1107310)], (18914 ^ _780461) ^ [_1107385] : [c_Int_OMin = _1107385, -(c_Int_OMin = c_Int_OBit1(_1107385))], (18920 ^ _780461) ^ [_1107478] : [c_Int_OBit1(_1107478) = c_Int_OMin, -(_1107478 = c_Int_OMin)], (18926 ^ _780461) ^ [_1107553] : [_1107553 = c_Int_OMin, -(c_Int_OBit1(_1107553) = c_Int_OMin)], (18932 ^ _780461) ^ [_1107646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1107646)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107646), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18938 ^ _780461) ^ [_1107741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107741), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1107741)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18944 ^ _780461) ^ [_1107854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1107854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1107854)))], (18950 ^ _780461) ^ [_1107937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1107937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1107937))))], (18956 ^ _780461) ^ [_1108038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108038)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108038), c_Int_OPls)))], (18962 ^ _780461) ^ [_1108133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108133), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108133)), c_Int_OPls)))], (18968 ^ _780461) ^ [_1108234] : [-(c_Int_OBit1(_1108234) = 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)), _1108234)), _1108234))], (18970 ^ _780461) ^ [_1108280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1108280)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1108280), c_Int_OMin)))], (18976 ^ _780461) ^ [_1108375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1108375), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1108375)), c_Int_OMin)))], (18982 ^ _780461) ^ [_1108488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1108488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1108488)))], (18988 ^ _780461) ^ [_1108571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1108571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1108571))))], (18994 ^ _780461) ^ [_1108672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1108672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1108672)))], (19000 ^ _780461) ^ [_1108755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1108755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1108755))))], (19006 ^ _780461) ^ [_1108856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108856)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108856), c_Int_OMin)))], (19012 ^ _780461) ^ [_1108951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108951), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1108951)), c_Int_OMin)))], (19018 ^ _780461) ^ [_1109064] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1109064)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1109064))))], (19024 ^ _780461) ^ [_1109159] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1109159))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1109159)))))], (19030 ^ _780461) ^ [_1109260] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1109260)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1109260))))], (19032 ^ _780461) ^ [_1109295, _1109297] : [c_Int_Oiszero(_1109295, hAPP(c_Int_Onumber__class_Onumber__of(_1109295), c_Int_OBit1(_1109297))), class_Int_Onumber__ring(_1109295), class_Int_Oring__char__0(_1109295)], (19042 ^ _780461) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (19044 ^ _780461) ^ [_1109453, _1109455] : [class_Int_Onumber__ring(_1109453), -(hAPP(c_Int_Onumber__class_Onumber__of(_1109453), c_Int_OBit1(_1109455)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109453), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109453), c_Groups_Oone__class_Oone(_1109453)), hAPP(c_Int_Onumber__class_Onumber__of(_1109453), _1109455))), hAPP(c_Int_Onumber__class_Onumber__of(_1109453), _1109455)))], (19050 ^ _780461) ^ [_1109598, _1109600] : [class_Int_Onumber__ring(_1109598), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109598), _1109600), hAPP(c_Int_Onumber__class_Onumber__of(_1109598), c_Int_OBit1(c_Int_OPls))) = _1109600)], (19056 ^ _780461) ^ [_1109699, _1109701] : [class_Int_Onumber__ring(_1109699), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109699), hAPP(c_Int_Onumber__class_Onumber__of(_1109699), c_Int_OBit1(c_Int_OPls))), _1109701) = _1109701)], (19062 ^ _780461) ^ [_1109800] : [class_Int_Onumber__ring(_1109800), -(hAPP(c_Int_Onumber__class_Onumber__of(_1109800), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1109800))], (19068 ^ _780461) ^ [_1109887] : [class_Int_Onumber__ring(_1109887), -(c_Groups_Oone__class_Oone(_1109887) = hAPP(c_Int_Onumber__class_Onumber__of(_1109887), c_Int_OBit1(c_Int_OPls)))], (19074 ^ _780461) ^ [_1109986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1109986)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109986), c_Int_OPls)))], (19080 ^ _780461) ^ [_1110081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110081), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1110081)), c_Int_OPls)))], (19086 ^ _780461) ^ [_1110194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1110194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1110194)))], (19092 ^ _780461) ^ [_1110277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1110277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1110277))))], (19098 ^ _780461) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (19100 ^ _780461) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (19102 ^ _780461) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (19104 ^ _780461) ^ [_1110420] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1110420)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1110420)))], (19106 ^ _780461) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (19108 ^ _780461) ^ [_1110471] : [class_Int_Onumber__ring(_1110471), c_Int_Oiszero(_1110471, hAPP(c_Int_Onumber__class_Onumber__of(_1110471), c_Int_OBit1(c_Int_OPls)))], (19114 ^ _780461) ^ [] : [-(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)))], (19116 ^ _780461) ^ [] : [-(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)))))], (19118 ^ _780461) ^ [_1110591, _1110593] : [class_Groups_Omonoid__mult(_1110591), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1110591), _1110593), 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(_1110591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110591), _1110593), _1110593)), _1110593))], (19124 ^ _780461) ^ [] : [-(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))))))], (19126 ^ _780461) ^ [_1110732] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1110732))) = 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)))), _1110732))], (19128 ^ _780461) ^ [] : [-(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)))))], (19130 ^ _780461) ^ [] : [-(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)))))], (19132 ^ _780461) ^ [_1110803, _1110805] : [class_Int_Onumber__ring(_1110803), class_Rings_Olinordered__idom(_1110803), 19139 ^ _780461 : [(19140 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110803), c_Groups_Oone__class_Oone(_1110803)), hAPP(c_Int_Onumber__class_Onumber__of(_1110803), _1110805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1110805)))], (19146 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1110805)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110803), c_Groups_Oone__class_Oone(_1110803)), hAPP(c_Int_Onumber__class_Onumber__of(_1110803), _1110805))))]]], (19152 ^ _780461) ^ [_1111108, _1111110] : [class_Int_Onumber__ring(_1111108), class_Rings_Olinordered__idom(_1111108), 19159 ^ _780461 : [(19160 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111108), hAPP(c_Int_Onumber__class_Onumber__of(_1111108), _1111110)), c_Groups_Oone__class_Oone(_1111108))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111110), c_Int_OBit1(c_Int_OPls))))], (19166 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111110), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111108), hAPP(c_Int_Onumber__class_Onumber__of(_1111108), _1111110)), c_Groups_Oone__class_Oone(_1111108))))]]], (19172 ^ _780461) ^ [_1111422, _1111424] : [class_Int_Onumber__ring(_1111422), class_Rings_Olinordered__idom(_1111422), 19179 ^ _780461 : [(19180 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111422), hAPP(c_Int_Onumber__class_Onumber__of(_1111422), _1111424)), c_Groups_Oone__class_Oone(_1111422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111424), c_Int_OBit1(c_Int_OPls))))], (19186 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111424), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111422), hAPP(c_Int_Onumber__class_Onumber__of(_1111422), _1111424)), c_Groups_Oone__class_Oone(_1111422))))]]], (19192 ^ _780461) ^ [_1111736, _1111738] : [class_Int_Onumber__ring(_1111736), class_Rings_Olinordered__idom(_1111736), 19199 ^ _780461 : [(19200 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111736), c_Groups_Oone__class_Oone(_1111736)), hAPP(c_Int_Onumber__class_Onumber__of(_1111736), _1111738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1111738)))], (19206 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1111738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1111736), c_Groups_Oone__class_Oone(_1111736)), hAPP(c_Int_Onumber__class_Onumber__of(_1111736), _1111738))))]]], (19212 ^ _780461) ^ [_1112041, _1112043] : [class_Int_Onumber__ring(_1112041), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112041), c_Groups_Oone__class_Oone(_1112041)), hAPP(c_Int_Onumber__class_Onumber__of(_1112041), _1112043)) = hAPP(c_Int_Onumber__class_Onumber__of(_1112041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1112043)))], (19218 ^ _780461) ^ [_1112162, _1112164] : [class_Int_Onumber__ring(_1112162), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112162), hAPP(c_Int_Onumber__class_Onumber__of(_1112162), _1112164)), c_Groups_Oone__class_Oone(_1112162)) = hAPP(c_Int_Onumber__class_Onumber__of(_1112162), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112164), c_Int_OBit1(c_Int_OPls))))], (19224 ^ _780461) ^ [_1112289, _1112291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1112289)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112291)), _1112289) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112291), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112289), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (19230 ^ _780461) ^ [_1112412, _1112414] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1112412, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1112414)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1112412, 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)))), _1112414)))], (19232 ^ _780461) ^ [_1112457, _1112459] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1112457))), _1112459) = 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)))), _1112457), _1112459))], (19234 ^ _780461) ^ [_1112502, _1112504] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1112502))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1112504)) = 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)))), _1112502), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1112504)))], (19236 ^ _780461) ^ [_1112553, _1112555] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1112553), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1112555)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1112553), 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)))), _1112555)))], (19238 ^ _780461) ^ [_1112611, _1112613] : [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), _1112611))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1112613)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1112611))) = 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), _1112613), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1112611)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19244 ^ _780461) ^ [_1112758, _1112760] : [-(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), _1112758)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1112760)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1112758))) = 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), _1112760)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1112758)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19250 ^ _780461) ^ [_1112840, _1112842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1112840), 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)))), _1112842)), 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)))), _1112840)) = 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), _1112842), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1112840))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19256 ^ _780461) ^ [_1112991, _1112993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112991)), -(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)))), _1112993))), 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)))), _1112991)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1112993), _1112991))], (19262 ^ _780461) ^ [_1113114, _1113116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113114), 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)))), _1113116))), 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)))), _1113114)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1113116), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1113114))], (19268 ^ _780461) ^ [_1113255, _1113257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113255)), -(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)))), _1113257)), 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)))), _1113255)) = 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, _1113257, _1113255))))], (19274 ^ _780461) ^ [_1113382, _1113384] : [class_Rings_Osemiring__1(_1113382), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113384)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1113382), 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)))), _1113384))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113382), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1113382), hAPP(c_Int_Onat, _1113384))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1113382), hAPP(c_Int_Onat, _1113384))))], (19284 ^ _780461) ^ [_1113598, _1113600] : [c_Int_OBit0(_1113598) = c_Int_OBit0(_1113600), -(_1113598 = _1113600)], (19290 ^ _780461) ^ [_1113679, _1113681] : [_1113679 = _1113681, -(c_Int_OBit0(_1113679) = c_Int_OBit0(_1113681))], (19296 ^ _780461) ^ [_1113781, _1113783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1113781)), c_Int_OBit0(_1113783))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113781), _1113783)))], (19302 ^ _780461) ^ [_1113882, _1113884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113882), _1113884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1113882)), c_Int_OBit0(_1113884))))], (19308 ^ _780461) ^ [_1114004, _1114006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1114004)), c_Int_OBit0(_1114006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114004), _1114006)))], (19314 ^ _780461) ^ [_1114105, _1114107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114105), _1114107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1114105)), c_Int_OBit0(_1114107))))], (19320 ^ _780461) ^ [_1114227, _1114229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1114227)), c_Int_OBit0(_1114229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114227), _1114229)))], (19326 ^ _780461) ^ [_1114328, _1114330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114328), _1114330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1114328)), c_Int_OBit0(_1114330))))], (19332 ^ _780461) ^ [_1114450, _1114452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1114450)), c_Int_OBit0(_1114452))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114450), _1114452)))], (19338 ^ _780461) ^ [_1114551, _1114553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114551), _1114553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1114551)), c_Int_OBit0(_1114553))))], (19344 ^ _780461) ^ [_1114670] : [c_Int_OBit0(_1114670) = c_Int_OPls, -(_1114670 = c_Int_OPls)], (19350 ^ _780461) ^ [_1114745] : [_1114745 = c_Int_OPls, -(c_Int_OBit0(_1114745) = c_Int_OPls)], (19356 ^ _780461) ^ [_1114838] : [c_Int_OPls = c_Int_OBit0(_1114838), -(c_Int_OPls = _1114838)], (19362 ^ _780461) ^ [_1114913] : [c_Int_OPls = _1114913, -(c_Int_OPls = c_Int_OBit0(_1114913))], (19368 ^ _780461) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (19370 ^ _780461) ^ [_1115024, _1115026] : [c_Int_OBit1(_1115024) = c_Int_OBit0(_1115026)], (19372 ^ _780461) ^ [_1115065, _1115067] : [c_Int_OBit0(_1115065) = c_Int_OBit1(_1115067)], (19374 ^ _780461) ^ [_1115094] : [-(c_Int_OBit0(_1115094) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1115094), _1115094))], (19376 ^ _780461) ^ [_1115125, _1115127] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1115125)), c_Int_OBit0(_1115127)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1115125), _1115127)))], (19378 ^ _780461) ^ [_1115168, _1115170] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1115168)), _1115170) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1115168), _1115170)))], (19380 ^ _780461) ^ [_1115209, _1115211] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1115209)), c_Int_OBit0(_1115211)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1115209), _1115211)))], (19382 ^ _780461) ^ [_1115252] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1115252)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1115252)))], (19384 ^ _780461) ^ [_1115294] : [c_Int_OBit0(_1115294) = c_Int_OMin], (19386 ^ _780461) ^ [_1115328] : [c_Int_OMin = c_Int_OBit0(_1115328)], (19388 ^ _780461) ^ [_1115365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1115365)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115365), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19394 ^ _780461) ^ [_1115460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115460), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1115460)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19400 ^ _780461) ^ [_1115573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1115573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1115573)))], (19406 ^ _780461) ^ [_1115656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1115656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1115656))))], (19412 ^ _780461) ^ [_1115757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1115757)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115757), c_Int_OPls)))], (19418 ^ _780461) ^ [_1115852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115852), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1115852)), c_Int_OPls)))], (19424 ^ _780461) ^ [_1115968, _1115970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1115968)), c_Int_OBit1(_1115970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1115968), _1115970)))], (19430 ^ _780461) ^ [_1116069, _1116071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116069), _1116071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1116069)), c_Int_OBit1(_1116071))))], (19436 ^ _780461) ^ [_1116191, _1116193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1116191)), c_Int_OBit1(_1116193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116191), _1116193)))], (19442 ^ _780461) ^ [_1116292, _1116294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116292), _1116294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1116292)), c_Int_OBit1(_1116294))))], (19448 ^ _780461) ^ [_1116411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116411)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116411), c_Int_OPls)))], (19454 ^ _780461) ^ [_1116506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116506), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1116506)), c_Int_OPls)))], (19460 ^ _780461) ^ [_1116619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1116619))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1116619)))], (19466 ^ _780461) ^ [_1116702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1116702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1116702))))], (19472 ^ _780461) ^ [_1116806, _1116808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1116806)), c_Int_OBit0(_1116808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116806), _1116808)))], (19478 ^ _780461) ^ [_1116907, _1116909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116907), _1116909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1116907)), c_Int_OBit0(_1116909))))], (19484 ^ _780461) ^ [_1117029, _1117031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1117029)), c_Int_OBit0(_1117031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117029), _1117031)))], (19490 ^ _780461) ^ [_1117130, _1117132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117130), _1117132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1117130)), c_Int_OBit0(_1117132))))], (19496 ^ _780461) ^ [_1117237, _1117239] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1117237)), c_Int_OBit0(_1117239)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117237), _1117239)))], (19498 ^ _780461) ^ [_1117280, _1117282] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1117280)), c_Int_OBit1(_1117282)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117280), _1117282)))], (19500 ^ _780461) ^ [_1117323] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1117323)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1117323)))], (19502 ^ _780461) ^ [_1117356, _1117358] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1117356)), c_Int_OBit1(_1117358)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1117356), _1117358)))], (19504 ^ _780461) ^ [_1117399, _1117401] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1117399)), c_Int_OBit0(_1117401)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1117399), _1117401)))], (19506 ^ _780461) ^ [_1117454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1117454)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1117454), c_Int_OMin)))], (19512 ^ _780461) ^ [_1117549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1117549), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1117549)), c_Int_OMin)))], (19518 ^ _780461) ^ [_1117662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1117662))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1117662)))], (19524 ^ _780461) ^ [_1117745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1117745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1117745))))], (19530 ^ _780461) ^ [_1117834, _1117836] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1117834))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1117836))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1117834)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1117836)))], (19532 ^ _780461) ^ [_1117899] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1117899)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1117899))))], (19538 ^ _780461) ^ [_1117994] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1117994))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1117994)))))], (19544 ^ _780461) ^ [_1118095] : [-(c_Int_Opred(c_Int_OBit1(_1118095)) = c_Int_OBit0(_1118095))], (19546 ^ _780461) ^ [_1118124] : [-(c_Int_Opred(c_Int_OBit0(_1118124)) = c_Int_OBit1(c_Int_Opred(_1118124)))], (19548 ^ _780461) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (19550 ^ _780461) ^ [_1118173, _1118175] : [class_Int_Onumber__ring(_1118173), class_Int_Oring__char__0(_1118173), 19557 ^ _780461 : [(19558 ^ _780461) ^ [] : [c_Int_Oiszero(_1118173, hAPP(c_Int_Onumber__class_Onumber__of(_1118173), c_Int_OBit0(_1118175))), -(c_Int_Oiszero(_1118173, hAPP(c_Int_Onumber__class_Onumber__of(_1118173), _1118175)))], (19564 ^ _780461) ^ [] : [c_Int_Oiszero(_1118173, hAPP(c_Int_Onumber__class_Onumber__of(_1118173), _1118175)), -(c_Int_Oiszero(_1118173, hAPP(c_Int_Onumber__class_Onumber__of(_1118173), c_Int_OBit0(_1118175))))]]], (19570 ^ _780461) ^ [_1118466] : [-(c_Int_Osucc(c_Int_OBit0(_1118466)) = c_Int_OBit1(_1118466))], (19572 ^ _780461) ^ [_1118495] : [-(c_Int_Osucc(c_Int_OBit1(_1118495)) = c_Int_OBit0(c_Int_Osucc(_1118495)))], (19574 ^ _780461) ^ [_1118526, _1118528] : [class_Int_Onumber__ring(_1118526), -(hAPP(c_Int_Onumber__class_Onumber__of(_1118526), c_Int_OBit0(_1118528)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118526), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118526), c_Groups_Ozero__class_Ozero(_1118526)), hAPP(c_Int_Onumber__class_Onumber__of(_1118526), _1118528))), hAPP(c_Int_Onumber__class_Onumber__of(_1118526), _1118528)))], (19580 ^ _780461) ^ [_1118686, _1118688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1118686)), c_Int_OBit1(_1118688))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118686), _1118688)))], (19586 ^ _780461) ^ [_1118787, _1118789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118787), _1118789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1118787)), c_Int_OBit1(_1118789))))], (19592 ^ _780461) ^ [_1118909, _1118911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1118909)), c_Int_OBit1(_1118911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118909), _1118911)))], (19598 ^ _780461) ^ [_1119010, _1119012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119010), _1119012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1119010)), c_Int_OBit1(_1119012))))], (19604 ^ _780461) ^ [_1119132, _1119134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1119132)), c_Int_OBit0(_1119134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119132), _1119134)))], (19610 ^ _780461) ^ [_1119233, _1119235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119233), _1119235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1119233)), c_Int_OBit0(_1119235))))], (19616 ^ _780461) ^ [_1119355, _1119357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1119355)), c_Int_OBit0(_1119357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119355), _1119357)))], (19622 ^ _780461) ^ [_1119456, _1119458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119456), _1119458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1119456)), c_Int_OBit0(_1119458))))], (19628 ^ _780461) ^ [_1119563, _1119565] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1119563)), _1119565) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1119563), _1119565))), _1119565))], (19630 ^ _780461) ^ [_1119622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1119622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1119622)))], (19636 ^ _780461) ^ [_1119705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1119705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1119705))))], (19642 ^ _780461) ^ [_1119806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1119806)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119806), c_Int_OMin)))], (19648 ^ _780461) ^ [_1119901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1119901), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1119901)), c_Int_OMin)))], (19654 ^ _780461) ^ [_1120002] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1120002)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1120002)))], (19656 ^ _780461) ^ [_1120035] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1120035)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1120035)))], (19658 ^ _780461) ^ [_1120068, _1120070] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1120068)), c_Int_OBit1(_1120070)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1120068)), _1120070)))], (19660 ^ _780461) ^ [_1120113, _1120115] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1120113)), c_Int_OBit1(_1120115)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120113), c_Int_Osucc(_1120115))))], (19662 ^ _780461) ^ [_1120158, _1120160] : [class_Int_Onumber__ring(_1120158), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120158), c_Groups_Oone__class_Oone(_1120158)), c_Groups_Oone__class_Oone(_1120158))), hAPP(c_Int_Onumber__class_Onumber__of(_1120158), _1120160)) = hAPP(c_Int_Onumber__class_Onumber__of(_1120158), c_Int_OBit0(_1120160)))], (19668 ^ _780461) ^ [_1120297] : [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), _1120297))), 19671 ^ _780461 : [(19672 ^ _780461) ^ [] : [-(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(_1120297)))))], (19674 ^ _780461) ^ [] : [-(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(_1120297)))))]]], (19676 ^ _780461) ^ [_1120436, _1120438] : [class_Int_Onumber__ring(_1120436), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120436), _1120438), hAPP(c_Int_Onumber__class_Onumber__of(_1120436), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120436), _1120438), _1120438))], (19682 ^ _780461) ^ [_1120553, _1120555] : [class_Int_Onumber__ring(_1120553), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120553), hAPP(c_Int_Onumber__class_Onumber__of(_1120553), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1120555) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120553), _1120555), _1120555))], (19688 ^ _780461) ^ [_1120670] : [class_Int_Onumber__ring(_1120670), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120670), c_Groups_Oone__class_Oone(_1120670)), c_Groups_Oone__class_Oone(_1120670)) = hAPP(c_Int_Onumber__class_Onumber__of(_1120670), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (19694 ^ _780461) ^ [_1120777] : [class_Rings_Osemiring__1(_1120777), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1120777), c_Groups_Ozero__class_Ozero(_1120777)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1120777))], (19700 ^ _780461) ^ [_1120874, _1120876] : [class_Rings_Oring__1__no__zero__divisors(_1120874), 19703 ^ _780461 : [(19704 ^ _780461) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1120874), _1120876), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1120874), -(_1120876 = c_Groups_Ozero__class_Ozero(_1120874))], (19710 ^ _780461) ^ [] : [_1120876 = c_Groups_Ozero__class_Ozero(_1120874), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1120874), _1120876), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1120874))]]], (19716 ^ _780461) ^ [] : [-(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))))], (19718 ^ _780461) ^ [] : [-(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))))], (19720 ^ _780461) ^ [_1121151, _1121153] : [class_Groups_Omonoid__mult(_1121151), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121151), _1121153), 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(_1121151), _1121153), _1121153))], (19726 ^ _780461) ^ [_1121258, _1121260] : [class_Rings_Ocomm__semiring__1(_1121258), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121258), _1121260), _1121260) = hAPP(hAPP(c_Power_Opower__class_Opower(_1121258), _1121260), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19732 ^ _780461) ^ [] : [-(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))))))], (19734 ^ _780461) ^ [_1121383] : [-(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)))), _1121383) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1121383)))], (19736 ^ _780461) ^ [_1121415] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121415), 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, _1121415)))], (19738 ^ _780461) ^ [_1121450] : [class_Rings_Osemiring__1(_1121450), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121450), c_Groups_Oone__class_Oone(_1121450)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1121450))], (19744 ^ _780461) ^ [_1121547, _1121549] : [class_Rings_Oring__1(_1121547), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121547), hAPP(c_Groups_Ouminus__class_Ouminus(_1121547), _1121549)), 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(_1121547), _1121549), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19750 ^ _780461) ^ [_1121664] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1121664), 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), _1121664), _1121664))], (19752 ^ _780461) ^ [_1121699] : [-(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)))), _1121699) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121699), _1121699))], (19754 ^ _780461) ^ [_1121731, _1121733, _1121735] : [class_Groups_Omonoid__mult(_1121731), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121731), _1121733), 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)))), _1121735)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1121731), hAPP(hAPP(c_Power_Opower__class_Opower(_1121731), _1121733), _1121735)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19760 ^ _780461) ^ [] : [-(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)))))], (19762 ^ _780461) ^ [] : [-(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)))))], (19764 ^ _780461) ^ [_1121898, _1121900] : [class_Rings_Olinordered__idom(_1121898), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121898), hAPP(c_Groups_Oabs__class_Oabs(_1121898), _1121900)), 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(_1121898), _1121900), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19770 ^ _780461) ^ [_1122015, _1122017] : [class_Rings_Olinordered__idom(_1122015), -(hAPP(c_Groups_Oabs__class_Oabs(_1122015), hAPP(hAPP(c_Power_Opower__class_Opower(_1122015), _1122017), 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(_1122015), _1122017), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19776 ^ _780461) ^ [] : [-(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))))], (19778 ^ _780461) ^ [_1122150] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1122150)), 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, _1122150, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19780 ^ _780461) ^ [_1122187] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1122187))), 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), _1122187), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (19782 ^ _780461) ^ [_1122231, _1122233] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1122231)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1122233))) = 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), _1122231), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122233))))], (19784 ^ _780461) ^ [_1122283] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122283), _1122283)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1122283)], (19786 ^ _780461) ^ [_1122318, _1122320, _1122322] : [class_Rings_Olinordered__semidom(_1122318), hAPP(hAPP(c_Power_Opower__class_Opower(_1122318), _1122320), 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(_1122318), _1122322), 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(_1122318), c_Groups_Ozero__class_Ozero(_1122318)), _1122320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122318), c_Groups_Ozero__class_Ozero(_1122318)), _1122322)), -(_1122320 = _1122322)], (19804 ^ _780461) ^ [_1122625, _1122627, _1122629] : [class_Rings_Olinordered__semidom(_1122625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122625), hAPP(hAPP(c_Power_Opower__class_Opower(_1122625), _1122627), 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(_1122625), _1122629), 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(_1122625), c_Groups_Ozero__class_Ozero(_1122625)), _1122629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122625), _1122627), _1122629)))], (19818 ^ _780461) ^ [_1122888, _1122890] : [class_Rings_Olinordered__idom(_1122888), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122888), c_Groups_Ozero__class_Ozero(_1122888)), hAPP(hAPP(c_Power_Opower__class_Opower(_1122888), _1122890), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19824 ^ _780461) ^ [_1122997, _1122999] : [class_Rings_Olinordered__idom(_1122997), 19827 ^ _780461 : [(19828 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122997), c_Groups_Ozero__class_Ozero(_1122997)), hAPP(hAPP(c_Power_Opower__class_Opower(_1122997), _1122999), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1122999 = c_Groups_Ozero__class_Ozero(_1122997)], (19834 ^ _780461) ^ [] : [-(_1122999 = c_Groups_Ozero__class_Ozero(_1122997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122997), c_Groups_Ozero__class_Ozero(_1122997)), hAPP(hAPP(c_Power_Opower__class_Opower(_1122997), _1122999), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (19840 ^ _780461) ^ [_1123221, _1123223] : [class_Rings_Olinordered__idom(_1123221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1123221), hAPP(hAPP(c_Power_Opower__class_Opower(_1123221), _1123223), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1123221)))], (19846 ^ _780461) ^ [_1123331, _1123333, _1123335] : [class_Rings_Olinordered__idom(_1123331), 19849 ^ _780461 : [(19850 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123331), hAPP(hAPP(c_Power_Opower__class_Opower(_1123331), _1123333), 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(_1123331), _1123335), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1123331), 19853 ^ _780461 : [(19854 ^ _780461) ^ [] : [-(_1123333 = c_Groups_Ozero__class_Ozero(_1123331))], (19856 ^ _780461) ^ [] : [-(_1123335 = c_Groups_Ozero__class_Ozero(_1123331))]]], (19858 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123331), hAPP(hAPP(c_Power_Opower__class_Opower(_1123331), _1123333), 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(_1123331), _1123335), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1123331)), _1123333 = c_Groups_Ozero__class_Ozero(_1123331), _1123335 = c_Groups_Ozero__class_Ozero(_1123331)]]], (19868 ^ _780461) ^ [_1123706, _1123708] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1123706), hAPP(c_Int_Onumber__class_Onumber__of(_1123706), _1123708)), 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(_1123706), hAPP(c_Int_Onumber__class_Onumber__of(_1123706), _1123708)), hAPP(c_Int_Onumber__class_Onumber__of(_1123706), _1123708))), class_Groups_Omonoid__mult(_1123706), class_Int_Onumber(_1123706)], (19878 ^ _780461) ^ [_1123893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123893), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1123893 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1123893 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19888 ^ _780461) ^ [] : [-(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))))], (19890 ^ _780461) ^ [_1124009, _1124011] : [class_Rings_Oring__1__no__zero__divisors(_1124009), 19893 ^ _780461 : [(19904 ^ _780461) ^ [] : [19905 ^ _780461 : [(19906 ^ _780461) ^ [] : [_1124011 = c_Groups_Oone__class_Oone(_1124009)], (19908 ^ _780461) ^ [] : [_1124011 = hAPP(c_Groups_Ouminus__class_Ouminus(_1124009), c_Groups_Oone__class_Oone(_1124009))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1124009), _1124011), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1124009))], (19894 ^ _780461) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1124009), _1124011), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1124009), -(_1124011 = c_Groups_Oone__class_Oone(_1124009)), -(_1124011 = hAPP(c_Groups_Ouminus__class_Ouminus(_1124009), c_Groups_Oone__class_Oone(_1124009)))]]], (19912 ^ _780461) ^ [_1124316, _1124318, _1124320] : [class_Rings_Ocomm__semiring__1(_1124316), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1124316), _1124318), 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)))), _1124320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124316), hAPP(hAPP(c_Power_Opower__class_Opower(_1124316), _1124318), _1124320)), hAPP(hAPP(c_Power_Opower__class_Opower(_1124316), _1124318), _1124320)))], (19918 ^ _780461) ^ [_1124463, _1124465, _1124467] : [class_Rings_Oring__1(_1124463), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1124463), hAPP(c_Groups_Ouminus__class_Ouminus(_1124463), _1124465)), 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)))), _1124467)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1124463), _1124465), 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)))), _1124467)))], (19924 ^ _780461) ^ [_1124594, _1124596, _1124598] : [class_Rings_Olinordered__semidom(_1124594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124594), hAPP(hAPP(c_Power_Opower__class_Opower(_1124594), _1124596), 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(_1124594), _1124598), 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(_1124594), c_Groups_Ozero__class_Ozero(_1124594)), _1124598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124594), _1124596), _1124598)))], (19938 ^ _780461) ^ [_1124857, _1124859, _1124861] : [class_Rings_Olinordered__idom(_1124857), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124857), c_Groups_Ozero__class_Ozero(_1124857)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124857), hAPP(hAPP(c_Power_Opower__class_Opower(_1124857), _1124859), 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(_1124857), _1124861), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (19944 ^ _780461) ^ [_1125000, _1125002, _1125004] : [class_Rings_Olinordered__idom(_1125000), 19947 ^ _780461 : [(19948 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125000), hAPP(hAPP(c_Power_Opower__class_Opower(_1125000), _1125002), 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(_1125000), _1125004), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1125000))), 19951 ^ _780461 : [(19952 ^ _780461) ^ [] : [-(_1125002 = c_Groups_Ozero__class_Ozero(_1125000))], (19954 ^ _780461) ^ [] : [-(_1125004 = c_Groups_Ozero__class_Ozero(_1125000))]]], (19956 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1125000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125000), hAPP(hAPP(c_Power_Opower__class_Opower(_1125000), _1125002), 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(_1125000), _1125004), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1125000)))), _1125002 = c_Groups_Ozero__class_Ozero(_1125000), _1125004 = c_Groups_Ozero__class_Ozero(_1125000)]]], (19966 ^ _780461) ^ [_1125396, _1125398, _1125400] : [class_Rings_Olinordered__idom(_1125396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125396), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125396), hAPP(hAPP(c_Power_Opower__class_Opower(_1125396), _1125398), 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(_1125396), _1125400), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1125396)))], (19972 ^ _780461) ^ [_1125540, _1125542, _1125544] : [class_Rings_Olinordered__idom(_1125540), 19975 ^ _780461 : [(19986 ^ _780461) ^ [] : [19987 ^ _780461 : [(19988 ^ _780461) ^ [] : [-(_1125542 = c_Groups_Ozero__class_Ozero(_1125540))], (19990 ^ _780461) ^ [] : [-(_1125544 = c_Groups_Ozero__class_Ozero(_1125540))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125540), c_Groups_Ozero__class_Ozero(_1125540)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125540), hAPP(hAPP(c_Power_Opower__class_Opower(_1125540), _1125542), 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(_1125540), _1125544), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (19976 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1125540), c_Groups_Ozero__class_Ozero(_1125540)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125540), hAPP(hAPP(c_Power_Opower__class_Opower(_1125540), _1125542), 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(_1125540), _1125544), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1125542 = c_Groups_Ozero__class_Ozero(_1125540), _1125544 = c_Groups_Ozero__class_Ozero(_1125540)]]], (19994 ^ _780461) ^ [_1125915, _1125917, _1125919] : [class_Int_Onumber__ring(_1125915), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1125915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125915), _1125917), _1125919)), 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(_1125915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1125915), hAPP(hAPP(c_Power_Opower__class_Opower(_1125915), _1125917), 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(_1125915), _1125919), 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(_1125915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125915), hAPP(c_Int_Onumber__class_Onumber__of(_1125915), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1125917)), _1125919)))], (20000 ^ _780461) ^ [_1126130, _1126132, _1126134] : [class_Rings_Olinordered__idom(_1126130), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1126130), c_Groups_Ozero__class_Ozero(_1126130)), hAPP(hAPP(c_Power_Opower__class_Opower(_1126130), _1126132), 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)))), _1126134)))))], (20006 ^ _780461) ^ [_1126247, _1126249, _1126251] : [class_Groups_Omonoid__mult(_1126247), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1126247), _1126249), 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)))), _1126251))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126247), _1126249), hAPP(hAPP(c_Power_Opower__class_Opower(_1126247), hAPP(hAPP(c_Power_Opower__class_Opower(_1126247), _1126249), _1126251)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (20012 ^ _780461) ^ [_1126400, _1126402, _1126404] : [class_Rings_Ocomm__semiring__1(_1126400), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1126400), _1126402), 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)))), _1126404))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126400), _1126402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126400), hAPP(hAPP(c_Power_Opower__class_Opower(_1126400), _1126402), _1126404)), hAPP(hAPP(c_Power_Opower__class_Opower(_1126400), _1126402), _1126404))))], (20018 ^ _780461) ^ [_1126569, _1126571] : [class_Rings_Oring__1(_1126569), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1126569), hAPP(c_Groups_Ouminus__class_Ouminus(_1126569), c_Groups_Oone__class_Oone(_1126569))), 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)))), _1126571)) = c_Groups_Oone__class_Oone(_1126569))], (20024 ^ _780461) ^ [_1126693, _1126695] : [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), _1126693))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1126695))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1126693))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126695)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126693)))], (20030 ^ _780461) ^ [_1126830, _1126832] : [-(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), _1126830)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1126832))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1126830))) = 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), _1126832)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126830)))], (20036 ^ _780461) ^ [_1126919] : [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, _1126919, 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, _1126919, 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))], (20042 ^ _780461) ^ [_1127010] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127010, 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, _1127010, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20048 ^ _780461) ^ [_1127107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1127107)), -(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), _1127107), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20054 ^ _780461) ^ [_1127202, _1127204, _1127206] : [class_Int_Onumber__ring(_1127202), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1127202), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1127202), _1127204), _1127206)), 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(_1127202), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1127202), hAPP(hAPP(c_Power_Opower__class_Opower(_1127202), _1127204), 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(_1127202), _1127206), 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(_1127202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127202), hAPP(c_Int_Onumber__class_Onumber__of(_1127202), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1127204)), _1127206)))], (20060 ^ _780461) ^ [_1127417, _1127419, _1127421] : [class_Rings_Olinordered__idom(_1127417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127417), c_Groups_Ozero__class_Ozero(_1127417)), hAPP(hAPP(c_Power_Opower__class_Opower(_1127417), _1127419), 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)))), _1127421))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127417), c_Groups_Ozero__class_Ozero(_1127417)), _1127419)))], (20070 ^ _780461) ^ [_1127612, _1127614, _1127616] : [class_Rings_Olinordered__idom(_1127612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127612), _1127614), c_Groups_Ozero__class_Ozero(_1127612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1127612), hAPP(hAPP(c_Power_Opower__class_Opower(_1127612), _1127614), 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)))), _1127616)))), c_Groups_Ozero__class_Ozero(_1127612))))], (20080 ^ _780461) ^ [_1127807, _1127809] : [class_Rings_Oring__1(_1127807), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1127807), hAPP(c_Groups_Ouminus__class_Ouminus(_1127807), c_Groups_Oone__class_Oone(_1127807))), 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)))), _1127809))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127807), c_Groups_Oone__class_Oone(_1127807)))], (20086 ^ _780461) ^ [_1127938, _1127940] : [class_Int_Onumber__ring(_1127938), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1127938), hAPP(c_Int_Onumber__class_Onumber__of(_1127938), 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)))), _1127940)) = c_Groups_Oone__class_Oone(_1127938))], (20092 ^ _780461) ^ [_1128049, _1128051] : [class_Int_Onumber__ring(_1128049), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1128049), hAPP(c_Int_Onumber__class_Onumber__of(_1128049), 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)))), _1128051))) = hAPP(c_Int_Onumber__class_Onumber__of(_1128049), c_Int_OMin))], (20098 ^ _780461) ^ [_1128172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128172)), -(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), _1128172), 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)))))))], (20104 ^ _780461) ^ [_1128285] : [_1128285 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1128285) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20110 ^ _780461) ^ [_1128361] : [-(_1128361 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 20113 ^ _780461 : [(20114 ^ _780461) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1128361, 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, _1128361) = 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), _1128361), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20120 ^ _780461) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1128361, 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, _1128361) = 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), _1128361), 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)))]]], (20126 ^ _780461) ^ [] : [-(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)))], (20128 ^ _780461) ^ [_1128639, _1128641] : [class_Fields_Olinordered__field__inverse__zero(_1128639), class_Int_Onumber__ring(_1128639), 20135 ^ _780461 : [(20136 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128639), c_Groups_Ozero__class_Ozero(_1128639)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128639), _1128641), hAPP(c_Int_Onumber__class_Onumber__of(_1128639), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128639), c_Groups_Ozero__class_Ozero(_1128639)), _1128641)))], (20142 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128639), c_Groups_Ozero__class_Ozero(_1128639)), _1128641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128639), c_Groups_Ozero__class_Ozero(_1128639)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128639), _1128641), hAPP(c_Int_Onumber__class_Onumber__of(_1128639), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (20148 ^ _780461) ^ [_1128989, _1128991] : [class_Fields_Olinordered__field__inverse__zero(_1128989), class_Int_Onumber__ring(_1128989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128989), c_Groups_Ozero__class_Ozero(_1128989)), _1128991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1128989), c_Groups_Ozero__class_Ozero(_1128989)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1128989), _1128991), hAPP(c_Int_Onumber__class_Onumber__of(_1128989), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20162 ^ _780461) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (20164 ^ _780461) ^ [_1129248, _1129250, _1129252, _1129254] : [20166 ^ _780461 : [(20167 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129248), 20165 ^ [_1129248, _1129250, _1129252, _1129254])))], (20169 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20165 ^ [_1129248, _1129250, _1129252, _1129254]), _1129250)))], (20171 ^ _780461) ^ [] : [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(_1129252, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 20165 ^ [_1129248, _1129250, _1129252, _1129254]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1129252, 20165 ^ [_1129248, _1129250, _1129252, _1129254])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1129248), _1129250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1129252, _1129248)), _1129254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129254), hAPP(_1129252, _1129250))), 20185 ^ _780461 : [(20186 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129248), 20184 ^ [_1129248, _1129250, _1129252, _1129254])))], (20188 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20184 ^ [_1129248, _1129250, _1129252, _1129254]), _1129250)))], (20190 ^ _780461) ^ [] : [-(hAPP(_1129252, 20184 ^ [_1129248, _1129250, _1129252, _1129254]) = _1129254)]]], (20192 ^ _780461) ^ [] : [-(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))], (20194 ^ _780461) ^ [_1129892, _1129894] : [class_Rings_Odivision__ring__inverse__zero(_1129892), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129892), _1129894), c_Groups_Ozero__class_Ozero(_1129892)) = c_Groups_Ozero__class_Ozero(_1129892))], (20200 ^ _780461) ^ [_1129991, _1129993] : [class_Rings_Odivision__ring(_1129991), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1129991), c_Groups_Ozero__class_Ozero(_1129991)), _1129993) = c_Groups_Ozero__class_Ozero(_1129991))], (20206 ^ _780461) ^ [_1130090, _1130092, _1130094, _1130096] : [class_Rings_Odivision__ring(_1130090), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130090), _1130092), _1130094)), _1130096) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130090), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130090), _1130092), _1130096)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130090), _1130094), _1130096)))], (20212 ^ _780461) ^ [_1130249, _1130251, _1130253, _1130255, _1130257] : [class_Fields_Ofield__inverse__zero(_1130249), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130249), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130249), _1130251), _1130253)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130249), _1130255), _1130257)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130249), _1130251), _1130255)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130249), _1130253), _1130257)))], (20218 ^ _780461) ^ [_1130426, _1130428, _1130430, _1130432] : [class_Rings_Odivision__ring(_1130426), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130426), _1130428), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130426), _1130430), _1130432)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130426), _1130428), _1130430)), _1130432))], (20224 ^ _780461) ^ [_1130569, _1130571, _1130573, _1130575] : [class_Rings_Odivision__ring(_1130569), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130569), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130569), _1130571), _1130573)), _1130575) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130569), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130569), _1130571), _1130575)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130569), _1130573), _1130575)))], (20230 ^ _780461) ^ [_1130728, _1130730] : [class_Rings_Odivision__ring(_1130728), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130728), _1130730), c_Groups_Oone__class_Oone(_1130728)) = _1130730)], (20236 ^ _780461) ^ [_1130823, _1130825, _1130827] : [class_Fields_Ofield__inverse__zero(_1130823), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130823), hAPP(c_Groups_Ouminus__class_Ouminus(_1130823), _1130825)), hAPP(c_Groups_Ouminus__class_Ouminus(_1130823), _1130827)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130823), _1130825), _1130827))], (20242 ^ _780461) ^ [_1130952, _1130954, _1130956] : [class_Fields_Ofield__inverse__zero(_1130952), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130952), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130952), _1130954), _1130956)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1130952), _1130954), hAPP(c_Groups_Ouminus__class_Ouminus(_1130952), _1130956)))], (20248 ^ _780461) ^ [_1131081, _1131083, _1131085] : [class_Rings_Odivision__ring(_1131081), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1131081), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131081), _1131083), _1131085)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131081), hAPP(c_Groups_Ouminus__class_Ouminus(_1131081), _1131083)), _1131085))], (20254 ^ _780461) ^ [_1131210, _1131212, _1131214, _1131216] : [class_Fields_Ofield__inverse__zero(_1131210), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1131210), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131210), _1131212), _1131214)), _1131216) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131210), hAPP(hAPP(c_Power_Opower__class_Opower(_1131210), _1131212), _1131216)), hAPP(hAPP(c_Power_Opower__class_Opower(_1131210), _1131214), _1131216)))], (20260 ^ _780461) ^ [_1131369, _1131371, _1131373] : [class_Fields_Olinordered__field__inverse__zero(_1131369), -(hAPP(c_Groups_Oabs__class_Oabs(_1131369), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131369), _1131371), _1131373)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1131369), hAPP(c_Groups_Oabs__class_Oabs(_1131369), _1131371)), hAPP(c_Groups_Oabs__class_Oabs(_1131369), _1131373)))], (20266 ^ _780461) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20268 ^ _780461) ^ [_1131526, _1131528] : [c_Nat__Transfer_Ois__nat(_1131526), c_Nat__Transfer_Ois__nat(_1131528), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1131526), _1131528)))], (20278 ^ _780461) ^ [_1131661] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1131661)))], (20280 ^ _780461) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20282 ^ _780461) ^ [_1131704, _1131706] : [c_Nat__Transfer_Ois__nat(_1131704), c_Nat__Transfer_Ois__nat(_1131706), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1131704), _1131706)))], (20292 ^ _780461) ^ [_1131839, _1131841] : [c_Nat__Transfer_Ois__nat(_1131839), c_Nat__Transfer_Ois__nat(_1131841), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1131839, _1131841)))], (20302 ^ _780461) ^ [_1131970, _1131972] : [c_Nat__Transfer_Ois__nat(_1131970), c_Nat__Transfer_Ois__nat(_1131972), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131970), _1131972)))], (20312 ^ _780461) ^ [_1132105, _1132107] : [c_Nat__Transfer_Ois__nat(_1132105), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1132105), _1132107)))], (20318 ^ _780461) ^ [_1132190, _1132192, _1132194] : [class_Fields_Olinordered__field__inverse__zero(_1132190), 20321 ^ _780461 : [(20322 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), c_Groups_Ozero__class_Ozero(_1132190)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132190), _1132192), _1132194))), 20327 ^ _780461 : [(20328 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), c_Groups_Ozero__class_Ozero(_1132190)), _1132192)))], (20330 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), c_Groups_Ozero__class_Ozero(_1132190)), _1132194)))]], 20331 ^ _780461 : [(20332 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), _1132192), c_Groups_Ozero__class_Ozero(_1132190))))], (20334 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), _1132194), c_Groups_Ozero__class_Ozero(_1132190))))]]], (20336 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), c_Groups_Ozero__class_Ozero(_1132190)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132190), _1132192), _1132194)))), 20337 ^ _780461 : [(20338 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), c_Groups_Ozero__class_Ozero(_1132190)), _1132192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), c_Groups_Ozero__class_Ozero(_1132190)), _1132194))], (20344 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), _1132192), c_Groups_Ozero__class_Ozero(_1132190))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132190), _1132194), c_Groups_Ozero__class_Ozero(_1132190)))]]]]], (20352 ^ _780461) ^ [_1132780, _1132782, _1132784] : [class_Fields_Olinordered__field__inverse__zero(_1132780), 20355 ^ _780461 : [(20356 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132780), _1132782), _1132784)), c_Groups_Ozero__class_Ozero(_1132780))), 20361 ^ _780461 : [(20362 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), c_Groups_Ozero__class_Ozero(_1132780)), _1132782)))], (20364 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), _1132784), c_Groups_Ozero__class_Ozero(_1132780))))]], 20365 ^ _780461 : [(20366 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), _1132782), c_Groups_Ozero__class_Ozero(_1132780))))], (20368 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), c_Groups_Ozero__class_Ozero(_1132780)), _1132784)))]]], (20370 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1132780), _1132782), _1132784)), c_Groups_Ozero__class_Ozero(_1132780)))), 20371 ^ _780461 : [(20372 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), c_Groups_Ozero__class_Ozero(_1132780)), _1132782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), _1132784), c_Groups_Ozero__class_Ozero(_1132780)))], (20378 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), _1132782), c_Groups_Ozero__class_Ozero(_1132780))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132780), c_Groups_Ozero__class_Ozero(_1132780)), _1132784))]]]]], (20386 ^ _780461) ^ [_1133370, _1133372, _1133374, _1133376] : [class_Fields_Olinordered__field__inverse__zero(_1133370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133370), _1133372), _1133374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133370), c_Groups_Ozero__class_Ozero(_1133370)), _1133376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133370), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133370), _1133372), _1133376)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133370), _1133374), _1133376))))], (20400 ^ _780461) ^ [_1133639, _1133641, _1133643, _1133645] : [class_Fields_Olinordered__field__inverse__zero(_1133639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133639), _1133641), _1133643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133639), _1133645), c_Groups_Ozero__class_Ozero(_1133639))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133639), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133639), _1133643), _1133645)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133639), _1133641), _1133645))))], (20414 ^ _780461) ^ [_1133908, _1133910, _1133912, _1133914] : [class_Fields_Olinordered__field(_1133908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133908), _1133910), _1133912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133908), _1133914), c_Groups_Ozero__class_Ozero(_1133908))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133908), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133908), _1133912), _1133914)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133908), _1133910), _1133914))))], (20428 ^ _780461) ^ [_1134177, _1134179, _1134181, _1134183] : [class_Fields_Olinordered__field(_1134177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134177), _1134179), _1134181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134177), c_Groups_Ozero__class_Ozero(_1134177)), _1134183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134177), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134177), _1134179), _1134183)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134177), _1134181), _1134183))))], (20442 ^ _780461) ^ [_1134446, _1134448, _1134450] : [class_Fields_Olinordered__field(_1134446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134446), _1134448), c_Groups_Ozero__class_Ozero(_1134446))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134446), _1134450), c_Groups_Ozero__class_Ozero(_1134446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134446), c_Groups_Ozero__class_Ozero(_1134446)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134446), _1134448), _1134450))))], (20456 ^ _780461) ^ [_1134701, _1134703, _1134705] : [class_Fields_Olinordered__field(_1134701), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134701), _1134703), c_Groups_Ozero__class_Ozero(_1134701))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134701), c_Groups_Ozero__class_Ozero(_1134701)), _1134705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134701), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134701), _1134703), _1134705)), c_Groups_Ozero__class_Ozero(_1134701))))], (20470 ^ _780461) ^ [_1134956, _1134958, _1134960] : [class_Fields_Olinordered__field(_1134956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134956), c_Groups_Ozero__class_Ozero(_1134956)), _1134958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134956), _1134960), c_Groups_Ozero__class_Ozero(_1134956))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134956), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1134956), _1134958), _1134960)), c_Groups_Ozero__class_Ozero(_1134956))))], (20484 ^ _780461) ^ [_1135211, _1135213, _1135215] : [class_Fields_Olinordered__field(_1135211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135211), c_Groups_Ozero__class_Ozero(_1135211)), _1135213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135211), c_Groups_Ozero__class_Ozero(_1135211)), _1135215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135211), c_Groups_Ozero__class_Ozero(_1135211)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135211), _1135213), _1135215))))], (20498 ^ _780461) ^ [_1135466, _1135468, _1135470] : [class_Fields_Olinordered__field__inverse__zero(_1135466), 20501 ^ _780461 : [(20502 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135466), _1135468), _1135470)), c_Groups_Ozero__class_Ozero(_1135466))), 20507 ^ _780461 : [(20508 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), c_Groups_Ozero__class_Ozero(_1135466)), _1135468)))], (20510 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), _1135470), c_Groups_Ozero__class_Ozero(_1135466))))]], 20511 ^ _780461 : [(20512 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), _1135468), c_Groups_Ozero__class_Ozero(_1135466))))], (20514 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), c_Groups_Ozero__class_Ozero(_1135466)), _1135470)))]]], (20516 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1135466), _1135468), _1135470)), c_Groups_Ozero__class_Ozero(_1135466)))), 20517 ^ _780461 : [(20518 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), c_Groups_Ozero__class_Ozero(_1135466)), _1135468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), _1135470), c_Groups_Ozero__class_Ozero(_1135466)))], (20524 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), _1135468), c_Groups_Ozero__class_Ozero(_1135466))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135466), c_Groups_Ozero__class_Ozero(_1135466)), _1135470))]]]]], (20532 ^ _780461) ^ [_1136056, _1136058, _1136060] : [class_Fields_Olinordered__field__inverse__zero(_1136056), 20535 ^ _780461 : [(20536 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), c_Groups_Ozero__class_Ozero(_1136056)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136056), _1136058), _1136060))), 20541 ^ _780461 : [(20542 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), c_Groups_Ozero__class_Ozero(_1136056)), _1136058)))], (20544 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), c_Groups_Ozero__class_Ozero(_1136056)), _1136060)))]], 20545 ^ _780461 : [(20546 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), _1136058), c_Groups_Ozero__class_Ozero(_1136056))))], (20548 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), _1136060), c_Groups_Ozero__class_Ozero(_1136056))))]]], (20550 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), c_Groups_Ozero__class_Ozero(_1136056)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136056), _1136058), _1136060)))), 20551 ^ _780461 : [(20552 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), c_Groups_Ozero__class_Ozero(_1136056)), _1136058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), c_Groups_Ozero__class_Ozero(_1136056)), _1136060))], (20558 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), _1136058), c_Groups_Ozero__class_Ozero(_1136056))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136056), _1136060), c_Groups_Ozero__class_Ozero(_1136056)))]]]]], (20566 ^ _780461) ^ [_1136646, _1136648, _1136650, _1136652] : [class_Fields_Ofield__inverse__zero(_1136646), 20569 ^ _780461 : [(20586 ^ _780461) ^ [] : [-(_1136648 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136646), _1136650), _1136652)), 20589 ^ _780461 : [(20590 ^ _780461) ^ [] : [_1136652 = c_Groups_Ozero__class_Ozero(_1136646)], (20592 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136646), _1136648), _1136652) = _1136650]], 20593 ^ _780461 : [(20594 ^ _780461) ^ [] : [-(_1136652 = c_Groups_Ozero__class_Ozero(_1136646))], (20596 ^ _780461) ^ [] : [_1136648 = c_Groups_Ozero__class_Ozero(_1136646)]]], (20570 ^ _780461) ^ [] : [_1136648 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1136646), _1136650), _1136652), 20573 ^ _780461 : [(20574 ^ _780461) ^ [] : [-(_1136652 = c_Groups_Ozero__class_Ozero(_1136646)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136646), _1136648), _1136652) = _1136650)], (20580 ^ _780461) ^ [] : [_1136652 = c_Groups_Ozero__class_Ozero(_1136646), -(_1136648 = c_Groups_Ozero__class_Ozero(_1136646))]]]]], (20600 ^ _780461) ^ [_1137140, _1137142, _1137144, _1137146] : [class_Fields_Ofield__inverse__zero(_1137140), 20603 ^ _780461 : [(20620 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137140), _1137142), _1137144) = _1137146), 20623 ^ _780461 : [(20624 ^ _780461) ^ [] : [_1137144 = c_Groups_Ozero__class_Ozero(_1137140)], (20626 ^ _780461) ^ [] : [_1137142 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137140), _1137146), _1137144)]], 20627 ^ _780461 : [(20628 ^ _780461) ^ [] : [-(_1137144 = c_Groups_Ozero__class_Ozero(_1137140))], (20630 ^ _780461) ^ [] : [_1137146 = c_Groups_Ozero__class_Ozero(_1137140)]]], (20604 ^ _780461) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137140), _1137142), _1137144) = _1137146, 20607 ^ _780461 : [(20608 ^ _780461) ^ [] : [-(_1137144 = c_Groups_Ozero__class_Ozero(_1137140)), -(_1137142 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137140), _1137146), _1137144))], (20614 ^ _780461) ^ [] : [_1137144 = c_Groups_Ozero__class_Ozero(_1137140), -(_1137146 = c_Groups_Ozero__class_Ozero(_1137140))]]]]], (20634 ^ _780461) ^ [_1137634, _1137636, _1137638, _1137640] : [class_Fields_Ofield__inverse__zero(_1137634), -(_1137636 = c_Groups_Ozero__class_Ozero(_1137634)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137634), _1137638), _1137636)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137634), _1137640), _1137636)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137634), _1137638), _1137640))], (20644 ^ _780461) ^ [_1137796, _1137798, _1137800, _1137802] : [class_Fields_Ofield__inverse__zero(_1137796), -(_1137798 = c_Groups_Ozero__class_Ozero(_1137796)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137796), _1137798), _1137800)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137796), _1137798), _1137802)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137796), _1137800), _1137802))], (20654 ^ _780461) ^ [_1137958, _1137960, _1137962, _1137964, _1137966] : [class_Fields_Ofield(_1137958), -(_1137960 = c_Groups_Ozero__class_Ozero(_1137958)), -(_1137962 = c_Groups_Ozero__class_Ozero(_1137958)), 20665 ^ _780461 : [(20666 ^ _780461) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137958), _1137964), _1137960) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137958), _1137966), _1137962), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137958), _1137964), _1137962) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137958), _1137966), _1137960))], (20672 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137958), _1137964), _1137962) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137958), _1137966), _1137960), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137958), _1137964), _1137960) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1137958), _1137966), _1137962))]]], (20678 ^ _780461) ^ [_1138407, _1138409, _1138411, _1138413] : [class_Rings_Odivision__ring(_1138407), -(_1138409 = c_Groups_Ozero__class_Ozero(_1138407)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138407), _1138411), _1138409) = _1138413, -(_1138411 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138407), _1138413), _1138409))], (20692 ^ _780461) ^ [_1138637, _1138639, _1138641, _1138643] : [class_Rings_Odivision__ring(_1138637), -(_1138639 = c_Groups_Ozero__class_Ozero(_1138637)), _1138641 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138637), _1138643), _1138639), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138637), _1138641), _1138639) = _1138643)], (20706 ^ _780461) ^ [_1138867, _1138869, _1138871, _1138873] : [class_Rings_Odivision__ring(_1138867), -(_1138869 = c_Groups_Ozero__class_Ozero(_1138867)), 20713 ^ _780461 : [(20714 ^ _780461) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138867), _1138871), _1138869) = _1138873, -(_1138871 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138867), _1138873), _1138869))], (20720 ^ _780461) ^ [] : [_1138871 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138867), _1138873), _1138869), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138867), _1138871), _1138869) = _1138873)]]], (20726 ^ _780461) ^ [_1139195, _1139197, _1139199, _1139201] : [class_Rings_Odivision__ring(_1139195), -(_1139197 = c_Groups_Ozero__class_Ozero(_1139195)), 20733 ^ _780461 : [(20734 ^ _780461) ^ [] : [_1139199 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139195), _1139201), _1139197), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139195), _1139199), _1139197) = _1139201)], (20740 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139195), _1139199), _1139197) = _1139201, -(_1139199 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139195), _1139201), _1139197))]]], (20746 ^ _780461) ^ [_1139523, _1139525, _1139527] : [class_Rings_Odivision__ring(_1139523), -(_1139525 = c_Groups_Ozero__class_Ozero(_1139523)), 20753 ^ _780461 : [(20754 ^ _780461) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139523), _1139527), _1139525) = c_Groups_Oone__class_Oone(_1139523), -(_1139527 = _1139525)], (20760 ^ _780461) ^ [] : [_1139527 = _1139525, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139523), _1139527), _1139525) = c_Groups_Oone__class_Oone(_1139523))]]], (20766 ^ _780461) ^ [_1139825, _1139827] : [class_Rings_Odivision__ring(_1139825), -(_1139827 = c_Groups_Ozero__class_Ozero(_1139825)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139825), _1139827), _1139827) = c_Groups_Oone__class_Oone(_1139825))], (20776 ^ _780461) ^ [_1139939, _1139941] : [class_Rings_Odivision__ring__inverse__zero(_1139939), 20779 ^ _780461 : [(20780 ^ _780461) ^ [] : [_1139941 = c_Groups_Ozero__class_Ozero(_1139939), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139939), _1139941), _1139941) = c_Groups_Ozero__class_Ozero(_1139939))], (20786 ^ _780461) ^ [] : [-(_1139941 = c_Groups_Ozero__class_Ozero(_1139939)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1139939), _1139941), _1139941) = c_Groups_Oone__class_Oone(_1139939))]]], (20792 ^ _780461) ^ [_1140161, _1140163, _1140165] : [class_Rings_Odivision__ring(_1140161), -(_1140163 = c_Groups_Ozero__class_Ozero(_1140161)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140161), hAPP(c_Groups_Ouminus__class_Ouminus(_1140161), _1140165)), hAPP(c_Groups_Ouminus__class_Ouminus(_1140161), _1140163)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140161), _1140165), _1140163))], (20802 ^ _780461) ^ [_1140309, _1140311, _1140313] : [class_Rings_Odivision__ring(_1140309), -(_1140311 = c_Groups_Ozero__class_Ozero(_1140309)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1140309), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140309), _1140313), _1140311)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140309), _1140313), hAPP(c_Groups_Ouminus__class_Ouminus(_1140309), _1140311)))], (20812 ^ _780461) ^ [_1140457, _1140459, _1140461, _1140463] : [class_Fields_Ofield(_1140457), -(_1140459 = c_Groups_Ozero__class_Ozero(_1140457)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1140457), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140457), _1140461), _1140459)), _1140463) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140457), hAPP(hAPP(c_Power_Opower__class_Opower(_1140457), _1140461), _1140463)), hAPP(hAPP(c_Power_Opower__class_Opower(_1140457), _1140459), _1140463)))], (20822 ^ _780461) ^ [_1140635, _1140637, _1140639] : [class_Fields_Olinordered__field(_1140635), -(_1140637 = c_Groups_Ozero__class_Ozero(_1140635)), -(hAPP(c_Groups_Oabs__class_Oabs(_1140635), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140635), _1140639), _1140637)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140635), hAPP(c_Groups_Oabs__class_Oabs(_1140635), _1140639)), hAPP(c_Groups_Oabs__class_Oabs(_1140635), _1140637)))], (20832 ^ _780461) ^ [_1140793, _1140795, _1140797] : [class_Fields_Ofield__inverse__zero(_1140793), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140793), c_Groups_Oone__class_Oone(_1140793)), hAPP(hAPP(c_Power_Opower__class_Opower(_1140793), _1140795), _1140797)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1140793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1140793), c_Groups_Oone__class_Oone(_1140793)), _1140795)), _1140797))], (20838 ^ _780461) ^ [_1140942, _1140944] : [c_Nat__Transfer_Ois__nat(_1140942), c_Nat__Transfer_Ois__nat(_1140944), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1140942, _1140944)))], (20848 ^ _780461) ^ [_1141071, _1141073, _1141075] : [class_Fields_Olinordered__field(_1141071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141071), _1141073), c_Groups_Ozero__class_Ozero(_1141071))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141071), _1141075), c_Groups_Ozero__class_Ozero(_1141071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141071), c_Groups_Ozero__class_Ozero(_1141071)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141071), _1141073), _1141075))))], (20862 ^ _780461) ^ [_1141326, _1141328, _1141330] : [class_Fields_Olinordered__field(_1141326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141326), _1141328), c_Groups_Ozero__class_Ozero(_1141326))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141326), c_Groups_Ozero__class_Ozero(_1141326)), _1141330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141326), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141326), _1141328), _1141330)), c_Groups_Ozero__class_Ozero(_1141326))))], (20876 ^ _780461) ^ [_1141581, _1141583, _1141585, _1141587, _1141589] : [class_Fields_Olinordered__field(_1141581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141581), c_Groups_Ozero__class_Ozero(_1141581)), _1141583)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141581), _1141583), _1141585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141581), c_Groups_Ozero__class_Ozero(_1141581)), _1141587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141581), _1141587), _1141589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141581), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141581), _1141583), _1141589)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1141581), _1141585), _1141587))))], (20898 ^ _780461) ^ [_1142004, _1142006, _1142008, _1142010, _1142012] : [class_Fields_Olinordered__field(_1142004), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142004), c_Groups_Ozero__class_Ozero(_1142004)), _1142006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142004), _1142006), _1142008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142004), c_Groups_Ozero__class_Ozero(_1142004)), _1142010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142004), _1142010), _1142012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142004), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142004), _1142006), _1142012)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142004), _1142008), _1142010))))], (20920 ^ _780461) ^ [_1142427, _1142429, _1142431, _1142433, _1142435] : [class_Fields_Olinordered__field(_1142427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142427), c_Groups_Ozero__class_Ozero(_1142427)), _1142429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142427), _1142429), _1142431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142427), c_Groups_Ozero__class_Ozero(_1142427)), _1142433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142427), _1142433), _1142435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142427), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142427), _1142429), _1142435)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142427), _1142431), _1142433))))], (20942 ^ _780461) ^ [_1142850, _1142852, _1142854] : [class_Fields_Olinordered__field(_1142850), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142850), c_Groups_Ozero__class_Ozero(_1142850)), _1142852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142850), _1142854), c_Groups_Ozero__class_Ozero(_1142850))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142850), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1142850), _1142852), _1142854)), c_Groups_Ozero__class_Ozero(_1142850))))], (20956 ^ _780461) ^ [_1143105, _1143107, _1143109] : [class_Fields_Olinordered__field(_1143105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143105), c_Groups_Ozero__class_Ozero(_1143105)), _1143107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143105), c_Groups_Ozero__class_Ozero(_1143105)), _1143109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143105), c_Groups_Ozero__class_Ozero(_1143105)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143105), _1143107), _1143109))))], (20970 ^ _780461) ^ [_1143360, _1143362, _1143364, _1143366] : [class_Fields_Olinordered__field(_1143360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143360), _1143362), _1143364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143360), _1143366), c_Groups_Ozero__class_Ozero(_1143360))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143360), c_Groups_Ozero__class_Ozero(_1143360)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143360), _1143362), _1143364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143360), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143360), _1143366), _1143362)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143360), _1143366), _1143364))))], (20988 ^ _780461) ^ [_1143719, _1143721, _1143723, _1143725] : [class_Fields_Olinordered__field(_1143719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143719), _1143721), _1143723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143719), c_Groups_Ozero__class_Ozero(_1143719)), _1143725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143719), c_Groups_Ozero__class_Ozero(_1143719)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143719), _1143723), _1143721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143719), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143719), _1143725), _1143723)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1143719), _1143725), _1143721))))], (21006 ^ _780461) ^ [_1144078, _1144080, _1144082, _1144084] : [class_Fields_Olinordered__field(_1144078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144078), _1144080), c_Groups_Ozero__class_Ozero(_1144078))), 21013 ^ _780461 : [(21014 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144078), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144078), _1144082), _1144080)), _1144084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144078), _1144084), _1144080)), _1144082)))], (21020 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144078), _1144084), _1144080)), _1144082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144078), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144078), _1144082), _1144080)), _1144084)))]]], (21026 ^ _780461) ^ [_1144459, _1144461, _1144463, _1144465] : [class_Fields_Olinordered__field(_1144459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144459), _1144461), c_Groups_Ozero__class_Ozero(_1144459))), 21033 ^ _780461 : [(21034 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144459), _1144463), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144459), _1144465), _1144461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144459), _1144465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144459), _1144463), _1144461))))], (21040 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144459), _1144465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144459), _1144463), _1144461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144459), _1144463), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144459), _1144465), _1144461))))]]], (21046 ^ _780461) ^ [_1144840, _1144842, _1144844, _1144846] : [class_Fields_Olinordered__field(_1144840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144840), c_Groups_Ozero__class_Ozero(_1144840)), _1144842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144840), _1144844), _1144842)), _1144846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144840), _1144844), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1144840), _1144846), _1144842))))], (21060 ^ _780461) ^ [_1145109, _1145111, _1145113, _1145115] : [class_Fields_Olinordered__field(_1145109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145109), c_Groups_Ozero__class_Ozero(_1145109)), _1145111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145109), _1145113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145109), _1145115), _1145111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145109), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145109), _1145113), _1145111)), _1145115)))], (21074 ^ _780461) ^ [_1145378, _1145380, _1145382, _1145384] : [class_Fields_Olinordered__field(_1145378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145378), c_Groups_Ozero__class_Ozero(_1145378)), _1145380)), 21081 ^ _780461 : [(21082 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145378), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145378), _1145382), _1145380)), _1145384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145378), _1145382), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145378), _1145384), _1145380))))], (21088 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145378), _1145382), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145378), _1145384), _1145380))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145378), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145378), _1145382), _1145380)), _1145384)))]]], (21094 ^ _780461) ^ [_1145759, _1145761, _1145763, _1145765] : [class_Fields_Olinordered__field(_1145759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145759), c_Groups_Ozero__class_Ozero(_1145759)), _1145761)), 21101 ^ _780461 : [(21102 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145759), _1145763), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145759), _1145765), _1145761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145759), _1145763), _1145761)), _1145765)))], (21108 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145759), _1145763), _1145761)), _1145765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145759), _1145763), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1145759), _1145765), _1145761))))]]], (21114 ^ _780461) ^ [_1146140, _1146142, _1146144, _1146146] : [class_Fields_Olinordered__field__inverse__zero(_1146140), 21117 ^ _780461 : [(21144 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146140), _1146142), _1146144)), _1146146))), 21147 ^ _780461 : [(21148 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), c_Groups_Ozero__class_Ozero(_1146140)), _1146144)))], (21150 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), _1146142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146140), _1146146), _1146144)))]], 21151 ^ _780461 : [(21152 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), c_Groups_Ozero__class_Ozero(_1146140)), _1146144))], (21154 ^ _780461) ^ [] : [21155 ^ _780461 : [(21156 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), _1146144), c_Groups_Ozero__class_Ozero(_1146140))))], (21158 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146140), _1146146), _1146144)), _1146142))]], 21159 ^ _780461 : [(21160 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), _1146144), c_Groups_Ozero__class_Ozero(_1146140)))], (21162 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), c_Groups_Ozero__class_Ozero(_1146140)), _1146146))]]]]], (21118 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1146140), _1146142), _1146144)), _1146146)), 21121 ^ _780461 : [(21122 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), c_Groups_Ozero__class_Ozero(_1146140)), _1146144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), _1146142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146140), _1146146), _1146144))))], (21128 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), c_Groups_Ozero__class_Ozero(_1146140)), _1146144))), 21131 ^ _780461 : [(21132 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), _1146144), c_Groups_Ozero__class_Ozero(_1146140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146140), _1146146), _1146144)), _1146142)))], (21138 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), _1146144), c_Groups_Ozero__class_Ozero(_1146140)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146140), c_Groups_Ozero__class_Ozero(_1146140)), _1146146)))]]]]]]], (21166 ^ _780461) ^ [_1147093, _1147095, _1147097, _1147099] : [class_Fields_Olinordered__field__inverse__zero(_1147093), 21169 ^ _780461 : [(21196 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147095), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147093), _1147097), _1147099)))), 21199 ^ _780461 : [(21200 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), c_Groups_Ozero__class_Ozero(_1147093)), _1147099)))], (21202 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147093), _1147095), _1147099)), _1147097))]], 21203 ^ _780461 : [(21204 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), c_Groups_Ozero__class_Ozero(_1147093)), _1147099))], (21206 ^ _780461) ^ [] : [21207 ^ _780461 : [(21208 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147099), c_Groups_Ozero__class_Ozero(_1147093))))], (21210 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147093), _1147095), _1147099)))]], 21211 ^ _780461 : [(21212 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147099), c_Groups_Ozero__class_Ozero(_1147093)))], (21214 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147095), c_Groups_Ozero__class_Ozero(_1147093)))]]]]], (21170 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147095), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1147093), _1147097), _1147099))), 21173 ^ _780461 : [(21174 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), c_Groups_Ozero__class_Ozero(_1147093)), _1147099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147093), _1147095), _1147099)), _1147097)))], (21180 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), c_Groups_Ozero__class_Ozero(_1147093)), _1147099))), 21183 ^ _780461 : [(21184 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147099), c_Groups_Ozero__class_Ozero(_1147093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147093), _1147095), _1147099))))], (21190 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147099), c_Groups_Ozero__class_Ozero(_1147093)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147093), _1147095), c_Groups_Ozero__class_Ozero(_1147093))))]]]]]]], (21218 ^ _780461) ^ [_1148058] : [c_Nat__Transfer_Ois__nat(_1148058), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148058)))], (21224 ^ _780461) ^ [_1148131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1148131)), -(c_Nat__Transfer_Ois__nat(_1148131))], (21230 ^ _780461) ^ [_1148210, _1148212, _1148214, _1148216] : [class_Fields_Ofield__inverse__zero(_1148210), -(_1148212 = c_Groups_Ozero__class_Ozero(_1148210)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148210), _1148214), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148210), _1148216), _1148212)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148210), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148210), _1148216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148210), _1148214), _1148212))), _1148212))], (21240 ^ _780461) ^ [_1148388, _1148390, _1148392, _1148394] : [class_Fields_Ofield(_1148388), -(_1148390 = c_Groups_Ozero__class_Ozero(_1148388)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148388), _1148392), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148388), _1148394), _1148390)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148388), _1148390), _1148392)), _1148394)), _1148390))], (21250 ^ _780461) ^ [_1148566, _1148568, _1148570, _1148572] : [class_Fields_Ofield__inverse__zero(_1148566), -(_1148568 = c_Groups_Ozero__class_Ozero(_1148566)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148566), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148566), _1148570), _1148568)), _1148572) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148566), _1148570), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148566), _1148572), _1148568))), _1148568))], (21260 ^ _780461) ^ [_1148744, _1148746, _1148748, _1148750] : [class_Fields_Ofield(_1148744), -(_1148746 = c_Groups_Ozero__class_Ozero(_1148744)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148744), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148744), _1148748), _1148746)), _1148750) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148744), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148744), _1148748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148744), _1148746), _1148750))), _1148746))], (21270 ^ _780461) ^ [_1148922, _1148924, _1148926, _1148928, _1148930] : [class_Fields_Ofield(_1148922), -(_1148924 = c_Groups_Ozero__class_Ozero(_1148922)), -(_1148926 = c_Groups_Ozero__class_Ozero(_1148922)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148922), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148922), _1148928), _1148924)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148922), _1148930), _1148926)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1148922), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148922), _1148928), _1148926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148922), _1148930), _1148924))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148922), _1148924), _1148926)))], (21284 ^ _780461) ^ [_1149169, _1149171, _1149173, _1149175, _1149177] : [class_Fields_Ofield(_1149169), -(_1149171 = c_Groups_Ozero__class_Ozero(_1149169)), -(_1149173 = c_Groups_Ozero__class_Ozero(_1149169)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149169), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149169), _1149175), _1149171)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149169), _1149177), _1149173)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149169), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149169), _1149175), _1149173)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149169), _1149177), _1149171))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149169), _1149171), _1149173)))], (21298 ^ _780461) ^ [_1149416, _1149418, _1149420, _1149422] : [class_Fields_Ofield(_1149416), -(_1149418 = c_Groups_Ozero__class_Ozero(_1149416)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149416), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149416), _1149420), _1149418)), _1149422) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149416), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149416), _1149420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149416), _1149418), _1149422))), _1149418))], (21308 ^ _780461) ^ [_1149594, _1149596, _1149598, _1149600] : [class_Fields_Ofield(_1149594), -(_1149596 = c_Groups_Ozero__class_Ozero(_1149594)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149594), _1149598), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149594), _1149600), _1149596)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149594), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149594), _1149596), _1149598)), _1149600)), _1149596))], (21318 ^ _780461) ^ [_1149772, _1149774, _1149776, _1149778] : [class_Fields_Ofield__inverse__zero(_1149772), class_Int_Onumber(_1149772), 21325 ^ _780461 : [(21342 ^ _780461) ^ [] : [-(_1149774 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149772), _1149776), hAPP(c_Int_Onumber__class_Onumber__of(_1149772), _1149778))), 21345 ^ _780461 : [(21346 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1149772), _1149778) = c_Groups_Ozero__class_Ozero(_1149772)], (21348 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149772), _1149774), hAPP(c_Int_Onumber__class_Onumber__of(_1149772), _1149778)) = _1149776]], 21349 ^ _780461 : [(21350 ^ _780461) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1149772), _1149778) = c_Groups_Ozero__class_Ozero(_1149772))], (21352 ^ _780461) ^ [] : [_1149774 = c_Groups_Ozero__class_Ozero(_1149772)]]], (21326 ^ _780461) ^ [] : [_1149774 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1149772), _1149776), hAPP(c_Int_Onumber__class_Onumber__of(_1149772), _1149778)), 21329 ^ _780461 : [(21330 ^ _780461) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1149772), _1149778) = c_Groups_Ozero__class_Ozero(_1149772)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149772), _1149774), hAPP(c_Int_Onumber__class_Onumber__of(_1149772), _1149778)) = _1149776)], (21336 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1149772), _1149778) = c_Groups_Ozero__class_Ozero(_1149772), -(_1149774 = c_Groups_Ozero__class_Ozero(_1149772))]]]]], (21356 ^ _780461) ^ [_1150382, _1150384, _1150386, _1150388] : [class_Fields_Ofield__inverse__zero(_1150382), class_Int_Onumber(_1150382), 21363 ^ _780461 : [(21380 ^ _780461) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1150382), _1150384) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150382), _1150386), _1150388)), 21383 ^ _780461 : [(21384 ^ _780461) ^ [] : [_1150388 = c_Groups_Ozero__class_Ozero(_1150382)], (21386 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150382), hAPP(c_Int_Onumber__class_Onumber__of(_1150382), _1150384)), _1150388) = _1150386]], 21387 ^ _780461 : [(21388 ^ _780461) ^ [] : [-(_1150388 = c_Groups_Ozero__class_Ozero(_1150382))], (21390 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1150382), _1150384) = c_Groups_Ozero__class_Ozero(_1150382)]]], (21364 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1150382), _1150384) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150382), _1150386), _1150388), 21367 ^ _780461 : [(21368 ^ _780461) ^ [] : [-(_1150388 = c_Groups_Ozero__class_Ozero(_1150382)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150382), hAPP(c_Int_Onumber__class_Onumber__of(_1150382), _1150384)), _1150388) = _1150386)], (21374 ^ _780461) ^ [] : [_1150388 = c_Groups_Ozero__class_Ozero(_1150382), -(hAPP(c_Int_Onumber__class_Onumber__of(_1150382), _1150384) = c_Groups_Ozero__class_Ozero(_1150382))]]]]], (21394 ^ _780461) ^ [_1150977, _1150979, _1150981, _1150983] : [class_Fields_Ofield__inverse__zero(_1150977), class_Int_Onumber(_1150977), 21401 ^ _780461 : [(21418 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150977), _1150979), _1150981) = hAPP(c_Int_Onumber__class_Onumber__of(_1150977), _1150983)), 21421 ^ _780461 : [(21422 ^ _780461) ^ [] : [_1150981 = c_Groups_Ozero__class_Ozero(_1150977)], (21424 ^ _780461) ^ [] : [_1150979 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150977), hAPP(c_Int_Onumber__class_Onumber__of(_1150977), _1150983)), _1150981)]], 21425 ^ _780461 : [(21426 ^ _780461) ^ [] : [-(_1150981 = c_Groups_Ozero__class_Ozero(_1150977))], (21428 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1150977), _1150983) = c_Groups_Ozero__class_Ozero(_1150977)]]], (21402 ^ _780461) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1150977), _1150979), _1150981) = hAPP(c_Int_Onumber__class_Onumber__of(_1150977), _1150983), 21405 ^ _780461 : [(21406 ^ _780461) ^ [] : [-(_1150981 = c_Groups_Ozero__class_Ozero(_1150977)), -(_1150979 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150977), hAPP(c_Int_Onumber__class_Onumber__of(_1150977), _1150983)), _1150981))], (21412 ^ _780461) ^ [] : [_1150981 = c_Groups_Ozero__class_Ozero(_1150977), -(hAPP(c_Int_Onumber__class_Onumber__of(_1150977), _1150983) = c_Groups_Ozero__class_Ozero(_1150977))]]]]], (21432 ^ _780461) ^ [_1151572, _1151574, _1151576, _1151578] : [class_Fields_Ofield__inverse__zero(_1151572), class_Int_Onumber(_1151572), 21439 ^ _780461 : [(21456 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151572), _1151574), hAPP(c_Int_Onumber__class_Onumber__of(_1151572), _1151576)) = _1151578), 21459 ^ _780461 : [(21460 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1151572), _1151576) = c_Groups_Ozero__class_Ozero(_1151572)], (21462 ^ _780461) ^ [] : [_1151574 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151572), _1151578), hAPP(c_Int_Onumber__class_Onumber__of(_1151572), _1151576))]], 21463 ^ _780461 : [(21464 ^ _780461) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1151572), _1151576) = c_Groups_Ozero__class_Ozero(_1151572))], (21466 ^ _780461) ^ [] : [_1151578 = c_Groups_Ozero__class_Ozero(_1151572)]]], (21440 ^ _780461) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1151572), _1151574), hAPP(c_Int_Onumber__class_Onumber__of(_1151572), _1151576)) = _1151578, 21443 ^ _780461 : [(21444 ^ _780461) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1151572), _1151576) = c_Groups_Ozero__class_Ozero(_1151572)), -(_1151574 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151572), _1151578), hAPP(c_Int_Onumber__class_Onumber__of(_1151572), _1151576)))], (21450 ^ _780461) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1151572), _1151576) = c_Groups_Ozero__class_Ozero(_1151572), -(_1151578 = c_Groups_Ozero__class_Ozero(_1151572))]]]]], (21470 ^ _780461) ^ [_1152182, _1152184, _1152186] : [class_Fields_Olinordered__field(_1152182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152182), _1152184), _1152186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152182), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152182), _1152184), _1152186)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152182), c_Groups_Oone__class_Oone(_1152182)), c_Groups_Oone__class_Oone(_1152182)))), _1152186)))], (21480 ^ _780461) ^ [_1152397, _1152399, _1152401] : [class_Fields_Olinordered__field(_1152397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152397), _1152399), _1152401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152397), _1152399), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152397), _1152399), _1152401)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1152397), c_Groups_Oone__class_Oone(_1152397)), c_Groups_Oone__class_Oone(_1152397))))))], (21490 ^ _780461) ^ [_1152612, _1152614] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152612), _1152614), hAPP(c_Int_Onumber__class_Onumber__of(_1152612), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1152612)), class_Fields_Ofield__inverse__zero(_1152612), class_Int_Onumber__ring(_1152612)], (21500 ^ _780461) ^ [_1152767, _1152769, _1152771] : [class_Fields_Olinordered__field__inverse__zero(_1152767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152767), c_Groups_Ozero__class_Ozero(_1152767)), _1152769)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152767), hAPP(c_Groups_Oabs__class_Oabs(_1152767), _1152771)), _1152769) = hAPP(c_Groups_Oabs__class_Oabs(_1152767), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152767), _1152771), _1152769)))], (21510 ^ _780461) ^ [_1152968, _1152970] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1152968), _1152970), hAPP(c_Int_Onumber__class_Onumber__of(_1152968), c_Int_OBit1(c_Int_OPls))) = _1152970), class_Fields_Ofield(_1152968), class_Int_Onumber__ring(_1152968)], (21520 ^ _780461) ^ [_1153119, _1153121] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153119), _1153121), hAPP(c_Int_Onumber__class_Onumber__of(_1153119), c_Int_OBit1(c_Int_OPls))) = _1153121), class_Fields_Ofield(_1153119), class_Int_Onumber__ring(_1153119)], (21530 ^ _780461) ^ [_1153270, _1153272] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153270), _1153272), hAPP(c_Int_Onumber__class_Onumber__of(_1153270), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1153270), _1153272)), class_Fields_Ofield__inverse__zero(_1153270), class_Int_Onumber__ring(_1153270)], (21540 ^ _780461) ^ [] : [-(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))], (21542 ^ _780461) ^ [_1153449, _1153451, _1153453, _1153455] : [class_Fields_Olinordered__field__inverse__zero(_1153449), 21545 ^ _780461 : [(21572 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153449), _1153451), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153449), _1153453), _1153455)))), 21575 ^ _780461 : [(21576 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153449), c_Groups_Ozero__class_Ozero(_1153449)), _1153455)))], (21578 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153449), _1153451), _1153455)), _1153453))]], 21579 ^ _780461 : [(21580 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153449), c_Groups_Ozero__class_Ozero(_1153449)), _1153455))], (21582 ^ _780461) ^ [] : [21583 ^ _780461 : [(21584 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153449), _1153455), c_Groups_Ozero__class_Ozero(_1153449))))], (21586 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153449), _1153453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153449), _1153451), _1153455)))]], 21587 ^ _780461 : [(21588 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153449), _1153455), c_Groups_Ozero__class_Ozero(_1153449)))], (21590 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153449), _1153451), c_Groups_Ozero__class_Ozero(_1153449)))]]]]], (21546 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153449), _1153451), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1153449), _1153453), _1153455))), 21549 ^ _780461 : [(21550 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153449), c_Groups_Ozero__class_Ozero(_1153449)), _1153455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153449), _1153451), _1153455)), _1153453)))], (21556 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153449), c_Groups_Ozero__class_Ozero(_1153449)), _1153455))), 21559 ^ _780461 : [(21560 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153449), _1153455), c_Groups_Ozero__class_Ozero(_1153449))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153449), _1153453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153449), _1153451), _1153455))))], (21566 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153449), _1153455), c_Groups_Ozero__class_Ozero(_1153449)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153449), _1153451), c_Groups_Ozero__class_Ozero(_1153449))))]]]]]]], (21594 ^ _780461) ^ [_1154402, _1154404, _1154406, _1154408] : [class_Fields_Olinordered__field__inverse__zero(_1154402), 21597 ^ _780461 : [(21624 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154402), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154402), _1154404), _1154406)), _1154408))), 21627 ^ _780461 : [(21628 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154402), c_Groups_Ozero__class_Ozero(_1154402)), _1154406)))], (21630 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154402), _1154404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154402), _1154408), _1154406)))]], 21631 ^ _780461 : [(21632 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154402), c_Groups_Ozero__class_Ozero(_1154402)), _1154406))], (21634 ^ _780461) ^ [] : [21635 ^ _780461 : [(21636 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154402), _1154406), c_Groups_Ozero__class_Ozero(_1154402))))], (21638 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154402), _1154408), _1154406)), _1154404))]], 21639 ^ _780461 : [(21640 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154402), _1154406), c_Groups_Ozero__class_Ozero(_1154402)))], (21642 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154402), c_Groups_Ozero__class_Ozero(_1154402)), _1154408))]]]]], (21598 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154402), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154402), _1154404), _1154406)), _1154408)), 21601 ^ _780461 : [(21602 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154402), c_Groups_Ozero__class_Ozero(_1154402)), _1154406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154402), _1154404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154402), _1154408), _1154406))))], (21608 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154402), c_Groups_Ozero__class_Ozero(_1154402)), _1154406))), 21611 ^ _780461 : [(21612 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154402), _1154406), c_Groups_Ozero__class_Ozero(_1154402))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154402), _1154408), _1154406)), _1154404)))], (21618 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154402), _1154406), c_Groups_Ozero__class_Ozero(_1154402)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154402), c_Groups_Ozero__class_Ozero(_1154402)), _1154408)))]]]]]]], (21646 ^ _780461) ^ [_1155355, _1155357, _1155359, _1155361] : [class_Fields_Olinordered__field(_1155355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155355), c_Groups_Ozero__class_Ozero(_1155355)), _1155357)), 21653 ^ _780461 : [(21654 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155355), _1155359), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155355), _1155361), _1155357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155355), _1155359), _1155357)), _1155361)))], (21660 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155355), _1155359), _1155357)), _1155361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155355), _1155359), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155355), _1155361), _1155357))))]]], (21666 ^ _780461) ^ [_1155736, _1155738, _1155740, _1155742] : [class_Fields_Olinordered__field(_1155736), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155736), c_Groups_Ozero__class_Ozero(_1155736)), _1155738)), 21673 ^ _780461 : [(21674 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155736), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155736), _1155740), _1155738)), _1155742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155736), _1155740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155736), _1155742), _1155738))))], (21680 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155736), _1155740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155736), _1155742), _1155738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155736), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1155736), _1155740), _1155738)), _1155742)))]]], (21686 ^ _780461) ^ [_1156117, _1156119, _1156121, _1156123] : [class_Fields_Olinordered__field(_1156117), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156117), c_Groups_Ozero__class_Ozero(_1156117)), _1156119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156117), _1156121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156117), _1156123), _1156119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156117), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156117), _1156121), _1156119)), _1156123)))], (21700 ^ _780461) ^ [_1156386, _1156388, _1156390, _1156392] : [class_Fields_Olinordered__field(_1156386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156386), c_Groups_Ozero__class_Ozero(_1156386)), _1156388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156386), _1156390), _1156388)), _1156392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156386), _1156390), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156386), _1156392), _1156388))))], (21714 ^ _780461) ^ [_1156655, _1156657, _1156659, _1156661] : [class_Fields_Olinordered__field(_1156655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156655), _1156657), c_Groups_Ozero__class_Ozero(_1156655))), 21721 ^ _780461 : [(21722 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156655), _1156659), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156655), _1156661), _1156657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156655), _1156661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156655), _1156659), _1156657))))], (21728 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156655), _1156661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156655), _1156659), _1156657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156655), _1156659), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156655), _1156661), _1156657))))]]], (21734 ^ _780461) ^ [_1157036, _1157038, _1157040, _1157042] : [class_Fields_Olinordered__field(_1157036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157036), _1157038), c_Groups_Ozero__class_Ozero(_1157036))), 21741 ^ _780461 : [(21742 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157036), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157036), _1157040), _1157038)), _1157042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157036), _1157042), _1157038)), _1157040)))], (21748 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157036), _1157042), _1157038)), _1157040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157036), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157036), _1157040), _1157038)), _1157042)))]]], (21754 ^ _780461) ^ [_1157417, _1157419, _1157421, _1157423] : [class_Fields_Olinordered__field(_1157417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157417), _1157419), _1157421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157417), c_Groups_Ozero__class_Ozero(_1157417)), _1157423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157417), c_Groups_Ozero__class_Ozero(_1157417)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157417), _1157421), _1157419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157417), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157417), _1157423), _1157421)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157417), _1157423), _1157419))))], (21772 ^ _780461) ^ [_1157776, _1157778, _1157780, _1157782] : [class_Fields_Olinordered__field__inverse__zero(_1157776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157776), _1157778), _1157780)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157776), _1157782), c_Groups_Ozero__class_Ozero(_1157776))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157776), c_Groups_Ozero__class_Ozero(_1157776)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157776), _1157778), _1157780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157776), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157776), _1157782), _1157778)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1157776), _1157782), _1157780))))], (21790 ^ _780461) ^ [_1158135, _1158137, _1158139, _1158141] : [class_Fields_Olinordered__field__inverse__zero(_1158135), class_Int_Onumber(_1158135), 21797 ^ _780461 : [(21824 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158135), _1158137), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139))), _1158141))), 21827 ^ _780461 : [(21828 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), c_Groups_Ozero__class_Ozero(_1158135)), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139))))], (21830 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), _1158137), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158135), _1158141), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139))))]], 21831 ^ _780461 : [(21832 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), c_Groups_Ozero__class_Ozero(_1158135)), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139)))], (21834 ^ _780461) ^ [] : [21835 ^ _780461 : [(21836 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139)), c_Groups_Ozero__class_Ozero(_1158135))))], (21838 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158135), _1158141), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139))), _1158137))]], 21839 ^ _780461 : [(21840 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139)), c_Groups_Ozero__class_Ozero(_1158135)))], (21842 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), c_Groups_Ozero__class_Ozero(_1158135)), _1158141))]]]]], (21798 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1158135), _1158137), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139))), _1158141)), 21801 ^ _780461 : [(21802 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), c_Groups_Ozero__class_Ozero(_1158135)), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), _1158137), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158135), _1158141), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139)))))], (21808 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), c_Groups_Ozero__class_Ozero(_1158135)), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139)))), 21811 ^ _780461 : [(21812 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139)), c_Groups_Ozero__class_Ozero(_1158135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158135), _1158141), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139))), _1158137)))], (21818 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), hAPP(c_Int_Onumber__class_Onumber__of(_1158135), _1158139)), c_Groups_Ozero__class_Ozero(_1158135)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158135), c_Groups_Ozero__class_Ozero(_1158135)), _1158141)))]]]]]]], (21846 ^ _780461) ^ [_1159249, _1159251, _1159253, _1159255] : [class_Fields_Olinordered__field__inverse__zero(_1159249), class_Int_Onumber(_1159249), 21853 ^ _780461 : [(21880 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159249), _1159251), _1159253)), hAPP(c_Int_Onumber__class_Onumber__of(_1159249), _1159255)))), 21883 ^ _780461 : [(21884 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), c_Groups_Ozero__class_Ozero(_1159249)), _1159253)))], (21886 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), _1159251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159249), hAPP(c_Int_Onumber__class_Onumber__of(_1159249), _1159255)), _1159253)))]], 21887 ^ _780461 : [(21888 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), c_Groups_Ozero__class_Ozero(_1159249)), _1159253))], (21890 ^ _780461) ^ [] : [21891 ^ _780461 : [(21892 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), _1159253), c_Groups_Ozero__class_Ozero(_1159249))))], (21894 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159249), hAPP(c_Int_Onumber__class_Onumber__of(_1159249), _1159255)), _1159253)), _1159251))]], 21895 ^ _780461 : [(21896 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), _1159253), c_Groups_Ozero__class_Ozero(_1159249)))], (21898 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), c_Groups_Ozero__class_Ozero(_1159249)), hAPP(c_Int_Onumber__class_Onumber__of(_1159249), _1159255)))]]]]], (21854 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1159249), _1159251), _1159253)), hAPP(c_Int_Onumber__class_Onumber__of(_1159249), _1159255))), 21857 ^ _780461 : [(21858 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), c_Groups_Ozero__class_Ozero(_1159249)), _1159253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), _1159251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159249), hAPP(c_Int_Onumber__class_Onumber__of(_1159249), _1159255)), _1159253))))], (21864 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), c_Groups_Ozero__class_Ozero(_1159249)), _1159253))), 21867 ^ _780461 : [(21868 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), _1159253), c_Groups_Ozero__class_Ozero(_1159249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159249), hAPP(c_Int_Onumber__class_Onumber__of(_1159249), _1159255)), _1159253)), _1159251)))], (21874 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), _1159253), c_Groups_Ozero__class_Ozero(_1159249)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159249), c_Groups_Ozero__class_Ozero(_1159249)), hAPP(c_Int_Onumber__class_Onumber__of(_1159249), _1159255))))]]]]]]], (21902 ^ _780461) ^ [_1160318, _1160320, _1160322, _1160324] : [class_Fields_Olinordered__field__inverse__zero(_1160318), class_Int_Onumber(_1160318), 21909 ^ _780461 : [(21936 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), hAPP(c_Int_Onumber__class_Onumber__of(_1160318), _1160320)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160318), _1160322), _1160324)))), 21939 ^ _780461 : [(21940 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), c_Groups_Ozero__class_Ozero(_1160318)), _1160324)))], (21942 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160318), hAPP(c_Int_Onumber__class_Onumber__of(_1160318), _1160320)), _1160324)), _1160322))]], 21943 ^ _780461 : [(21944 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), c_Groups_Ozero__class_Ozero(_1160318)), _1160324))], (21946 ^ _780461) ^ [] : [21947 ^ _780461 : [(21948 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), _1160324), c_Groups_Ozero__class_Ozero(_1160318))))], (21950 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), _1160322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160318), hAPP(c_Int_Onumber__class_Onumber__of(_1160318), _1160320)), _1160324)))]], 21951 ^ _780461 : [(21952 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), _1160324), c_Groups_Ozero__class_Ozero(_1160318)))], (21954 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), hAPP(c_Int_Onumber__class_Onumber__of(_1160318), _1160320)), c_Groups_Ozero__class_Ozero(_1160318)))]]]]], (21910 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), hAPP(c_Int_Onumber__class_Onumber__of(_1160318), _1160320)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1160318), _1160322), _1160324))), 21913 ^ _780461 : [(21914 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), c_Groups_Ozero__class_Ozero(_1160318)), _1160324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160318), hAPP(c_Int_Onumber__class_Onumber__of(_1160318), _1160320)), _1160324)), _1160322)))], (21920 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), c_Groups_Ozero__class_Ozero(_1160318)), _1160324))), 21923 ^ _780461 : [(21924 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), _1160324), c_Groups_Ozero__class_Ozero(_1160318))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), _1160322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160318), hAPP(c_Int_Onumber__class_Onumber__of(_1160318), _1160320)), _1160324))))], (21930 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), _1160324), c_Groups_Ozero__class_Ozero(_1160318)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160318), hAPP(c_Int_Onumber__class_Onumber__of(_1160318), _1160320)), c_Groups_Ozero__class_Ozero(_1160318))))]]]]]]], (21958 ^ _780461) ^ [_1161387, _1161389, _1161391, _1161393] : [class_Fields_Olinordered__field__inverse__zero(_1161387), class_Int_Onumber(_1161387), 21965 ^ _780461 : [(21992 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), _1161389), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161387), _1161391), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393))))), 21995 ^ _780461 : [(21996 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), c_Groups_Ozero__class_Ozero(_1161387)), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393))))], (21998 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161387), _1161389), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393))), _1161391))]], 21999 ^ _780461 : [(22000 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), c_Groups_Ozero__class_Ozero(_1161387)), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393)))], (22002 ^ _780461) ^ [] : [22003 ^ _780461 : [(22004 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393)), c_Groups_Ozero__class_Ozero(_1161387))))], (22006 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), _1161391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161387), _1161389), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393))))]], 22007 ^ _780461 : [(22008 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393)), c_Groups_Ozero__class_Ozero(_1161387)))], (22010 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), _1161389), c_Groups_Ozero__class_Ozero(_1161387)))]]]]], (21966 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), _1161389), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1161387), _1161391), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393)))), 21969 ^ _780461 : [(21970 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), c_Groups_Ozero__class_Ozero(_1161387)), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161387), _1161389), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393))), _1161391)))], (21976 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), c_Groups_Ozero__class_Ozero(_1161387)), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393)))), 21979 ^ _780461 : [(21980 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393)), c_Groups_Ozero__class_Ozero(_1161387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), _1161391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161387), _1161389), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393)))))], (21986 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), hAPP(c_Int_Onumber__class_Onumber__of(_1161387), _1161393)), c_Groups_Ozero__class_Ozero(_1161387)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161387), _1161389), c_Groups_Ozero__class_Ozero(_1161387))))]]]]]]], (22014 ^ _780461) ^ [_1162501, _1162503, _1162505, _1162507] : [class_Fields_Ofield(_1162501), -(_1162503 = c_Groups_Ozero__class_Ozero(_1162501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162505), _1162507)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1162501), _1162503), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1162507), _1162505)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162501), hAPP(hAPP(c_Power_Opower__class_Opower(_1162501), _1162503), _1162507)), hAPP(hAPP(c_Power_Opower__class_Opower(_1162501), _1162503), _1162505)))], (22028 ^ _780461) ^ [_1162785, _1162787] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162785), hAPP(c_Int_Onumber__class_Onumber__of(_1162785), c_Int_OMin)), _1162787) = hAPP(c_Groups_Ouminus__class_Ouminus(_1162785), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162785), c_Groups_Oone__class_Oone(_1162785)), _1162787))), class_Fields_Ofield__inverse__zero(_1162785), class_Int_Onumber__ring(_1162785)], (22038 ^ _780461) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (22040 ^ _780461) ^ [_1162984, _1162986, _1162988, _1162990] : [class_Fields_Olinordered__field__inverse__zero(_1162984), class_Int_Onumber(_1162984), 22047 ^ _780461 : [(22074 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162984), _1162986), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162984), _1162988), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990))))), 22077 ^ _780461 : [(22078 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162984), c_Groups_Ozero__class_Ozero(_1162984)), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990))))], (22080 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162984), _1162986), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990))), _1162988))]], 22081 ^ _780461 : [(22082 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162984), c_Groups_Ozero__class_Ozero(_1162984)), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990)))], (22084 ^ _780461) ^ [] : [22085 ^ _780461 : [(22086 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162984), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990)), c_Groups_Ozero__class_Ozero(_1162984))))], (22088 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162984), _1162988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162984), _1162986), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990))))]], 22089 ^ _780461 : [(22090 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162984), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990)), c_Groups_Ozero__class_Ozero(_1162984)))], (22092 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162984), _1162986), c_Groups_Ozero__class_Ozero(_1162984)))]]]]], (22048 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162984), _1162986), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1162984), _1162988), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990)))), 22051 ^ _780461 : [(22052 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162984), c_Groups_Ozero__class_Ozero(_1162984)), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162984), _1162986), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990))), _1162988)))], (22058 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162984), c_Groups_Ozero__class_Ozero(_1162984)), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990)))), 22061 ^ _780461 : [(22062 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162984), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990)), c_Groups_Ozero__class_Ozero(_1162984))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162984), _1162988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162984), _1162986), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990)))))], (22068 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162984), hAPP(c_Int_Onumber__class_Onumber__of(_1162984), _1162990)), c_Groups_Ozero__class_Ozero(_1162984)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162984), _1162986), c_Groups_Ozero__class_Ozero(_1162984))))]]]]]]], (22096 ^ _780461) ^ [_1164098, _1164100, _1164102, _1164104] : [class_Fields_Olinordered__field__inverse__zero(_1164098), class_Int_Onumber(_1164098), 22103 ^ _780461 : [(22130 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164098), hAPP(c_Int_Onumber__class_Onumber__of(_1164098), _1164100)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164098), _1164102), _1164104)))), 22133 ^ _780461 : [(22134 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164098), c_Groups_Ozero__class_Ozero(_1164098)), _1164104)))], (22136 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164098), hAPP(c_Int_Onumber__class_Onumber__of(_1164098), _1164100)), _1164104)), _1164102))]], 22137 ^ _780461 : [(22138 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164098), c_Groups_Ozero__class_Ozero(_1164098)), _1164104))], (22140 ^ _780461) ^ [] : [22141 ^ _780461 : [(22142 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164098), _1164104), c_Groups_Ozero__class_Ozero(_1164098))))], (22144 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164098), _1164102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164098), hAPP(c_Int_Onumber__class_Onumber__of(_1164098), _1164100)), _1164104)))]], 22145 ^ _780461 : [(22146 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164098), _1164104), c_Groups_Ozero__class_Ozero(_1164098)))], (22148 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164098), hAPP(c_Int_Onumber__class_Onumber__of(_1164098), _1164100)), c_Groups_Ozero__class_Ozero(_1164098)))]]]]], (22104 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164098), hAPP(c_Int_Onumber__class_Onumber__of(_1164098), _1164100)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1164098), _1164102), _1164104))), 22107 ^ _780461 : [(22108 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164098), c_Groups_Ozero__class_Ozero(_1164098)), _1164104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164098), hAPP(c_Int_Onumber__class_Onumber__of(_1164098), _1164100)), _1164104)), _1164102)))], (22114 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164098), c_Groups_Ozero__class_Ozero(_1164098)), _1164104))), 22117 ^ _780461 : [(22118 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164098), _1164104), c_Groups_Ozero__class_Ozero(_1164098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164098), _1164102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164098), hAPP(c_Int_Onumber__class_Onumber__of(_1164098), _1164100)), _1164104))))], (22124 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164098), _1164104), c_Groups_Ozero__class_Ozero(_1164098)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164098), hAPP(c_Int_Onumber__class_Onumber__of(_1164098), _1164100)), c_Groups_Ozero__class_Ozero(_1164098))))]]]]]]], (22152 ^ _780461) ^ [_1165167, _1165169, _1165171, _1165173] : [class_Fields_Olinordered__field__inverse__zero(_1165167), class_Int_Onumber(_1165167), 22159 ^ _780461 : [(22186 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165167), _1165169), _1165171)), hAPP(c_Int_Onumber__class_Onumber__of(_1165167), _1165173)))), 22189 ^ _780461 : [(22190 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165167), c_Groups_Ozero__class_Ozero(_1165167)), _1165171)))], (22192 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165167), _1165169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165167), hAPP(c_Int_Onumber__class_Onumber__of(_1165167), _1165173)), _1165171)))]], 22193 ^ _780461 : [(22194 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165167), c_Groups_Ozero__class_Ozero(_1165167)), _1165171))], (22196 ^ _780461) ^ [] : [22197 ^ _780461 : [(22198 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165167), _1165171), c_Groups_Ozero__class_Ozero(_1165167))))], (22200 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165167), hAPP(c_Int_Onumber__class_Onumber__of(_1165167), _1165173)), _1165171)), _1165169))]], 22201 ^ _780461 : [(22202 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165167), _1165171), c_Groups_Ozero__class_Ozero(_1165167)))], (22204 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165167), c_Groups_Ozero__class_Ozero(_1165167)), hAPP(c_Int_Onumber__class_Onumber__of(_1165167), _1165173)))]]]]], (22160 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1165167), _1165169), _1165171)), hAPP(c_Int_Onumber__class_Onumber__of(_1165167), _1165173))), 22163 ^ _780461 : [(22164 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165167), c_Groups_Ozero__class_Ozero(_1165167)), _1165171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165167), _1165169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165167), hAPP(c_Int_Onumber__class_Onumber__of(_1165167), _1165173)), _1165171))))], (22170 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165167), c_Groups_Ozero__class_Ozero(_1165167)), _1165171))), 22173 ^ _780461 : [(22174 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165167), _1165171), c_Groups_Ozero__class_Ozero(_1165167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165167), hAPP(c_Int_Onumber__class_Onumber__of(_1165167), _1165173)), _1165171)), _1165169)))], (22180 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165167), _1165171), c_Groups_Ozero__class_Ozero(_1165167)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165167), c_Groups_Ozero__class_Ozero(_1165167)), hAPP(c_Int_Onumber__class_Onumber__of(_1165167), _1165173))))]]]]]]], (22208 ^ _780461) ^ [_1166236, _1166238, _1166240, _1166242] : [class_Fields_Olinordered__field__inverse__zero(_1166236), class_Int_Onumber(_1166236), 22215 ^ _780461 : [(22242 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166236), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166236), _1166238), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240))), _1166242))), 22245 ^ _780461 : [(22246 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166236), c_Groups_Ozero__class_Ozero(_1166236)), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240))))], (22248 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166236), _1166238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166236), _1166242), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240))))]], 22249 ^ _780461 : [(22250 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166236), c_Groups_Ozero__class_Ozero(_1166236)), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240)))], (22252 ^ _780461) ^ [] : [22253 ^ _780461 : [(22254 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166236), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240)), c_Groups_Ozero__class_Ozero(_1166236))))], (22256 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166236), _1166242), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240))), _1166238))]], 22257 ^ _780461 : [(22258 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166236), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240)), c_Groups_Ozero__class_Ozero(_1166236)))], (22260 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166236), c_Groups_Ozero__class_Ozero(_1166236)), _1166242))]]]]], (22216 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166236), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1166236), _1166238), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240))), _1166242)), 22219 ^ _780461 : [(22220 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166236), c_Groups_Ozero__class_Ozero(_1166236)), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166236), _1166238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166236), _1166242), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240)))))], (22226 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166236), c_Groups_Ozero__class_Ozero(_1166236)), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240)))), 22229 ^ _780461 : [(22230 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166236), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240)), c_Groups_Ozero__class_Ozero(_1166236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166236), _1166242), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240))), _1166238)))], (22236 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166236), hAPP(c_Int_Onumber__class_Onumber__of(_1166236), _1166240)), c_Groups_Ozero__class_Ozero(_1166236)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166236), c_Groups_Ozero__class_Ozero(_1166236)), _1166242)))]]]]]]], (22264 ^ _780461) ^ [_1167359, _1167361] : [_1167359 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1167359, _1167361) = _1167361)], (22270 ^ _780461) ^ [_1167436, _1167438] : [-(_1167436 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1167436, _1167438) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1167436), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1167438)))], (22276 ^ _780461) ^ [] : [-(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))], (22278 ^ _780461) ^ [] : [-(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))], (22280 ^ _780461) ^ [_1167525, _1167527, _1167529] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1167525, _1167527, _1167529, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1167527)], (22282 ^ _780461) ^ [_1167566, _1167568] : [22283 ^ _780461 : [(22284 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1167566), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (22286 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1167568), _1167566))]], -(c_Random_Olog(_1167566, _1167568) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (22290 ^ _780461) ^ [_1167701, _1167703] : [-(c_Random_Olog(_1167701, _1167703) = 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(_1167701, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1167703), _1167701)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1167701), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1167703), _1167701)))], (22300 ^ _780461) ^ [_1167771, _1167773, _1167775] : [class_Fields_Olinordered__field(_1167771), 22306 ^ _780461 : [(22307 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167771), c_Groups_Ozero__class_Ozero(_1167771)), 22305 ^ [_1167771, _1167773, _1167775])))], (22309 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167771), _1167773), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167771), _1167775), 22305 ^ [_1167771, _1167773, _1167775])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167771), _1167773), _1167775)))], (22313 ^ _780461) ^ [_1168061, _1168063, _1168065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1168061), _1168063)), -(c_Random_Ominus__shift(_1168065, _1168061, _1168063) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1168065), _1168061)), _1168063))], (22319 ^ _780461) ^ [_1168176, _1168178, _1168180] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1168176), _1168178))), -(c_Random_Ominus__shift(_1168180, _1168176, _1168178) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1168176), _1168178))], (22325 ^ _780461) ^ [_1168240, _1168242] : [_1168240 = _1168242, -(c_Random_Oinc__shift(_1168240, _1168242) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (22331 ^ _780461) ^ [_1168317, _1168319] : [-(_1168317 = _1168319), -(c_Random_Oinc__shift(_1168317, _1168319) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1168319), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (22337 ^ _780461) ^ [_1168364] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1168364)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1168364)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22339 ^ _780461) ^ [_1168401] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1168401)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1168401)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22341 ^ _780461) ^ [_1168436, _1168438] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1168436), _1168438) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1168436), _1168438))], (22343 ^ _780461) ^ [_1168488, _1168490] : [c_Code__Numeral_OSuc__code__numeral(_1168488) = c_Code__Numeral_OSuc__code__numeral(_1168490), -(_1168488 = _1168490)], (22349 ^ _780461) ^ [_1168569, _1168571] : [_1168569 = _1168571, -(c_Code__Numeral_OSuc__code__numeral(_1168569) = c_Code__Numeral_OSuc__code__numeral(_1168571))], (22355 ^ _780461) ^ [_1168665] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1168665)], (22357 ^ _780461) ^ [_1168699] : [c_Code__Numeral_OSuc__code__numeral(_1168699) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (22359 ^ _780461) ^ [_1168724, _1168726, _1168728, _1168730] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1168724, _1168726, _1168728, c_Code__Numeral_OSuc__code__numeral(_1168730)) = hAPP(_1168728, _1168730))], (22361 ^ _780461) ^ [_1168763] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1168763)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1168763)], (22363 ^ _780461) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (22365 ^ _780461) ^ [_1168812] : [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), _1168812))), 22368 ^ _780461 : [(22369 ^ _780461) ^ [] : [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), _1168812)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1168812)) = 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), _1168812))))], (22375 ^ _780461) ^ [] : [-(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), _1168812))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1168812)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1168812)), 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), _1168812)))))]]], (22381 ^ _780461) ^ [_1169111, _1169113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1169111), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169113)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169111)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169113))], (22387 ^ _780461) ^ [_1169222, _1169224] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1169222), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169224)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169222)) = 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), _1169224), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1169222)))), 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)))], (22393 ^ _780461) ^ [_1169295, _1169297, _1169299, _1169301] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1169295, _1169297, _1169299, c_Code__Numeral_OSuc__code__numeral(_1169301)) = hAPP(hAPP(_1169299, _1169301), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1169295, _1169297, _1169299, _1169301)))], (22395 ^ _780461) ^ [_1169342, _1169344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1169342), _1169344)), -(c_Divides_Odivmod__nat(_1169344, _1169342) = 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), _1169344), _1169342)), _1169342))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1169344), _1169342), _1169342)))], (22405 ^ _780461) ^ [_1169559] : [-(_1169559 = 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)), _1169559)))], (22411 ^ _780461) ^ [_1169591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1169591)), _1169591 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22417 ^ _780461) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (22419 ^ _780461) ^ [_1169706, _1169708] : [hAPP(c_Code__Numeral_Oof__nat, _1169706) = hAPP(c_Code__Numeral_Oof__nat, _1169708), -(_1169706 = _1169708)], (22425 ^ _780461) ^ [_1169791, _1169793] : [_1169791 = _1169793, -(hAPP(c_Code__Numeral_Oof__nat, _1169791) = hAPP(c_Code__Numeral_Oof__nat, _1169793))], (22431 ^ _780461) ^ [_1169882] : [-(c_Divides_Odivmod__nat(_1169882, 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)), _1169882))], (22433 ^ _780461) ^ [_1169911, _1169913, _1169915, _1169917] : [class_Groups_Ouminus(_1169911), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1169913, _1169911)), _1169915), _1169917) = hAPP(c_Groups_Ouminus__class_Ouminus(_1169911), hAPP(_1169915, _1169917)))], (22439 ^ _780461) ^ [_1170028, _1170030, _1170032, _1170034, _1170036] : [class_Groups_Ominus(_1170028), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1170030, _1170028)), _1170032), _1170034), _1170036) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1170028), hAPP(_1170032, _1170036)), hAPP(_1170034, _1170036)))], (22445 ^ _780461) ^ [_1170180, _1170182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1170180)), _1170182)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170180), _1170182)))], (22451 ^ _780461) ^ [_1170283, _1170285] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170283), _1170285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1170283)), _1170285)))], (22457 ^ _780461) ^ [_1170392, _1170394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170392), _1170394)), -(c_Divides_Odivmod__nat(_1170392, _1170394) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170392))], (22463 ^ _780461) ^ [_1170491] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170491) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1170491)))], (22465 ^ _780461) ^ [_1170523, _1170525] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1170523), hAPP(c_Nat_OSuc, _1170525)) = 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), _1170523), _1170525)))], (22467 ^ _780461) ^ [_1170568] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1170568)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170568)), 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))))], (22469 ^ _780461) ^ [_1170605, _1170607] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1170605)), hAPP(c_Code__Numeral_Oof__nat, _1170607)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1170605), _1170607)))], (22471 ^ _780461) ^ [_1170651, _1170653] : [-(c_Divides_Odivmod__nat(_1170651, _1170653) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1170651), _1170653)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1170651, _1170653)))], (22473 ^ _780461) ^ [_1170695, _1170697, _1170699] : [class_Int_Onumber__ring(_1170695), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1170695), _1170697), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1170699))) = hAPP(hAPP(c_HOL_OLet(_1170695, _1170695), hAPP(hAPP(c_Power_Opower__class_Opower(_1170695), _1170697), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170699))), hAPP(hAPP(c_COMBS(_1170695, _1170695, _1170695), c_Groups_Otimes__class_Otimes(_1170695)), c_COMBI(_1170695))))], (22479 ^ _780461) ^ [_1170866, _1170868] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1170866), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1170868))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1170866), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170868))), 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))))], (22481 ^ _780461) ^ [_1170917, _1170919, _1170921] : [class_Int_Onumber__ring(_1170917), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1170917), hAPP(c_Int_Onumber__class_Onumber__of(_1170917), _1170919)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1170921))) = hAPP(hAPP(c_HOL_OLet(_1170917, _1170917), hAPP(hAPP(c_Power_Opower__class_Opower(_1170917), hAPP(c_Int_Onumber__class_Onumber__of(_1170917), _1170919)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1170921))), hAPP(hAPP(c_COMBS(_1170917, _1170917, _1170917), c_Groups_Otimes__class_Otimes(_1170917)), c_COMBI(_1170917))))], (22487 ^ _780461) ^ [_1171117, _1171119] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1171117)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1171119)), hAPP(c_Int_Onat, _1171117)) = hAPP(c_Int_Onat, _1171119))], (22493 ^ _780461) ^ [_1171222, _1171224] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1171222))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1171224)), hAPP(c_Int_Onat, _1171222)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1171224), _1171222)), 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)))], (22499 ^ _780461) ^ [_1171286, _1171288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171286), 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)), _1171288)), -(c_Divides_OnegDivAlg(_1171286, _1171288) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1171286), _1171288)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1171286, _1171288)))], (22509 ^ _780461) ^ [_1171467] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1171467) = 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), _1171467), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (22511 ^ _780461) ^ [_1171502, _1171504] : [class_Rings_Osemiring__1(_1171502), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1171502), _1171504) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1171502, hAPP(hAPP(c_COMBC(_1171502, _1171502, _1171502), c_Groups_Oplus__class_Oplus(_1171502)), c_Groups_Oone__class_Oone(_1171502)), _1171504, c_Groups_Ozero__class_Ozero(_1171502)))], (22517 ^ _780461) ^ [_1171629, _1171631, _1171633] : [-(hAPP(c_Divides_Oadjust(_1171629), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1171631), _1171633)) = 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), _1171633), _1171629)), 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)))), _1171631)), 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)))), _1171631)), _1171633))))], (22519 ^ _780461) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22521 ^ _780461) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (22523 ^ _780461) ^ [_1171760, _1171762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1171760)), hAPP(c_Code__Numeral_Oof__nat, _1171762))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1171760), _1171762)))], (22529 ^ _780461) ^ [_1171865, _1171867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1171865), _1171867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1171865)), hAPP(c_Code__Numeral_Oof__nat, _1171867))))], (22535 ^ _780461) ^ [_1171991, _1171993] : [hAPP(c_Nat_OSuc, _1171991) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1171993), -(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(_1171993))), 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)), _1171991))))))], (22541 ^ _780461) ^ [_1172114, _1172116] : [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(_1172116))), 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)), _1172114))))), -(hAPP(c_Nat_OSuc, _1172114) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172116))], (22547 ^ _780461) ^ [_1172258, _1172260] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172258) = hAPP(c_Nat_OSuc, _1172260), -(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(_1172258))), 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)), _1172260))))))], (22553 ^ _780461) ^ [_1172381, _1172383] : [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(_1172381))), 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)), _1172383))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172381) = hAPP(c_Nat_OSuc, _1172383))], (22559 ^ _780461) ^ [_1172510, _1172512, _1172514, _1172516] : [-(c_Nat_Onat_Onat__case(_1172510, _1172512, _1172514, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172516)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1172510), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1172516))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1172510, _1172510), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1172510, tc_fun(_1172510, _1172510)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1172510, tc_fun(_1172510, _1172510)), tc_Int_Oint), c_If(_1172510)), c_Nat__Numeral_Oneg)), _1172512)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1172510, tc_Int_Oint), _1172514), c_Int_Onat))))], (22561 ^ _780461) ^ [_1172612, _1172614, _1172616, _1172618] : [-(hAPP(c_Nat_Onat_Onat__rec(_1172612, _1172614, _1172616), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172618)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1172612), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1172618))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1172612, _1172612), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1172612, tc_fun(_1172612, _1172612)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1172612, tc_fun(_1172612, _1172612)), tc_Int_Oint), c_If(_1172612)), c_Nat__Numeral_Oneg)), _1172614)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1172612, _1172612), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1172612, _1172612), tc_Int_Oint), _1172616), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1172612, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1172612, _1172614, _1172616)), c_Int_Onat)))))], (22563 ^ _780461) ^ [_1172743, _1172745] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1172743)), hAPP(c_Code__Numeral_Oof__nat, _1172745)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1172743), _1172745)))], (22565 ^ _780461) ^ [_1172804, _1172806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1172804)), hAPP(c_Code__Numeral_Oof__nat, _1172806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1172804), _1172806)))], (22571 ^ _780461) ^ [_1172909, _1172911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1172909), _1172911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1172909)), hAPP(c_Code__Numeral_Oof__nat, _1172911))))], (22577 ^ _780461) ^ [_1173026] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1173026))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1173026)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22583 ^ _780461) ^ [_1173115] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1173115)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1173115)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173115)), 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)))))], (22589 ^ _780461) ^ [_1173185, _1173187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1173185)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173187))), -(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(_1173187))), 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), _1173185)), c_Int_Onat))))))], (22595 ^ _780461) ^ [_1173330, _1173332] : [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(_1173332))), 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), _1173330)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1173330)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173332))))], (22601 ^ _780461) ^ [_1173496, _1173498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173496)), hAPP(c_Nat_OSuc, _1173498))), -(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(_1173496))), 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)), _1173498)))))], (22607 ^ _780461) ^ [_1173623, _1173625] : [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(_1173623))), 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)), _1173625)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173623)), hAPP(c_Nat_OSuc, _1173625))))], (22613 ^ _780461) ^ [_1173771, _1173773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173771)), hAPP(c_Nat_OSuc, _1173773))), -(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(_1173771))), 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)), _1173773)))))], (22619 ^ _780461) ^ [_1173898, _1173900] : [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(_1173898))), 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)), _1173900)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1173898)), hAPP(c_Nat_OSuc, _1173900))))], (22625 ^ _780461) ^ [_1174046, _1174048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1174046)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174048))), -(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(_1174048))), 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), _1174046)), c_Int_Onat))))))], (22631 ^ _780461) ^ [_1174191, _1174193] : [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(_1174193))), 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), _1174191)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1174191)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174193))))], (22637 ^ _780461) ^ [_1174342, _1174344] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1174342)), hAPP(c_Code__Numeral_Oof__nat, _1174344)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174342), _1174344)))], (22639 ^ _780461) ^ [_1174388, _1174390, _1174392, _1174394, _1174396] : [-(c_Nat_Onat_Onat__case(_1174388, _1174390, _1174392, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174394)), _1174396)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1174388), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1174394))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1174388, _1174388), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1174388, tc_fun(_1174388, _1174388)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1174388, tc_fun(_1174388, _1174388)), tc_Int_Oint), c_If(_1174388)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1174388, _1174390, _1174392, _1174396))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1174388, tc_Int_Oint), _1174392), 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)), _1174396)))))], (22641 ^ _780461) ^ [_1174506, _1174508, _1174510, _1174512, _1174514] : [-(hAPP(c_Nat_Onat_Onat__rec(_1174506, _1174508, _1174510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174512)), _1174514)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1174506), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1174512))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1174506, _1174506), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1174506, tc_fun(_1174506, _1174506)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1174506, tc_fun(_1174506, _1174506)), tc_Int_Oint), c_If(_1174506)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1174506, _1174508, _1174510), _1174514))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1174506, _1174506), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1174506, _1174506), tc_Int_Oint), _1174510), 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)), _1174514))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1174506, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1174506, _1174508, _1174510)), 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)), _1174514))))))], (22643 ^ _780461) ^ [_1174658, _1174660, _1174662] : [class_Int_Onumber__ring(_1174658), 22646 ^ _780461 : [(22647 ^ _780461) ^ [] : [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), _1174660))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1174658), _1174662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1174660))) = hAPP(hAPP(c_HOL_OLet(_1174658, _1174658), hAPP(hAPP(c_Power_Opower__class_Opower(_1174658), _1174662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174660))), hAPP(hAPP(c_COMBS(_1174658, _1174658, _1174658), hAPP(hAPP(c_COMBB(_1174658, tc_fun(_1174658, _1174658), _1174658), c_Groups_Otimes__class_Otimes(_1174658)), hAPP(c_Groups_Otimes__class_Otimes(_1174658), _1174662))), c_COMBI(_1174658))))], (22653 ^ _780461) ^ [] : [-(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), _1174660)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1174658), _1174662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1174660))) = c_Groups_Oone__class_Oone(_1174658))]]], (22659 ^ _780461) ^ [_1175025, _1175027] : [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), _1175025))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1175027), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1175025))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1175027), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1175025))), 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), _1175027))), c_COMBI(tc_Int_Oint))))], (22665 ^ _780461) ^ [_1175182, _1175184] : [-(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), _1175182)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1175184), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1175182))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22671 ^ _780461) ^ [_1175245, _1175247] : [22672 ^ _780461 : [(22673 ^ _780461) ^ [] : [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), _1175245), _1175247)))], (22675 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1175247), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1175245, _1175247) = 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), _1175245), _1175247)))], (22679 ^ _780461) ^ [_1175404, _1175406] : [-(c_Divides_OnegDivAlg(_1175404, _1175406) = hAPP(c_Divides_Oadjust(_1175406), c_Divides_OnegDivAlg(_1175404, 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)))), _1175406)))), -(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), _1175404), _1175406)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1175406), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22689 ^ _780461) ^ [_1175476, _1175478, _1175480] : [class_Int_Onumber__ring(_1175476), 22692 ^ _780461 : [(22693 ^ _780461) ^ [] : [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), _1175478))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1175476), hAPP(c_Int_Onumber__class_Onumber__of(_1175476), _1175480)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1175478))) = hAPP(hAPP(c_HOL_OLet(_1175476, _1175476), hAPP(hAPP(c_Power_Opower__class_Opower(_1175476), hAPP(c_Int_Onumber__class_Onumber__of(_1175476), _1175480)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1175478))), hAPP(hAPP(c_COMBS(_1175476, _1175476, _1175476), hAPP(hAPP(c_COMBB(_1175476, tc_fun(_1175476, _1175476), _1175476), c_Groups_Otimes__class_Otimes(_1175476)), hAPP(c_Groups_Otimes__class_Otimes(_1175476), hAPP(c_Int_Onumber__class_Onumber__of(_1175476), _1175480)))), c_COMBI(_1175476))))], (22699 ^ _780461) ^ [] : [-(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), _1175478)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1175476), hAPP(c_Int_Onumber__class_Onumber__of(_1175476), _1175480)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1175478))) = c_Groups_Oone__class_Oone(_1175476))]]], (22705 ^ _780461) ^ [_1175874, _1175876, _1175878] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1175874, _1175876, _1175878, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1175876)], (22707 ^ _780461) ^ [_1175906, _1175908] : [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), _1175906))), 22710 ^ _780461 : [(22711 ^ _780461) ^ [] : [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), _1175908)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175906)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175908), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175906)) = 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), _1175908)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175906))))], (22717 ^ _780461) ^ [] : [-(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), _1175908)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175906))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175908), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175906)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175906)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1175908), 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), _1175906)))))]]], (22723 ^ _780461) ^ [_1176254, _1176256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176254)), 22726 ^ _780461 : [(22727 ^ _780461) ^ [] : [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), _1176256), _1176254))), -(c_Divides_OnegDivAlg(_1176256, _1176254) = 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), _1176256), _1176254)))], (22733 ^ _780461) ^ [] : [-(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), _1176256), _1176254)))), -(c_Divides_OnegDivAlg(_1176256, _1176254) = hAPP(c_Divides_Oadjust(_1176254), c_Divides_OnegDivAlg(_1176256, 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)))), _1176254))))]]], (22739 ^ _780461) ^ [_1176527, _1176529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176527), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1176529, _1176527) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176529), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176527)))], (22745 ^ _780461) ^ [_1176633, _1176635] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176633), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 22748 ^ _780461 : [(22749 ^ _780461) ^ [] : [22750 ^ _780461 : [(22751 ^ _780461) ^ [] : [_1176635 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22753 ^ _780461) ^ [] : [_1176633 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1176635, _1176633) = 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)))], (22757 ^ _780461) ^ [] : [-(c_Nitpick_Onorm__frac(_1176635, _1176633) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1176635), _1176633)), 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), _1176635))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1176633)))), -(_1176635 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1176633 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (22767 ^ _780461) ^ [_1176931] : [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), _1176931))), 22770 ^ _780461 : [(22771 ^ _780461) ^ [] : [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), _1176931))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1176931)) = 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)))], (22777 ^ _780461) ^ [] : [-(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), _1176931)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1176931)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1176931)), 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), _1176931)))))]]], (22783 ^ _780461) ^ [_1177200, _1177202] : [22784 ^ _780461 : [(22785 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177200), _1177202))], (22787 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177202), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1177200, _1177202) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177200))], (22791 ^ _780461) ^ [_1177341, _1177343] : [-(c_Divides_OposDivAlg(_1177341, _1177343) = hAPP(c_Divides_Oadjust(_1177343), c_Divides_OposDivAlg(_1177341, 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)))), _1177343)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177341), _1177343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177343), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22801 ^ _780461) ^ [_1177410] : [-(c_Divides_Oadjust(_1177410) = 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)), _1177410))))), 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)), _1177410))))), 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))))))))], (22803 ^ _780461) ^ [_1177471, _1177473] : [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), _1177471))), 22806 ^ _780461 : [(22807 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177473)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177471))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177473), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177471)) = 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), _1177473)))], (22813 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177473)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177471)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177473), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177471)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177471)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1177473), 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), _1177471)))))]]], (22819 ^ _780461) ^ [_1177789] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1177789) = 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)))], (22821 ^ _780461) ^ [_1177815, _1177817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177817)), -(c_Divides_OposDivAlg(_1177815, _1177817) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1177815), _1177817)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1177815, _1177817)))], (22831 ^ _780461) ^ [_1177990, _1177992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177990)), 22834 ^ _780461 : [(22835 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177992), _1177990)), -(c_Divides_OposDivAlg(_1177992, _1177990) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177992))], (22841 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177992), _1177990))), -(c_Divides_OposDivAlg(_1177992, _1177990) = hAPP(c_Divides_Oadjust(_1177990), c_Divides_OposDivAlg(_1177992, 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)))), _1177990))))]]], (22847 ^ _780461) ^ [_1178230, _1178232] : [class_Rings_Oring__1(_1178230), 22850 ^ _780461 : [(22851 ^ _780461) ^ [] : [_1178232 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1178230), _1178232) = c_Groups_Ozero__class_Ozero(_1178230))], (22857 ^ _780461) ^ [] : [-(_1178232 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22860 ^ _780461 : [(22861 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178232), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1178230), _1178232) = hAPP(c_Groups_Ouminus__class_Ouminus(_1178230), hAPP(c_Int_Oring__1__class_Oof__int(_1178230), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178232))))], (22867 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178232), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1178230), _1178232) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1178230), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1178230, _1178230)), tc_fun(tc_Int_Oint, _1178230)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1178230, _1178230), _1178230), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1178230, _1178230)), tc_fun(tc_Int_Oint, _1178230)), tc_Int_Oint), c_COMBB(tc_fun(_1178230, _1178230), _1178230, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1178230, tc_fun(tc_fun(_1178230, _1178230), _1178230), tc_Int_Oint), c_HOL_OLet(_1178230, _1178230)), c_Int_Oring__1__class_Oof__int(_1178230)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1178230, _1178230), tc_fun(_1178230, _1178230)), hAPP(hAPP(c_COMBB(tc_fun(_1178230, tc_fun(_1178230, _1178230)), tc_fun(tc_fun(_1178230, _1178230), tc_fun(_1178230, _1178230)), tc_Int_Oint), c_COMBS(_1178230, _1178230, _1178230)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1178230, _1178230), tc_fun(_1178230, tc_fun(_1178230, _1178230))), hAPP(hAPP(c_COMBB(tc_fun(_1178230, tc_fun(_1178230, _1178230)), tc_fun(tc_fun(_1178230, _1178230), tc_fun(_1178230, tc_fun(_1178230, _1178230))), tc_Int_Oint), c_COMBB(_1178230, tc_fun(_1178230, _1178230), _1178230)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1178230, tc_fun(_1178230, _1178230)), tc_Int_Oint), c_If(_1178230)), 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(_1178230, _1178230, _1178230), c_Groups_Oplus__class_Oplus(_1178230)), c_COMBI(_1178230))))), hAPP(hAPP(c_COMBC(_1178230, _1178230, _1178230), hAPP(hAPP(c_COMBB(_1178230, tc_fun(_1178230, _1178230), _1178230), c_Groups_Oplus__class_Oplus(_1178230)), hAPP(hAPP(c_COMBS(_1178230, _1178230, _1178230), c_Groups_Oplus__class_Oplus(_1178230)), c_COMBI(_1178230)))), c_Groups_Oone__class_Oone(_1178230))))), c_Divides_Odivmod__int(_1178232, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (22873 ^ _780461) ^ [_1179143] : [-(c_Hoare__Mirabelle_OMGT(_1179143) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _1179143), c_Natural_Oevalc(_1179143)))], (22875 ^ _780461) ^ [_1179176, _1179178, _1179180, _1179182, _1179184] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1179176, _1179178), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1179180), _1179182))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1179178)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1179184), _1179176), _1179178), 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), _1179184), _1179180)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1179184), _1179182)), _1179178))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1179184), _1179182), _1179178)))))], (22885 ^ _780461) ^ [_1179445, _1179447, _1179449, _1179451, _1179453] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1179445, _1179447), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1179449), _1179451))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1179447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1179453)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1179445, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1179447), _1179453)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1179449), _1179453)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1179447), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1179449, _1179453))), _1179451)))))], (22899 ^ _780461) ^ [_1179752, _1179754] : [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), _1179752), _1179754))), 22902 ^ _780461 : [(22903 ^ _780461) ^ [] : [22904 ^ _780461 : [(22905 ^ _780461) ^ [] : [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), _1179752), _1179754)))], (22907 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179754), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1179752, _1179754) = 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), _1179752), _1179754)))], (22911 ^ _780461) ^ [] : [-(c_Divides_OnegDivAlg(_1179752, _1179754) = hAPP(c_Divides_Oadjust(_1179754), c_Divides_OnegDivAlg(_1179752, 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)))), _1179754)))), -(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), _1179752), _1179754)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179754), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (22921 ^ _780461) ^ [_1180099, _1180101, _1180103, _1180105] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1180099, _1180101), _1180103)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1180099, _1180101), _1180105)), -(_1180103 = _1180105)], (22931 ^ _780461) ^ [_1180256, _1180258, _1180260, _1180262] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1180256, _1180258), _1180260)), hBOOL(hAPP(hAPP(_1180258, _1180262), _1180260)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1180256, _1180258), _1180262)))], (22951 ^ _780461) ^ [_1180627, _1180629, _1180631] : [22953 ^ _780461 : [(22954 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1180629, 22952 ^ [_1180627, _1180629, _1180631]), _1180631)))], (22956 ^ _780461) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1180627, _1180629), 22952 ^ [_1180627, _1180629, _1180631]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1180627, _1180629), _1180631)))], (22941 ^ _780461) ^ [_1180441, _1180443, _1180445] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1180441, _1180443), _1180445)), 22944 ^ _780461 : [(22945 ^ _780461) ^ [_1180526] : [hBOOL(hAPP(hAPP(_1180443, _1180526), _1180445)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1180441, _1180443), _1180526)))]]], (22970 ^ _780461) ^ [_1181017, _1181019, _1181021] : [22972 ^ _780461 : [(22973 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1181019, 22971 ^ [_1181017, _1181019, _1181021]), _1181021)))], (22975 ^ _780461) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1181017, _1181019), 22971 ^ [_1181017, _1181019, _1181021]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1181017, _1181019), _1181021)))], (22960 ^ _780461) ^ [_1180831, _1180833, _1180835] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1180831, _1180833), _1180835)), 22963 ^ _780461 : [(22964 ^ _780461) ^ [_1180916] : [hBOOL(hAPP(hAPP(_1180833, _1180916), _1180835)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1180831, _1180833), _1180916)))]]], (22979 ^ _780461) ^ [_1181203, _1181205, _1181207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1181203, tc_fun(_1181203, tc_HOL_Obool))), _1181205), _1181207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1181203, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1181203, _1181207)), c_Wellfounded_Oaccp(_1181203, _1181205))))], (22985 ^ _780461) ^ [_1181340, _1181342, _1181344] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1181340, _1181342), _1181344)), -(c_Divides_Odivmod__nat(_1181340, _1181342) = _1181344)], (22991 ^ _780461) ^ [_1181435, _1181437] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1181435, _1181437), c_Divides_Odivmod__nat(_1181435, _1181437))))], (22993 ^ _780461) ^ [_1181468, _1181470, _1181472, _1181474] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1181468, _1181470), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1181472), _1181474))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1181468, _1181470) = _1181474)], (22999 ^ _780461) ^ [_1181579, _1181581, _1181583, _1181585] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1181579, _1181581), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1181583), _1181585))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1181579), _1181581) = _1181583)], (23005 ^ _780461) ^ [_1181694, _1181696] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1181694, _1181696), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1181694), _1181696)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1181694, _1181696)))))], (23007 ^ _780461) ^ [_1181740, _1181742] : [-(c_Divides_Odivmod__int(_1181740, _1181742) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181740), _1181742)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1181740, _1181742)))], (23009 ^ _780461) ^ [_1181784, _1181786, _1181788, _1181790, _1181792, _1181794, _1181796] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1181784, _1181786), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1181788), _1181790))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1181792, _1181786), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1181794), _1181796))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1181786)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1181784), _1181792), _1181786), 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), _1181788), _1181794)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1181790), _1181796)), _1181786))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1181790), _1181796), _1181786)))))], (23023 ^ _780461) ^ [_1182145, _1182147] : [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), _1182145), _1182147))), 23026 ^ _780461 : [(23027 ^ _780461) ^ [] : [23028 ^ _780461 : [(23029 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182145), _1182147))], (23031 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182147), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1182145, _1182147) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182145))], (23035 ^ _780461) ^ [] : [-(c_Divides_OposDivAlg(_1182145, _1182147) = hAPP(c_Divides_Oadjust(_1182147), c_Divides_OposDivAlg(_1182145, 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)))), _1182147)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182145), _1182147))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182147), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23045 ^ _780461) ^ [_1182468, _1182470] : [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), _1182468), _1182470))), 23048 ^ _780461 : [(23049 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182470), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1182468, _1182470) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182468), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182470)))], (23055 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182470), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23058 ^ _780461 : [(23059 ^ _780461) ^ [] : [23060 ^ _780461 : [(23061 ^ _780461) ^ [] : [_1182468 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23063 ^ _780461) ^ [] : [_1182470 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1182468, _1182470) = 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)))], (23067 ^ _780461) ^ [] : [-(c_Nitpick_Onorm__frac(_1182468, _1182470) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1182468), _1182470)), 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), _1182468))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182470)))), -(_1182468 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1182470 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (23077 ^ _780461) ^ [] : [-(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)))))], (23105 ^ _780461) ^ [_1183357, _1183359] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183357))), 23108 ^ _780461 : [(23109 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183359)), -(c_Divides_Odivmod__int(_1183357, _1183359) = c_Divides_OnegDivAlg(_1183357, _1183359))], (23115 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183359))), -(c_Divides_Odivmod__int(_1183357, _1183359) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183357), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183359))))]]], (23079 ^ _780461) ^ [_1182987, _1182989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182987)), 23082 ^ _780461 : [(23083 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182989)), -(c_Divides_Odivmod__int(_1182987, _1182989) = c_Divides_OposDivAlg(_1182987, _1182989))], (23089 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182989))), 23092 ^ _780461 : [(23093 ^ _780461) ^ [] : [_1182987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1182987, _1182989) = 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)))], (23099 ^ _780461) ^ [] : [-(_1182987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1182987, _1182989) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182987), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182989))))]]]]], (23121 ^ _780461) ^ [_1183585, _1183587, _1183589] : [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), _1183585), _1183587))), -(hBOOL(hAPP(hAPP(_1183589, _1183585), _1183587))), 23128 ^ _780461 : [(23129 ^ _780461) ^ [] : [-(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), 23126 ^ [_1183585, _1183587, _1183589]), 23127 ^ [_1183585, _1183587, _1183589]))))], (23141 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1183589, 23126 ^ [_1183585, _1183587, _1183589]), 23127 ^ [_1183585, _1183587, _1183589]))], (23131 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1183589, 23126 ^ [_1183585, _1183587, _1183589]), 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)))), 23127 ^ [_1183585, _1183587, _1183589])))), -(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), 23126 ^ [_1183585, _1183587, _1183589]), 23127 ^ [_1183585, _1183587, _1183589])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23127 ^ [_1183585, _1183587, _1183589]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23145 ^ _780461) ^ [_1184080, _1184082] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1184080), _1184082)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1184080), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1184082)))], (23147 ^ _780461) ^ [_1184123, _1184125, _1184127, _1184129, _1184131] : [hBOOL(hAPP(hAPP(_1184123, _1184125), _1184127)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184129, _1184131, tc_HOL_Obool), _1184123), hAPP(hAPP(c_Product__Type_OPair(_1184129, _1184131), _1184125), _1184127))))], (23153 ^ _780461) ^ [_1184252, _1184254, _1184256, _1184258, _1184260] : [hBOOL(hAPP(hAPP(_1184252, _1184254), _1184256)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1184258, _1184260, tc_HOL_Obool), _1184252), hAPP(hAPP(c_Product__Type_OPair(_1184258, _1184260), _1184254), _1184256))))], (23159 ^ _780461) ^ [_1184381, _1184383, _1184385] : [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), _1184381), _1184383))), -(hBOOL(hAPP(hAPP(_1184385, _1184381), _1184383))), 23166 ^ _780461 : [(23167 ^ _780461) ^ [] : [-(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), 23164 ^ [_1184381, _1184383, _1184385]), 23165 ^ [_1184381, _1184383, _1184385]))))], (23179 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1184385, 23164 ^ [_1184381, _1184383, _1184385]), 23165 ^ [_1184381, _1184383, _1184385]))], (23169 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1184385, 23164 ^ [_1184381, _1184383, _1184385]), 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)))), 23165 ^ [_1184381, _1184383, _1184385])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23164 ^ [_1184381, _1184383, _1184385]), 23165 ^ [_1184381, _1184383, _1184385]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23165 ^ [_1184381, _1184383, _1184385]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23183 ^ _780461) ^ [_1184867, _1184869] : [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), _1184867), _1184869))), 23186 ^ _780461 : [(23187 ^ _780461) ^ [] : [_1184869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1184867, _1184869) = _1184867)], (23193 ^ _780461) ^ [] : [-(_1184869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1184867, _1184869) = c_Nitpick_Onat__gcd(_1184869, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1184867, _1184869)))]]], (23199 ^ _780461) ^ [_1185094, _1185096] : [_1185094 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1185094, _1185096) = 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)))], (23205 ^ _780461) ^ [_1185172, _1185174] : [-(_1185172 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23208 ^ _780461 : [(23209 ^ _780461) ^ [] : [_1185174 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1185172, _1185174) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185172))], (23215 ^ _780461) ^ [] : [-(_1185174 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1185172, _1185174) = 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, _1185174))), 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)), _1185174)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185172))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185174), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185172), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1185172, _1185174)), 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), _1185174))))), c_Divides_Opdivmod(_1185172, _1185174)))))]]], (23221 ^ _780461) ^ [_1185532, _1185534, _1185536, _1185538, _1185540, _1185542] : [-(hAPP(c_Product__Type_Oapsnd(_1185532, _1185534, _1185536, _1185538), hAPP(hAPP(c_Product__Type_OPair(_1185536, _1185532), _1185540), _1185542)) = hAPP(hAPP(c_Product__Type_OPair(_1185536, _1185534), _1185540), hAPP(_1185538, _1185542)))], (23223 ^ _780461) ^ [_1185612, _1185614, _1185616] : [hBOOL(hAPP(_1185612, 23224 ^ [_1185612, _1185614, _1185616])), 23227 ^ _780461 : [(23228 ^ _780461) ^ [_1185723, _1185725] : [-(hBOOL(hAPP(_1185612, hAPP(hAPP(c_Product__Type_OPair(_1185614, _1185616), _1185725), _1185723))))]]], (23230 ^ _780461) ^ [_1185759, _1185761, _1185763] : [hBOOL(hAPP(_1185759, hAPP(hAPP(c_Product__Type_OPair(_1185761, _1185763), 23231 ^ [_1185759, _1185761, _1185763]), 23232 ^ [_1185759, _1185761, _1185763]))), 23235 ^ _780461 : [(23236 ^ _780461) ^ [_1185906] : [-(hBOOL(hAPP(_1185759, _1185906)))]]], (23238 ^ _780461) ^ [_1185964, _1185966, _1185968, _1185970, _1185972, _1185974] : [hAPP(hAPP(c_Product__Type_OPair(_1185964, _1185966), _1185968), _1185970) = hAPP(hAPP(c_Product__Type_OPair(_1185964, _1185966), _1185972), _1185974), 23241 ^ _780461 : [(23242 ^ _780461) ^ [] : [-(_1185968 = _1185972)], (23244 ^ _780461) ^ [] : [-(_1185970 = _1185974)]]], (23246 ^ _780461) ^ [_1186107, _1186109, _1186111, _1186113, _1186115, _1186117] : [-(hAPP(hAPP(c_Product__Type_OPair(_1186107, _1186109), _1186111), _1186113) = hAPP(hAPP(c_Product__Type_OPair(_1186107, _1186109), _1186115), _1186117)), _1186111 = _1186115, _1186113 = _1186117], (23256 ^ _780461) ^ [_1186290, _1186292, _1186294, _1186296, _1186298, _1186300] : [hAPP(hAPP(c_Product__Type_OPair(_1186290, _1186292), _1186294), _1186296) = hAPP(hAPP(c_Product__Type_OPair(_1186290, _1186292), _1186298), _1186300), 23259 ^ _780461 : [(23260 ^ _780461) ^ [] : [-(_1186294 = _1186298)], (23262 ^ _780461) ^ [] : [-(_1186296 = _1186300)]]], (23264 ^ _780461) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (23266 ^ _780461) ^ [_1186459, _1186461, _1186463, _1186465, _1186467, _1186469] : [_1186459 = _1186461, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186463, _1186465, _1186467), _1186469), _1186459) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186463, _1186465, _1186467), _1186469), _1186461))], (23272 ^ _780461) ^ [_1186584, _1186586, _1186588, _1186590, _1186592, _1186594] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186584, _1186586, _1186588), _1186590), hAPP(hAPP(c_Product__Type_OPair(_1186584, _1186586), _1186592), _1186594)) = hAPP(hAPP(_1186590, _1186592), _1186594))], (23274 ^ _780461) ^ [_1186642, _1186644, _1186646, _1186648, _1186650, _1186652] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186642, _1186644, _1186646), _1186648), hAPP(hAPP(c_Product__Type_OPair(_1186642, _1186644), _1186650), _1186652)) = hAPP(hAPP(_1186648, _1186650), _1186652))], (23276 ^ _780461) ^ [_1186700, _1186702, _1186704, _1186706, _1186708] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186700, _1186702, tc_HOL_Obool), _1186704), hAPP(hAPP(c_Product__Type_OPair(_1186700, _1186702), _1186706), _1186708))), -(hBOOL(hAPP(hAPP(_1186704, _1186706), _1186708)))], (23282 ^ _780461) ^ [_1186829, _1186831, _1186833, _1186835] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1186829, _1186831, _1186833), hAPP(hAPP(c_COMBB(tc_fun(_1186831, tc_prod(_1186829, _1186831)), tc_fun(_1186831, _1186833), _1186829), hAPP(c_COMBB(tc_prod(_1186829, _1186831), _1186833, _1186831), _1186835)), c_Product__Type_OPair(_1186829, _1186831))) = _1186835)], (23284 ^ _780461) ^ [_1186897, _1186899, _1186901, _1186903, _1186905, _1186907, _1186909, _1186911] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186897, _1186899, _1186901), _1186903), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186905, _1186907, tc_prod(_1186897, _1186899)), _1186909), _1186911)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1186905, _1186907, _1186901), hAPP(hAPP(c_COMBB(tc_fun(_1186907, tc_prod(_1186897, _1186899)), tc_fun(_1186907, _1186901), _1186905), hAPP(c_COMBB(tc_prod(_1186897, _1186899), _1186901, _1186907), hAPP(c_Product__Type_Oprod_Oprod__case(_1186897, _1186899, _1186901), _1186903))), _1186909)), _1186911))], (23286 ^ _780461) ^ [_1187003, _1187005] : [-(c_Divides_Opdivmod(_1187003, _1187005) = 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), _1187003)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1187005))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1187003), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1187005))))], (23288 ^ _780461) ^ [_1187068, _1187070] : [_1187068 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1187070, _1187068) = 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), _1187070)))], (23294 ^ _780461) ^ [_1187157, _1187159] : [-(_1187157 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1187159, _1187157) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1187159), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1187157)))], (23300 ^ _780461) ^ [_1187216, _1187218] : [_1187216 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1187216, _1187218) = 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)))], (23306 ^ _780461) ^ [_1187294, _1187296] : [-(_1187294 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23309 ^ _780461 : [(23310 ^ _780461) ^ [] : [_1187296 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1187294, _1187296) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187294))], (23316 ^ _780461) ^ [] : [-(_1187296 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1187294, _1187296) = 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, _1187296))), 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, _1187294)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1187296))), c_Divides_Opdivmod(_1187294, _1187296)), 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), _1187296))))), c_Divides_Opdivmod(_1187294, _1187296)))))]]], (23322 ^ _780461) ^ [_1187606, _1187608] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1187606, _1187608) = 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), _1187606), _1187608)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1187606, _1187608)))], (23324 ^ _780461) ^ [_1187650, _1187652, _1187654, _1187656, _1187658] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187650, _1187652), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187654), _1187656))), -(_1187652 = 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)), _1187658)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187650, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1187652), _1187658)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1187654), _1187658)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1187652), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1187654, _1187658))), _1187656)))))], (23338 ^ _780461) ^ [_1187956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1187956)), 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), _1187956)) = 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), _1187956))))))], (23344 ^ _780461) ^ [_1188091, _1188093] : [-(c_Divides_Odivmod__int__rel(_1188091, _1188093) = 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, _1188091))), 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), _1188093)))))), 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)), _1188093))), 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)), _1188093))))), 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)), _1188093)))), 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), _1188093))), 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))))))))], (23346 ^ _780461) ^ [_1188206, _1188208, _1188210] : [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), _1188206), _1188208))), -(hBOOL(hAPP(hAPP(_1188210, _1188206), _1188208))), 23353 ^ _780461 : [(23354 ^ _780461) ^ [] : [-(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), 23351 ^ [_1188206, _1188208, _1188210]), 23352 ^ [_1188206, _1188208, _1188210]))))], (23362 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1188210, 23351 ^ [_1188206, _1188208, _1188210]), 23352 ^ [_1188206, _1188208, _1188210]))], (23356 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23352 ^ [_1188206, _1188208, _1188210]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1188210, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23351 ^ [_1188206, _1188208, _1188210])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 23352 ^ [_1188206, _1188208, _1188210]))))]]], (23366 ^ _780461) ^ [_1188679, _1188681, _1188683, _1188685, _1188687, _1188689, _1188691] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1188679, _1188681, tc_fun(_1188683, tc_HOL_Obool)), _1188685), hAPP(hAPP(c_Product__Type_OPair(_1188679, _1188681), _1188687), _1188689)), _1188691)), -(hBOOL(hAPP(hAPP(hAPP(_1188685, _1188687), _1188689), _1188691)))], (23372 ^ _780461) ^ [_1188830, _1188832, _1188834, _1188836] : [-(hAPP(c_Product__Type_Osnd(_1188830, _1188832), hAPP(hAPP(c_Product__Type_OPair(_1188830, _1188832), _1188834), _1188836)) = _1188836)], (23374 ^ _780461) ^ [_1188874, _1188876, _1188878, _1188880, _1188882] : [hAPP(c_Product__Type_Osnd(_1188874, _1188876), hAPP(hAPP(c_Product__Type_OPair(_1188874, _1188876), _1188878), _1188880)) = _1188882, -(_1188880 = _1188882)], (23380 ^ _780461) ^ [_1189014, _1189016, _1189018, _1189020, _1189022, _1189024] : [hAPP(c_Product__Type_Oapsnd(_1189014, _1189016, _1189018, _1189020), _1189022) = hAPP(c_Product__Type_Oapsnd(_1189014, _1189016, _1189018, _1189024), _1189022), -(hAPP(_1189020, hAPP(c_Product__Type_Osnd(_1189018, _1189014), _1189022)) = hAPP(_1189024, hAPP(c_Product__Type_Osnd(_1189018, _1189014), _1189022)))], (23386 ^ _780461) ^ [_1189163, _1189165, _1189167, _1189169, _1189171, _1189173] : [hAPP(_1189169, hAPP(c_Product__Type_Osnd(_1189167, _1189163), _1189171)) = hAPP(_1189173, hAPP(c_Product__Type_Osnd(_1189167, _1189163), _1189171)), -(hAPP(c_Product__Type_Oapsnd(_1189163, _1189165, _1189167, _1189169), _1189171) = hAPP(c_Product__Type_Oapsnd(_1189163, _1189165, _1189167, _1189173), _1189171))], (23392 ^ _780461) ^ [_1189318, _1189320, _1189322, _1189324, _1189326] : [-(hAPP(c_Product__Type_Osnd(_1189318, _1189320), hAPP(c_Product__Type_Oapsnd(_1189322, _1189320, _1189318, _1189324), _1189326)) = hAPP(_1189324, hAPP(c_Product__Type_Osnd(_1189318, _1189322), _1189326)))], (23394 ^ _780461) ^ [_1189372, _1189374, _1189376] : [-(hAPP(c_Product__Type_Osnd(_1189372, _1189374), _1189376) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1189372, _1189374, _1189374), hAPP(c_COMBK(tc_fun(_1189374, _1189374), _1189372), c_COMBI(_1189374))), _1189376))], (23396 ^ _780461) ^ [_1189426, _1189428] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189426, _1189428) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1189426, _1189428)))], (23398 ^ _780461) ^ [_1189457] : [-(_1189457 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1189457), 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)))))], (23404 ^ _780461) ^ [_1189496, _1189498, _1189500] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189496, _1189496), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189498), _1189500))), -(_1189496 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1189500 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23414 ^ _780461) ^ [_1189612, _1189614, _1189616, _1189618, _1189620, _1189622] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189612, _1189614), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189616), _1189618))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189612, _1189614), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189620), _1189622))), -(_1189614 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1189616 = _1189620)], (23428 ^ _780461) ^ [_1189816, _1189818, _1189820, _1189822, _1189824, _1189826] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189816, _1189818), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189820), _1189822))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189816, _1189818), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189824), _1189826))), -(_1189818 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1189822 = _1189826)], (23442 ^ _780461) ^ [_1190020, _1190022, _1190024] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1190020), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1190022)), _1190024)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190020, _1190022), hAPP(c_Divides_OnegateSnd, _1190024))))], (23448 ^ _780461) ^ [_1190133, _1190135] : [-(_1190133 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190135, _1190133), c_Divides_Odivmod__int(_1190135, _1190133))))], (23454 ^ _780461) ^ [_1190177, _1190179, _1190181] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190177, _1190177), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1190179), _1190181))), -(_1190177 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1190179 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (23464 ^ _780461) ^ [_1190293, _1190295, _1190297, _1190299] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190293, _1190295), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1190297), _1190299))), -(_1190295 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190293, _1190295) = _1190299)], (23474 ^ _780461) ^ [_1190419, _1190421, _1190423, _1190425] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190419, _1190421), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1190423), _1190425))), -(_1190421 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190419), _1190421) = _1190423)], (23484 ^ _780461) ^ [_1190549, _1190551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190549), 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)), _1190551)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190549, _1190551), c_Divides_OnegDivAlg(_1190549, _1190551))))], (23494 ^ _780461) ^ [_1190708, _1190710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190708), 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)), _1190710)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190708, _1190710) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1190708, _1190710)))], (23504 ^ _780461) ^ [_1190867, _1190869] : [-(_1190867 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190869, _1190867), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190869), _1190867)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1190869, _1190867)))))], (23510 ^ _780461) ^ [_1190924, _1190926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190926)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190924, _1190926), c_Divides_OposDivAlg(_1190924, _1190926))))], (23520 ^ _780461) ^ [_1191077, _1191079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191079)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1191077, _1191079) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1191077, _1191079)))], (23530 ^ _780461) ^ [_1191234] : [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), _1191234))), -(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), _1191234)) = 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), _1191234))))], (23536 ^ _780461) ^ [_1191351, _1191353, _1191355, _1191357, _1191359, _1191361, _1191363] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1191351, _1191353), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1191355), _1191357))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1191359, _1191353), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1191361), _1191363))), -(_1191353 = 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), _1191351), _1191359), _1191353), 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), _1191355), _1191361)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191357), _1191363)), _1191353))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191357), _1191363), _1191353)))))], (23550 ^ _780461) ^ [_1191661, _1191663, _1191665, _1191667] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1191661, _1191663), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1191665), _1191667))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1191661), _1191663), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1191667), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1191665)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1191665)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1191667), 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), _1191663), _1191667))))))], (23556 ^ _780461) ^ [_1191888, _1191890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191890), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1191888, _1191890) = 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), _1191888), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1191890)))))], (23566 ^ _780461) ^ [_1192078, _1192080] : [23567 ^ _780461 : [(23568 ^ _780461) ^ [] : [_1192078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23570 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1192080), _1192078))]], -(c_Divides_Odivmod__nat(_1192080, _1192078) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1192080))], (23574 ^ _780461) ^ [_1192209, _1192211] : [-(c_Divides_Odivmod__nat(_1192211, _1192209) = 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), _1192211), _1192209), _1192209))), -(_1192209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1192211), _1192209)))], (23584 ^ _780461) ^ [_1192274, _1192276, _1192278, _1192280] : [_1192274 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192276), _1192278)), _1192280), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192274, _1192276), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192278), _1192280)))), 23591 ^ _780461 : [(23592 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192276)))], (23594 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192280), _1192276))]], 23599 ^ _780461 : [(23600 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192276))], (23602 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192276), _1192280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192280), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (23610 ^ _780461) ^ [_1192736, _1192738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192736), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192738), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1192736, _1192738) = 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), _1192736), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1192738)))))], (23620 ^ _780461) ^ [_1192923, _1192925, _1192927, _1192929, _1192931] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192923, _1192925), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192927), _1192929))), -(_1192925 = 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), _1192931), _1192923), _1192925), 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), _1192931), _1192927)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192931), _1192929)), _1192925))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192931), _1192929), _1192925)))))], (23630 ^ _780461) ^ [_1193145, _1193147, _1193149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1193145, tc_HOL_Obool)), _1193147), _1193149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1193145, tc_HOL_Obool)), _1193149), _1193147)), -(_1193147 = _1193149)], (23640 ^ _780461) ^ [_1193318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1193318)), 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), _1193318)) = 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), _1193318))))))], (23646 ^ _780461) ^ [_1193451, _1193453, _1193455] : [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), _1193451), _1193453))), -(hBOOL(hAPP(hAPP(_1193455, _1193451), _1193453))), 23653 ^ _780461 : [(23654 ^ _780461) ^ [] : [-(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), 23651 ^ [_1193451, _1193453, _1193455]), 23652 ^ [_1193451, _1193453, _1193455]))))], (23662 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1193455, 23651 ^ [_1193451, _1193453, _1193455]), 23652 ^ [_1193451, _1193453, _1193455]))], (23656 ^ _780461) ^ [] : [-(23652 ^ [_1193451, _1193453, _1193455] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1193455, 23652 ^ [_1193451, _1193453, _1193455]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 23651 ^ [_1193451, _1193453, _1193455], 23652 ^ [_1193451, _1193453, _1193455]))))]]], (23666 ^ _780461) ^ [_1193873, _1193875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193873), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193875), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1193873), _1193875) = 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), _1193873), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1193875)))))], (23676 ^ _780461) ^ [_1194064, _1194066] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1194064)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1194066)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1194066))), 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), _1194064)), c_Int_Onat)))))], (23678 ^ _780461) ^ [_1194127, _1194129, _1194131] : [class_Orderings_Olinorder(_1194127), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194127), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194127), _1194129), _1194131)), _1194129)))], (23684 ^ _780461) ^ [_1194234, _1194236, _1194238] : [class_Orderings_Olinorder(_1194234), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194234), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194234), _1194236), _1194238)), _1194238)))], (23690 ^ _780461) ^ [_1194341, _1194343, _1194345] : [class_Orderings_Olinorder(_1194341), 23693 ^ _780461 : [(23694 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194341), _1194343), _1194345)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194341), _1194343), _1194345) = _1194343)], (23700 ^ _780461) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194341), _1194343), _1194345) = _1194343, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194341), _1194343), _1194345)))]]], (23706 ^ _780461) ^ [_1194597, _1194599, _1194601, _1194603] : [class_Orderings_Olinorder(_1194597), 23709 ^ _780461 : [(23710 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194597), _1194599), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194597), _1194601), _1194603))), 23713 ^ _780461 : [(23714 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194597), _1194599), _1194601)))], (23716 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194597), _1194599), _1194603)))]]], (23718 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194597), _1194599), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194597), _1194601), _1194603)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194597), _1194599), _1194601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194597), _1194599), _1194603))]]], (23728 ^ _780461) ^ [_1194977, _1194979, _1194981, _1194983] : [class_Orderings_Olinorder(_1194977), 23731 ^ _780461 : [(23742 ^ _780461) ^ [] : [23743 ^ _780461 : [(23744 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194977), _1194979), _1194983))], (23746 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194977), _1194981), _1194983))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194977), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194977), _1194979), _1194981)), _1194983)))], (23732 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194977), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1194977), _1194979), _1194981)), _1194983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194977), _1194979), _1194983))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194977), _1194981), _1194983)))]]], (23750 ^ _780461) ^ [_1195326, _1195328, _1195330, _1195332] : [class_Orderings_Olinorder(_1195326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195326), _1195328), _1195330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195326), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195326), _1195328), _1195332)), _1195330)))], (23760 ^ _780461) ^ [_1195505, _1195507, _1195509, _1195511] : [class_Orderings_Olinorder(_1195505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195505), _1195507), _1195509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195505), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195505), _1195511), _1195507)), _1195509)))], (23770 ^ _780461) ^ [_1195684, _1195686, _1195688] : [class_Orderings_Olinorder(_1195684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195684), _1195686), _1195688)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195684), _1195686), _1195688) = _1195686)], (23780 ^ _780461) ^ [_1195845, _1195847, _1195849] : [class_Orderings_Olinorder(_1195845), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195845), _1195847), _1195849)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1195845), _1195849), _1195847) = _1195847)], (23790 ^ _780461) ^ [_1196006, _1196008, _1196010, _1196012] : [class_Orderings_Olinorder(_1196006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196006), _1196008), _1196010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196006), _1196008), _1196012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196006), _1196008), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196006), _1196010), _1196012))))], (23804 ^ _780461) ^ [_1196255, _1196257, _1196259, _1196261] : [class_Orderings_Olinorder(_1196255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196255), _1196257), _1196259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196255), _1196257), _1196261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196255), _1196257), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196255), _1196259), _1196261))))], (23818 ^ _780461) ^ [_1196504, _1196506, _1196508, _1196510, _1196512] : [class_Orderings_Olinorder(_1196504), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196504), _1196506), _1196508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196504), _1196510), _1196512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196504), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196504), _1196506), _1196510)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196504), _1196508), _1196512))))], (23832 ^ _780461) ^ [_1196775, _1196777, _1196779, _1196781] : [class_Orderings_Olinorder(_1196775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196775), _1196777), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1196775), _1196779), _1196781))), 23839 ^ _780461 : [(23840 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196775), _1196777), _1196779)))], (23842 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196775), _1196777), _1196781)))]]], (23844 ^ _780461) ^ [_1196998] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1196998) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23846 ^ _780461) ^ [_1197024] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1197024), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23848 ^ _780461) ^ [_1197053, _1197055, _1197057, _1197059] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1197053), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197053), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197053), _1197055), _1197057)), _1197059) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197053), _1197055), _1197059)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197053), _1197057), _1197059)))], (23854 ^ _780461) ^ [_1197212, _1197214, _1197216, _1197218] : [class_Groups_Oordered__ab__group__add(_1197212), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1197212), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197212), _1197214), _1197216)), _1197218) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197212), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1197212), _1197214), _1197218)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1197212), _1197216), _1197218)))], (23860 ^ _780461) ^ [_1197371, _1197373, _1197375, _1197377] : [class_Orderings_Olinorder(_1197371), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197371), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197371), _1197373), _1197375)), _1197377) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197371), _1197373), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197371), _1197375), _1197377)))], (23866 ^ _780461) ^ [_1197514, _1197516, _1197518, _1197520] : [class_Orderings_Olinorder(_1197514), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197514), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197514), _1197516), _1197518)), _1197520) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197514), _1197516), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197514), _1197518), _1197520)))], (23872 ^ _780461) ^ [_1197657, _1197659, _1197661, _1197663] : [class_Orderings_Olinorder(_1197657), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197657), _1197659), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197657), _1197661), _1197663)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197657), _1197661), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197657), _1197659), _1197663)))], (23878 ^ _780461) ^ [_1197800, _1197802, _1197804, _1197806] : [class_Orderings_Olinorder(_1197800), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197800), _1197802), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197800), _1197804), _1197806)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197800), _1197804), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197800), _1197802), _1197806)))], (23884 ^ _780461) ^ [_1197943, _1197945, _1197947] : [class_Orderings_Olinorder(_1197943), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197943), _1197945), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197943), _1197945), _1197947)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1197943), _1197945), _1197947))], (23890 ^ _780461) ^ [_1198068, _1198070, _1198072] : [class_Orderings_Olinorder(_1198068), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198068), _1198070), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198068), _1198070), _1198072)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198068), _1198070), _1198072))], (23896 ^ _780461) ^ [_1198193, _1198195, _1198197] : [class_Orderings_Olinorder(_1198193), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198193), _1198195), _1198197) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198193), _1198197), _1198195))], (23902 ^ _780461) ^ [_1198302, _1198304, _1198306] : [class_Orderings_Olinorder(_1198302), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198302), _1198304), _1198306) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198302), _1198306), _1198304))], (23908 ^ _780461) ^ [_1198411, _1198413] : [class_Orderings_Olinorder(_1198411), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198411), _1198413), _1198413) = _1198413)], (23914 ^ _780461) ^ [_1198502, _1198504, _1198506, _1198508] : [class_Orderings_Olinorder(_1198502), 23917 ^ _780461 : [(23918 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198502), _1198504), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198502), _1198506), _1198508))), 23921 ^ _780461 : [(23922 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198502), _1198504), _1198506)))], (23924 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198502), _1198504), _1198508)))]]], (23926 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198502), _1198504), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198502), _1198506), _1198508)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198502), _1198504), _1198506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198502), _1198504), _1198508))]]], (23936 ^ _780461) ^ [_1198882, _1198884, _1198886, _1198888] : [class_Orderings_Olinorder(_1198882), 23939 ^ _780461 : [(23950 ^ _780461) ^ [] : [23951 ^ _780461 : [(23952 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198882), _1198884), _1198888))], (23954 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198882), _1198886), _1198888))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198882), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198882), _1198884), _1198886)), _1198888)))], (23940 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198882), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1198882), _1198884), _1198886)), _1198888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198882), _1198884), _1198888))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1198882), _1198886), _1198888)))]]], (23958 ^ _780461) ^ [_1199231, _1199233, _1199235, _1199237] : [class_Orderings_Olinorder(_1199231), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199231), _1199233), _1199235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199231), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199231), _1199233), _1199237)), _1199235)))], (23968 ^ _780461) ^ [_1199410, _1199412, _1199414, _1199416] : [class_Orderings_Olinorder(_1199410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199410), _1199412), _1199414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1199410), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1199410), _1199416), _1199412)), _1199414)))], (23978 ^ _780461) ^ [_1199589, _1199591] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199589)), hAPP(c_Nat_OSuc, _1199591)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1199589), _1199591)))], (23980 ^ _780461) ^ [_1199635, _1199637, _1199639] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1199635), _1199637)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1199639), _1199637)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1199635), _1199639)), _1199637))], (23982 ^ _780461) ^ [_1199692, _1199694, _1199696, _1199698, _1199700] : [hAPP(c_Product__Type_Ofst(_1199692, _1199694), hAPP(hAPP(c_Product__Type_OPair(_1199692, _1199694), _1199696), _1199698)) = _1199700, -(_1199696 = _1199700)], (23988 ^ _780461) ^ [_1199805, _1199807, _1199809, _1199811] : [-(hAPP(c_Product__Type_Ofst(_1199805, _1199807), hAPP(hAPP(c_Product__Type_OPair(_1199805, _1199807), _1199809), _1199811)) = _1199809)], (23990 ^ _780461) ^ [_1199849, _1199851, _1199853, _1199855] : [hAPP(c_Product__Type_Ofst(_1199849, _1199851), _1199853) = hAPP(c_Product__Type_Ofst(_1199849, _1199851), _1199855), hAPP(c_Product__Type_Osnd(_1199849, _1199851), _1199853) = hAPP(c_Product__Type_Osnd(_1199849, _1199851), _1199855), -(_1199853 = _1199855)], (24000 ^ _780461) ^ [_1200055, _1200057, _1200059, _1200061] : [_1200055 = _1200057, 24003 ^ _780461 : [(24004 ^ _780461) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1200059, _1200061), _1200055) = hAPP(c_Product__Type_Ofst(_1200059, _1200061), _1200057))], (24006 ^ _780461) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1200059, _1200061), _1200055) = hAPP(c_Product__Type_Osnd(_1200059, _1200061), _1200057))]]], (24008 ^ _780461) ^ [_1200206, _1200208, _1200210, _1200212] : [-(_1200206 = _1200208), hAPP(c_Product__Type_Ofst(_1200210, _1200212), _1200206) = hAPP(c_Product__Type_Ofst(_1200210, _1200212), _1200208), hAPP(c_Product__Type_Osnd(_1200210, _1200212), _1200206) = hAPP(c_Product__Type_Osnd(_1200210, _1200212), _1200208)], (24018 ^ _780461) ^ [_1200393, _1200395, _1200397, _1200399, _1200401] : [-(hAPP(c_Product__Type_Ofst(_1200393, _1200395), hAPP(c_Product__Type_Oapsnd(_1200397, _1200395, _1200393, _1200399), _1200401)) = hAPP(c_Product__Type_Ofst(_1200393, _1200397), _1200401))], (24020 ^ _780461) ^ [_1200444, _1200446, _1200448] : [-(hAPP(c_Product__Type_Ofst(_1200444, _1200446), _1200448) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200444, _1200446, _1200444), c_COMBK(_1200444, _1200446)), _1200448))], (24022 ^ _780461) ^ [_1200490, _1200492, _1200494] : [class_Int_Onumber(_1200490), class_Orderings_Oord(_1200490), 24029 ^ _780461 : [(24030 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200490), hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200492)), hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200494))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200490), hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200492)), hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200494)) = hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200492))], (24036 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200490), hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200492)), hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200494)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1200490), hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200492)), hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200494)) = hAPP(c_Int_Onumber__class_Onumber__of(_1200490), _1200494))]]], (24042 ^ _780461) ^ [_1200882, _1200884, _1200886] : [-(_1200882 = hAPP(hAPP(c_Product__Type_OPair(_1200884, _1200886), hAPP(c_Product__Type_Ofst(_1200884, _1200886), _1200882)), hAPP(c_Product__Type_Osnd(_1200884, _1200886), _1200882)))], (24044 ^ _780461) ^ [_1200930, _1200932, _1200934] : [-(hAPP(hAPP(c_Product__Type_OPair(_1200930, _1200932), hAPP(c_Product__Type_Ofst(_1200930, _1200932), _1200934)), hAPP(c_Product__Type_Osnd(_1200930, _1200932), _1200934)) = _1200934)], (24046 ^ _780461) ^ [_1200978, _1200980, _1200982, _1200984, _1200986] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200978, _1200980, _1200982), _1200984), _1200986) = hAPP(hAPP(_1200984, hAPP(c_Product__Type_Ofst(_1200978, _1200980), _1200986)), hAPP(c_Product__Type_Osnd(_1200978, _1200980), _1200986)))], (24048 ^ _780461) ^ [_1201037, _1201039] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1201037), _1201039) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1201037, _1201039)))], (24050 ^ _780461) ^ [_1201074, _1201076] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1201074, _1201076) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1201074, _1201076)))], (24052 ^ _780461) ^ [_1201109, _1201111, _1201113, _1201115, _1201117] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1201109, _1201111, _1201113), _1201115), _1201117) = hAPP(hAPP(_1201115, hAPP(c_Product__Type_Ofst(_1201109, _1201111), _1201117)), hAPP(c_Product__Type_Osnd(_1201109, _1201111), _1201117)))], (24054 ^ _780461) ^ [_1201168, _1201170, _1201172, _1201174, _1201176, _1201178] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1201168, _1201170), _1201170, _1201172), hAPP(hAPP(c_COMBB(_1201174, tc_fun(_1201170, _1201172), tc_prod(_1201168, _1201170)), _1201176), hAPP(hAPP(c_COMBB(_1201168, _1201174, tc_prod(_1201168, _1201170)), _1201178), c_Product__Type_Ofst(_1201168, _1201170)))), c_Product__Type_Osnd(_1201168, _1201170)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1201168, _1201170, _1201172), hAPP(hAPP(c_COMBB(_1201174, tc_fun(_1201170, _1201172), _1201168), _1201176), _1201178)))], (24056 ^ _780461) ^ [_1201269, _1201271, _1201273, _1201275, _1201277] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1201269, _1201271, _1201273), _1201275), _1201277) = hAPP(hAPP(_1201275, hAPP(c_Product__Type_Ofst(_1201269, _1201271), _1201277)), hAPP(c_Product__Type_Osnd(_1201269, _1201271), _1201277)))], (24058 ^ _780461) ^ [_1201328, _1201330, _1201332] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201328, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201328, tc_HOL_Obool)), _1201330), _1201332)), _1201330)))], (24060 ^ _780461) ^ [_1201376, _1201378, _1201380, _1201382, _1201384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201376, tc_HOL_Obool)), _1201378), _1201380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201376, tc_HOL_Obool)), _1201382), _1201384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201376, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201376, tc_HOL_Obool)), _1201378), _1201384)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201376, tc_HOL_Obool)), _1201380), _1201382))))], (24070 ^ _780461) ^ [_1201621, _1201623, _1201625, _1201627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201621, tc_HOL_Obool)), _1201623), _1201625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201621, tc_HOL_Obool)), _1201625), _1201627)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201621, tc_HOL_Obool)), _1201625), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201621, tc_HOL_Obool)), _1201627), _1201623)) = _1201623)], (24080 ^ _780461) ^ [_1201860, _1201862, _1201864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1201860, tc_HOL_Obool)), _1201862), _1201864)), 24083 ^ _780461 : [(24084 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201860, tc_HOL_Obool)), _1201862), _1201864)))], (24086 ^ _780461) ^ [] : [_1201862 = _1201864]]], (24088 ^ _780461) ^ [_1202009, _1202011, _1202013] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1202009, tc_HOL_Obool)), _1202011), _1202013))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202009, tc_HOL_Obool)), _1202011), _1202013)), -(_1202011 = _1202013)], (24108 ^ _780461) ^ [_1202333, _1202335, _1202337] : [24109 ^ _780461 : [(24110 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1202333, tc_HOL_Obool)), _1202335), _1202337))], (24112 ^ _780461) ^ [] : [_1202335 = _1202337]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202333, tc_HOL_Obool)), _1202335), _1202337)))], (24098 ^ _780461) ^ [_1202205, _1202207, _1202209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202205, tc_HOL_Obool)), _1202207), _1202209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1202205, tc_HOL_Obool)), _1202207), _1202209))), -(_1202207 = _1202209)], (24116 ^ _780461) ^ [_1202492, _1202494, _1202496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1202492, tc_HOL_Obool)), _1202494), _1202496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202492, tc_HOL_Obool)), _1202494), _1202496)))], (24122 ^ _780461) ^ [_1202611, _1202613, _1202615, _1202617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1202611, tc_HOL_Obool)), _1202613), _1202615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202611, tc_HOL_Obool)), _1202615), _1202617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1202611, tc_HOL_Obool)), _1202613), _1202617)))], (24132 ^ _780461) ^ [_1202808, _1202810, _1202812, _1202814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1202808, tc_HOL_Obool)), _1202810), _1202812)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1202808, tc_HOL_Obool)), _1202812), _1202814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1202808, tc_HOL_Obool)), _1202810), _1202814)))], (24142 ^ _780461) ^ [_1203005, _1203007, _1203009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203005, tc_HOL_Obool)), _1203007), _1203009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203005, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203005, tc_HOL_Obool)), _1203009)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203005, tc_HOL_Obool)), _1203007))))], (24148 ^ _780461) ^ [_1203174, _1203176, _1203178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203174, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203174, tc_HOL_Obool)), _1203176)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203174, tc_HOL_Obool)), _1203178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203174, tc_HOL_Obool)), _1203178), _1203176)))], (24154 ^ _780461) ^ [_1203321, _1203323, _1203325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203321, tc_HOL_Obool)), _1203325), _1203323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203321, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203321, tc_HOL_Obool)), _1203323)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1203321, tc_HOL_Obool)), _1203325))))], (24160 ^ _780461) ^ [_1203474, _1203476] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203474, tc_HOL_Obool)), _1203476), _1203476)))], (24162 ^ _780461) ^ [_1203527, _1203529, _1203531] : [_1203527 = _1203529, 24165 ^ _780461 : [(24166 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203531, tc_HOL_Obool)), _1203527), _1203529)))], (24168 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203531, tc_HOL_Obool)), _1203529), _1203527)))]]], (24170 ^ _780461) ^ [_1203668, _1203670, _1203672] : [-(_1203668 = _1203670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203672, tc_HOL_Obool)), _1203668), _1203670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203672, tc_HOL_Obool)), _1203670), _1203668))], (24180 ^ _780461) ^ [_1203843, _1203845, _1203847] : [_1203843 = _1203845, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203847, tc_HOL_Obool)), _1203843), _1203845)))], (24186 ^ _780461) ^ [_1203942, _1203944, _1203946] : [_1203942 = _1203944, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203946, tc_HOL_Obool)), _1203944), _1203942)))], (24192 ^ _780461) ^ [_1204041, _1204043, _1204045, _1204047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204041, tc_HOL_Obool)), _1204043), _1204045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204041, tc_HOL_Obool)), _1204045), _1204047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204041, tc_HOL_Obool)), _1204043), _1204047)))], (24202 ^ _780461) ^ [_1204238, _1204240, _1204242] : [_1204238 = _1204240, 24205 ^ _780461 : [(24206 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204242, tc_HOL_Obool)), _1204238), _1204240)))], (24208 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1204242, tc_HOL_Obool)), _1204240), _1204238)))]]], (24210 ^ _780461) ^ [_1204387, _1204389] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204387)), _1204389) = 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), _1204387)), _1204389))], (24212 ^ _780461) ^ [_1204432, _1204434] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1204432), hAPP(c_Nat_OSuc, _1204434)) = 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)), _1204434)), _1204432))], (24214 ^ _780461) ^ [_1204477, _1204479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204477), 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)), _1204479)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204477), _1204479) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1204477, _1204479)))], (24224 ^ _780461) ^ [_1204644, _1204646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204646)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204644), _1204646) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1204644, _1204646)))], (24234 ^ _780461) ^ [_1204805] : [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), _1204805))), -(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), _1204805)) = 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), _1204805))))], (24240 ^ _780461) ^ [_1204920, _1204922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204922), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1204920), _1204922) = 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), _1204920), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204922)))))], (24250 ^ _780461) ^ [_1205105, _1205107] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1205105)), hAPP(c_Nat_OSuc, _1205107)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1205105))), 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)), _1205107)))))], (24252 ^ _780461) ^ [_1205162, _1205164, _1205166, _1205168, _1205170] : [-(c_Product__Type_Oprod_Oprod__size(_1205162, _1205164, _1205166, _1205168, _1205170) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1205166, hAPP(c_Product__Type_Ofst(_1205162, _1205164), _1205170))), hAPP(_1205168, hAPP(c_Product__Type_Osnd(_1205162, _1205164), _1205170)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24254 ^ _780461) ^ [_1205229, _1205231, _1205233, _1205235, _1205237, _1205239] : [hBOOL(hAPP(_1205229, _1205231)), hBOOL(hAPP(_1205233, _1205235)), 24261 ^ _780461 : [(24262 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1205229, hAPP(c_Product__Type_Ofst(_1205237, _1205239), hAPP(hAPP(c_Product__Type_OPair(_1205237, _1205239), _1205231), _1205235)))))], (24264 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1205233, hAPP(c_Product__Type_Osnd(_1205237, _1205239), hAPP(hAPP(c_Product__Type_OPair(_1205237, _1205239), _1205231), _1205235)))))]]], (24266 ^ _780461) ^ [_1205476, _1205478, _1205480, _1205482, _1205484] : [hBOOL(hAPP(hAPP(_1205476, _1205478), _1205480)), -(hBOOL(hAPP(hAPP(_1205476, hAPP(c_Product__Type_Osnd(_1205482, _1205484), hAPP(hAPP(c_Product__Type_OPair(_1205482, _1205484), _1205480), _1205478))), hAPP(c_Product__Type_Ofst(_1205482, _1205484), hAPP(hAPP(c_Product__Type_OPair(_1205482, _1205484), _1205480), _1205478)))))], (24272 ^ _780461) ^ [_1205639] : [class_Orderings_Oord(_1205639), -(c_Orderings_Oord__class_Omin(_1205639) = c_Orderings_Oord_Omin(_1205639, c_Orderings_Oord__class_Oless__eq(_1205639)))], (24278 ^ _780461) ^ [_1205726, _1205728, _1205730, _1205732, _1205734, _1205736] : [-(c_Product__Type_Oprod_Oprod__rec(_1205726, _1205728, _1205730, _1205732, hAPP(hAPP(c_Product__Type_OPair(_1205726, _1205728), _1205734), _1205736)) = hAPP(hAPP(_1205732, _1205734), _1205736))], (24280 ^ _780461) ^ [_1205798, _1205800, _1205802] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1205798, tc_HOL_Obool)), _1205800) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1205798, tc_HOL_Obool)), _1205802), -(_1205800 = _1205802)], (24286 ^ _780461) ^ [_1205905, _1205907, _1205909] : [_1205907 = _1205909, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1205905, tc_HOL_Obool)), _1205907) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1205905, tc_HOL_Obool)), _1205909))], (24292 ^ _780461) ^ [_1206018, _1206020] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1206018, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1206018, tc_HOL_Obool)), _1206020)) = _1206020)], (24294 ^ _780461) ^ [_1206059, _1206061, _1206063] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206059, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206059, tc_HOL_Obool)), _1206061), _1206063)), _1206063) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206059, tc_HOL_Obool)), _1206061), _1206063))], (24296 ^ _780461) ^ [_1206119, _1206121, _1206123, _1206125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1206119, tc_HOL_Obool)), _1206121), _1206123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1206119, tc_HOL_Obool)), _1206123), _1206125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1206119, tc_HOL_Obool)), _1206121), _1206125)))], (24306 ^ _780461) ^ [_1206316, _1206318] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206316), _1206318) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1206316, _1206318)))], (24340 ^ _780461) ^ [_1206907, _1206909, _1206911] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1206907, _1206909), _1206911))), _1206907 = 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), _1206911)), _1206909)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1206911)), 24347 ^ _780461 : [(24348 ^ _780461) ^ [] : [-(_1206909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24350 ^ _780461) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1206911) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 24351 ^ _780461 : [(24352 ^ _780461) ^ [] : [_1206909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24354 ^ _780461) ^ [] : [24355 ^ _780461 : [(24356 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206909)))], (24358 ^ _780461) ^ [] : [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), _1206911))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1206911)), _1206909))]], 24363 ^ _780461 : [(24364 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206909))], (24366 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206909), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1206911))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1206911)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (24308 ^ _780461) ^ [_1206371, _1206373, _1206375] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1206371, _1206373), _1206375)), 24311 ^ _780461 : [(24312 ^ _780461) ^ [] : [-(_1206371 = 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), _1206375)), _1206373)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1206375)))], (24314 ^ _780461) ^ [] : [_1206373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1206375) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24320 ^ _780461) ^ [] : [-(_1206373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24323 ^ _780461 : [(24324 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206373)), 24327 ^ _780461 : [(24328 ^ _780461) ^ [] : [-(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), _1206375))))], (24330 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1206375)), _1206373)))]]], (24332 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206373))), 24335 ^ _780461 : [(24336 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206373), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1206375))))], (24338 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1206375)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (24374 ^ _780461) ^ [_1207516, _1207518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1207516)), -(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(_1207516), _1207518))), _1207516)))], (24380 ^ _780461) ^ [_1207623, _1207625] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1207623), _1207625) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1207623, 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)))), _1207625))))], (24382 ^ _780461) ^ [_1207661, _1207663] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207661)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1207663)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1207663))), 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, _1207661))), 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), _1207661)), c_Int_Onat)))))], (24384 ^ _780461) ^ [_1207733, _1207735] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1207733)), hAPP(c_Nat_OSuc, _1207735)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1207733))), 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, _1207735))), 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)), _1207735)))))], (24386 ^ _780461) ^ [_1207799, _1207801, _1207803, _1207805, _1207807, _1207809, _1207811] : [-(hAPP(c_Product__Type_Oapsnd(_1207799, _1207801, _1207803, _1207805), hAPP(c_Product__Type_Oapfst(_1207807, _1207803, _1207799, _1207809), _1207811)) = hAPP(hAPP(c_Product__Type_OPair(_1207803, _1207801), hAPP(_1207809, hAPP(c_Product__Type_Ofst(_1207807, _1207799), _1207811))), hAPP(_1207805, hAPP(c_Product__Type_Osnd(_1207807, _1207799), _1207811))))], (24388 ^ _780461) ^ [_1207877, _1207879, _1207881, _1207883] : [class_Orderings_Olinorder(_1207877), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1207877), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207877), _1207879), _1207881)), _1207883) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1207877), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1207877), _1207879), _1207883)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1207877), _1207881), _1207883)))], (24394 ^ _780461) ^ [_1208036, _1208038, _1208040, _1208042] : [class_Orderings_Olinorder(_1208036), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208036), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208036), _1208038), _1208040)), _1208042) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208036), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208036), _1208038), _1208042)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208036), _1208040), _1208042)))], (24400 ^ _780461) ^ [_1208195, _1208197, _1208199, _1208201] : [class_Orderings_Olinorder(_1208195), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208195), _1208197), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208195), _1208199), _1208201)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208195), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208195), _1208197), _1208199)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208195), _1208197), _1208201)))], (24406 ^ _780461) ^ [_1208354, _1208356, _1208358, _1208360] : [class_Orderings_Olinorder(_1208354), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208354), _1208356), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208354), _1208358), _1208360)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208354), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208354), _1208356), _1208358)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208354), _1208356), _1208360)))], (24412 ^ _780461) ^ [_1208513, _1208515, _1208517] : [class_Orderings_Olinorder(_1208513), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208513), _1208515), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208513), _1208515), _1208517)) = _1208515)], (24418 ^ _780461) ^ [_1208622, _1208624, _1208626] : [class_Orderings_Olinorder(_1208622), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208622), _1208624), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1208622), _1208624), _1208626)) = _1208624)], (24424 ^ _780461) ^ [_1208731, _1208733, _1208735, _1208737] : [class_Orderings_Olinorder(_1208731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208731), _1208733), _1208735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208731), _1208733), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208731), _1208737), _1208735))))], (24434 ^ _780461) ^ [_1208910, _1208912, _1208914, _1208916] : [class_Orderings_Olinorder(_1208910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208910), _1208912), _1208914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208910), _1208912), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1208910), _1208914), _1208916))))], (24444 ^ _780461) ^ [_1209089, _1209091, _1209093, _1209095] : [class_Orderings_Olinorder(_1209089), 24447 ^ _780461 : [(24448 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209089), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209089), _1209091), _1209093)), _1209095)), 24451 ^ _780461 : [(24452 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209089), _1209091), _1209095)))], (24454 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209089), _1209093), _1209095)))]]], (24456 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209089), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209089), _1209091), _1209093)), _1209095))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209089), _1209091), _1209095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209089), _1209093), _1209095))]]], (24466 ^ _780461) ^ [_1209469, _1209471, _1209473, _1209475] : [class_Orderings_Olinorder(_1209469), 24469 ^ _780461 : [(24480 ^ _780461) ^ [] : [24481 ^ _780461 : [(24482 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209469), _1209471), _1209473))], (24484 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209469), _1209471), _1209475))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209469), _1209471), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209469), _1209473), _1209475))))], (24470 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209469), _1209471), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209469), _1209473), _1209475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209469), _1209471), _1209473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209469), _1209471), _1209475)))]]], (24488 ^ _780461) ^ [_1209818, _1209820, _1209822, _1209824] : [class_Groups_Oordered__ab__group__add(_1209818), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1209818), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209818), _1209820), _1209822)), _1209824) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209818), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1209818), _1209820), _1209824)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1209818), _1209822), _1209824)))], (24494 ^ _780461) ^ [_1209977, _1209979, _1209981] : [class_Orderings_Olinorder(_1209977), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209977), _1209979), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1209977), _1209979), _1209981))))], (24500 ^ _780461) ^ [_1210084, _1210086, _1210088] : [class_Orderings_Olinorder(_1210084), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210084), _1210086), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210084), _1210088), _1210086))))], (24506 ^ _780461) ^ [_1210191, _1210193, _1210195] : [class_Orderings_Olinorder(_1210191), 24509 ^ _780461 : [(24510 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210191), _1210193), _1210195)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210191), _1210193), _1210195) = _1210195)], (24516 ^ _780461) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210191), _1210193), _1210195) = _1210195, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210191), _1210193), _1210195)))]]], (24522 ^ _780461) ^ [_1210447, _1210449, _1210451, _1210453] : [class_Orderings_Olinorder(_1210447), 24525 ^ _780461 : [(24536 ^ _780461) ^ [] : [24537 ^ _780461 : [(24538 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210447), _1210449), _1210451))], (24540 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210447), _1210449), _1210453))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210447), _1210449), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210447), _1210451), _1210453))))], (24526 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210447), _1210449), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210447), _1210451), _1210453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210447), _1210449), _1210451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210447), _1210449), _1210453)))]]], (24544 ^ _780461) ^ [_1210796, _1210798, _1210800, _1210802] : [class_Orderings_Olinorder(_1210796), 24547 ^ _780461 : [(24548 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210796), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210796), _1210798), _1210800)), _1210802)), 24551 ^ _780461 : [(24552 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210796), _1210798), _1210802)))], (24554 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210796), _1210800), _1210802)))]]], (24556 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210796), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1210796), _1210798), _1210800)), _1210802))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210796), _1210798), _1210802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210796), _1210800), _1210802))]]], (24566 ^ _780461) ^ [_1211176, _1211178, _1211180, _1211182] : [class_Orderings_Olinorder(_1211176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211176), _1211178), _1211180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211176), _1211178), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211176), _1211180), _1211182))))], (24576 ^ _780461) ^ [_1211355, _1211357, _1211359, _1211361] : [class_Orderings_Olinorder(_1211355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211355), _1211357), _1211359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211355), _1211357), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211355), _1211361), _1211359))))], (24586 ^ _780461) ^ [_1211534, _1211536, _1211538] : [class_Orderings_Olinorder(_1211534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211534), _1211536), _1211538)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211534), _1211536), _1211538) = _1211538)], (24596 ^ _780461) ^ [_1211695, _1211697, _1211699] : [class_Orderings_Olinorder(_1211695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211695), _1211697), _1211699)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211695), _1211699), _1211697) = _1211699)], (24606 ^ _780461) ^ [_1211856, _1211858, _1211860, _1211862] : [class_Orderings_Olinorder(_1211856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211856), _1211858), _1211860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211856), _1211862), _1211860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211856), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1211856), _1211858), _1211862)), _1211860)))], (24620 ^ _780461) ^ [_1212105, _1212107, _1212109, _1212111] : [class_Orderings_Olinorder(_1212105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212105), _1212107), _1212109)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212105), _1212111), _1212109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212105), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212105), _1212107), _1212111)), _1212109)))], (24634 ^ _780461) ^ [_1212354, _1212356, _1212358, _1212360, _1212362] : [class_Orderings_Olinorder(_1212354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212354), _1212356), _1212358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212354), _1212360), _1212362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212354), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212354), _1212356), _1212360)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212354), _1212358), _1212362))))], (24648 ^ _780461) ^ [_1212625, _1212627, _1212629, _1212631] : [class_Orderings_Olinorder(_1212625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212625), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212625), _1212627), _1212629)), _1212631)), 24655 ^ _780461 : [(24656 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212625), _1212627), _1212631)))], (24658 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212625), _1212629), _1212631)))]]], (24660 ^ _780461) ^ [_1212848] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212848) = _1212848)], (24662 ^ _780461) ^ [_1212874] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1212874), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1212874)], (24664 ^ _780461) ^ [_1212903, _1212905] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1212903)), hAPP(c_Nat_OSuc, _1212905)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1212903), _1212905)))], (24666 ^ _780461) ^ [_1212949, _1212951, _1212953, _1212955] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1212949), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212949), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212949), _1212951), _1212953)), _1212955) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1212949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212949), _1212951), _1212955)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1212949), _1212953), _1212955)))], (24672 ^ _780461) ^ [_1213108, _1213110, _1213112, _1213114] : [class_Orderings_Olinorder(_1213108), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213108), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213108), _1213110), _1213112)), _1213114) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213108), _1213110), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213108), _1213112), _1213114)))], (24678 ^ _780461) ^ [_1213251, _1213253, _1213255, _1213257] : [class_Orderings_Olinorder(_1213251), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213251), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213251), _1213253), _1213255)), _1213257) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213251), _1213253), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213251), _1213255), _1213257)))], (24684 ^ _780461) ^ [_1213394, _1213396, _1213398, _1213400] : [class_Orderings_Olinorder(_1213394), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213394), _1213396), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213394), _1213398), _1213400)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213394), _1213398), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213394), _1213396), _1213400)))], (24690 ^ _780461) ^ [_1213537, _1213539, _1213541, _1213543] : [class_Orderings_Olinorder(_1213537), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213537), _1213539), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213537), _1213541), _1213543)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213537), _1213541), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213537), _1213539), _1213543)))], (24696 ^ _780461) ^ [_1213680, _1213682, _1213684] : [class_Orderings_Olinorder(_1213680), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213680), _1213682), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213680), _1213682), _1213684)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213680), _1213682), _1213684))], (24702 ^ _780461) ^ [_1213805, _1213807, _1213809] : [class_Orderings_Olinorder(_1213805), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213805), _1213807), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213805), _1213807), _1213809)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213805), _1213807), _1213809))], (24708 ^ _780461) ^ [_1213930, _1213932, _1213934] : [class_Orderings_Olinorder(_1213930), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213930), _1213932), _1213934) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1213930), _1213934), _1213932))], (24714 ^ _780461) ^ [_1214039, _1214041, _1214043] : [class_Orderings_Olinorder(_1214039), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1214039), _1214041), _1214043) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1214039), _1214043), _1214041))], (24720 ^ _780461) ^ [_1214148, _1214150] : [class_Orderings_Olinorder(_1214148), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1214148), _1214150), _1214150) = _1214150)], (24726 ^ _780461) ^ [_1214239, _1214241, _1214243, _1214245, _1214247, _1214249] : [-(hAPP(c_Product__Type_Oapfst(_1214239, _1214241, _1214243, _1214245), hAPP(hAPP(c_Product__Type_OPair(_1214239, _1214243), _1214247), _1214249)) = hAPP(hAPP(c_Product__Type_OPair(_1214241, _1214243), hAPP(_1214245, _1214247)), _1214249))], (24728 ^ _780461) ^ [_1214328, _1214330, _1214332, _1214334, _1214336, _1214338] : [hAPP(c_Product__Type_Oapfst(_1214328, _1214330, _1214332, _1214334), _1214336) = hAPP(c_Product__Type_Oapfst(_1214328, _1214330, _1214332, _1214338), _1214336), -(hAPP(_1214334, hAPP(c_Product__Type_Ofst(_1214328, _1214332), _1214336)) = hAPP(_1214338, hAPP(c_Product__Type_Ofst(_1214328, _1214332), _1214336)))], (24734 ^ _780461) ^ [_1214477, _1214479, _1214481, _1214483, _1214485, _1214487] : [hAPP(_1214483, hAPP(c_Product__Type_Ofst(_1214477, _1214481), _1214485)) = hAPP(_1214487, hAPP(c_Product__Type_Ofst(_1214477, _1214481), _1214485)), -(hAPP(c_Product__Type_Oapfst(_1214477, _1214479, _1214481, _1214483), _1214485) = hAPP(c_Product__Type_Oapfst(_1214477, _1214479, _1214481, _1214487), _1214485))], (24740 ^ _780461) ^ [_1214632, _1214634, _1214636, _1214638, _1214640] : [-(hAPP(c_Product__Type_Ofst(_1214632, _1214634), hAPP(c_Product__Type_Oapfst(_1214636, _1214632, _1214634, _1214638), _1214640)) = hAPP(_1214638, hAPP(c_Product__Type_Ofst(_1214636, _1214634), _1214640)))], (24742 ^ _780461) ^ [_1214686, _1214688, _1214690, _1214692, _1214694] : [-(hAPP(c_Product__Type_Osnd(_1214686, _1214688), hAPP(c_Product__Type_Oapfst(_1214690, _1214686, _1214688, _1214692), _1214694)) = hAPP(c_Product__Type_Osnd(_1214690, _1214688), _1214694))], (24744 ^ _780461) ^ [_1214737, _1214739, _1214741] : [class_Int_Onumber(_1214737), class_Orderings_Oord(_1214737), 24751 ^ _780461 : [(24752 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214737), hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214739)), hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214741))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1214737), hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214739)), hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214741)) = hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214741))], (24758 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214737), hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214739)), hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214741)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1214737), hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214739)), hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214741)) = hAPP(c_Int_Onumber__class_Onumber__of(_1214737), _1214739))]]], (24764 ^ _780461) ^ [_1215129, _1215131, _1215133, _1215135] : [class_Orderings_Olinorder(_1215129), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215129), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215129), _1215131), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215129), _1215133), _1215135))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215129), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215129), _1215131), _1215133)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215129), _1215131), _1215135)))))], (24770 ^ _780461) ^ [_1215302, _1215304, _1215306, _1215308] : [class_Orderings_Olinorder(_1215302), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215302), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215302), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215302), _1215304), _1215306)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215302), _1215304), _1215308))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215302), _1215304), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215302), _1215306), _1215308)))))], (24776 ^ _780461) ^ [_1215475, _1215477, _1215479] : [class_Groups_Olinordered__ab__group__add(_1215475), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1215475), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215475), _1215477), _1215479)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215475), hAPP(c_Groups_Ouminus__class_Ouminus(_1215475), _1215477)), hAPP(c_Groups_Ouminus__class_Ouminus(_1215475), _1215479)))], (24782 ^ _780461) ^ [_1215614, _1215616, _1215618] : [class_Groups_Olinordered__ab__group__add(_1215614), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1215614), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215614), _1215616), _1215618)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215614), hAPP(c_Groups_Ouminus__class_Ouminus(_1215614), _1215616)), hAPP(c_Groups_Ouminus__class_Ouminus(_1215614), _1215618)))], (24788 ^ _780461) ^ [_1215753, _1215755] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1215753), _1215755)), _1215755) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1215753), _1215755))], (24790 ^ _780461) ^ [_1215796, _1215798, _1215800, _1215802, _1215804, _1215806, _1215808] : [-(hAPP(c_Product__Type_Oapsnd(_1215796, _1215798, _1215800, _1215802), hAPP(c_Product__Type_Oapfst(_1215804, _1215800, _1215796, _1215806), _1215808)) = hAPP(c_Product__Type_Oapfst(_1215804, _1215800, _1215798, _1215806), hAPP(c_Product__Type_Oapsnd(_1215796, _1215798, _1215804, _1215802), _1215808)))], (24792 ^ _780461) ^ [_1215863, _1215865] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1215863)), _1215865) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1215863), 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), _1215863)), _1215865))], (24794 ^ _780461) ^ [_1215911, _1215913] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1215911), hAPP(c_Nat_OSuc, _1215913)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1215913), 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)), _1215913)), _1215911))], (24796 ^ _780461) ^ [_1215959, _1215961, _1215963, _1215965, _1215967, _1215969, _1215971] : [-(hAPP(c_Product__Type_Oapfst(_1215959, _1215961, _1215963, _1215965), hAPP(c_Product__Type_Oapsnd(_1215967, _1215963, _1215959, _1215969), _1215971)) = hAPP(hAPP(c_Product__Type_OPair(_1215961, _1215963), hAPP(_1215965, hAPP(c_Product__Type_Ofst(_1215959, _1215967), _1215971))), hAPP(_1215969, hAPP(c_Product__Type_Osnd(_1215959, _1215967), _1215971))))], (24798 ^ _780461) ^ [_1216037] : [class_Orderings_Olinorder(_1216037), -(c_Orderings_Oord_Omin(_1216037, hAPP(c_COMBC(_1216037, _1216037, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1216037))) = c_Orderings_Oord__class_Omax(_1216037))], (24804 ^ _780461) ^ [_1216138] : [class_Orderings_Oord(_1216138), -(c_Orderings_Oord__class_Omax(_1216138) = c_Orderings_Oord_Omax(_1216138, c_Orderings_Oord__class_Oless__eq(_1216138)))], (24810 ^ _780461) ^ [_1216221] : [-(_1216221 = 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, _1216221)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1216221))))], (24816 ^ _780461) ^ [_1216272] : [-(c_Nitpick_Ozero__frac(_1216272) = c_Nitpick_OAbs__Frac(_1216272, 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))))], (24818 ^ _780461) ^ [_1216300, _1216302, _1216304, _1216306] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1216300, _1216302, _1216304, _1216306) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1216300, _1216302), _1216304), _1216306)))], (24820 ^ _780461) ^ [_1216360, _1216362] : [hAPP(c_Code__Numeral_Onat__of, _1216360) = hAPP(c_Code__Numeral_Onat__of, _1216362), -(_1216360 = _1216362)], (24826 ^ _780461) ^ [_1216445, _1216447] : [_1216445 = _1216447, -(hAPP(c_Code__Numeral_Onat__of, _1216445) = hAPP(c_Code__Numeral_Onat__of, _1216447))], (24832 ^ _780461) ^ [_1216551, _1216553] : [hAPP(c_Code__Numeral_Onat__of, _1216551) = hAPP(c_Code__Numeral_Onat__of, _1216553), -(_1216551 = _1216553)], (24838 ^ _780461) ^ [_1216636, _1216638] : [_1216636 = _1216638, -(hAPP(c_Code__Numeral_Onat__of, _1216636) = hAPP(c_Code__Numeral_Onat__of, _1216638))], (24844 ^ _780461) ^ [_1216727] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1216727)) = _1216727)], (24846 ^ _780461) ^ [_1216756] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1216756)) = _1216756)], (24848 ^ _780461) ^ [_1216785] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1216785)) = _1216785)], (24850 ^ _780461) ^ [_1216829, _1216831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1216829), _1216831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1216829)), hAPP(c_Code__Numeral_Onat__of, _1216831))))], (24856 ^ _780461) ^ [_1216934, _1216936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1216934)), hAPP(c_Code__Numeral_Onat__of, _1216936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1216934), _1216936)))], (24862 ^ _780461) ^ [_1217045] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1217045)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1217045))], (24864 ^ _780461) ^ [_1217092, _1217094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1217092), _1217094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1217092)), hAPP(c_Code__Numeral_Onat__of, _1217094))))], (24870 ^ _780461) ^ [_1217197, _1217199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1217197)), hAPP(c_Code__Numeral_Onat__of, _1217199))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1217197), _1217199)))], (24876 ^ _780461) ^ [_1217308] : [-(hAPP(c_Code__Numeral_Onat__of, _1217308) = c_Code__Numeral_Onat__of__aux(_1217308, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24878 ^ _780461) ^ [_1217337, _1217339] : [-(c_Code__Numeral_Onat__of__aux(_1217337, _1217339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1217337)), _1217339))], (24880 ^ _780461) ^ [_1217374, _1217376] : [class_Orderings_Olinorder(_1217374), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1217374), _1217376), _1217376) = _1217376)], (24886 ^ _780461) ^ [_1217465, _1217467] : [class_Orderings_Olinorder(_1217465), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217465), _1217467), _1217467) = _1217467)], (24892 ^ _780461) ^ [_1217556] : [class_Orderings_Olinorder(_1217556), -(c_Orderings_Oord_Omax(_1217556, hAPP(c_COMBC(_1217556, _1217556, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1217556))) = c_Orderings_Oord__class_Omin(_1217556))], (24898 ^ _780461) ^ [_1217657] : [-(c_Code__Numeral_OSuc__code__numeral(_1217657) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1217657))))], (24900 ^ _780461) ^ [_1217691, _1217693] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1217691), _1217693) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1217691)), hAPP(c_Code__Numeral_Onat__of, _1217693))))], (24902 ^ _780461) ^ [_1217737, _1217739] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1217737), _1217739) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1217737)), hAPP(c_Code__Numeral_Onat__of, _1217739))))], (24904 ^ _780461) ^ [_1217783, _1217785] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1217783), _1217785) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1217783)), hAPP(c_Code__Numeral_Onat__of, _1217785))))], (24906 ^ _780461) ^ [_1217829, _1217831] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1217829), _1217831) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1217829)), hAPP(c_Code__Numeral_Onat__of, _1217831))))], (24908 ^ _780461) ^ [_1217875, _1217877] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1217875, _1217877) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1217875), hAPP(c_Code__Numeral_Onat__of, _1217877))))], (24910 ^ _780461) ^ [_1217917] : [-(c_Nitpick_Oone__frac(_1217917) = c_Nitpick_OAbs__Frac(_1217917, 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))))], (24912 ^ _780461) ^ [_1217945, _1217947] : [-(c_Nitpick_Onumber__of__frac(_1217945, _1217947) = c_Nitpick_OAbs__Frac(_1217945, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1217947), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (24914 ^ _780461) ^ [_1217982, _1217984, _1217986] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1217982), _1217984), _1217986) = c_Nitpick_OAbs__Frac(_1217982, c_Nitpick_Onorm__frac(_1217984, _1217986)))], (24916 ^ _780461) ^ [_1218023, _1218025, _1218027, _1218029] : [-(c_Sum__Type_Osum_Osum__case(_1218023, _1218025, _1218027, hAPP(hAPP(c_COMBB(tc_sum(_1218023, _1218027), _1218025, _1218023), _1218029), c_Sum__Type_OInl(_1218023, _1218027)), hAPP(hAPP(c_COMBB(tc_sum(_1218023, _1218027), _1218025, _1218027), _1218029), c_Sum__Type_OInr(_1218027, _1218023))) = _1218029)], (24918 ^ _780461) ^ [_1218108, _1218110, _1218112, _1218114, _1218116] : [_1218108 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1218110, _1218112, _1218108, _1218114), _1218116) = hAPP(c_Product__Type_OPair(_1218110, _1218112), _1218116))], (24924 ^ _780461) ^ [_1218213, _1218215, _1218217, _1218219, _1218221] : [-(_1218213 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1218215, _1218217, _1218213, _1218219), _1218221) = hAPP(hAPP(c_Product__Type_Oscomp(_1218217, _1218215, _1218217, tc_prod(_1218215, _1218217)), hAPP(_1218219, _1218221)), c_Random_Oiterate(_1218215, _1218217, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1218213), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1218219)))], (24930 ^ _780461) ^ [_1218293, _1218295, _1218297, _1218299, _1218301, _1218303, _1218305, _1218307, _1218309] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1218293, _1218295, _1218297, _1218299), hAPP(hAPP(c_Product__Type_Oscomp(_1218293, _1218301, _1218303, tc_prod(_1218295, _1218297)), _1218305), _1218307)), _1218309) = hAPP(hAPP(c_Product__Type_Oscomp(_1218293, _1218301, _1218303, _1218299), _1218305), hAPP(hAPP(c_COMBC(_1218301, tc_fun(_1218295, tc_fun(_1218297, _1218299)), tc_fun(_1218303, _1218299)), hAPP(hAPP(c_COMBB(tc_fun(_1218303, tc_prod(_1218295, _1218297)), tc_fun(tc_fun(_1218295, tc_fun(_1218297, _1218299)), tc_fun(_1218303, _1218299)), _1218301), c_Product__Type_Oscomp(_1218303, _1218295, _1218297, _1218299)), _1218307)), _1218309)))], (24932 ^ _780461) ^ [_1218420, _1218422, _1218424, _1218426, _1218428] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1218420, _1218422, _1218424, hAPP(c_COMBK(_1218422, _1218420), _1218426), hAPP(c_COMBK(_1218422, _1218424), _1218426)), _1218428) = _1218426)], (24934 ^ _780461) ^ [_1218472, _1218474, _1218476, _1218478, _1218480, _1218482, _1218484] : [c_Sum__Type_Osum_Osum__case(_1218472, _1218474, _1218476, _1218478, _1218480) = c_Sum__Type_Osum_Osum__case(_1218472, _1218474, _1218476, _1218482, _1218484), 24937 ^ _780461 : [(24938 ^ _780461) ^ [] : [-(_1218478 = _1218482)], (24940 ^ _780461) ^ [] : [-(_1218480 = _1218484)]]], (24942 ^ _780461) ^ [_1218613, _1218615, _1218617, _1218619, _1218621, _1218623, _1218625] : [_1218613 = _1218615, -(hAPP(c_Sum__Type_Osum_Osum__case(_1218617, _1218619, _1218621, _1218623, _1218625), _1218613) = hAPP(c_Sum__Type_Osum_Osum__case(_1218617, _1218619, _1218621, _1218623, _1218625), _1218615))], (24948 ^ _780461) ^ [_1218736, _1218738, _1218740, _1218742] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1218736, _1218738, _1218740, tc_prod(_1218738, _1218740)), _1218742), c_Product__Type_OPair(_1218738, _1218740)) = _1218742)], (24950 ^ _780461) ^ [_1218782, _1218784, _1218786, _1218788, _1218790] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1218782, _1218784, _1218782, _1218786), hAPP(c_Product__Type_OPair(_1218784, _1218782), _1218788)), _1218790) = hAPP(_1218790, _1218788))], (24952 ^ _780461) ^ [_1218833, _1218835, _1218837, _1218839, _1218841, _1218843, _1218845] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1218833, _1218835, _1218837, _1218839), _1218841), _1218843), _1218845) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1218835, _1218837, _1218839), _1218843), hAPP(_1218841, _1218845)))], (24954 ^ _780461) ^ [_1218895, _1218897, _1218899, _1218901, _1218903, _1218905] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1218895, _1218897, _1218899, _1218901, _1218903), hAPP(c_Sum__Type_OInr(_1218899, _1218895), _1218905)) = hAPP(_1218903, _1218905))], (24956 ^ _780461) ^ [_1218946, _1218948, _1218950, _1218952, _1218954, _1218956] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1218946, _1218948, _1218950, _1218952, _1218954), hAPP(c_Sum__Type_OInl(_1218946, _1218950), _1218956)) = hAPP(_1218952, _1218956))], (24958 ^ _780461) ^ [_1218997, _1218999, _1219001, _1219003, _1219005, _1219007, _1219009] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1218997, _1218999, _1219001, _1219003), _1219005), _1219007), _1219009) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1218999, _1219001, _1219003), _1219007), hAPP(_1219005, _1219009)))], (24960 ^ _780461) ^ [_1219059, _1219061, _1219063, _1219065, _1219067, _1219069, _1219071] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1219059, _1219061, _1219063, _1219065), _1219067), _1219069), _1219071) = hAPP(hAPP(_1219069, hAPP(c_Product__Type_Ofst(_1219061, _1219063), hAPP(_1219067, _1219071))), hAPP(c_Product__Type_Osnd(_1219061, _1219063), hAPP(_1219067, _1219071))))], (24962 ^ _780461) ^ [_1219132, _1219134, _1219136] : [-(c_Nitpick_Oplus__frac(_1219132, _1219134, _1219136) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1219132), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1219132), _1219134), hAPP(c_Nitpick_Odenom(_1219132), _1219136))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1219132), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1219132), tc_Int_Oint), c_Nitpick_Ofrac(_1219132)), 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(_1219132), _1219134))), 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(_1219132), _1219134))))), 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(_1219132), _1219136))), 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(_1219132), _1219136)))))), c_COMBI(tc_Int_Oint))))], (24964 ^ _780461) ^ [_1219263, _1219265, _1219267] : [-(c_Product__Type_Ointernal__split(_1219263, _1219265, _1219267) = c_Product__Type_Oprod_Oprod__case(_1219263, _1219265, _1219267))], (24966 ^ _780461) ^ [] : [-(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)))], (24968 ^ _780461) ^ [_1219334, _1219336, _1219338, _1219340, _1219342] : [_1219334 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1219336, _1219338, _1219340, _1219342), _1219334) = c_Lazy__Sequence_Oempty(_1219338))], (24974 ^ _780461) ^ [_1219431, _1219433, _1219435, _1219437, _1219439] : [-(_1219431 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1219433, _1219435, _1219437, _1219439), _1219431) = c_Lazy__Sequence_Obind(_1219433, _1219435, hAPP(_1219437, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1219431), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1219433, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1219435)), _1219439), _1219431)))], (24980 ^ _780461) ^ [_1219527, _1219529, _1219531, _1219533, _1219535] : [_1219527 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1219529, _1219531, _1219533, _1219535), _1219527) = c_Lazy__Sequence_Ohit__bound(_1219531))], (24986 ^ _780461) ^ [_1219624, _1219626, _1219628, _1219630, _1219632] : [-(_1219624 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1219626, _1219628, _1219630, _1219632), _1219624) = c_Lazy__Sequence_Ohb__bind(_1219626, _1219628, hAPP(_1219630, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1219624), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1219626, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1219628))), _1219632), _1219624)))], (24992 ^ _780461) ^ [_1219704, _1219706, _1219708, _1219710, _1219712, _1219714] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1219704, _1219706, _1219708), _1219710), hAPP(hAPP(c_Product__Type_OPair(_1219704, _1219706), _1219712), _1219714)) = hAPP(hAPP(_1219710, _1219712), _1219714))], (24994 ^ _780461) ^ [_1219762, _1219764, _1219766] : [-(c_Nitpick_Otimes__frac(_1219762, _1219764, _1219766) = hAPP(hAPP(c_Nitpick_Ofrac(_1219762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1219762), _1219764)), hAPP(c_Nitpick_Onum(_1219762), _1219766))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1219762), _1219764)), hAPP(c_Nitpick_Odenom(_1219762), _1219766))))], (24996 ^ _780461) ^ [_1219833, _1219835, _1219837] : [-(c_Nitpick_Oof__frac(_1219835, _1219833, _1219837) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219833), hAPP(c_Int_Oring__1__class_Oof__int(_1219833), hAPP(c_Nitpick_Onum(_1219835), _1219837))), hAPP(c_Int_Oring__1__class_Oof__int(_1219833), hAPP(c_Nitpick_Odenom(_1219835), _1219837)))), class_Rings_Oinverse(_1219833), class_Rings_Oring__1(_1219833)], (25006 ^ _780461) ^ [_1220026, _1220028] : [-(c_Nitpick_Oinverse__frac(_1220026, _1220028) = hAPP(hAPP(c_Nitpick_Ofrac(_1220026), hAPP(c_Nitpick_Odenom(_1220026), _1220028)), hAPP(c_Nitpick_Onum(_1220026), _1220028)))], (25008 ^ _780461) ^ [_1220072, _1220074] : [-(c_Nitpick_Ouminus__frac(_1220072, _1220074) = c_Nitpick_OAbs__Frac(_1220072, 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(_1220072), _1220074))), hAPP(c_Nitpick_Odenom(_1220072), _1220074))))], (25010 ^ _780461) ^ [_1220122, _1220124, _1220126, _1220128, _1220130, _1220132, _1220134] : [-(c_New__Random__Sequence_Opos__decr__bind(_1220122, _1220124, _1220126, _1220128, _1220130, _1220132, _1220134) = c_New__DSequence_Opos__decr__bind(_1220122, _1220124, hAPP(hAPP(hAPP(_1220126, _1220130), _1220132), _1220134), hAPP(hAPP(c_COMBC(_1220122, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1220124))), hAPP(hAPP(c_COMBC(_1220122, 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(_1220124)))), hAPP(hAPP(c_COMBC(_1220122, 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(_1220124))))), _1220128), _1220130)), _1220132)), _1220134)))], (25012 ^ _780461) ^ [_1220251, _1220253, _1220255] : [c_Nitpick_Oless__frac(_1220251, _1220253, _1220255), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1220251), c_Nitpick_Oplus__frac(_1220251, _1220253, c_Nitpick_Ouminus__frac(_1220251, _1220255)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25018 ^ _780461) ^ [_1220362, _1220364, _1220366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1220362), c_Nitpick_Oplus__frac(_1220362, _1220364, c_Nitpick_Ouminus__frac(_1220362, _1220366)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1220362, _1220364, _1220366))], (25024 ^ _780461) ^ [_1220497, _1220499, _1220501] : [c_Nitpick_Oless__eq__frac(_1220497, _1220499, _1220501), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1220497), c_Nitpick_Oplus__frac(_1220497, _1220499, c_Nitpick_Ouminus__frac(_1220497, _1220501)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25030 ^ _780461) ^ [_1220608, _1220610, _1220612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1220608), c_Nitpick_Oplus__frac(_1220608, _1220610, c_Nitpick_Ouminus__frac(_1220608, _1220612)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1220608, _1220610, _1220612))], (25036 ^ _780461) ^ [_1220725, _1220727, _1220729, _1220731, _1220733, _1220735, _1220737] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1220725, _1220727, _1220729, _1220731, _1220733, _1220735, _1220737) = c_New__DSequence_Oneg__decr__bind(_1220725, _1220727, hAPP(hAPP(hAPP(_1220729, _1220733), _1220735), _1220737), hAPP(hAPP(c_COMBC(_1220725, 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(_1220727)))), hAPP(hAPP(c_COMBC(_1220725, 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(_1220727))))), hAPP(hAPP(c_COMBC(_1220725, 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(_1220727)))))), _1220731), _1220733)), _1220735)), _1220737)))], (25038 ^ _780461) ^ [_1220842, _1220844, _1220846, _1220848, _1220850] : [-(hAPP(c_New__DSequence_Oneg__bind(_1220842, _1220844, _1220846, _1220848), _1220850) = c_Lazy__Sequence_Ohb__bind(_1220842, _1220844, hAPP(_1220846, _1220850), hAPP(hAPP(c_COMBC(_1220842, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1220844))), _1220848), _1220850)))], (25040 ^ _780461) ^ [_1220903, _1220905] : [-(hAPP(c_New__DSequence_Opos__empty(_1220903), _1220905) = c_Lazy__Sequence_Oempty(_1220903))], (25042 ^ _780461) ^ [_1220935, _1220937, _1220939, _1220941] : [-(c_New__Random__Sequence_Opos__empty(_1220935, _1220937, _1220939, _1220941) = c_New__DSequence_Opos__empty(_1220935))], (25044 ^ _780461) ^ [_1220971, _1220973, _1220975, _1220977, _1220979, _1220981, _1220983] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1220971, _1220973, _1220975, _1220977), _1220979), _1220981), _1220983) = c_New__DSequence_Oneg__bind(_1220971, _1220973, hAPP(hAPP(hAPP(_1220975, _1220979), _1220981), _1220983), hAPP(hAPP(c_COMBC(_1220971, 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(_1220973)))), hAPP(hAPP(c_COMBC(_1220971, 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(_1220973))))), hAPP(hAPP(c_COMBC(_1220971, 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(_1220973)))))), _1220977), _1220979)), _1220981)), _1220983)))], (25046 ^ _780461) ^ [_1221094, _1221096, _1221098, _1221100, _1221102] : [-(hAPP(c_New__DSequence_Opos__bind(_1221094, _1221096, _1221098, _1221100), _1221102) = c_Lazy__Sequence_Obind(_1221094, _1221096, hAPP(_1221098, _1221102), hAPP(hAPP(c_COMBC(_1221094, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1221096)), _1221100), _1221102)))], (25048 ^ _780461) ^ [_1221153, _1221155, _1221157, _1221159, _1221161, _1221163] : [hBOOL(hAPP(hAPP(_1221153, _1221155), _1221157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1221159, tc_fun(_1221161, tc_HOL_Obool))), _1221153), _1221163)), -(hBOOL(hAPP(hAPP(_1221163, _1221155), _1221157)))], (25058 ^ _780461) ^ [_1221344, _1221346, _1221348, _1221350, _1221352, _1221354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1221344, tc_fun(_1221346, tc_HOL_Obool))), _1221348), _1221350)), hBOOL(hAPP(hAPP(_1221348, _1221352), _1221354)), -(hBOOL(hAPP(hAPP(_1221350, _1221352), _1221354)))], (25068 ^ _780461) ^ [_1221535, _1221537, _1221539, _1221541] : [hBOOL(hAPP(_1221535, _1221537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1221539, tc_HOL_Obool)), _1221535), _1221541)), -(hBOOL(hAPP(_1221541, _1221537)))], (25078 ^ _780461) ^ [_1221700, _1221702, _1221704, _1221706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1221700, tc_HOL_Obool)), _1221702), _1221704)), hBOOL(hAPP(_1221702, _1221706)), -(hBOOL(hAPP(_1221704, _1221706)))], (25088 ^ _780461) ^ [_1221865, _1221867, _1221869, _1221871, _1221873, _1221875, _1221877] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1221865, _1221867, _1221869, _1221871), _1221873), _1221875), _1221877) = c_New__DSequence_Opos__bind(_1221865, _1221867, hAPP(hAPP(hAPP(_1221869, _1221873), _1221875), _1221877), hAPP(hAPP(c_COMBC(_1221865, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1221867))), hAPP(hAPP(c_COMBC(_1221865, 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(_1221867)))), hAPP(hAPP(c_COMBC(_1221865, 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(_1221867))))), _1221871), _1221873)), _1221875)), _1221877)))], (25090 ^ _780461) ^ [_1221982, _1221984, _1221986] : [-(c_HOL_OThe(tc_prod(_1221982, _1221984), hAPP(c_Product__Type_Oprod_Oprod__case(_1221982, _1221984, tc_HOL_Obool), _1221986)) = c_HOL_OThe(tc_prod(_1221982, _1221984), hAPP(hAPP(c_COMBS(tc_prod(_1221982, _1221984), _1221984, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1221982, tc_fun(_1221984, tc_HOL_Obool), tc_prod(_1221982, _1221984)), _1221986), c_Product__Type_Ofst(_1221982, _1221984))), c_Product__Type_Osnd(_1221982, _1221984))))], (25092 ^ _780461) ^ [_1222078, _1222080, _1222082, _1222084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1222078), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1222080, _1222082, _1222078, _1222084) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222080)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1222080)))], (25098 ^ _780461) ^ [_1222209, _1222211, _1222213, _1222215] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1222209), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1222211, _1222213, _1222209, _1222215) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1222211, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm)), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1222213, _1222215)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1222211, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1222211, _1222213, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1222209), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1222215))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1222211, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211))))), tc_prod(_1222211, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1222211)), hAPP(hAPP(c_COMBB(_1222211, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1222211)))), tc_prod(_1222211, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1222211)), c_Product__Type_Ofst(_1222211, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (25104 ^ _780461) ^ [_1222588, _1222590, _1222592, _1222594, _1222596, _1222598, _1222600] : [hBOOL(hAPP(hAPP(_1222588, hAPP(c_Product__Type_Osnd(_1222590, _1222592), _1222594)), hAPP(c_Product__Type_Ofst(_1222590, _1222592), _1222594))), 25111 ^ _780461 : [(25112 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1222588, 25110 ^ [_1222588, _1222590, _1222592, _1222594, _1222596, _1222598, _1222600]), 25109 ^ [_1222588, _1222590, _1222592, _1222594, _1222596, _1222598, _1222600])))], (25114 ^ _780461) ^ [] : [hBOOL(hAPP(_1222596, hAPP(hAPP(_1222598, 25109 ^ [_1222588, _1222590, _1222592, _1222594, _1222596, _1222598, _1222600]), 25110 ^ [_1222588, _1222590, _1222592, _1222594, _1222596, _1222598, _1222600])))]], -(hBOOL(hAPP(_1222596, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1222590, _1222592, _1222600), _1222598), _1222594))))], (25118 ^ _780461) ^ [_1222994, _1222996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1222994), _1222996)), -(c_Quickcheck_Obeyond(_1222994, _1222996) = _1222996)], (25124 ^ _780461) ^ [_1223081, _1223083] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1223081), _1223083))), -(c_Quickcheck_Obeyond(_1223081, _1223083) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (25130 ^ _780461) ^ [_1223127] : [-(c_Quickcheck_Obeyond(_1223127, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (25132 ^ _780461) ^ [_1223153, _1223155, _1223157] : [-(c_HOL_OThe(tc_prod(_1223153, _1223155), _1223157) = c_HOL_OThe(tc_prod(_1223153, _1223155), hAPP(c_Product__Type_Oprod_Oprod__case(_1223153, _1223155, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1223155, tc_prod(_1223153, _1223155)), tc_fun(_1223155, tc_HOL_Obool), _1223153), hAPP(c_COMBB(tc_prod(_1223153, _1223155), tc_HOL_Obool, _1223155), _1223157)), c_Product__Type_OPair(_1223153, _1223155)))))], (25134 ^ _780461) ^ [_1223231, _1223233, _1223235, _1223237] : [-(c_HOL_OThe(tc_prod(_1223231, _1223233), hAPP(c_Product__Type_Oprod_Oprod__case(_1223231, _1223233, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1223231, tc_fun(_1223233, tc_HOL_Obool), tc_fun(_1223233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1223233, tc_HOL_Obool), tc_fun(_1223233, tc_HOL_Obool)), _1223231), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1223233)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1223231), c_fconj), hAPP(c_fequal, _1223235)))), hAPP(c_fequal, _1223237)))) = hAPP(hAPP(c_Product__Type_OPair(_1223231, _1223233), _1223235), _1223237))], (25136 ^ _780461) ^ [_1223337, _1223339] : [-(c_Divides_Odivmod__nat(_1223337, _1223339) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1223337, _1223339)))], (25138 ^ _780461) ^ [_1223371, _1223373, _1223375] : [-(c_Random__Sequence_Oempty(_1223371, _1223373, _1223375) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1223371)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1223371)))], (25140 ^ _780461) ^ [_1223420, _1223422, _1223424, _1223426] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1223420), _1223422), _1223424), _1223426) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1223420)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1223420), _1223422)))], (25142 ^ _780461) ^ [_1223481, _1223483] : [-(c_HOL_OThe(_1223481, hAPP(hAPP(c_COMBC(_1223481, _1223481, tc_HOL_Obool), c_fequal), _1223483)) = _1223483)], (25144 ^ _780461) ^ [_1223519, _1223521] : [-(c_HOL_OThe(_1223519, hAPP(c_fequal, _1223521)) = _1223521)], (25146 ^ _780461) ^ [_1223550, _1223552, _1223554, _1223556, _1223558, _1223560] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1223550, _1223552, _1223554, _1223556), _1223558), _1223560) = hAPP(_1223556, hAPP(hAPP(c_Product__Type_OPair(_1223550, _1223552), _1223558), _1223560)))], (25148 ^ _780461) ^ [_1223606, _1223608, _1223610, _1223612, _1223614] : [hBOOL(hAPP(_1223606, hAPP(hAPP(c_Product__Type_OPair(_1223608, _1223610), _1223612), _1223614))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1223608, _1223610, tc_HOL_Obool, _1223606), _1223612), _1223614)))], (25154 ^ _780461) ^ [_1223731, _1223733, _1223735, _1223737, _1223739] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1223731, _1223733, tc_HOL_Obool, _1223735), _1223737), _1223739)), -(hBOOL(hAPP(_1223735, hAPP(hAPP(c_Product__Type_OPair(_1223731, _1223733), _1223737), _1223739))))], (25160 ^ _780461) ^ [_1223856, _1223858, _1223860, _1223862, _1223864] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1223856, _1223858, tc_HOL_Obool, _1223860), _1223862), _1223864)), -(hBOOL(hAPP(_1223860, hAPP(hAPP(c_Product__Type_OPair(_1223856, _1223858), _1223862), _1223864))))], (25166 ^ _780461) ^ [_1223981, _1223983, _1223985, _1223987, _1223989, _1223991] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1223981, _1223983, _1223985, _1223987), _1223989), _1223991) = hAPP(_1223987, hAPP(hAPP(c_Product__Type_OPair(_1223981, _1223983), _1223989), _1223991)))], (25168 ^ _780461) ^ [_1224037, _1224039, _1224041, _1224043] : [-(c_Product__Type_Ocurry(_1224037, _1224039, _1224041, hAPP(c_Product__Type_Oprod_Oprod__case(_1224037, _1224039, _1224041), _1224043)) = _1224043)], (25170 ^ _780461) ^ [_1224078, _1224080, _1224082, _1224084] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1224078, _1224080, _1224082), c_Product__Type_Ocurry(_1224078, _1224080, _1224082, _1224084)) = _1224084)], (25182 ^ _780461) ^ [_1224320, _1224322, _1224324] : [25184 ^ _780461 : [(25185 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1224320), 25183 ^ [_1224320, _1224322, _1224324]), _1224324)))], (25187 ^ _780461) ^ [] : [hBOOL(hAPP(_1224322, 25183 ^ [_1224320, _1224322, _1224324]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1224320, _1224322), _1224324)))], (25172 ^ _780461) ^ [_1224137, _1224139, _1224141] : [hBOOL(hAPP(c_Predicate_OPowp(_1224137, _1224139), _1224141)), 25175 ^ _780461 : [(25176 ^ _780461) ^ [_1224221] : [hBOOL(hAPP(hAPP(c_member(_1224137), _1224221), _1224141)), -(hBOOL(hAPP(_1224139, _1224221)))]]], (25191 ^ _780461) ^ [_1224500, _1224502, _1224504] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1224500), _1224502)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1224500), _1224504))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1224500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1224502), _1224504)))], (25201 ^ _780461) ^ [_1224681, _1224683, _1224685, _1224687, _1224689, _1224691, _1224693, _1224695] : [c_Hoare__Mirabelle_Ohoare__derivs(_1224681, _1224683, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1224681)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1224681), _1224685), hAPP(c_Com_Ocom_OBODY, _1224687)), hAPP(hAPP(c_COMBC(_1224681, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1224681), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1224689)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), hAPP(hAPP(c_COMBB(tc_Com_Ostate, tc_fun(tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), tc_Com_Ostate), c_Natural_Oupdate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Oloc, tc_Nat_Onat), tc_Com_Ostate), c_Natural_Osetlocs), hAPP(c_Natural_Ogetlocs, _1224691)))), _1224693)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Oloc, tc_Nat_Onat), c_Natural_Ogetlocs), c_Com_ORes))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1224681), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1224681, _1224683, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1224681)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1224681), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1224681), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _1224691)))), hAPP(hAPP(c_COMBC(_1224681, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1224681), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1224685)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), hAPP(hAPP(c_COMBB(tc_Com_Ostate, tc_fun(tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), tc_Com_Ostate), c_Natural_Oupdate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Oloc, tc_Nat_Onat), tc_Com_Ostate), c_Natural_Osetlocs), c_Natural_Onewlocs))), c_Com_Ovname_OLoc(c_Com_OArg))), _1224695)))), c_Com_Ocom_OCall(_1224693, _1224687, _1224695)), _1224689)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1224681), tc_HOL_Obool)))))], (25207 ^ _780461) ^ [_1225066, _1225068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225066)), 25210 ^ _780461 : [(25211 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1225068), _1225066)), _1225066)), -(_1225068 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (25217 ^ _780461) ^ [] : [_1225068 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1225068), _1225066)), _1225066)))]]], (25223 ^ _780461) ^ [_1225310, _1225312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225310)), 25226 ^ _780461 : [(25227 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1225310), _1225312)), _1225310)), -(_1225312 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (25233 ^ _780461) ^ [] : [_1225312 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1225310), _1225312)), _1225310)))]]], (25239 ^ _780461) ^ [_1225554] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1225554), _1225554)))], (25241 ^ _780461) ^ [_1225582, _1225584] : [class_Rings_Ocomm__semiring__1(_1225582), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1225582), _1225584), c_Groups_Ozero__class_Ozero(_1225582))))], (25247 ^ _780461) ^ [_1225675, _1225677] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1225675, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1225675, tc_HOL_Obool))), _1225677)))], (25249 ^ _780461) ^ [_1225715] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1225715)))], (25251 ^ _780461) ^ [_1225740, _1225742, _1225744] : [hBOOL(hAPP(hAPP(c_member(_1225742), _1225740), c_Orderings_Obot__class_Obot(tc_fun(_1225742, tc_HOL_Obool)))), -(hBOOL(hAPP(_1225744, _1225740)))], (25257 ^ _780461) ^ [_1225847, _1225849, _1225851, _1225853, _1225855] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1225847, _1225849, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1225847)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1225847), hAPP(hAPP(c_COMBC(_1225847, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1225847), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1225851)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1225853)), _1225855))), c_Com_Ocom_OAss(_1225853, _1225855)), _1225851)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1225847), tc_HOL_Obool)))))], (25259 ^ _780461) ^ [_1225939, _1225941, _1225943, _1225945, _1225947] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1225939, _1225941, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1225939)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1225939), hAPP(hAPP(c_COMBC(_1225939, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1225939), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1225943)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _1225945)), _1225947))), c_Com_Ocom_OAss(_1225945, _1225947)), _1225943)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1225939), tc_HOL_Obool)))))], (25261 ^ _780461) ^ [_1226031, _1226033, _1226035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1226031, tc_HOL_Obool)), _1226033), hAPP(hAPP(c_Set_Oinsert(_1226031), _1226035), c_Orderings_Obot__class_Obot(tc_fun(_1226031, tc_HOL_Obool))))), -(_1226033 = c_Orderings_Obot__class_Obot(tc_fun(_1226031, tc_HOL_Obool))), -(_1226033 = hAPP(hAPP(c_Set_Oinsert(_1226031), _1226035), c_Orderings_Obot__class_Obot(tc_fun(_1226031, tc_HOL_Obool))))], (25271 ^ _780461) ^ [_1226220, _1226222, _1226224] : [c_Orderings_Obot__class_Obot(tc_fun(_1226220, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_1226220), _1226222), _1226224)], (25273 ^ _780461) ^ [_1226275, _1226277, _1226279] : [hAPP(hAPP(c_Set_Oinsert(_1226275), _1226277), _1226279) = c_Orderings_Obot__class_Obot(tc_fun(_1226275, tc_HOL_Obool))], (25275 ^ _780461) ^ [_1226315, _1226317, _1226319] : [-(hAPP(hAPP(c_Set_Oinsert(_1226315), _1226317), hAPP(hAPP(c_Set_Oinsert(_1226315), _1226317), _1226319)) = hAPP(hAPP(c_Set_Oinsert(_1226315), _1226317), _1226319))], (25277 ^ _780461) ^ [_1226366, _1226368, _1226370, _1226372] : [-(hAPP(hAPP(c_Set_Oinsert(_1226366), _1226368), hAPP(hAPP(c_Set_Oinsert(_1226366), _1226370), _1226372)) = hAPP(hAPP(c_Set_Oinsert(_1226366), _1226370), hAPP(hAPP(c_Set_Oinsert(_1226366), _1226368), _1226372)))], (25279 ^ _780461) ^ [_1226451, _1226453, _1226455, _1226457, _1226459] : [hAPP(hAPP(c_Set_Oinsert(_1226451), _1226453), hAPP(hAPP(c_Set_Oinsert(_1226451), _1226455), c_Orderings_Obot__class_Obot(tc_fun(_1226451, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1226451), _1226457), hAPP(hAPP(c_Set_Oinsert(_1226451), _1226459), c_Orderings_Obot__class_Obot(tc_fun(_1226451, tc_HOL_Obool)))), 25284 ^ _780461 : [(25285 ^ _780461) ^ [] : [-(_1226453 = _1226457)], (25287 ^ _780461) ^ [] : [-(_1226455 = _1226459)]], 25288 ^ _780461 : [(25289 ^ _780461) ^ [] : [-(_1226453 = _1226459)], (25291 ^ _780461) ^ [] : [-(_1226455 = _1226457)]]], (25293 ^ _780461) ^ [_1226713, _1226715, _1226717, _1226719, _1226721] : [-(hAPP(hAPP(c_Set_Oinsert(_1226713), _1226715), hAPP(hAPP(c_Set_Oinsert(_1226713), _1226717), c_Orderings_Obot__class_Obot(tc_fun(_1226713, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_1226713), _1226719), hAPP(hAPP(c_Set_Oinsert(_1226713), _1226721), c_Orderings_Obot__class_Obot(tc_fun(_1226713, tc_HOL_Obool))))), 25294 ^ _780461 : [(25295 ^ _780461) ^ [] : [_1226715 = _1226719, _1226717 = _1226721], (25301 ^ _780461) ^ [] : [_1226715 = _1226721, _1226717 = _1226719]]], (25319 ^ _780461) ^ [_1227164, _1227166, _1227168, _1227170] : [25320 ^ _780461 : [(25321 ^ _780461) ^ [] : [_1227166 = _1227170], (25323 ^ _780461) ^ [] : [hBOOL(hAPP(_1227168, _1227170))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1227164), _1227166), _1227168), _1227170)))], (25309 ^ _780461) ^ [_1227050, _1227052, _1227054, _1227056] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_1227050), _1227052), _1227054), _1227056)), -(_1227052 = _1227056), -(hBOOL(hAPP(_1227054, _1227056)))], (25327 ^ _780461) ^ [_1227309, _1227311, _1227313] : [hAPP(hAPP(c_Set_Oinsert(_1227309), _1227311), c_Orderings_Obot__class_Obot(tc_fun(_1227309, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_1227309), _1227313), c_Orderings_Obot__class_Obot(tc_fun(_1227309, tc_HOL_Obool))), -(_1227311 = _1227313)], (25333 ^ _780461) ^ [_1227440, _1227442, _1227444] : [class_Rings_Olinordered__idom(_1227440), hAPP(c_Groups_Oabs__class_Oabs(_1227440), _1227442) = hAPP(c_Groups_Oabs__class_Oabs(_1227440), _1227444), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227440), _1227442), _1227444)))], (25343 ^ _780461) ^ [_1227605, _1227607, _1227609] : [class_Rings_Olinordered__idom(_1227605), 25346 ^ _780461 : [(25347 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227605), hAPP(c_Groups_Oabs__class_Oabs(_1227605), _1227607)), _1227609)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227605), _1227607), _1227609)))], (25353 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227605), _1227607), _1227609)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227605), hAPP(c_Groups_Oabs__class_Oabs(_1227605), _1227607)), _1227609)))]]], (25359 ^ _780461) ^ [_1227873, _1227875, _1227877] : [class_Rings_Olinordered__idom(_1227873), 25362 ^ _780461 : [(25363 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227873), _1227875), hAPP(c_Groups_Oabs__class_Oabs(_1227873), _1227877))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227873), _1227875), _1227877)))], (25369 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227873), _1227875), _1227877)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1227873), _1227875), hAPP(c_Groups_Oabs__class_Oabs(_1227873), _1227877))))]]], (25375 ^ _780461) ^ [_1228141, _1228143, _1228145, _1228147, _1228149, _1228151, _1228153] : [c_Hoare__Mirabelle_Ohoare__derivs(_1228141, _1228143, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1228141)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1228141), _1228145), _1228147), _1228149)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1228141), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1228141, _1228143, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1228141)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1228141), _1228149), _1228151), _1228153)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1228141), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1228141, _1228143, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1228141)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1228141), _1228145), c_Com_Ocom_OSemi(_1228147, _1228151)), _1228153)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1228141), tc_HOL_Obool)))))], (25385 ^ _780461) ^ [_1228470, _1228472, _1228474] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1228470, _1228472, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1228470)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1228470), _1228474), c_Com_Ocom_OSKIP), _1228474)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1228470), tc_HOL_Obool)))))], (25387 ^ _780461) ^ [_1228526, _1228528, _1228530] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1228526, _1228528, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1228526)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1228526), _1228530), c_Com_Ocom_OSKIP), _1228530)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1228526), tc_HOL_Obool)))))], (25389 ^ _780461) ^ [_1228582, _1228584] : [class_Rings_Ocomm__semiring__1(_1228582), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228582), c_Groups_Ozero__class_Ozero(_1228582)), _1228584)), -(_1228584 = c_Groups_Ozero__class_Ozero(_1228582))], (25399 ^ _780461) ^ [_1228731, _1228733, _1228735, _1228737] : [class_Rings_Ocomm__semiring__1(_1228731), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228731), _1228733), _1228735)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228731), _1228733), _1228737)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228731), _1228733), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228731), _1228735), _1228737))))], (25413 ^ _780461) ^ [_1228980, _1228982] : [class_Rings_Ocomm__semiring__1(_1228980), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1228980), c_Groups_Oone__class_Oone(_1228980)), _1228982)))], (25419 ^ _780461) ^ [_1229073, _1229075, _1229077] : [class_Orderings_Obot(_1229073), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1229075, _1229073)), _1229077) = c_Orderings_Obot__class_Obot(_1229073))], (25425 ^ _780461) ^ [_1229170, _1229172, _1229174, _1229176] : [c_Hoare__Mirabelle_Ohoare__derivs(_1229170, _1229172, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1229170)), _1229174), _1229176)), 25428 ^ _780461 : [(25429 ^ _780461) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1229170, _1229172, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1229170)), _1229174), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1229170), tc_HOL_Obool)))))], (25431 ^ _780461) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1229170, _1229172, _1229176))]]], (25433 ^ _780461) ^ [_1229337, _1229339, _1229341, _1229343] : [c_Hoare__Mirabelle_Ohoare__derivs(_1229337, _1229339, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1229337)), _1229341), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1229337), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1229337, _1229339, _1229343), -(c_Hoare__Mirabelle_Ohoare__derivs(_1229337, _1229339, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1229337)), _1229341), _1229343)))], (25443 ^ _780461) ^ [_1229534, _1229536, _1229538, _1229540] : [c_Hoare__Mirabelle_Ohoare__derivs(_1229534, _1229536, _1229538), c_Hoare__Mirabelle_Ohoare__derivs(_1229534, _1229540, _1229536), -(c_Hoare__Mirabelle_Ohoare__derivs(_1229534, _1229540, _1229538))], (25453 ^ _780461) ^ [_1229677, _1229679] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1229677, _1229679, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1229677), tc_HOL_Obool))))], (25455 ^ _780461) ^ [_1229710, _1229712] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1229710, _1229712, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1229710), tc_HOL_Obool))))], (25457 ^ _780461) ^ [_1229758, _1229760] : [_1229758 = _1229760, 25460 ^ _780461 : [(25461 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229758), _1229760)))], (25463 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229760), _1229758)))]]], (25465 ^ _780461) ^ [_1229877, _1229879] : [-(_1229877 = _1229879), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229877), _1229879)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1229879), _1229877))], (25475 ^ _780461) ^ [_1230043, _1230045] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230043), _1230045)), 25480 ^ _780461 : [(25481 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230043), _1230045)))], (25483 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230045), _1230043))]], -(_1230043 = _1230045)], (25487 ^ _780461) ^ [_1230233, _1230235] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230233), _1230235))), 25488 ^ _780461 : [(25495 ^ _780461) ^ [] : [_1230233 = _1230235], (25489 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230233), _1230235)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230235), _1230233)))]]], (25499 ^ _780461) ^ [_1230443, _1230445] : [25506 ^ _780461 : [(25507 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230443), _1230445)))], (25509 ^ _780461) ^ [] : [_1230443 = _1230445]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230443), _1230445)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230445), _1230443)))], (25511 ^ _780461) ^ [_1230635, _1230637] : [25518 ^ _780461 : [(25519 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230635), _1230637)))], (25521 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230637), _1230635))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230635), _1230637)), -(_1230635 = _1230637)], (25523 ^ _780461) ^ [_1230832, _1230834] : [-(_1230832 = _1230834), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230832), _1230834)), 25530 ^ _780461 : [(25531 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230832), _1230834)))], (25533 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1230834), _1230832))]]], (25535 ^ _780461) ^ [_1231023, _1231025] : [_1231023 = _1231025, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231023), _1231025)))], (25541 ^ _780461) ^ [_1231110, _1231112] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231110), _1231112)), 25544 ^ _780461 : [(25545 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231112), _1231110)), -(_1231112 = _1231110)], (25551 ^ _780461) ^ [] : [_1231112 = _1231110, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231112), _1231110)))]]], (25557 ^ _780461) ^ [_1231342, _1231344] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231342), _1231344)), 25562 ^ _780461 : [(25563 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231342), _1231344)))], (25565 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231344), _1231342))]], -(_1231342 = _1231344)], (25569 ^ _780461) ^ [_1231536, _1231538] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231536), _1231538)), -(_1231536 = _1231538), 25576 ^ _780461 : [(25577 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231536), _1231538)))], (25579 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231538), _1231536))]]], (25581 ^ _780461) ^ [_1231732, _1231734, _1231736] : [_1231732 = _1231734, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231734), _1231736)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231732), _1231736)))], (25591 ^ _780461) ^ [_1231885, _1231887, _1231889] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231885), _1231887)), _1231887 = _1231889, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1231885), _1231889)))], (25601 ^ _780461) ^ [_1232038, _1232040] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232038), _1232040)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232040), _1232038)), -(_1232038 = _1232040)], (25611 ^ _780461) ^ [_1232187, _1232189] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232187), _1232189)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232189), _1232187)), -(_1232187 = _1232189)], (25621 ^ _780461) ^ [_1232336, _1232338, _1232340] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232336), _1232338)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232338), _1232340)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232336), _1232340)))], (25631 ^ _780461) ^ [_1232499, _1232501, _1232503] : [_1232499 = _1232501, 25642 ^ _780461 : [(25643 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232499), _1232503)))], (25645 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232503), _1232499))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232501), _1232503)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232503), _1232501)))], (25647 ^ _780461) ^ [_1232763, _1232765, _1232767] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232763), _1232765)), 25658 ^ _780461 : [(25659 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232763), _1232767)))], (25661 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232767), _1232763))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232765), _1232767)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1232767), _1232765)))], (25663 ^ _780461) ^ [_1233037, _1233039] : [_1233037 = _1233039, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233037), _1233039)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233039), _1233037)))], (25673 ^ _780461) ^ [_1233190, _1233192] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233190), _1233192)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233192), _1233190))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233192), _1233190)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233190), _1233192)))], (25687 ^ _780461) ^ [_1233420, _1233422] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233420), _1233422))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233420), _1233422)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233422), _1233420)))], (25697 ^ _780461) ^ [_1233582, _1233584] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233582), _1233584)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233584), _1233582))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233584), _1233582)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233582), _1233584)))], (25711 ^ _780461) ^ [_1233812, _1233814] : [_1233812 = _1233814, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233812), _1233814)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233814), _1233812)))], (25721 ^ _780461) ^ [_1233965, _1233967] : [_1233967 = _1233965, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233965), _1233967)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1233967), _1233965)))], (25731 ^ _780461) ^ [_1234118, _1234120, _1234122] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234118), _1234120)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234120), _1234118))), _1234120 = _1234122, 25742 ^ _780461 : [(25743 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234118), _1234122)))], (25745 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234122), _1234118))]]], (25747 ^ _780461) ^ [_1234384, _1234386, _1234388] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234384), _1234386)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234386), _1234384))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234386), _1234388)), 25758 ^ _780461 : [(25759 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234384), _1234388)))], (25761 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234388), _1234384))]]], (25763 ^ _780461) ^ [_1234660, _1234662] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234660), _1234662)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234662), _1234660))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234662), _1234660)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234660), _1234662)))], (25777 ^ _780461) ^ [_1234890, _1234892, _1234894] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234890), _1234892)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234892), _1234890))), 25792 ^ _780461 : [(25793 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234890), _1234894)))], (25795 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234894), _1234890))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234892), _1234894)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1234894), _1234892)))], (25797 ^ _780461) ^ [_1235233, _1235235] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235233), _1235235)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235235), _1235233))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235235), _1235233)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1235233), _1235235)))], (25811 ^ _780461) ^ [_1235463, _1235465] : [class_Rings_Ocomm__semiring__1(_1235463), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235463), _1235465), _1235465)))], (25817 ^ _780461) ^ [_1235552, _1235554, _1235556, _1235558] : [class_Rings_Ocomm__semiring__1(_1235552), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235552), _1235554), _1235556)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235552), _1235556), _1235558)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235552), _1235554), _1235558)))], (25831 ^ _780461) ^ [_1235785, _1235787, _1235789, _1235791] : [class_Divides_Osemiring__div(_1235785), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235785), _1235787), _1235789)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235785), _1235787), _1235791)), 25842 ^ _780461 : [(25843 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235785), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1235785), _1235789), _1235787)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1235785), _1235791), _1235787))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235785), _1235789), _1235791)))], (25849 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235785), _1235789), _1235791)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1235785), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1235785), _1235789), _1235787)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1235785), _1235791), _1235787))))]]], (25855 ^ _780461) ^ [_1236232, _1236234, _1236236, _1236238] : [class_Rings_Ocomm__semiring__1(_1236232), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236232), _1236234), _1236236)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236232), hAPP(hAPP(c_Power_Opower__class_Opower(_1236232), _1236234), _1236238)), hAPP(hAPP(c_Power_Opower__class_Opower(_1236232), _1236236), _1236238))))], (25865 ^ _780461) ^ [_1236427, _1236429, _1236431, _1236433] : [class_Divides_Osemiring__div(_1236427), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236427), _1236429), c_Divides_Odiv__class_Omod(_1236427, _1236431, _1236433))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236427), _1236429), _1236433)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236427), _1236429), _1236431)))], (25879 ^ _780461) ^ [_1236668, _1236670, _1236672, _1236674] : [class_Divides_Osemiring__div(_1236668), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236668), _1236670), _1236672)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236668), _1236670), _1236674)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236668), _1236670), c_Divides_Odiv__class_Omod(_1236668, _1236672, _1236674))))], (25893 ^ _780461) ^ [_1236909, _1236911, _1236913, _1236915] : [class_Divides_Osemiring__div(_1236909), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1236909), _1236911), _1236913)), -(c_Divides_Odiv__class_Omod(_1236909, c_Divides_Odiv__class_Omod(_1236909, _1236915, _1236913), _1236911) = c_Divides_Odiv__class_Omod(_1236909, _1236915, _1236911))], (25903 ^ _780461) ^ [_1237082, _1237084, _1237086, _1237088] : [class_Divides_Osemiring__div(_1237082), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237082), _1237084), _1237086)), 25910 ^ _780461 : [(25911 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237082), _1237084), c_Divides_Odiv__class_Omod(_1237082, _1237088, _1237086))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237082), _1237084), _1237088)))], (25917 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237082), _1237084), _1237088)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237082), _1237084), c_Divides_Odiv__class_Omod(_1237082, _1237088, _1237086))))]]], (25923 ^ _780461) ^ [_1237423, _1237425, _1237427] : [class_Rings_Ocomm__semiring__1(_1237423), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237423), _1237425), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237423), _1237425), _1237427))))], (25929 ^ _780461) ^ [_1237530, _1237532, _1237534] : [class_Rings_Ocomm__semiring__1(_1237530), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237530), _1237532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237530), _1237534), _1237532))))], (25935 ^ _780461) ^ [_1237637, _1237639, _1237641, _1237643] : [class_Rings_Ocomm__semiring__1(_1237637), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237637), _1237639), _1237641)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237637), _1237639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237637), _1237641), _1237643))))], (25945 ^ _780461) ^ [_1237816, _1237818, _1237820, _1237822] : [class_Rings_Ocomm__semiring__1(_1237816), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237816), _1237818), _1237820)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237816), _1237818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237816), _1237822), _1237820))))], (25955 ^ _780461) ^ [_1237995, _1237997, _1237999, _1238001, _1238003] : [class_Rings_Ocomm__semiring__1(_1237995), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237995), _1237997), _1237999)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237995), _1238001), _1238003)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1237995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237995), _1237997), _1238001)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237995), _1237999), _1238003))))], (25969 ^ _780461) ^ [_1238266, _1238268, _1238270, _1238272] : [class_Rings_Odvd(_1238266), _1238268 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238266), _1238270), _1238272), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238266), _1238270), _1238268)))], (25979 ^ _780461) ^ [_1238431, _1238433, _1238435, _1238437] : [class_Rings_Ocomm__semiring__1(_1238431), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238431), _1238433), _1238435)), _1238437)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238431), _1238433), _1238437)))], (25989 ^ _780461) ^ [_1238610, _1238612, _1238614, _1238616] : [class_Rings_Ocomm__semiring__1(_1238610), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238610), _1238612), _1238614)), _1238616)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1238610), _1238614), _1238616)))], (25999 ^ _780461) ^ [_1238789, _1238791, _1238793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1238789), tc_HOL_Obool)), _1238791), _1238793)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1238789, _1238793, _1238791))], (26005 ^ _780461) ^ [_1238894, _1238896, _1238898, _1238900] : [c_Hoare__Mirabelle_Ohoare__derivs(_1238894, _1238896, _1238898), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1238894), tc_HOL_Obool)), _1238900), _1238898)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1238894, _1238896, _1238900))], (26015 ^ _780461) ^ [_1239059, _1239061, _1239063, _1239065] : [c_Hoare__Mirabelle_Ohoare__derivs(_1239059, _1239061, _1239063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_1239059), tc_HOL_Obool)), _1239061), _1239065)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1239059, _1239065, _1239063))], (26025 ^ _780461) ^ [_1239224, _1239226, _1239228] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239224), _1239226)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239224), _1239228)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239224), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1239226), _1239228))))], (26035 ^ _780461) ^ [_1239399, _1239401, _1239403, _1239405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239399, tc_HOL_Obool)), _1239401), _1239403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239399, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1239399), _1239405), _1239401)), hAPP(hAPP(c_Set_Oinsert(_1239399), _1239405), _1239403))))], (26041 ^ _780461) ^ [_1239552, _1239554, _1239556, _1239558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239552, tc_HOL_Obool)), _1239554), _1239556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239552, tc_HOL_Obool)), _1239554), hAPP(hAPP(c_Set_Oinsert(_1239552), _1239558), _1239556))))], (26047 ^ _780461) ^ [_1239689, _1239691, _1239693] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239689, tc_HOL_Obool)), _1239691), hAPP(hAPP(c_Set_Oinsert(_1239689), _1239693), _1239691))))], (26049 ^ _780461) ^ [_1239749, _1239751] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239749), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1239751), _1239749))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239749), _1239751)))], (26055 ^ _780461) ^ [_1239854, _1239856] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239854), _1239856)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1239854), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1239856), _1239854))))], (26061 ^ _780461) ^ [_1239965, _1239967, _1239969, _1239971] : [class_Rings_Ocomm__ring__1(_1239965), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239965), _1239967), _1239969)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239965), _1239967), _1239971)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1239965), _1239967), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1239965), _1239969), _1239971))))], (26075 ^ _780461) ^ [_1240214, _1240216, _1240218] : [class_Rings_Ocomm__ring__1(_1240214), 26078 ^ _780461 : [(26079 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240214), _1240216), hAPP(c_Groups_Ouminus__class_Ouminus(_1240214), _1240218))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240214), _1240216), _1240218)))], (26085 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240214), _1240216), _1240218)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240214), _1240216), hAPP(c_Groups_Ouminus__class_Ouminus(_1240214), _1240218))))]]], (26091 ^ _780461) ^ [_1240482, _1240484, _1240486] : [class_Rings_Ocomm__ring__1(_1240482), 26094 ^ _780461 : [(26095 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240482), hAPP(c_Groups_Ouminus__class_Ouminus(_1240482), _1240484)), _1240486)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240482), _1240484), _1240486)))], (26101 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240482), _1240484), _1240486)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1240482), hAPP(c_Groups_Ouminus__class_Ouminus(_1240482), _1240484)), _1240486)))]]], (26107 ^ _780461) ^ [_1240750, _1240752, _1240754] : [class_Orderings_Obot(_1240750), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1240752, _1240750)), _1240754) = c_Orderings_Obot__class_Obot(_1240750))], (26113 ^ _780461) ^ [_1240847, _1240849, _1240851, _1240853, _1240855] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1240847, _1240849, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1240847)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1240847), hAPP(hAPP(c_COMBC(_1240847, 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)), _1240847), 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)), _1240847), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _1240851))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _1240853))), c_Com_Ocom_OWhile(_1240853, _1240855)), _1240851)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1240847), tc_HOL_Obool)))))], (26115 ^ _780461) ^ [_1240943, _1240945, _1240947, _1240949] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1240943, tc_HOL_Obool)), _1240945), hAPP(hAPP(c_Set_Oinsert(_1240943), _1240947), _1240949)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1240943, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1240943, tc_HOL_Obool)), _1240945), _1240949)), hAPP(hAPP(c_Set_Oinsert(_1240943), _1240947), c_Orderings_Obot__class_Obot(tc_fun(_1240943, tc_HOL_Obool)))))], (26117 ^ _780461) ^ [_1241026, _1241028, _1241030, _1241032] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241026, tc_HOL_Obool)), _1241028), hAPP(hAPP(c_Set_Oinsert(_1241026), _1241030), _1241032)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241026, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241026, tc_HOL_Obool)), _1241028), hAPP(hAPP(c_Set_Oinsert(_1241026), _1241030), c_Orderings_Obot__class_Obot(tc_fun(_1241026, tc_HOL_Obool))))), _1241032))], (26119 ^ _780461) ^ [_1241109, _1241111, _1241113] : [-(hAPP(hAPP(c_Set_Oinsert(_1241109), _1241111), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241109, tc_HOL_Obool)), _1241113), hAPP(hAPP(c_Set_Oinsert(_1241109), _1241111), c_Orderings_Obot__class_Obot(tc_fun(_1241109, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_1241109), _1241111), _1241113))], (26121 ^ _780461) ^ [_1241188] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1241188), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1241188 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (26127 ^ _780461) ^ [_1241269] : [_1241269 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1241269), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (26133 ^ _780461) ^ [_1241371, _1241373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241371, tc_HOL_Obool)), _1241373), c_Orderings_Obot__class_Obot(tc_fun(_1241371, tc_HOL_Obool)))), -(_1241373 = c_Orderings_Obot__class_Obot(tc_fun(_1241371, tc_HOL_Obool)))], (26139 ^ _780461) ^ [_1241484, _1241486] : [_1241486 = c_Orderings_Obot__class_Obot(tc_fun(_1241484, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241484, tc_HOL_Obool)), _1241486), c_Orderings_Obot__class_Obot(tc_fun(_1241484, tc_HOL_Obool)))))], (26145 ^ _780461) ^ [_1241603, _1241605] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241603, tc_HOL_Obool)), _1241605), _1241605) = c_Orderings_Obot__class_Obot(tc_fun(_1241603, tc_HOL_Obool)))], (26147 ^ _780461) ^ [_1241644, _1241646] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241644, tc_HOL_Obool)), _1241646), c_Orderings_Obot__class_Obot(tc_fun(_1241644, tc_HOL_Obool))) = _1241646)], (26149 ^ _780461) ^ [_1241685, _1241687] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1241685, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1241685, tc_HOL_Obool))), _1241687) = c_Orderings_Obot__class_Obot(tc_fun(_1241685, tc_HOL_Obool)))], (26151 ^ _780461) ^ [_1241743, _1241745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1241743, tc_HOL_Obool)), _1241745), c_Orderings_Obot__class_Obot(tc_fun(_1241743, tc_HOL_Obool))))], (26153 ^ _780461) ^ [_1241783, _1241785, _1241787, _1241789, _1241791] : [c_Hoare__Mirabelle_Ohoare__derivs(_1241783, _1241785, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1241783)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1241783), _1241787), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1241789))), _1241791)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1241783), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1241783, _1241785, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1241783)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1241783), _1241787), hAPP(c_Com_Ocom_OBODY, _1241789)), _1241791)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1241783), tc_HOL_Obool)))))], (26159 ^ _780461) ^ [_1242000, _1242002, _1242004, _1242006, _1242008] : [c_Hoare__Mirabelle_Ohoare__derivs(_1242000, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1242000)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1242000), _1242002), hAPP(c_Com_Ocom_OBODY, _1242004)), _1242006)), _1242008), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1242000)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1242000), _1242002), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1242004))), _1242006)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1242000), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1242000, _1242008, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1242000)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1242000), _1242002), hAPP(c_Com_Ocom_OBODY, _1242004)), _1242006)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1242000), tc_HOL_Obool)))))], (26165 ^ _780461) ^ [_1242265, _1242267] : [class_Orderings_Obot(_1242265), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242265), c_Orderings_Obot__class_Obot(_1242265)), _1242267)))], (26171 ^ _780461) ^ [_1242358, _1242360, _1242362, _1242364] : [class_Rings_Oidom(_1242358), 26174 ^ _780461 : [(26185 ^ _780461) ^ [] : [26186 ^ _780461 : [(26187 ^ _780461) ^ [] : [_1242360 = c_Groups_Ozero__class_Ozero(_1242358)], (26189 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242358), _1242362), _1242364))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242358), _1242360), _1242362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242358), _1242360), _1242364))))], (26175 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242358), _1242360), _1242362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242358), _1242360), _1242364))), -(_1242360 = c_Groups_Ozero__class_Ozero(_1242358)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242358), _1242362), _1242364)))]]], (26193 ^ _780461) ^ [_1242716, _1242718, _1242720, _1242722] : [class_Rings_Oidom(_1242716), 26196 ^ _780461 : [(26207 ^ _780461) ^ [] : [26208 ^ _780461 : [(26209 ^ _780461) ^ [] : [_1242720 = c_Groups_Ozero__class_Ozero(_1242716)], (26211 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242716), _1242718), _1242722))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242716), _1242718), _1242720)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242716), _1242722), _1242720))))], (26197 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242716), _1242718), _1242720)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242716), _1242722), _1242720))), -(_1242720 = c_Groups_Ozero__class_Ozero(_1242716)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1242716), _1242718), _1242722)))]]], (26215 ^ _780461) ^ [_1243074, _1243076, _1243078] : [class_Divides_Osemiring__div(_1243074), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243074), _1243076), _1243078)), -(c_Divides_Odiv__class_Omod(_1243074, _1243078, _1243076) = c_Groups_Ozero__class_Ozero(_1243074))], (26225 ^ _780461) ^ [_1243231, _1243233, _1243235] : [class_Divides_Osemiring__div(_1243231), 26228 ^ _780461 : [(26229 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243231), _1243233), _1243235)), -(c_Divides_Odiv__class_Omod(_1243231, _1243235, _1243233) = c_Groups_Ozero__class_Ozero(_1243231))], (26235 ^ _780461) ^ [] : [c_Divides_Odiv__class_Omod(_1243231, _1243235, _1243233) = c_Groups_Ozero__class_Ozero(_1243231), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243231), _1243233), _1243235)))]]], (26241 ^ _780461) ^ [_1243481, _1243483, _1243485, _1243487] : [class_Divides_Osemiring__div(_1243481), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243481), _1243483), _1243485)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243481), _1243483), _1243487)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1243481), _1243485), _1243487)), _1243483) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1243481), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243481), _1243485), _1243483)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243481), _1243487), _1243483)))], (26255 ^ _780461) ^ [_1243780, _1243782, _1243784] : [class_Divides_Osemiring__div(_1243780), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243780), _1243782), _1243784)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243780), _1243782), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243780), _1243784), _1243782)) = _1243784)], (26265 ^ _780461) ^ [_1243957, _1243959, _1243961, _1243963] : [class_Divides_Osemiring__div(_1243957), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1243957), _1243959), _1243961)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243957), _1243963), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243957), _1243961), _1243959)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1243957), _1243963), _1243961)), _1243959))], (26275 ^ _780461) ^ [_1244170, _1244172, _1244174] : [class_Divides_Osemiring__div(_1244170), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244170), _1244172), _1244174)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244170), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244170), _1244174), _1244172)), _1244172) = _1244174)], (26285 ^ _780461) ^ [_1244347, _1244349, _1244351, _1244353] : [class_Divides_Osemiring__div(_1244347), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244347), _1244349), _1244351)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244347), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244347), _1244351), _1244349)), _1244353) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244347), _1244351), _1244353)), _1244349))], (26295 ^ _780461) ^ [_1244560, _1244562, _1244564, _1244566, _1244568] : [class_Divides_Osemiring__div(_1244560), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244560), _1244562), _1244564)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244560), _1244566), _1244568)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244560), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244560), _1244564), _1244562)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244560), _1244568), _1244566)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244560), _1244564), _1244568)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1244560), _1244562), _1244566)))], (26309 ^ _780461) ^ [_1244881, _1244883, _1244885] : [class_Divides_Oring__div(_1244881), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1244881), _1244883), _1244885)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244881), hAPP(c_Groups_Ouminus__class_Ouminus(_1244881), _1244885)), _1244883) = hAPP(c_Groups_Ouminus__class_Ouminus(_1244881), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244881), _1244885), _1244883)))], (26319 ^ _780461) ^ [_1245078, _1245080, _1245082] : [class_Divides_Oring__div(_1245078), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245078), _1245080), _1245082)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1245078), _1245082), hAPP(c_Groups_Ouminus__class_Ouminus(_1245078), _1245080)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1245078), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1245078), _1245082), _1245080)))], (26329 ^ _780461) ^ [_1245275, _1245277, _1245279, _1245281] : [class_Rings_Ocomm__semiring__1(_1245275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245277), _1245279)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245275), hAPP(hAPP(c_Power_Opower__class_Opower(_1245275), _1245281), _1245277)), hAPP(hAPP(c_Power_Opower__class_Opower(_1245275), _1245281), _1245279))))], (26339 ^ _780461) ^ [_1245466, _1245468, _1245470, _1245472, _1245474] : [class_Rings_Ocomm__semiring__1(_1245466), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245466), _1245468), _1245470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245472), _1245474)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245466), hAPP(hAPP(c_Power_Opower__class_Opower(_1245466), _1245468), _1245472)), hAPP(hAPP(c_Power_Opower__class_Opower(_1245466), _1245470), _1245474))))], (26353 ^ _780461) ^ [_1245733, _1245735, _1245737, _1245739, _1245741] : [class_Rings_Ocomm__semiring__1(_1245733), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245733), hAPP(hAPP(c_Power_Opower__class_Opower(_1245733), _1245735), _1245737)), _1245739)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245741), _1245737)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1245733), hAPP(hAPP(c_Power_Opower__class_Opower(_1245733), _1245735), _1245741)), _1245739)))], (26367 ^ _780461) ^ [_1246000, _1246002, _1246004, _1246006] : [class_Divides_Osemiring__div(_1246000), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1246000), _1246002), _1246004)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1246000), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246000), _1246004), _1246002)), _1246006) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246000), hAPP(hAPP(c_Power_Opower__class_Opower(_1246000), _1246004), _1246006)), hAPP(hAPP(c_Power_Opower__class_Opower(_1246000), _1246002), _1246006)))], (26377 ^ _780461) ^ [_1246229, _1246231, _1246233, _1246235, _1246237, _1246239, _1246241, _1246243] : [c_Hoare__Mirabelle_Ohoare__derivs(_1246229, _1246231, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1246229)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1246229), _1246233), _1246235), hAPP(hAPP(c_COMBC(_1246229, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1246229), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1246237)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_1246239))), hAPP(hAPP(c_Natural_Ogetlocs, _1246241), _1246239))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1246229), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1246229, _1246231, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1246229)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1246229), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1246229), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _1246241)))), hAPP(hAPP(c_COMBC(_1246229, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _1246229), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _1246233)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_1246239))), _1246243)))), c_Com_Ocom_OLocal(_1246239, _1246243, _1246235)), _1246237)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1246229), tc_HOL_Obool)))))], (26383 ^ _780461) ^ [_1246628] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246628), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1246628 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (26389 ^ _780461) ^ [_1246709] : [_1246709 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246709), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (26395 ^ _780461) ^ [_1246796, _1246798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1246796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246796), _1246798)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246798), _1246796))], (26415 ^ _780461) ^ [_1247100, _1247102, _1247104] : [26416 ^ _780461 : [(26417 ^ _780461) ^ [] : [_1247100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26419 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247102), _1247104))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247100), _1247102)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1247100), _1247104))))], (26405 ^ _780461) ^ [_1246968, _1246970, _1246972] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246968), _1246970)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246968), _1246972))), -(_1246968 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1246970), _1246972)))], (26423 ^ _780461) ^ [_1247263, _1247265, _1247267] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247263), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247265), _1247267))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247263), _1247267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247267), _1247265)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247263), _1247265)))], (26437 ^ _780461) ^ [_1247502, _1247504, _1247506] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247504), _1247506))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247502), _1247504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1247506), _1247504)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1247502), _1247506)))], (26451 ^ _780461) ^ [_1247756, _1247758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247756, tc_HOL_Obool)), _1247758), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1247756, tc_HOL_Obool)), _1247758))), -(_1247758 = c_Orderings_Obot__class_Obot(tc_fun(_1247756, tc_HOL_Obool)))], (26457 ^ _780461) ^ [_1247875, _1247877] : [_1247877 = c_Orderings_Obot__class_Obot(tc_fun(_1247875, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247875, tc_HOL_Obool)), _1247877), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1247875, tc_HOL_Obool)), _1247877))))], (26463 ^ _780461) ^ [_1248000, _1248002, _1248004] : [class_Rings_Odvd(_1248000), class_Rings_Osemiring__0(_1248000), 26470 ^ _780461 : [(26471 ^ _780461) ^ [] : [26472 ^ _780461 : [(26473 ^ _780461) ^ [_1248192] : [hBOOL(hAPP(_1248002, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248000), _1248004), _1248192)))]], 26475 ^ _780461 : [(26476 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248000), _1248004), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248000), 26474 ^ [_1248000, _1248002, _1248004]), c_Groups_Ozero__class_Ozero(_1248000)))))], (26478 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1248002, 26474 ^ [_1248000, _1248002, _1248004])))]]], (26480 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1248002, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248000), _1248004), 26487 ^ [_1248000, _1248002, _1248004])))), 26481 ^ _780461 : [(26482 ^ _780461) ^ [_1248329] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248000), _1248004), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248000), _1248329), c_Groups_Ozero__class_Ozero(_1248000)))), hBOOL(hAPP(_1248002, _1248329))]]]]], (26491 ^ _780461) ^ [_1248502, _1248504, _1248506, _1248508] : [class_Rings_Ocomm__ring(_1248502), class_Rings_Odvd(_1248502), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248502), _1248504), _1248506)), 26502 ^ _780461 : [(26503 ^ _780461) ^ [_1248755, _1248757] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248502), _1248504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248502), _1248757), _1248508))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248502), _1248504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1248502), _1248757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248502), _1248755), _1248506))), _1248508))))], (26509 ^ _780461) ^ [_1248928, _1248930] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248502), _1248504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1248502), _1248930), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248502), _1248928), _1248506))), _1248508))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1248502), _1248504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1248502), _1248930), _1248508))))]]], (26515 ^ _780461) ^ [_1249115, _1249117, _1249119, _1249121] : [class_Rings_Ocomm__ring(_1249115), class_Rings_Odvd(_1249115), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249115), _1249117), _1249119)), 26526 ^ _780461 : [(26527 ^ _780461) ^ [_1249368, _1249370] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249115), _1249117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249115), _1249370), _1249121))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249115), _1249117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249115), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1249115), _1249370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249115), _1249368), _1249119))), _1249121))))], (26533 ^ _780461) ^ [_1249541, _1249543] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249115), _1249117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249115), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1249115), _1249543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249115), _1249541), _1249119))), _1249121))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249115), _1249117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1249115), _1249543), _1249121))))]]], (26539 ^ _780461) ^ [_1249728, _1249730, _1249732] : [class_Divides_Osemiring__div(_1249728), class_Int_Onumber(_1249728), 26546 ^ _780461 : [(26547 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249728), hAPP(c_Int_Onumber__class_Onumber__of(_1249728), _1249730)), hAPP(c_Int_Onumber__class_Onumber__of(_1249728), _1249732))), -(c_Divides_Odiv__class_Omod(_1249728, hAPP(c_Int_Onumber__class_Onumber__of(_1249728), _1249732), hAPP(c_Int_Onumber__class_Onumber__of(_1249728), _1249730)) = c_Groups_Ozero__class_Ozero(_1249728))], (26553 ^ _780461) ^ [] : [c_Divides_Odiv__class_Omod(_1249728, hAPP(c_Int_Onumber__class_Onumber__of(_1249728), _1249732), hAPP(c_Int_Onumber__class_Onumber__of(_1249728), _1249730)) = c_Groups_Ozero__class_Ozero(_1249728), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1249728), hAPP(c_Int_Onumber__class_Onumber__of(_1249728), _1249730)), hAPP(c_Int_Onumber__class_Onumber__of(_1249728), _1249732))))]]], (26559 ^ _780461) ^ [_1250092, _1250094, _1250096, _1250098, _1250100] : [class_Divides_Osemiring__div(_1250092), -(_1250094 = c_Groups_Ozero__class_Ozero(_1250092)), -(_1250096 = c_Groups_Ozero__class_Ozero(_1250092)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1250092), _1250094), _1250098)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1250092), _1250096), _1250100)), 26578 ^ _780461 : [(26579 ^ _780461) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250092), _1250098), _1250094) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250092), _1250100), _1250096), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250092), _1250098), _1250096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250092), _1250094), _1250100))], (26585 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250092), _1250098), _1250096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250092), _1250094), _1250100), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250092), _1250098), _1250094) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250092), _1250100), _1250096))]]], (26591 ^ _780461) ^ [_1250685, _1250687, _1250689, _1250691] : [class_Divides_Osemiring__div(_1250685), -(_1250687 = c_Groups_Ozero__class_Ozero(_1250685)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1250685), _1250687), _1250689)), 26602 ^ _780461 : [(26603 ^ _780461) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250685), _1250689), _1250687) = _1250691, -(_1250689 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250685), _1250691), _1250687))], (26609 ^ _780461) ^ [] : [_1250689 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250685), _1250691), _1250687), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1250685), _1250689), _1250687) = _1250691)]]], (26615 ^ _780461) ^ [_1251083, _1251085] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1251083), _1251085)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1251085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1251083), _1251085)))], (26625 ^ _780461) ^ [_1251236, _1251238, _1251240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1251236)), 26628 ^ _780461 : [(26629 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251236), _1251238)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251236), _1251240))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1251238), _1251240)))], (26635 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1251238), _1251240)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251236), _1251238)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251236), _1251240))))]]], (26641 ^ _780461) ^ [_1251519, _1251521, _1251523] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251519), _1251521)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251519), _1251523))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1251519)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1251521), _1251523)))], (26651 ^ _780461) ^ [_1251700, _1251702, _1251704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1251700, tc_HOL_Obool)), _1251702), _1251704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1251700, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1251700, _1251702)), c_Predicate_OPowp(_1251700, _1251704))))], (26657 ^ _780461) ^ [_1251837, _1251839, _1251841] : [class_Rings_Ocomm__semiring__1(_1251837), 26662 ^ _780461 : [(26663 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1251839))], (26665 ^ _780461) ^ [] : [_1251841 = c_Groups_Oone__class_Oone(_1251837)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1251837), _1251841), hAPP(hAPP(c_Power_Opower__class_Opower(_1251837), _1251841), _1251839))))], (26669 ^ _780461) ^ [_1252044, _1252046] : [-(c_Set_Othe__elem(_1252044, _1252046) = c_HOL_OThe(_1252044, hAPP(hAPP(c_COMBB(tc_fun(_1252044, tc_HOL_Obool), tc_HOL_Obool, _1252044), hAPP(c_fequal, _1252046)), hAPP(hAPP(c_COMBC(_1252044, tc_fun(_1252044, tc_HOL_Obool), tc_fun(_1252044, tc_HOL_Obool)), c_Set_Oinsert(_1252044)), c_Orderings_Obot__class_Obot(tc_fun(_1252044, tc_HOL_Obool))))))], (26671 ^ _780461) ^ [_1252114, _1252116] : [-(c_Set_Othe__elem(_1252114, hAPP(hAPP(c_Set_Oinsert(_1252114), _1252116), c_Orderings_Obot__class_Obot(tc_fun(_1252114, tc_HOL_Obool)))) = _1252116)], (26673 ^ _780461) ^ [_1252155, _1252157] : [-(c_Option_Oset(_1252155, hAPP(c_Option_Ooption_OSome(_1252155), _1252157)) = hAPP(hAPP(c_Set_Oinsert(_1252155), _1252157), c_Orderings_Obot__class_Obot(tc_fun(_1252155, tc_HOL_Obool))))], (26675 ^ _780461) ^ [_1252201, _1252203, _1252205, _1252207] : [class_Orderings_Oorder(_1252201), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1252201, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1252203), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252201), hAPP(_1252203, _1252205)), hAPP(_1252203, _1252207)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252205), _1252207)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252207), _1252205)))], (26693 ^ _780461) ^ [_1252501, _1252503, _1252505, _1252507] : [class_Orderings_Oorder(_1252501), c_Orderings_Oorder_Omono(tc_Nat_Onat, _1252501, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252503), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1252505), _1252507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252501), hAPP(_1252503, _1252505)), hAPP(_1252503, _1252507))))], (26707 ^ _780461) ^ [_1252732, _1252734, _1252736] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252732), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1252734, _1252736))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252732), _1252736)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252732), _1252734)))], (26717 ^ _780461) ^ [_1252903, _1252905, _1252907] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252903), _1252905)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252903), _1252907)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1252903), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1252905, _1252907))))], (26727 ^ _780461) ^ [_1253089, _1253091] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253089), _1253091)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253089), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1253091))))], (26733 ^ _780461) ^ [_1253188, _1253190] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253188), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1253190))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253188), _1253190)))], (26739 ^ _780461) ^ [_1253308, _1253310] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253308), _1253310)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1253308)), _1253310)))], (26745 ^ _780461) ^ [_1253407, _1253409] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1253407)), _1253409)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253407), _1253409)))], (26751 ^ _780461) ^ [_1253512, _1253514, _1253516] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1253514), _1253516))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253512), _1253516)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253512), _1253514)))], (26761 ^ _780461) ^ [_1253687, _1253689] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253687), _1253689)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253689), _1253687)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253687) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253689))], (26771 ^ _780461) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26773 ^ _780461) ^ [_1253866, _1253868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253868)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253866), _1253868)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1253868), _1253866)), -(_1253866 = _1253868)], (26791 ^ _780461) ^ [_1254127, _1254129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254127), _1254129)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254129), _1254127))], (26801 ^ _780461) ^ [_1254281, _1254283, _1254285] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254281), _1254283)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254281), _1254285))), -(_1254281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254283), _1254285)))], (26811 ^ _780461) ^ [_1254418, _1254420, _1254422] : [-(_1254418 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26814 ^ _780461 : [(26815 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254420), _1254422)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254418), _1254420)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254418), _1254422))))], (26821 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254418), _1254420)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254418), _1254422))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254420), _1254422)))]]], (26827 ^ _780461) ^ [_1254695, _1254697, _1254699, _1254701, _1254703] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254695), _1254697)), 26830 ^ _780461 : [(26831 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1254699), _1254701))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1254699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254703), _1254697))), _1254701))))], (26837 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1254699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1254703), _1254697))), _1254701))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1254695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1254699), _1254701))))]]], (26843 ^ _780461) ^ [_1255050, _1255052, _1255054] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1255050), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1255052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255050), _1255054)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1255050), _1255052)))], (26849 ^ _780461) ^ [_1255169, _1255171, _1255173] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1255169), _1255171)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1255169), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1255171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255169), _1255173)))))], (26855 ^ _780461) ^ [_1255309, _1255311] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1255309), _1255311)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255309)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255311))))], (26861 ^ _780461) ^ [_1255414, _1255416] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255414)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255416))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1255414), _1255416)))], (26867 ^ _780461) ^ [_1255540, _1255542] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255540)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255542))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1255540), _1255542)))], (26873 ^ _780461) ^ [_1255645, _1255647] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1255645), _1255647)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255645)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1255647))))], (26879 ^ _780461) ^ [_1255756, _1255758] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1255756), _1255758)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255756), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1255758), _1255756)) = _1255758)], (26885 ^ _780461) ^ [_1255885, _1255887, _1255889] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1255885, _1255887) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1255889, _1255887), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1255887), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1255885), _1255889))))], (26891 ^ _780461) ^ [_1255998, _1256000, _1256002] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1256000), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1255998), _1256002))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1255998, _1256000) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1256002, _1256000))], (26897 ^ _780461) ^ [_1256129] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1256129), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256129) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (26903 ^ _780461) ^ [_1256216] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256216) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1256216), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (26909 ^ _780461) ^ [_1256309, _1256311] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1256309), _1256311)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1256311), _1256309)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256311)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256309)))], (26915 ^ _780461) ^ [_1256438, _1256440] : [class_Orderings_Oorder(_1256438), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1256438, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1256440), -(c_Orderings_Oorder_Omono(tc_Nat_Onat, _1256438, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1256440))], (26925 ^ _780461) ^ [_1256573, _1256575] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1256573), _1256575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1256573), _1256575)))], (26935 ^ _780461) ^ [_1256741, _1256743] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1256741)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1256743))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1256743), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1256741)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26941 ^ _780461) ^ [_1256856, _1256858] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1256858), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1256856)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1256856)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1256858))))], (26947 ^ _780461) ^ [_1256976, _1256978] : [-(_1256976 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1256978), _1256976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256978)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256976))))], (26957 ^ _780461) ^ [_1257135, _1257137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257137)), 26964 ^ _780461 : [(26965 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1257135)), hAPP(c_Int_Onat, _1257137))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1257135), _1257137)))], (26971 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1257135), _1257137)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1257135)), hAPP(c_Int_Onat, _1257137))))]]], (26977 ^ _780461) ^ [_1257449, _1257451] : [-(_1257449 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 26980 ^ _780461 : [(26981 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1257449), _1257451)), _1257449)), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1257451) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (26987 ^ _780461) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1257451) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1257449), _1257451)), _1257449)))]]], (26993 ^ _780461) ^ [_1257711, _1257713] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1257711), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1257713))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1257711))), _1257713)))], (26999 ^ _780461) ^ [_1257822, _1257824] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1257822))), _1257824)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1257822), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1257824))))], (27005 ^ _780461) ^ [_1257954, _1257956] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1257954)), _1257956)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1257954), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1257956)))))], (27011 ^ _780461) ^ [_1258065, _1258067] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1258065), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1258067)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258065)), _1258067)))], (27017 ^ _780461) ^ [_1258182] : [-(c_Option_Oset(_1258182, c_Option_Ooption_ONone(_1258182)) = c_Orderings_Obot__class_Obot(tc_fun(_1258182, tc_HOL_Obool)))], (27019 ^ _780461) ^ [_1258230, _1258232] : [c_Option_Oset(_1258230, _1258232) = c_Orderings_Obot__class_Obot(tc_fun(_1258230, tc_HOL_Obool)), -(_1258232 = c_Option_Ooption_ONone(_1258230))], (27025 ^ _780461) ^ [_1258323, _1258325] : [_1258325 = c_Option_Ooption_ONone(_1258323), -(c_Option_Oset(_1258323, _1258325) = c_Orderings_Obot__class_Obot(tc_fun(_1258323, tc_HOL_Obool)))], (27047 ^ _780461) ^ [_1258649, _1258651] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1258649)), _1258651))), 27050 ^ _780461 : [(27051 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258649)))], (27053 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1258649), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258651)))]], 27054 ^ _780461 : [(27055 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258649))], (27057 ^ _780461) ^ [] : [_1258651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (27031 ^ _780461) ^ [_1258437, _1258439] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Int_Onat, _1258437)), _1258439)), 27034 ^ _780461 : [(27035 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258437)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1258437), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258439))))], (27041 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258437))), -(_1258439 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (27061 ^ _780461) ^ [_1258893, _1258895, _1258897, _1258899, _1258901] : [27064 ^ _780461 : [(27065 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1258893, 27062 ^ [_1258893, _1258895, _1258897, _1258899, _1258901]), 27063 ^ [_1258893, _1258895, _1258897, _1258899, _1258901])))], (27067 ^ _780461) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1258895, _1258897, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1258895)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1258895), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1258895), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 27063 ^ [_1258893, _1258895, _1258897, _1258899, _1258901]))), _1258899), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _1258895), hAPP(_1258901, 27062 ^ [_1258893, _1258895, _1258897, _1258899, _1258901])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1258895), tc_HOL_Obool))))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1258895, _1258897, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1258895)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1258895), _1258893), _1258899), _1258901)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1258895), tc_HOL_Obool)))))], (27071 ^ _780461) ^ [_1259315, _1259317, _1259319, _1259321, _1259323, _1259325] : [c_Hoare__Mirabelle_Ohoare__derivs(_1259315, _1259317, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1259315)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1259315), _1259319), _1259321), _1259323)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1259315), tc_HOL_Obool)))), 27078 ^ _780461 : [(27079 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1259323, 27076 ^ [_1259315, _1259317, _1259319, _1259321, _1259323, _1259325]), 27077 ^ [_1259315, _1259317, _1259319, _1259321, _1259323, _1259325])))], (27081 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1259325, 27076 ^ [_1259315, _1259317, _1259319, _1259321, _1259323, _1259325]), 27077 ^ [_1259315, _1259317, _1259319, _1259321, _1259323, _1259325]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1259315, _1259317, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1259315)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1259315), _1259319), _1259321), _1259325)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1259315), tc_HOL_Obool)))))], (27085 ^ _780461) ^ [_1259744, _1259746, _1259748, _1259750, _1259752, _1259754] : [c_Hoare__Mirabelle_Ohoare__derivs(_1259744, _1259746, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1259744)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1259744), _1259748), _1259750), _1259752)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1259744), tc_HOL_Obool)))), 27092 ^ _780461 : [(27093 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1259754, 27090 ^ [_1259744, _1259746, _1259748, _1259750, _1259752, _1259754]), 27091 ^ [_1259744, _1259746, _1259748, _1259750, _1259752, _1259754])))], (27095 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1259748, 27090 ^ [_1259744, _1259746, _1259748, _1259750, _1259752, _1259754]), 27091 ^ [_1259744, _1259746, _1259748, _1259750, _1259752, _1259754]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_1259744, _1259746, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1259744)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1259744), _1259754), _1259750), _1259752)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1259744), tc_HOL_Obool)))))], (27125 ^ _780461) ^ [_1260721, _1260723, _1260725, _1260727] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1260721, tc_HOL_Obool)), _1260723), hAPP(hAPP(c_Set_Oinsert(_1260721), _1260725), _1260727)))), 27128 ^ _780461 : [(27129 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260721), _1260725), _1260727)))], (27131 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1260721, tc_HOL_Obool)), _1260723), _1260727))]], 27132 ^ _780461 : [(27133 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1260721), _1260725), _1260727))], (27135 ^ _780461) ^ [] : [27136 ^ _780461 : [(27137 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260721), _1260725), _1260723)))], (27139 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1260721, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260721, tc_HOL_Obool)), _1260723), hAPP(hAPP(c_Set_Oinsert(_1260721), _1260725), c_Orderings_Obot__class_Obot(tc_fun(_1260721, tc_HOL_Obool))))), _1260727))]], 27140 ^ _780461 : [(27141 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1260721), _1260725), _1260723))], (27143 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260721, tc_HOL_Obool)), _1260723), _1260727))]]]]], (27099 ^ _780461) ^ [_1260194, _1260196, _1260198, _1260200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1260194, tc_HOL_Obool)), _1260196), hAPP(hAPP(c_Set_Oinsert(_1260194), _1260198), _1260200))), 27102 ^ _780461 : [(27103 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1260194), _1260198), _1260200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1260194, tc_HOL_Obool)), _1260196), _1260200)))], (27109 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260194), _1260198), _1260200))), 27112 ^ _780461 : [(27113 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1260194), _1260198), _1260196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1260194, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260194, tc_HOL_Obool)), _1260196), hAPP(hAPP(c_Set_Oinsert(_1260194), _1260198), c_Orderings_Obot__class_Obot(tc_fun(_1260194, tc_HOL_Obool))))), _1260200)))], (27119 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1260194), _1260198), _1260196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260194, tc_HOL_Obool)), _1260196), _1260200)))]]]]], (27147 ^ _780461) ^ [_1261260, _1261262, _1261264, _1261266] : [_1261260 = _1261262, 27152 ^ _780461 : [(27153 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261264), _1261266), _1261260)))], (27155 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261264), _1261266), _1261262)))]], 27156 ^ _780461 : [(27157 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1261264), _1261266), _1261260))], (27159 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1261264), _1261266), _1261262))]]], (27161 ^ _780461) ^ [_1261535, _1261537] : [hBOOL(hAPP(hAPP(c_member(_1261535), _1261537), c_Orderings_Obot__class_Obot(tc_fun(_1261535, tc_HOL_Obool))))], (27163 ^ _780461) ^ [_1261572, _1261574, _1261576, _1261578] : [hBOOL(hAPP(hAPP(c_member(_1261572), _1261574), hAPP(hAPP(c_Set_Oinsert(_1261572), _1261576), _1261578))), -(_1261574 = _1261576), -(hBOOL(hAPP(hAPP(c_member(_1261572), _1261574), _1261578)))], (27173 ^ _780461) ^ [_1261712, _1261714, _1261716, _1261718] : [27174 ^ _780461 : [(27175 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1261712), _1261714), _1261716))], (27177 ^ _780461) ^ [] : [_1261714 = _1261718]], -(hBOOL(hAPP(hAPP(c_member(_1261712), _1261714), hAPP(hAPP(c_Set_Oinsert(_1261712), _1261718), _1261716))))], (27181 ^ _780461) ^ [_1261877, _1261879, _1261881, _1261883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261877, tc_HOL_Obool)), _1261879), _1261881)), hBOOL(hAPP(hAPP(c_member(_1261877), _1261883), _1261879)), -(hBOOL(hAPP(hAPP(c_member(_1261877), _1261883), _1261881)))], (27191 ^ _780461) ^ [_1262062, _1262064, _1262066, _1262068] : [hBOOL(hAPP(hAPP(c_member(_1262062), _1262064), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262062, tc_HOL_Obool)), _1262066), _1262068))), 27194 ^ _780461 : [(27195 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1262062), _1262064), _1262066)))], (27197 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1262062), _1262064), _1262068))]]], (27199 ^ _780461) ^ [_1262241, _1262243, _1262245, _1262247] : [hBOOL(hAPP(hAPP(c_member(_1262241), _1262243), _1262245)), -(hBOOL(hAPP(hAPP(c_member(_1262241), _1262243), _1262247))), -(hBOOL(hAPP(hAPP(c_member(_1262241), _1262243), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262241, tc_HOL_Obool)), _1262245), _1262247))))], (27209 ^ _780461) ^ [_1262397, _1262399, _1262401] : [-(hBOOL(hAPP(hAPP(c_member(_1262397), _1262399), _1262401))), -(hBOOL(hAPP(hAPP(c_member(_1262397), _1262399), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262397, tc_HOL_Obool)), _1262401))))], (27215 ^ _780461) ^ [_1262457, _1262459, _1262461, _1262463, _1262465, _1262467, _1262469] : [hBOOL(hAPP(hAPP(c_member(_1262457), _1262459), hAPP(hAPP(_1262461, _1262463), _1262465))), -(hBOOL(hAPP(hAPP(c_member(_1262457), _1262459), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1262467, _1262469, tc_fun(_1262457, tc_HOL_Obool)), _1262461), hAPP(hAPP(c_Product__Type_OPair(_1262467, _1262469), _1262463), _1262465)))))], (27221 ^ _780461) ^ [_1262628, _1262630, _1262632] : [-(hBOOL(hAPP(hAPP(c_member(_1262628), _1262630), hAPP(hAPP(c_Set_Oinsert(_1262628), _1262630), _1262632))))], (27223 ^ _780461) ^ [_1262679, _1262681] : [-(hBOOL(hAPP(hAPP(c_member(_1262679), 27224 ^ [_1262679, _1262681]), _1262681))), -(_1262681 = c_Orderings_Obot__class_Obot(tc_fun(_1262679, tc_HOL_Obool)))], (27230 ^ _780461) ^ [_1262730, _1262732] : [_1262732 = c_Orderings_Obot__class_Obot(tc_fun(_1262730, tc_HOL_Obool)), 27233 ^ _780461 : [(27234 ^ _780461) ^ [_1262810] : [hBOOL(hAPP(hAPP(c_member(_1262730), _1262810), _1262732))]]], (27236 ^ _780461) ^ [_1262861, _1262863] : [27237 ^ _780461 : [(27238 ^ _780461) ^ [_1262914] : [hBOOL(hAPP(hAPP(c_member(_1262861), _1262914), _1262863))]], _1262863 = c_Orderings_Obot__class_Obot(tc_fun(_1262861, tc_HOL_Obool))], (27242 ^ _780461) ^ [_1262970, _1262972] : [-(_1262972 = c_Orderings_Obot__class_Obot(tc_fun(_1262970, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1262970), 27245 ^ [_1262970, _1262972]), _1262972)))], (27249 ^ _780461) ^ [_1263039, _1263041] : [hBOOL(hAPP(hAPP(c_member(_1263039), _1263041), c_Orderings_Obot__class_Obot(tc_fun(_1263039, tc_HOL_Obool))))], (27261 ^ _780461) ^ [_1263231, _1263233, _1263235, _1263237] : [27262 ^ _780461 : [(27263 ^ _780461) ^ [] : [_1263233 = _1263235], (27265 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1263231), _1263233), _1263237))]], -(hBOOL(hAPP(hAPP(c_member(_1263231), _1263233), hAPP(hAPP(c_Set_Oinsert(_1263231), _1263235), _1263237))))], (27251 ^ _780461) ^ [_1263097, _1263099, _1263101, _1263103] : [hBOOL(hAPP(hAPP(c_member(_1263097), _1263099), hAPP(hAPP(c_Set_Oinsert(_1263097), _1263101), _1263103))), -(_1263099 = _1263101), -(hBOOL(hAPP(hAPP(c_member(_1263097), _1263099), _1263103)))], (27269 ^ _780461) ^ [_1263395, _1263397, _1263399, _1263401] : [-(hBOOL(hAPP(hAPP(c_member(_1263395), _1263397), _1263399))), -(hBOOL(hAPP(hAPP(c_member(_1263395), _1263397), _1263401))), 27276 ^ _780461 : [(27277 ^ _780461) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_1263395), _1263397), _1263399) = hAPP(hAPP(c_Set_Oinsert(_1263395), _1263397), _1263401), -(_1263399 = _1263401)], (27283 ^ _780461) ^ [] : [_1263399 = _1263401, -(hAPP(hAPP(c_Set_Oinsert(_1263395), _1263397), _1263399) = hAPP(hAPP(c_Set_Oinsert(_1263395), _1263397), _1263401))]]], (27289 ^ _780461) ^ [_1263740, _1263742, _1263744] : [_1263740 = c_Orderings_Obot__class_Obot(tc_fun(_1263742, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_1263742), _1263744), _1263740))], (27295 ^ _780461) ^ [_1263844, _1263846, _1263848, _1263850] : [hBOOL(hAPP(hAPP(c_member(_1263844), _1263846), _1263848)), -(hBOOL(hAPP(hAPP(c_member(_1263844), _1263846), hAPP(hAPP(c_Set_Oinsert(_1263844), _1263850), _1263848))))], (27301 ^ _780461) ^ [_1263969, _1263971, _1263973] : [hBOOL(hAPP(hAPP(c_member(_1263969), _1263971), _1263973)), -(hAPP(hAPP(c_Set_Oinsert(_1263969), _1263971), _1263973) = _1263973)], (27307 ^ _780461) ^ [_1264078, _1264080, _1264082, _1264084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264078, tc_HOL_Obool)), _1264080), _1264082)), hBOOL(hAPP(hAPP(c_member(_1264078), _1264084), _1264080)), -(hBOOL(hAPP(hAPP(c_member(_1264078), _1264084), _1264082)))], (27317 ^ _780461) ^ [_1264263, _1264265, _1264267, _1264269] : [hBOOL(hAPP(hAPP(c_member(_1264263), _1264265), _1264267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264263, tc_HOL_Obool)), _1264267), _1264269)), -(hBOOL(hAPP(hAPP(c_member(_1264263), _1264265), _1264269)))], (27327 ^ _780461) ^ [_1264448, _1264450, _1264452, _1264454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264448, tc_HOL_Obool)), _1264450), _1264452)), hBOOL(hAPP(hAPP(c_member(_1264448), _1264454), _1264450)), -(hBOOL(hAPP(hAPP(c_member(_1264448), _1264454), _1264452)))], (27337 ^ _780461) ^ [_1264651, _1264653, _1264655] : [hBOOL(hAPP(hAPP(c_member(_1264651), _1264653), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264651, tc_HOL_Obool)), _1264655))), hBOOL(hAPP(hAPP(c_member(_1264651), _1264653), _1264655))], (27343 ^ _780461) ^ [_1264769, _1264771, _1264773] : [-(hBOOL(hAPP(hAPP(c_member(_1264769), _1264771), _1264773))), -(hBOOL(hAPP(hAPP(c_member(_1264769), _1264771), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264769, tc_HOL_Obool)), _1264773))))], (27349 ^ _780461) ^ [_1264831, _1264833, _1264835] : [hBOOL(hAPP(hAPP(c_member(_1264831), _1264833), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264831, tc_HOL_Obool)), _1264835))), hBOOL(hAPP(hAPP(c_member(_1264831), _1264833), _1264835))], (27355 ^ _780461) ^ [_1264955, _1264957, _1264959] : [hBOOL(hAPP(hAPP(c_member(_1264955), _1264957), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264955, tc_HOL_Obool)), _1264959))), hBOOL(hAPP(hAPP(c_member(_1264955), _1264957), _1264959))], (27361 ^ _780461) ^ [_1265097, _1265099, _1265101] : [hAPP(hAPP(c_COMBC(_1265097, tc_fun(_1265097, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265097)), _1265099) = hAPP(hAPP(c_COMBC(_1265097, tc_fun(_1265097, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265097)), _1265101), -(_1265099 = _1265101)], (27367 ^ _780461) ^ [_1265232, _1265234, _1265236] : [_1265234 = _1265236, -(hAPP(hAPP(c_COMBC(_1265232, tc_fun(_1265232, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265232)), _1265234) = hAPP(hAPP(c_COMBC(_1265232, tc_fun(_1265232, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265232)), _1265236))], (27373 ^ _780461) ^ [_1265391, _1265393, _1265395] : [hBOOL(hAPP(hAPP(c_member(_1265391), _1265393), hAPP(c_fequal, _1265395))), -(_1265393 = _1265395)], (27379 ^ _780461) ^ [_1265486, _1265488, _1265490] : [_1265488 = _1265490, -(hBOOL(hAPP(hAPP(c_member(_1265486), _1265488), hAPP(c_fequal, _1265490))))], (27385 ^ _780461) ^ [_1265608, _1265610, _1265612, _1265614] : [hBOOL(hAPP(hAPP(c_member(_1265608), _1265610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265608, tc_HOL_Obool)), _1265612), _1265614))), 27388 ^ _780461 : [(27389 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1265608), _1265610), _1265612)))], (27391 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1265608), _1265610), _1265614))]]], (27393 ^ _780461) ^ [_1265783, _1265785, _1265787, _1265789] : [-(hBOOL(hAPP(hAPP(c_member(_1265783), _1265785), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265783, tc_HOL_Obool)), _1265787), _1265789)))), hBOOL(hAPP(hAPP(c_member(_1265783), _1265785), _1265787)), -(hBOOL(hAPP(hAPP(c_member(_1265783), _1265785), _1265789)))], (27403 ^ _780461) ^ [_1265989, _1265991, _1265993, _1265995] : [hBOOL(hAPP(hAPP(c_member(_1265989), _1265991), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265989, tc_HOL_Obool)), _1265993), _1265995))), -(hBOOL(hAPP(hAPP(c_member(_1265989), _1265991), _1265993)))], (27409 ^ _780461) ^ [_1266120, _1266122, _1266124, _1266126] : [hBOOL(hAPP(hAPP(c_member(_1266120), _1266122), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266120, tc_HOL_Obool)), _1266124), _1266126))), hBOOL(hAPP(hAPP(c_member(_1266120), _1266122), _1266126))], (27415 ^ _780461) ^ [_1266270, _1266272, _1266274] : [hBOOL(hAPP(hAPP(c_member(_1266270), _1266272), _1266274)), -(hBOOL(hAPP(_1266274, _1266272)))], (27421 ^ _780461) ^ [_1266363, _1266365, _1266367] : [hBOOL(hAPP(_1266367, _1266365)), -(hBOOL(hAPP(hAPP(c_member(_1266363), _1266365), _1266367)))], (27427 ^ _780461) ^ [_1266462, _1266464, _1266466, _1266468] : [_1266462 = _1266464, 27430 ^ _780461 : [(27431 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1266466), _1266468), _1266462)), -(hBOOL(hAPP(hAPP(c_member(_1266466), _1266468), _1266464)))], (27437 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1266466), _1266468), _1266464)), -(hBOOL(hAPP(hAPP(c_member(_1266466), _1266468), _1266462)))]]], (27443 ^ _780461) ^ [_1266723, _1266725, _1266727, _1266729] : [_1266723 = _1266725, 27446 ^ _780461 : [(27447 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1266727), _1266723), _1266729)), -(hBOOL(hAPP(hAPP(c_member(_1266727), _1266725), _1266729)))], (27453 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1266727), _1266725), _1266729)), -(hBOOL(hAPP(hAPP(c_member(_1266727), _1266723), _1266729)))]]], (27459 ^ _780461) ^ [_1266984, _1266986, _1266988, _1266990] : [_1266984 = _1266986, hBOOL(hAPP(hAPP(c_member(_1266988), _1266986), _1266990)), -(hBOOL(hAPP(hAPP(c_member(_1266988), _1266984), _1266990)))], (27469 ^ _780461) ^ [_1267149, _1267151, _1267153, _1267155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1267149, tc_HOL_Obool)), _1267151), _1267153)), hBOOL(hAPP(hAPP(c_member(_1267149), _1267155), _1267151)), -(hBOOL(hAPP(hAPP(c_member(_1267149), _1267155), _1267153)))], (27479 ^ _780461) ^ [_1267349, _1267351] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1267349, tc_HOL_Obool)), _1267351)), -(hBOOL(hAPP(hAPP(c_member(_1267349), _1267351), c_Orderings_Obot__class_Obot(tc_fun(_1267349, tc_HOL_Obool)))))], (27485 ^ _780461) ^ [_1267460, _1267462] : [hBOOL(hAPP(hAPP(c_member(_1267460), _1267462), c_Orderings_Obot__class_Obot(tc_fun(_1267460, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1267460, tc_HOL_Obool)), _1267462)))], (27491 ^ _780461) ^ [_1267598, _1267600, _1267602, _1267604] : [hAPP(hAPP(c_COMBC(_1267598, tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_fun(_1267600, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1267600, tc_fun(tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_fun(_1267600, tc_HOL_Obool)), _1267598), c_COMBC(_1267600, tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1267600, tc_prod(_1267598, _1267600)), tc_fun(_1267600, tc_fun(tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_HOL_Obool)), _1267598), hAPP(c_COMBB(tc_prod(_1267598, _1267600), tc_fun(tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_HOL_Obool), _1267600), c_member(tc_prod(_1267598, _1267600)))), c_Product__Type_OPair(_1267598, _1267600)))), _1267602) = hAPP(hAPP(c_COMBC(_1267598, tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_fun(_1267600, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1267600, tc_fun(tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_fun(_1267600, tc_HOL_Obool)), _1267598), c_COMBC(_1267600, tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1267600, tc_prod(_1267598, _1267600)), tc_fun(_1267600, tc_fun(tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_HOL_Obool)), _1267598), hAPP(c_COMBB(tc_prod(_1267598, _1267600), tc_fun(tc_fun(tc_prod(_1267598, _1267600), tc_HOL_Obool), tc_HOL_Obool), _1267600), c_member(tc_prod(_1267598, _1267600)))), c_Product__Type_OPair(_1267598, _1267600)))), _1267604), -(_1267602 = _1267604)], (27497 ^ _780461) ^ [_1268147, _1268149, _1268151, _1268153] : [_1268151 = _1268153, -(hAPP(hAPP(c_COMBC(_1268147, tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_fun(_1268149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268149, tc_fun(tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_fun(_1268149, tc_HOL_Obool)), _1268147), c_COMBC(_1268149, tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268149, tc_prod(_1268147, _1268149)), tc_fun(_1268149, tc_fun(tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_HOL_Obool)), _1268147), hAPP(c_COMBB(tc_prod(_1268147, _1268149), tc_fun(tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_HOL_Obool), _1268149), c_member(tc_prod(_1268147, _1268149)))), c_Product__Type_OPair(_1268147, _1268149)))), _1268151) = hAPP(hAPP(c_COMBC(_1268147, tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_fun(_1268149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268149, tc_fun(tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_fun(_1268149, tc_HOL_Obool)), _1268147), c_COMBC(_1268149, tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1268149, tc_prod(_1268147, _1268149)), tc_fun(_1268149, tc_fun(tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_HOL_Obool)), _1268147), hAPP(c_COMBB(tc_prod(_1268147, _1268149), tc_fun(tc_fun(tc_prod(_1268147, _1268149), tc_HOL_Obool), tc_HOL_Obool), _1268149), c_member(tc_prod(_1268147, _1268149)))), c_Product__Type_OPair(_1268147, _1268149)))), _1268153))], (27503 ^ _780461) ^ [_1268723, _1268725, _1268727, _1268729] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1268723, tc_fun(_1268725, tc_HOL_Obool))), _1268727), _1268729)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1268723, _1268725)), hAPP(hAPP(c_Product__Type_OPair(_1268723, _1268725), _1268727), _1268729)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1268723, _1268725), tc_HOL_Obool)))))], (27509 ^ _780461) ^ [_1268880, _1268882, _1268884, _1268886] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1268880, _1268882)), hAPP(hAPP(c_Product__Type_OPair(_1268880, _1268882), _1268884), _1268886)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1268880, _1268882), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1268880, tc_fun(_1268882, tc_HOL_Obool))), _1268884), _1268886)))], (27515 ^ _780461) ^ [_1269061, _1269063, _1269065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269061, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1269061, tc_fun(_1269061, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269061)), _1269063)), hAPP(hAPP(c_COMBC(_1269061, tc_fun(_1269061, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269061)), _1269065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269061, tc_HOL_Obool)), _1269063), _1269065)))], (27521 ^ _780461) ^ [_1269236, _1269238, _1269240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269236, tc_HOL_Obool)), _1269238), _1269240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269236, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1269236, tc_fun(_1269236, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269236)), _1269238)), hAPP(hAPP(c_COMBC(_1269236, tc_fun(_1269236, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269236)), _1269240))))], (27527 ^ _780461) ^ [_1269435, _1269437, _1269439] : [hBOOL(hAPP(hAPP(c_member(_1269435), _1269437), hAPP(hAPP(c_Set_Oinsert(_1269435), _1269439), c_Orderings_Obot__class_Obot(tc_fun(_1269435, tc_HOL_Obool))))), -(_1269437 = _1269439)], (27533 ^ _780461) ^ [_1269550, _1269552, _1269554] : [_1269552 = _1269554, -(hBOOL(hAPP(hAPP(c_member(_1269550), _1269552), hAPP(hAPP(c_Set_Oinsert(_1269550), _1269554), c_Orderings_Obot__class_Obot(tc_fun(_1269550, tc_HOL_Obool))))))], (27539 ^ _780461) ^ [_1269671, _1269673, _1269675] : [hBOOL(hAPP(hAPP(c_member(_1269671), _1269673), hAPP(hAPP(c_Set_Oinsert(_1269671), _1269675), c_Orderings_Obot__class_Obot(tc_fun(_1269671, tc_HOL_Obool))))), -(_1269673 = _1269675)], (27545 ^ _780461) ^ [_1269789, _1269791, _1269793, _1269795] : [-(hBOOL(hAPP(hAPP(c_member(_1269789), _1269791), _1269793))), 27548 ^ _780461 : [(27549 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269789, tc_HOL_Obool)), _1269793), hAPP(hAPP(c_Set_Oinsert(_1269789), _1269791), _1269795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269789, tc_HOL_Obool)), _1269793), _1269795)))], (27555 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269789, tc_HOL_Obool)), _1269793), _1269795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1269789, tc_HOL_Obool)), _1269793), hAPP(hAPP(c_Set_Oinsert(_1269789), _1269791), _1269795))))]]], (27561 ^ _780461) ^ [_1270118, _1270120, _1270122, _1270124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270118, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1270118), _1270120), _1270122)), _1270124)), 27564 ^ _780461 : [(27565 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270118), _1270120), _1270124)))], (27567 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270118, tc_HOL_Obool)), _1270122), _1270124)))]]], (27569 ^ _780461) ^ [_1270291, _1270293, _1270295, _1270297] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270291, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1270291), _1270293), _1270295)), _1270297))), hBOOL(hAPP(hAPP(c_member(_1270291), _1270293), _1270297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1270291, tc_HOL_Obool)), _1270295), _1270297))], (27579 ^ _780461) ^ [_1270515, _1270517, _1270519, _1270521] : [hBOOL(hAPP(hAPP(c_member(_1270515), _1270517), _1270519)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270515, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1270515), _1270517), _1270521)), _1270519) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270515, tc_HOL_Obool)), _1270521), _1270519))], (27585 ^ _780461) ^ [_1270664, _1270666, _1270668, _1270670] : [-(hBOOL(hAPP(hAPP(c_member(_1270664), _1270666), _1270668))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270664, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1270664), _1270666), _1270670)), _1270668) = hAPP(hAPP(c_Set_Oinsert(_1270664), _1270666), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270664, tc_HOL_Obool)), _1270670), _1270668)))], (27591 ^ _780461) ^ [_1270751, _1270753, _1270755, _1270757] : [hBOOL(hAPP(hAPP(c_member(_1270751), _1270753), _1270755)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270751, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1270751), _1270753), _1270757)), _1270755) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270751, tc_HOL_Obool)), _1270757), _1270755))], (27597 ^ _780461) ^ [_1270924, _1270926, _1270928] : [hBOOL(hAPP(hAPP(c_member(_1270924), _1270926), c_Option_Oset(_1270924, _1270928))), -(_1270928 = hAPP(c_Option_Ooption_OSome(_1270924), _1270926))], (27603 ^ _780461) ^ [_1271029, _1271031, _1271033] : [_1271033 = hAPP(c_Option_Ooption_OSome(_1271029), _1271031), -(hBOOL(hAPP(hAPP(c_member(_1271029), _1271031), c_Option_Oset(_1271029, _1271033))))], (27609 ^ _780461) ^ [_1271161, _1271163, _1271165, _1271167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271161, tc_fun(_1271163, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1271161, tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_fun(_1271163, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271163, tc_fun(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_fun(_1271163, tc_HOL_Obool)), _1271161), c_COMBC(_1271163, tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271163, tc_prod(_1271161, _1271163)), tc_fun(_1271163, tc_fun(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_HOL_Obool)), _1271161), hAPP(c_COMBB(tc_prod(_1271161, _1271163), tc_fun(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_HOL_Obool), _1271163), c_member(tc_prod(_1271161, _1271163)))), c_Product__Type_OPair(_1271161, _1271163)))), _1271165)), hAPP(hAPP(c_COMBC(_1271161, tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_fun(_1271163, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271163, tc_fun(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_fun(_1271163, tc_HOL_Obool)), _1271161), c_COMBC(_1271163, tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271163, tc_prod(_1271161, _1271163)), tc_fun(_1271163, tc_fun(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_HOL_Obool)), _1271161), hAPP(c_COMBB(tc_prod(_1271161, _1271163), tc_fun(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool), tc_HOL_Obool), _1271163), c_member(tc_prod(_1271161, _1271163)))), c_Product__Type_OPair(_1271161, _1271163)))), _1271167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1271161, _1271163), tc_HOL_Obool)), _1271165), _1271167)))], (27615 ^ _780461) ^ [_1271762, _1271764, _1271766, _1271768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool)), _1271766), _1271768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271762, tc_fun(_1271764, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1271762, tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_fun(_1271764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271764, tc_fun(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_fun(_1271764, tc_HOL_Obool)), _1271762), c_COMBC(_1271764, tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271764, tc_prod(_1271762, _1271764)), tc_fun(_1271764, tc_fun(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_HOL_Obool)), _1271762), hAPP(c_COMBB(tc_prod(_1271762, _1271764), tc_fun(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_HOL_Obool), _1271764), c_member(tc_prod(_1271762, _1271764)))), c_Product__Type_OPair(_1271762, _1271764)))), _1271766)), hAPP(hAPP(c_COMBC(_1271762, tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_fun(_1271764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271764, tc_fun(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_fun(_1271764, tc_HOL_Obool)), _1271762), c_COMBC(_1271764, tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271764, tc_prod(_1271762, _1271764)), tc_fun(_1271764, tc_fun(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_HOL_Obool)), _1271762), hAPP(c_COMBB(tc_prod(_1271762, _1271764), tc_fun(tc_fun(tc_prod(_1271762, _1271764), tc_HOL_Obool), tc_HOL_Obool), _1271764), c_member(tc_prod(_1271762, _1271764)))), c_Product__Type_OPair(_1271762, _1271764)))), _1271768))))], (27621 ^ _780461) ^ [_1272365, _1272367, _1272369] : [-(hBOOL(hAPP(hAPP(c_member(_1272365), _1272367), _1272369))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272365, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1272365), _1272367), _1272369)), hAPP(hAPP(c_Set_Oinsert(_1272365), _1272367), c_Orderings_Obot__class_Obot(tc_fun(_1272365, tc_HOL_Obool)))) = _1272369)], (27627 ^ _780461) ^ [_1272442, _1272444, _1272446] : [hBOOL(hAPP(hAPP(c_member(_1272442), _1272444), _1272446)), -(hAPP(hAPP(c_Set_Oinsert(_1272442), _1272444), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272442, tc_HOL_Obool)), _1272446), hAPP(hAPP(c_Set_Oinsert(_1272442), _1272444), c_Orderings_Obot__class_Obot(tc_fun(_1272442, tc_HOL_Obool))))) = _1272446)], (27649 ^ _780461) ^ [_1272952, _1272954, _1272956, _1272958] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272952, tc_HOL_Obool)), _1272954), hAPP(hAPP(c_Set_Oinsert(_1272952), _1272956), _1272958)))), 27652 ^ _780461 : [(27653 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1272952), _1272956), _1272954)))], (27655 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272952, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272952, tc_HOL_Obool)), _1272954), hAPP(hAPP(c_Set_Oinsert(_1272952), _1272956), c_Orderings_Obot__class_Obot(tc_fun(_1272952, tc_HOL_Obool))))), _1272958))]], 27656 ^ _780461 : [(27657 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1272952), _1272956), _1272954))], (27659 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272952, tc_HOL_Obool)), _1272954), _1272958))]]], (27633 ^ _780461) ^ [_1272620, _1272622, _1272624, _1272626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272620, tc_HOL_Obool)), _1272622), hAPP(hAPP(c_Set_Oinsert(_1272620), _1272624), _1272626))), 27636 ^ _780461 : [(27637 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1272620), _1272624), _1272622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272620, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1272620, tc_HOL_Obool)), _1272622), hAPP(hAPP(c_Set_Oinsert(_1272620), _1272624), c_Orderings_Obot__class_Obot(tc_fun(_1272620, tc_HOL_Obool))))), _1272626)))], (27643 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1272620), _1272624), _1272622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272620, tc_HOL_Obool)), _1272622), _1272626)))]]], (27663 ^ _780461) ^ [_1273316, _1273318, _1273320, _1273322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273316, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273316, tc_HOL_Obool)), _1273318), hAPP(hAPP(c_Set_Oinsert(_1273316), _1273320), c_Orderings_Obot__class_Obot(tc_fun(_1273316, tc_HOL_Obool))))), _1273322)), hBOOL(hAPP(hAPP(c_member(_1273316), _1273320), _1273318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1273316, tc_HOL_Obool)), _1273318), hAPP(hAPP(c_Set_Oinsert(_1273316), _1273320), _1273322))))], (27673 ^ _780461) ^ [_1273595, _1273597, _1273599, _1273601, _1273603] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1273595, _1273597, _1273599), _1273601), _1273603)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1273595, _1273597)), hAPP(hAPP(c_Product__Type_OPair(_1273595, _1273597), _1273601), _1273603)), _1273599)))], (27679 ^ _780461) ^ [_1273730, _1273732, _1273734, _1273736, _1273738] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1273730, _1273732)), hAPP(hAPP(c_Product__Type_OPair(_1273730, _1273732), _1273736), _1273738)), _1273734)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1273730, _1273732, _1273734), _1273736), _1273738)))], (27685 ^ _780461) ^ [_1273871, _1273873, _1273875, _1273877, _1273879, _1273881, _1273883] : [hBOOL(hAPP(hAPP(c_member(_1273871), _1273873), _1273875)), c_Nitpick_Ofold__graph_H(_1273871, _1273877, _1273879, _1273881, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273871, tc_HOL_Obool)), _1273875), hAPP(hAPP(c_Set_Oinsert(_1273871), _1273873), c_Orderings_Obot__class_Obot(tc_fun(_1273871, tc_HOL_Obool)))), _1273883), -(c_Nitpick_Ofold__graph_H(_1273871, _1273877, _1273879, _1273881, _1273875, hAPP(hAPP(_1273879, _1273873), _1273883)))], (27695 ^ _780461) ^ [_1274125, _1274127] : [c_Nitpick_Orefl_H(_1274125, _1274127), 27698 ^ _780461 : [(27699 ^ _780461) ^ [_1274203] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1274125, _1274125)), hAPP(hAPP(c_Product__Type_OPair(_1274125, _1274125), _1274203), _1274203)), _1274127)))]]], (27701 ^ _780461) ^ [_1274245, _1274247] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1274245, _1274245)), hAPP(hAPP(c_Product__Type_OPair(_1274245, _1274245), 27702 ^ [_1274245, _1274247]), 27702 ^ [_1274245, _1274247])), _1274247)), -(c_Nitpick_Orefl_H(_1274245, _1274247))], (27708 ^ _780461) ^ [_1274424, _1274426, _1274428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274424, tc_HOL_Obool)), _1274426), hAPP(hAPP(c_Set_Oinsert(_1274424), _1274428), c_Orderings_Obot__class_Obot(tc_fun(_1274424, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1274424, _1274428, _1274426) = _1274428)], (27714 ^ _780461) ^ [_1274551, _1274553, _1274555] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1274551, tc_HOL_Obool)), _1274553), hAPP(hAPP(c_Set_Oinsert(_1274551), _1274555), c_Orderings_Obot__class_Obot(tc_fun(_1274551, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1274551, _1274555, _1274553) = c_HOL_OThe(_1274551, hAPP(hAPP(c_COMBC(_1274551, tc_fun(_1274551, tc_HOL_Obool), tc_HOL_Obool), c_member(_1274551)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1274551, tc_HOL_Obool)), _1274553), hAPP(hAPP(c_Set_Oinsert(_1274551), _1274555), c_Orderings_Obot__class_Obot(tc_fun(_1274551, tc_HOL_Obool)))))))], (27720 ^ _780461) ^ [_1274678, _1274680, _1274682, _1274684] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1274678, tc_fun(_1274680, tc_HOL_Obool))), _1274682), _1274684))], (27722 ^ _780461) ^ [_1274720, _1274722, _1274724] : [_1274720 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1274722, _1274722), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1274722, _1274722), tc_HOL_Obool)), _1274720), _1274724)))], (27728 ^ _780461) ^ [_1274841, _1274843, _1274845, _1274847] : [-(c_Nitpick_Ofold__graph_H(_1274841, _1274843, _1274845, _1274847, c_Orderings_Obot__class_Obot(tc_fun(_1274841, tc_HOL_Obool)), _1274847))], (27730 ^ _780461) ^ [_1274879, _1274881, _1274883, _1274885] : [-(c_Nitpick_Ofold__graph_H(_1274879, _1274881, _1274883, _1274885, c_Orderings_Obot__class_Obot(tc_fun(_1274879, tc_HOL_Obool)), _1274885))], (27732 ^ _780461) ^ [_1274938, _1274940, _1274942, _1274944] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1274938, _1274938)), hAPP(hAPP(c_Product__Type_OPair(_1274938, _1274938), _1274940), _1274942)), hAPP(c_Wellfounded_Omeasure(_1274938), _1274944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1274944, _1274940)), hAPP(_1274944, _1274942))))], (27738 ^ _780461) ^ [_1275085, _1275087, _1275089, _1275091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1275091, _1275087)), hAPP(_1275091, _1275089))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1275085, _1275085)), hAPP(hAPP(c_Product__Type_OPair(_1275085, _1275085), _1275087), _1275089)), hAPP(c_Wellfounded_Omeasure(_1275085), _1275091))))], (27744 ^ _780461) ^ [_1275238, _1275240, _1275242, _1275244, _1275246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1275238, _1275240)), hAPP(_1275238, _1275242))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1275244, _1275244)), hAPP(hAPP(c_Product__Type_OPair(_1275244, _1275244), _1275240), _1275242)), _1275246)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1275244, _1275244)), hAPP(hAPP(c_Product__Type_OPair(_1275244, _1275244), _1275240), _1275242)), c_Wellfounded_Omlex__prod(_1275244, _1275238, _1275246))))], (27754 ^ _780461) ^ [_1275485, _1275487, _1275489, _1275491, _1275493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1275485, _1275487)), hAPP(_1275485, _1275489))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1275491, _1275491)), hAPP(hAPP(c_Product__Type_OPair(_1275491, _1275491), _1275487), _1275489)), c_Wellfounded_Omlex__prod(_1275491, _1275485, _1275493))))], (27760 ^ _780461) ^ [_1275636, _1275638] : [class_Int_Onumber__ring(_1275636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1275638)), -(hBOOL(hAPP(hAPP(c_member(_1275636), hAPP(c_Int_Onumber__class_Onumber__of(_1275636), _1275638)), c_Nat_Osemiring__1__class_ONats(_1275636))))], (27770 ^ _780461) ^ [_1275795] : [class_Rings_Osemiring__1(_1275795), -(hBOOL(hAPP(hAPP(c_member(_1275795), c_Groups_Ozero__class_Ozero(_1275795)), c_Nat_Osemiring__1__class_ONats(_1275795))))], (27776 ^ _780461) ^ [_1275890, _1275892, _1275894] : [class_Rings_Osemiring__1(_1275890), hBOOL(hAPP(hAPP(c_member(_1275890), _1275892), c_Nat_Osemiring__1__class_ONats(_1275890))), hBOOL(hAPP(hAPP(c_member(_1275890), _1275894), c_Nat_Osemiring__1__class_ONats(_1275890))), -(hBOOL(hAPP(hAPP(c_member(_1275890), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1275890), _1275892), _1275894)), c_Nat_Osemiring__1__class_ONats(_1275890))))], (27790 ^ _780461) ^ [_1276145, _1276147, _1276149] : [class_Rings_Osemiring__1(_1276145), hBOOL(hAPP(hAPP(c_member(_1276145), _1276147), c_Nat_Osemiring__1__class_ONats(_1276145))), hBOOL(hAPP(hAPP(c_member(_1276145), _1276149), c_Nat_Osemiring__1__class_ONats(_1276145))), -(hBOOL(hAPP(hAPP(c_member(_1276145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276145), _1276147), _1276149)), c_Nat_Osemiring__1__class_ONats(_1276145))))], (27804 ^ _780461) ^ [_1276400] : [class_Rings_Osemiring__1(_1276400), -(hBOOL(hAPP(hAPP(c_member(_1276400), c_Groups_Oone__class_Oone(_1276400)), c_Nat_Osemiring__1__class_ONats(_1276400))))], (27810 ^ _780461) ^ [_1276495, _1276497] : [class_Rings_Osemiring__1(_1276495), -(hBOOL(hAPP(hAPP(c_member(_1276495), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1276495), _1276497)), c_Nat_Osemiring__1__class_ONats(_1276495))))], (27816 ^ _780461) ^ [_1276598, _1276600] : [class_Rings_Olinordered__idom(_1276598), hBOOL(hAPP(hAPP(c_member(_1276598), _1276600), c_Int_Oring__1__class_OInts(_1276598))), 27823 ^ _780461 : [(27824 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276598), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1276598), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1276598), c_Groups_Oone__class_Oone(_1276598)), _1276600)), _1276600)), c_Groups_Ozero__class_Ozero(_1276598))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276598), _1276600), c_Groups_Ozero__class_Ozero(_1276598))))], (27830 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276598), _1276600), c_Groups_Ozero__class_Ozero(_1276598))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276598), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1276598), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1276598), c_Groups_Oone__class_Oone(_1276598)), _1276600)), _1276600)), c_Groups_Ozero__class_Ozero(_1276598))))]]], (27836 ^ _780461) ^ [_1277011, _1277013, _1277015, _1277017, _1277019, _1277021, _1277023] : [c_Nitpick_Ofold__graph_H(_1277011, _1277013, _1277015, _1277017, _1277019, hAPP(hAPP(_1277015, _1277021), _1277023)), 27841 ^ _780461 : [(27842 ^ _780461) ^ [] : [-(_1277019 = c_Orderings_Obot__class_Obot(tc_fun(_1277011, tc_HOL_Obool)))], (27844 ^ _780461) ^ [] : [-(hAPP(hAPP(_1277015, _1277021), _1277023) = _1277017)]], 27847 ^ _780461 : [(27848 ^ _780461) ^ [] : [-(hAPP(hAPP(_1277015, _1277021), _1277023) = hAPP(hAPP(_1277015, 27845 ^ [_1277011, _1277013, _1277015, _1277017, _1277019, _1277021, _1277023]), 27846 ^ [_1277011, _1277013, _1277015, _1277017, _1277019, _1277021, _1277023]))], (27850 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277011), 27845 ^ [_1277011, _1277013, _1277015, _1277017, _1277019, _1277021, _1277023]), _1277019)))], (27852 ^ _780461) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1277011, _1277013, _1277015, _1277017, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277011, tc_HOL_Obool)), _1277019), hAPP(hAPP(c_Set_Oinsert(_1277011), 27845 ^ [_1277011, _1277013, _1277015, _1277017, _1277019, _1277021, _1277023]), c_Orderings_Obot__class_Obot(tc_fun(_1277011, tc_HOL_Obool)))), 27846 ^ [_1277011, _1277013, _1277015, _1277017, _1277019, _1277021, _1277023]))]]], (27854 ^ _780461) ^ [_1277448, _1277450, _1277452, _1277454, _1277456, _1277458, _1277460] : [-(c_Nitpick_Ofold__graph_H(_1277448, _1277450, _1277452, _1277454, _1277456, hAPP(hAPP(_1277452, _1277458), _1277460))), 27855 ^ _780461 : [(27856 ^ _780461) ^ [] : [_1277456 = c_Orderings_Obot__class_Obot(tc_fun(_1277448, tc_HOL_Obool)), hAPP(hAPP(_1277452, _1277458), _1277460) = _1277454], (27862 ^ _780461) ^ [_1277677, _1277679] : [hAPP(hAPP(_1277452, _1277458), _1277460) = hAPP(hAPP(_1277452, _1277679), _1277677), hBOOL(hAPP(hAPP(c_member(_1277448), _1277679), _1277456)), c_Nitpick_Ofold__graph_H(_1277448, _1277450, _1277452, _1277454, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277448, tc_HOL_Obool)), _1277456), hAPP(hAPP(c_Set_Oinsert(_1277448), _1277679), c_Orderings_Obot__class_Obot(tc_fun(_1277448, tc_HOL_Obool)))), _1277677)]]], (27874 ^ _780461) ^ [_1278002, _1278004, _1278006, _1278008, _1278010, _1278012, _1278014, _1278016] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1278002, _1278004), tc_prod(_1278002, _1278004))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1278002, _1278004), tc_prod(_1278002, _1278004)), hAPP(hAPP(c_Product__Type_OPair(_1278002, _1278004), _1278006), _1278008)), hAPP(hAPP(c_Product__Type_OPair(_1278002, _1278004), _1278010), _1278012))), c_Wellfounded_Olex__prod(_1278002, _1278004, _1278014, _1278016))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1278002, _1278002)), hAPP(hAPP(c_Product__Type_OPair(_1278002, _1278002), _1278006), _1278010)), _1278014))), 27881 ^ _780461 : [(27882 ^ _780461) ^ [] : [-(_1278006 = _1278010)], (27884 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1278004, _1278004)), hAPP(hAPP(c_Product__Type_OPair(_1278004, _1278004), _1278008), _1278012)), _1278016)))]]], (27886 ^ _780461) ^ [_1278327, _1278329, _1278331, _1278333, _1278335, _1278337, _1278339, _1278341] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1278327, _1278329), tc_prod(_1278327, _1278329))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1278327, _1278329), tc_prod(_1278327, _1278329)), hAPP(hAPP(c_Product__Type_OPair(_1278327, _1278329), _1278331), _1278333)), hAPP(hAPP(c_Product__Type_OPair(_1278327, _1278329), _1278335), _1278337))), c_Wellfounded_Olex__prod(_1278327, _1278329, _1278339, _1278341)))), 27887 ^ _780461 : [(27888 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1278327, _1278327)), hAPP(hAPP(c_Product__Type_OPair(_1278327, _1278327), _1278331), _1278335)), _1278339))], (27890 ^ _780461) ^ [] : [_1278331 = _1278335, hBOOL(hAPP(hAPP(c_member(tc_prod(_1278329, _1278329)), hAPP(hAPP(c_Product__Type_OPair(_1278329, _1278329), _1278333), _1278337)), _1278341))]]], (27898 ^ _780461) ^ [_1278702, _1278704, _1278706, _1278708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1278702), _1278704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1278706), _1278708)), -(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), _1278702), _1278706)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1278704), _1278708))), c_FunDef_Opair__less)))], (27908 ^ _780461) ^ [_1278905] : [class_Rings_Oring__1(_1278905), -(hBOOL(hAPP(hAPP(c_member(_1278905), c_Groups_Ozero__class_Ozero(_1278905)), c_Int_Oring__1__class_OInts(_1278905))))], (27914 ^ _780461) ^ [_1279000, _1279002, _1279004] : [class_Rings_Oring__1(_1279000), hBOOL(hAPP(hAPP(c_member(_1279000), _1279002), c_Int_Oring__1__class_OInts(_1279000))), hBOOL(hAPP(hAPP(c_member(_1279000), _1279004), c_Int_Oring__1__class_OInts(_1279000))), -(hBOOL(hAPP(hAPP(c_member(_1279000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279000), _1279002), _1279004)), c_Int_Oring__1__class_OInts(_1279000))))], (27928 ^ _780461) ^ [_1279255, _1279257, _1279259] : [class_Rings_Oring__1(_1279255), hBOOL(hAPP(hAPP(c_member(_1279255), _1279257), c_Int_Oring__1__class_OInts(_1279255))), hBOOL(hAPP(hAPP(c_member(_1279255), _1279259), c_Int_Oring__1__class_OInts(_1279255))), -(hBOOL(hAPP(hAPP(c_member(_1279255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279255), _1279257), _1279259)), c_Int_Oring__1__class_OInts(_1279255))))], (27942 ^ _780461) ^ [_1279510, _1279512, _1279514] : [class_Rings_Oring__1(_1279510), hBOOL(hAPP(hAPP(c_member(_1279510), _1279512), c_Int_Oring__1__class_OInts(_1279510))), hBOOL(hAPP(hAPP(c_member(_1279510), _1279514), c_Int_Oring__1__class_OInts(_1279510))), -(hBOOL(hAPP(hAPP(c_member(_1279510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1279510), _1279512), _1279514)), c_Int_Oring__1__class_OInts(_1279510))))], (27956 ^ _780461) ^ [_1279765, _1279767] : [class_Int_Onumber__ring(_1279765), -(hBOOL(hAPP(hAPP(c_member(_1279765), hAPP(c_Int_Onumber__class_Onumber__of(_1279765), _1279767)), c_Int_Oring__1__class_OInts(_1279765))))], (27962 ^ _780461) ^ [_1279868] : [class_Rings_Oring__1(_1279868), -(hBOOL(hAPP(hAPP(c_member(_1279868), c_Groups_Oone__class_Oone(_1279868)), c_Int_Oring__1__class_OInts(_1279868))))], (27968 ^ _780461) ^ [_1279963, _1279965] : [class_Rings_Oring__1(_1279963), hBOOL(hAPP(hAPP(c_member(_1279963), _1279965), c_Int_Oring__1__class_OInts(_1279963))), -(hBOOL(hAPP(hAPP(c_member(_1279963), hAPP(c_Groups_Ouminus__class_Ouminus(_1279963), _1279965)), c_Int_Oring__1__class_OInts(_1279963))))], (27978 ^ _780461) ^ [_1280136, _1280138] : [class_Rings_Oring__1(_1280136), -(hBOOL(hAPP(hAPP(c_member(_1280136), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1280136), _1280138)), c_Int_Oring__1__class_OInts(_1280136))))], (27984 ^ _780461) ^ [_1280239, _1280241, _1280243] : [class_Rings_Oring__1(_1280239), hBOOL(hAPP(hAPP(c_member(_1280239), _1280241), c_Int_Oring__1__class_OInts(_1280239))), -(hBOOL(hAPP(hAPP(c_member(_1280239), hAPP(hAPP(c_Power_Opower__class_Opower(_1280239), _1280241), _1280243)), c_Int_Oring__1__class_OInts(_1280239))))], (27994 ^ _780461) ^ [_1280422, _1280424] : [class_Rings_Oring__1(_1280422), -(hBOOL(hAPP(hAPP(c_member(_1280422), hAPP(c_Int_Oring__1__class_Oof__int(_1280422), _1280424)), c_Int_Oring__1__class_OInts(_1280422))))], (28000 ^ _780461) ^ [_1280525, _1280527] : [class_Int_Oring__char__0(_1280525), hBOOL(hAPP(hAPP(c_member(_1280525), _1280527), c_Int_Oring__1__class_OInts(_1280525))), 28007 ^ _780461 : [(28008 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280525), _1280527), _1280527) = c_Groups_Ozero__class_Ozero(_1280525), -(_1280527 = c_Groups_Ozero__class_Ozero(_1280525))], (28014 ^ _780461) ^ [] : [_1280527 = c_Groups_Ozero__class_Ozero(_1280525), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280525), _1280527), _1280527) = c_Groups_Ozero__class_Ozero(_1280525))]]], (28020 ^ _780461) ^ [_1280836, _1280838, _1280840, _1280842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1280836), _1280838)), -(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), _1280836), _1280840)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1280838), _1280842))), c_FunDef_Opair__less)))], (28026 ^ _780461) ^ [_1280973, _1280975] : [class_Int_Oring__char__0(_1280973), hBOOL(hAPP(hAPP(c_member(_1280973), _1280975), c_Int_Oring__1__class_OInts(_1280973))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280973), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280973), c_Groups_Oone__class_Oone(_1280973)), _1280975)), _1280975) = c_Groups_Ozero__class_Ozero(_1280973)], (28036 ^ _780461) ^ [_1281159, _1281161, _1281163, _1281165, _1281167, _1281169, _1281171] : [hBOOL(hAPP(_1281159, _1281161)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1281163, _1281163)), hAPP(hAPP(c_Product__Type_OPair(_1281163, _1281163), _1281165), _1281167)), hAPP(_1281169, _1281161))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1281171, _1281163), tc_prod(_1281171, _1281163))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1281171, _1281163), tc_prod(_1281171, _1281163)), hAPP(hAPP(c_Product__Type_OPair(_1281171, _1281163), _1281161), _1281165)), hAPP(hAPP(c_Product__Type_OPair(_1281171, _1281163), _1281161), _1281167))), c_Recdef_Osame__fst(_1281171, _1281163, _1281159, _1281169))))], (28046 ^ _780461) ^ [_1281464, _1281466, _1281468, _1281470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1281464), _1281466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1281468), _1281470)), -(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), _1281464), _1281468)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1281466), _1281470))), c_FunDef_Opair__leq)))], (28056 ^ _780461) ^ [_1281667, _1281669, _1281671, _1281673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1281667), _1281669)), 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)), _1281671), _1281667)), 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)), _1281673), _1281669)), 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)), _1281671), _1281673)), _1281669)), c_FunDef_Omax__strict)))], (28070 ^ _780461) ^ [_1281948, _1281950, _1281952, _1281954] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1281948), _1281950)), 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)), _1281948), _1281952)), 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)), _1281950), _1281954)), 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)), _1281950), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1281952), _1281954))), c_FunDef_Omin__strict)))], (28084 ^ _780461) ^ [_1282225] : [-(_1282225 = 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)), _1282225), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (28090 ^ _780461) ^ [_1282270, _1282272, _1282274, _1282276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1282270), _1282272)), -(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), _1282270), _1282274)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1282272), _1282276))), c_FunDef_Opair__leq)))], (28096 ^ _780461) ^ [_1282407, _1282409, _1282411, _1282413] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1282407), _1282409)), 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)), _1282407), _1282411)), 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)), _1282409), _1282413)), 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)), _1282409), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1282411), _1282413))), c_FunDef_Omin__weak)))], (28110 ^ _780461) ^ [_1282688, _1282690, _1282692, _1282694] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1282688), _1282690)), 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)), _1282692), _1282688)), 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)), _1282694), _1282690)), 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)), _1282692), _1282694)), _1282690)), c_FunDef_Omax__weak)))], (28124 ^ _780461) ^ [_1282969] : [-(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)), _1282969), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (28126 ^ _780461) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (28128 ^ _780461) ^ [] : [-(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)))))], (28130 ^ _780461) ^ [] : [-(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)))], (28132 ^ _780461) ^ [] : [-(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)))], (28134 ^ _780461) ^ [_1283090, _1283092] : [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), _1283090), _1283092)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1283090), _1283092)))], (28140 ^ _780461) ^ [_1283195, _1283197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1283195), _1283197)), -(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), _1283195), _1283197)), c_Wellfounded_Oless__than)))], (28146 ^ _780461) ^ [_1283306, _1283308, _1283310, _1283312] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283306, tc_HOL_Obool)), _1283308), _1283310), _1283312)), -(hBOOL(hAPP(_1283308, _1283312))), -(hBOOL(hAPP(_1283310, _1283312)))], (28156 ^ _780461) ^ [_1283436, _1283438, _1283440, _1283442] : [28157 ^ _780461 : [(28158 ^ _780461) ^ [] : [hBOOL(hAPP(_1283436, _1283438))], (28160 ^ _780461) ^ [] : [hBOOL(hAPP(_1283440, _1283438))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283442, tc_HOL_Obool)), _1283440), _1283436), _1283438)))], (28164 ^ _780461) ^ [_1283591, _1283593, _1283595, _1283597] : [hBOOL(hAPP(hAPP(c_member(_1283591), _1283593), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283591, tc_HOL_Obool)), _1283595), _1283597))), -(hBOOL(hAPP(hAPP(c_member(_1283591), _1283593), _1283595))), -(hBOOL(hAPP(hAPP(c_member(_1283591), _1283593), _1283597)))], (28174 ^ _780461) ^ [_1283751, _1283753, _1283755, _1283757] : [28175 ^ _780461 : [(28176 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1283751), _1283753), _1283755))], (28178 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1283751), _1283753), _1283757))]], -(hBOOL(hAPP(hAPP(c_member(_1283751), _1283753), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283751, tc_HOL_Obool)), _1283757), _1283755))))], (28182 ^ _780461) ^ [_1283936, _1283938, _1283940] : [class_Lattices_Obounded__lattice__bot(_1283936), 28185 ^ _780461 : [(28186 ^ _780461) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283936), _1283938), _1283940) = c_Orderings_Obot__class_Obot(_1283936), 28189 ^ _780461 : [(28190 ^ _780461) ^ [] : [-(_1283938 = c_Orderings_Obot__class_Obot(_1283936))], (28192 ^ _780461) ^ [] : [-(_1283940 = c_Orderings_Obot__class_Obot(_1283936))]]], (28194 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283936), _1283938), _1283940) = c_Orderings_Obot__class_Obot(_1283936)), _1283938 = c_Orderings_Obot__class_Obot(_1283936), _1283940 = c_Orderings_Obot__class_Obot(_1283936)]]], (28204 ^ _780461) ^ [_1284263, _1284265] : [class_Lattices_Obounded__lattice__bot(_1284263), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284263), _1284265), c_Orderings_Obot__class_Obot(_1284263)) = _1284265)], (28210 ^ _780461) ^ [_1284358, _1284360] : [class_Lattices_Obounded__lattice__bot(_1284358), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284358), c_Orderings_Obot__class_Obot(_1284358)), _1284360) = _1284360)], (28216 ^ _780461) ^ [_1284471, _1284473, _1284475] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284471, tc_HOL_Obool)), _1284473), _1284475) = c_Orderings_Obot__class_Obot(tc_fun(_1284471, tc_HOL_Obool)), 28219 ^ _780461 : [(28220 ^ _780461) ^ [] : [-(_1284473 = c_Orderings_Obot__class_Obot(tc_fun(_1284471, tc_HOL_Obool)))], (28222 ^ _780461) ^ [] : [-(_1284475 = c_Orderings_Obot__class_Obot(tc_fun(_1284471, tc_HOL_Obool)))]]], (28224 ^ _780461) ^ [_1284624, _1284626, _1284628] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284624, tc_HOL_Obool)), _1284626), _1284628) = c_Orderings_Obot__class_Obot(tc_fun(_1284624, tc_HOL_Obool))), _1284626 = c_Orderings_Obot__class_Obot(tc_fun(_1284624, tc_HOL_Obool)), _1284628 = c_Orderings_Obot__class_Obot(tc_fun(_1284624, tc_HOL_Obool))], (28234 ^ _780461) ^ [_1284811, _1284813] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284811, tc_HOL_Obool)), _1284813), c_Orderings_Obot__class_Obot(tc_fun(_1284811, tc_HOL_Obool))) = _1284813)], (28236 ^ _780461) ^ [_1284852, _1284854] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284852, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1284852, tc_HOL_Obool))), _1284854) = _1284854)], (28238 ^ _780461) ^ [_1284893, _1284895, _1284897, _1284899] : [class_Lattices_Osemilattice__sup(_1284893), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284893), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1284893), _1284895), _1284897)), _1284899)), 28245 ^ _780461 : [(28246 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284893), _1284895), _1284899)))], (28248 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284893), _1284897), _1284899)))]]], (28250 ^ _780461) ^ [_1285116, _1285118, _1285120, _1285122, _1285124] : [class_Lattices_Osemilattice__sup(_1285116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285116), _1285118), _1285120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285116), _1285122), _1285124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285116), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285116), _1285118), _1285122)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285116), _1285120), _1285124))))], (28264 ^ _780461) ^ [_1285387, _1285389, _1285391, _1285393] : [class_Lattices_Osemilattice__sup(_1285387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285387), _1285389), _1285391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285387), _1285393), _1285391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285387), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285387), _1285389), _1285393)), _1285391)))], (28278 ^ _780461) ^ [_1285636, _1285638, _1285640, _1285642] : [class_Lattices_Osemilattice__sup(_1285636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285636), _1285638), _1285640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285636), _1285642), _1285640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285636), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285636), _1285638), _1285642)), _1285640)))], (28292 ^ _780461) ^ [_1285885, _1285887, _1285889] : [class_Lattices_Osemilattice__sup(_1285885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285885), _1285887), _1285889)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1285885), _1285889), _1285887) = _1285889)], (28302 ^ _780461) ^ [_1286046, _1286048, _1286050] : [class_Lattices_Osemilattice__sup(_1286046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286046), _1286048), _1286050)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286046), _1286048), _1286050) = _1286050)], (28312 ^ _780461) ^ [_1286207, _1286209, _1286211, _1286213] : [class_Lattices_Osemilattice__sup(_1286207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286207), _1286209), _1286211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286207), _1286209), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286207), _1286213), _1286211))))], (28322 ^ _780461) ^ [_1286386, _1286388, _1286390, _1286392] : [class_Lattices_Osemilattice__sup(_1286386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286386), _1286388), _1286390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286386), _1286388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286386), _1286390), _1286392))))], (28332 ^ _780461) ^ [_1286565, _1286567, _1286569, _1286571] : [class_Lattices_Osemilattice__sup(_1286565), 28335 ^ _780461 : [(28336 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286565), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286565), _1286567), _1286569)), _1286571)), 28339 ^ _780461 : [(28340 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286565), _1286567), _1286571)))], (28342 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286565), _1286569), _1286571)))]]], (28344 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286565), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286565), _1286567), _1286569)), _1286571))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286565), _1286567), _1286571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286565), _1286569), _1286571))]]], (28354 ^ _780461) ^ [_1286945, _1286947, _1286949] : [class_Lattices_Osemilattice__sup(_1286945), 28357 ^ _780461 : [(28358 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286945), _1286947), _1286949)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286945), _1286947), _1286949) = _1286949)], (28364 ^ _780461) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286945), _1286947), _1286949) = _1286949, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286945), _1286947), _1286949)))]]], (28370 ^ _780461) ^ [_1287201, _1287203, _1287205] : [class_Lattices_Osemilattice__sup(_1287201), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287201), _1287203), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287201), _1287205), _1287203))))], (28376 ^ _780461) ^ [_1287308, _1287310, _1287312] : [class_Lattices_Olattice(_1287308), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287308), _1287310), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287308), _1287312), _1287310))))], (28382 ^ _780461) ^ [_1287415, _1287417, _1287419] : [class_Lattices_Osemilattice__sup(_1287415), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287415), _1287417), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287415), _1287417), _1287419))))], (28388 ^ _780461) ^ [_1287522, _1287524, _1287526] : [class_Lattices_Olattice(_1287522), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287522), _1287524), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287522), _1287524), _1287526))))], (28394 ^ _780461) ^ [_1287629, _1287631, _1287633, _1287635, _1287637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287629, tc_HOL_Obool)), _1287631), _1287633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287629, tc_HOL_Obool)), _1287635), _1287637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287629, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287629, tc_HOL_Obool)), _1287631), _1287635)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287629, tc_HOL_Obool)), _1287633), _1287637))))], (28404 ^ _780461) ^ [_1287874, _1287876, _1287878, _1287880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287874, tc_HOL_Obool)), _1287876), _1287878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287874, tc_HOL_Obool)), _1287880), _1287878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287874, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287874, tc_HOL_Obool)), _1287876), _1287880)), _1287878)))], (28414 ^ _780461) ^ [_1288093, _1288095, _1288097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288093, tc_HOL_Obool)), _1288095), _1288097)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288093, tc_HOL_Obool)), _1288097), _1288095) = _1288097)], (28420 ^ _780461) ^ [_1288214, _1288216, _1288218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288214, tc_HOL_Obool)), _1288216), _1288218)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288214, tc_HOL_Obool)), _1288216), _1288218) = _1288218)], (28426 ^ _780461) ^ [_1288353, _1288355, _1288357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288353, tc_HOL_Obool)), _1288355), _1288357)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288353, tc_HOL_Obool)), _1288355), _1288357) = _1288357)], (28432 ^ _780461) ^ [_1288470, _1288472, _1288474] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288470, tc_HOL_Obool)), _1288472), _1288474) = _1288474, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288470, tc_HOL_Obool)), _1288472), _1288474)))], (28438 ^ _780461) ^ [_1288593, _1288595, _1288597] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288593, tc_HOL_Obool)), _1288595), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288593, tc_HOL_Obool)), _1288597), _1288595))))], (28440 ^ _780461) ^ [_1288641, _1288643, _1288645] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288641, tc_HOL_Obool)), _1288643), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288641, tc_HOL_Obool)), _1288643), _1288645))))], (28442 ^ _780461) ^ [_1288689, _1288691, _1288693, _1288695] : [hBOOL(hAPP(_1288689, _1288691)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288693, tc_HOL_Obool)), _1288689), _1288695), _1288691)))], (28448 ^ _780461) ^ [_1288800, _1288802, _1288804, _1288806] : [hBOOL(hAPP(_1288800, _1288802)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288804, tc_HOL_Obool)), _1288806), _1288800), _1288802)))], (28454 ^ _780461) ^ [_1288911, _1288913, _1288915] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288911, tc_HOL_Obool)), _1288913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288911, tc_HOL_Obool)), _1288915), _1288913)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288911, tc_HOL_Obool)), _1288913), _1288915))], (28456 ^ _780461) ^ [_1288971, _1288973, _1288975] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288971, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288971, tc_HOL_Obool)), _1288973), _1288975)), _1288975) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288971, tc_HOL_Obool)), _1288973), _1288975))], (28458 ^ _780461) ^ [_1289031, _1289033, _1289035, _1289037] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289031, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289031, tc_HOL_Obool)), _1289033), _1289035)), _1289037) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289031, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289031, tc_HOL_Obool)), _1289033), _1289037)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289031, tc_HOL_Obool)), _1289035), _1289037)))], (28460 ^ _780461) ^ [_1289115, _1289117] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289115, tc_HOL_Obool)), _1289117), _1289117) = _1289117)], (28462 ^ _780461) ^ [_1289151, _1289153, _1289155] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289151, tc_HOL_Obool)), _1289153), _1289155) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289151, tc_HOL_Obool)), _1289155), _1289153))], (28464 ^ _780461) ^ [_1289200, _1289202, _1289204] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289200, tc_HOL_Obool)), _1289202), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289200, tc_HOL_Obool)), _1289202), _1289204)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289200, tc_HOL_Obool)), _1289202), _1289204))], (28466 ^ _780461) ^ [_1289260, _1289262, _1289264, _1289266] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289260, tc_HOL_Obool)), _1289262), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289260, tc_HOL_Obool)), _1289264), _1289266)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289260, tc_HOL_Obool)), _1289264), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289260, tc_HOL_Obool)), _1289262), _1289266)))], (28468 ^ _780461) ^ [_1289333, _1289335, _1289337, _1289339] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289333, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289333, tc_HOL_Obool)), _1289335), _1289337)), _1289339) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289333, tc_HOL_Obool)), _1289335), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289333, tc_HOL_Obool)), _1289337), _1289339)))], (28470 ^ _780461) ^ [_1289427, _1289429, _1289431, _1289433] : [28471 ^ _780461 : [(28472 ^ _780461) ^ [_1289537] : [hBOOL(hAPP(hAPP(c_member(_1289427), _1289537), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289427, tc_HOL_Obool)), _1289429), _1289431))), hBOOL(hAPP(_1289433, _1289537))]], 28480 ^ _780461 : [(28481 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1289427), 28479 ^ [_1289427, _1289429, _1289431, _1289433]), _1289429)))], (28483 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1289433, 28479 ^ [_1289427, _1289429, _1289431, _1289433])))]], 28485 ^ _780461 : [(28486 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1289427), 28484 ^ [_1289427, _1289429, _1289431, _1289433]), _1289431)))], (28488 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1289433, 28484 ^ [_1289427, _1289429, _1289431, _1289433])))]]], (28490 ^ _780461) ^ [_1289826, _1289828, _1289830, _1289832] : [28504 ^ _780461 : [(28505 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1289826), 28503 ^ [_1289826, _1289828, _1289830, _1289832]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289826, tc_HOL_Obool)), _1289828), _1289830))))], (28507 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1289832, 28503 ^ [_1289826, _1289828, _1289830, _1289832])))]], 28491 ^ _780461 : [(28492 ^ _780461) ^ [_1289939] : [hBOOL(hAPP(hAPP(c_member(_1289826), _1289939), _1289828)), hBOOL(hAPP(_1289832, _1289939))], (28498 ^ _780461) ^ [_1290035] : [hBOOL(hAPP(hAPP(c_member(_1289826), _1290035), _1289830)), hBOOL(hAPP(_1289832, _1290035))]]], (28528 ^ _780461) ^ [_1290672, _1290674, _1290676, _1290678] : [28532 ^ _780461 : [(28533 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290672), 28531 ^ [_1290672, _1290674, _1290676, _1290678]), _1290674)))], (28535 ^ _780461) ^ [] : [hBOOL(hAPP(_1290678, 28531 ^ [_1290672, _1290674, _1290676, _1290678]))]], 28537 ^ _780461 : [(28538 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290672), 28536 ^ [_1290672, _1290674, _1290676, _1290678]), _1290676)))], (28540 ^ _780461) ^ [] : [hBOOL(hAPP(_1290678, 28536 ^ [_1290672, _1290674, _1290676, _1290678]))]], 28541 ^ _780461 : [(28542 ^ _780461) ^ [_1291005] : [hBOOL(hAPP(hAPP(c_member(_1290672), _1291005), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290672, tc_HOL_Obool)), _1290674), _1290676))), -(hBOOL(hAPP(_1290678, _1291005)))]]], (28509 ^ _780461) ^ [_1290250, _1290252, _1290254, _1290256] : [28511 ^ _780461 : [(28512 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290250), 28510 ^ [_1290250, _1290252, _1290254, _1290256]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290250, tc_HOL_Obool)), _1290252), _1290254))))], (28514 ^ _780461) ^ [] : [hBOOL(hAPP(_1290256, 28510 ^ [_1290250, _1290252, _1290254, _1290256]))]], 28515 ^ _780461 : [(28516 ^ _780461) ^ [_1290470] : [hBOOL(hAPP(hAPP(c_member(_1290250), _1290470), _1290252)), -(hBOOL(hAPP(_1290256, _1290470)))], (28522 ^ _780461) ^ [_1290567] : [hBOOL(hAPP(hAPP(c_member(_1290250), _1290567), _1290254)), -(hBOOL(hAPP(_1290256, _1290567)))]]], (28548 ^ _780461) ^ [_1291136, _1291138] : [class_Lattices_Osemilattice__sup(_1291136), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291136), _1291138), _1291138) = _1291138)], (28554 ^ _780461) ^ [_1291227, _1291229] : [class_Lattices_Osemilattice__sup(_1291227), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291227), _1291229), _1291229) = _1291229)], (28560 ^ _780461) ^ [_1291318, _1291320, _1291322] : [class_Lattices_Osemilattice__sup(_1291318), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291318), _1291320), _1291322) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291318), _1291322), _1291320))], (28566 ^ _780461) ^ [_1291427, _1291429, _1291431] : [class_Lattices_Olattice(_1291427), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291427), _1291429), _1291431) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291427), _1291431), _1291429))], (28572 ^ _780461) ^ [_1291536, _1291538, _1291540] : [class_Lattices_Osemilattice__sup(_1291536), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291536), _1291538), _1291540) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291536), _1291540), _1291538))], (28578 ^ _780461) ^ [_1291645, _1291647, _1291649] : [class_Lattices_Osemilattice__sup(_1291645), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291645), _1291647), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291645), _1291647), _1291649)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291645), _1291647), _1291649))], (28584 ^ _780461) ^ [_1291770, _1291772, _1291774] : [class_Lattices_Olattice(_1291770), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291770), _1291772), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291770), _1291772), _1291774)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291770), _1291772), _1291774))], (28590 ^ _780461) ^ [_1291895, _1291897, _1291899] : [class_Lattices_Osemilattice__sup(_1291895), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291895), _1291897), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291895), _1291897), _1291899)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291895), _1291897), _1291899))], (28596 ^ _780461) ^ [_1292020, _1292022, _1292024, _1292026] : [class_Lattices_Osemilattice__sup(_1292020), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292020), _1292022), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292020), _1292024), _1292026)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292020), _1292024), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292020), _1292022), _1292026)))], (28602 ^ _780461) ^ [_1292163, _1292165, _1292167, _1292169] : [class_Lattices_Olattice(_1292163), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292163), _1292165), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292163), _1292167), _1292169)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292163), _1292167), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292163), _1292165), _1292169)))], (28608 ^ _780461) ^ [_1292306, _1292308, _1292310, _1292312] : [class_Lattices_Osemilattice__sup(_1292306), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292306), _1292308), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292306), _1292310), _1292312)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292306), _1292310), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292306), _1292308), _1292312)))], (28614 ^ _780461) ^ [_1292449, _1292451, _1292453, _1292455] : [class_Lattices_Osemilattice__sup(_1292449), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292449), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292449), _1292451), _1292453)), _1292455) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292449), _1292451), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292449), _1292453), _1292455)))], (28620 ^ _780461) ^ [_1292592, _1292594, _1292596, _1292598] : [class_Lattices_Olattice(_1292592), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292592), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292592), _1292594), _1292596)), _1292598) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292592), _1292594), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292592), _1292596), _1292598)))], (28626 ^ _780461) ^ [_1292735, _1292737, _1292739, _1292741] : [class_Lattices_Osemilattice__sup(_1292735), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292735), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292735), _1292737), _1292739)), _1292741) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292735), _1292737), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292735), _1292739), _1292741)))], (28632 ^ _780461) ^ [_1292878, _1292880, _1292882, _1292884, _1292886] : [class_Lattices_Olattice(_1292878), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292880, _1292878)), _1292882), _1292884), _1292886) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292878), hAPP(_1292882, _1292886)), hAPP(_1292884, _1292886)))], (28638 ^ _780461) ^ [_1293015, _1293017, _1293019, _1293021] : [class_Lattices_Osemilattice__sup(_1293015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293015), _1293017), _1293019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293015), _1293017), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1293015), _1293019), _1293021))))], (28648 ^ _780461) ^ [_1293194, _1293196, _1293198, _1293200] : [class_Lattices_Osemilattice__sup(_1293194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293194), _1293196), _1293198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293194), _1293196), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1293194), _1293200), _1293198))))], (28658 ^ _780461) ^ [_1293373, _1293375, _1293377, _1293379, _1293381] : [class_Lattices_Olattice(_1293373), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293375, _1293373)), _1293377), _1293379), _1293381) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1293373), hAPP(_1293377, _1293381)), hAPP(_1293379, _1293381)))], (28664 ^ _780461) ^ [_1293510, _1293512] : [class_Lattices_Olattice(_1293510), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1293510), _1293512), _1293512) = _1293512)], (28670 ^ _780461) ^ [_1293601] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1293601) = c_Orderings_Oord__class_Omax(_1293601)), class_Lattices_Osemilattice__sup(_1293601), class_Orderings_Olinorder(_1293601)], (28680 ^ _780461) ^ [_1293730, _1293732, _1293734, _1293736] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293730, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1293730), _1293732), _1293734)), _1293736) = hAPP(hAPP(c_Set_Oinsert(_1293730), _1293732), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293730, tc_HOL_Obool)), _1293734), _1293736)))], (28682 ^ _780461) ^ [_1293797, _1293799, _1293801, _1293803] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293797, tc_HOL_Obool)), _1293799), hAPP(hAPP(c_Set_Oinsert(_1293797), _1293801), _1293803)) = hAPP(hAPP(c_Set_Oinsert(_1293797), _1293801), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293797, tc_HOL_Obool)), _1293799), _1293803)))], (28694 ^ _780461) ^ [_1294039, _1294041, _1294043, _1294045] : [28695 ^ _780461 : [(28696 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1294039), _1294041), _1294043))], (28698 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1294039), _1294041), _1294045))]], -(hBOOL(hAPP(hAPP(c_member(_1294039), _1294041), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294039, tc_HOL_Obool)), _1294043), _1294045))))], (28684 ^ _780461) ^ [_1293885, _1293887, _1293889, _1293891] : [hBOOL(hAPP(hAPP(c_member(_1293885), _1293887), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293885, tc_HOL_Obool)), _1293889), _1293891))), -(hBOOL(hAPP(hAPP(c_member(_1293885), _1293887), _1293889))), -(hBOOL(hAPP(hAPP(c_member(_1293885), _1293887), _1293891)))], (28702 ^ _780461) ^ [_1294224, _1294226, _1294228, _1294230] : [hBOOL(hAPP(hAPP(c_member(_1294224), _1294226), _1294228)), -(hBOOL(hAPP(hAPP(c_member(_1294224), _1294226), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294224, tc_HOL_Obool)), _1294228), _1294230))))], (28708 ^ _780461) ^ [_1294355, _1294357, _1294359, _1294361] : [hBOOL(hAPP(hAPP(c_member(_1294355), _1294357), _1294359)), -(hBOOL(hAPP(hAPP(c_member(_1294355), _1294357), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294355, tc_HOL_Obool)), _1294361), _1294359))))], (28714 ^ _780461) ^ [_1294507, _1294509, _1294511, _1294513] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294507, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1294507, tc_fun(_1294507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1294507)), _1294509)), hAPP(hAPP(c_COMBC(_1294507, tc_fun(_1294507, tc_HOL_Obool), tc_HOL_Obool), c_member(_1294507)), _1294511)), _1294513)), -(hBOOL(hAPP(hAPP(c_member(_1294507), _1294513), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294507, tc_HOL_Obool)), _1294509), _1294511))))], (28720 ^ _780461) ^ [_1294706, _1294708, _1294710, _1294712] : [hBOOL(hAPP(hAPP(c_member(_1294706), _1294712), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294706, tc_HOL_Obool)), _1294708), _1294710))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294706, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1294706, tc_fun(_1294706, tc_HOL_Obool), tc_HOL_Obool), c_member(_1294706)), _1294708)), hAPP(hAPP(c_COMBC(_1294706, tc_fun(_1294706, tc_HOL_Obool), tc_HOL_Obool), c_member(_1294706)), _1294710)), _1294712)))], (28726 ^ _780461) ^ [_1294911, _1294913, _1294915] : [-(hAPP(hAPP(c_Set_Oinsert(_1294911), _1294913), _1294915) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294911, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1294911), _1294913), c_Orderings_Obot__class_Obot(tc_fun(_1294911, tc_HOL_Obool)))), _1294915))], (28728 ^ _780461) ^ [_1294991, _1294993, _1294995, _1294997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1294991, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1294991, tc_HOL_Obool)), _1294993), _1294995)), _1294997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1294991, tc_HOL_Obool)), _1294993), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294991, tc_HOL_Obool)), _1294995), _1294997))))], (28734 ^ _780461) ^ [_1295152, _1295154, _1295156, _1295158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1295152, tc_HOL_Obool)), _1295154), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295152, tc_HOL_Obool)), _1295156), _1295158))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1295152, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1295152, tc_HOL_Obool)), _1295154), _1295156)), _1295158)))], (28740 ^ _780461) ^ [_1295319, _1295321, _1295323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1295319, tc_HOL_Obool)), _1295321), _1295323)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295319, tc_HOL_Obool)), _1295321), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1295319, tc_HOL_Obool)), _1295323), _1295321)) = _1295323)], (28746 ^ _780461) ^ [_1295462, _1295464, _1295466] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1295462, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1295462, tc_HOL_Obool)), _1295464), _1295466)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295462, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1295462, tc_HOL_Obool)), _1295464)), _1295466))], (28748 ^ _780461) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (28750 ^ _780461) ^ [] : [-(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)))))], (28752 ^ _780461) ^ [_1295563, _1295565, _1295567] : [-(c_Wellfounded_Omlex__prod(_1295563, _1295565, _1295567) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1295563), _1295563), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1295563, c_Wellfounded_Oless__than, _1295567)), hAPP(hAPP(c_COMBS(_1295563, _1295563, tc_prod(tc_Nat_Onat, _1295563)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1295563, tc_prod(tc_Nat_Onat, _1295563)), _1295563), c_Product__Type_OPair(tc_Nat_Onat, _1295563)), _1295565)), c_COMBI(_1295563))))], (28754 ^ _780461) ^ [_1295666, _1295668, _1295670, _1295672] : [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), _1295666), _1295668)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1295670), _1295672))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295666), _1295672) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295670), _1295668))], (28760 ^ _780461) ^ [_1295813, _1295815, _1295817, _1295819] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295813), _1295819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1295817), _1295815), -(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), _1295813), _1295815)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1295817), _1295819))), c_Int_Ointrel)))], (28766 ^ _780461) ^ [_1295966, _1295968, _1295970, _1295972] : [c_FunDef_Oreduction__pair(_1295966, _1295968), -(c_FunDef_Oreduction__pair(_1295970, hAPP(hAPP(c_FunDef_Orp__inv__image(_1295966, _1295970), _1295968), _1295972)))], (28772 ^ _780461) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (28774 ^ _780461) ^ [_1296083, _1296085] : [-(c_FunDef_Orp__inv__image(_1296083, _1296085) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool), tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool), tc_fun(tc_fun(_1296085, _1296083), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool), tc_fun(tc_fun(_1296085, _1296083), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool), tc_fun(tc_fun(_1296085, _1296083), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1296085, _1296083), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)), tc_fun(tc_fun(_1296085, _1296083), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool), tc_fun(tc_fun(_1296085, _1296083), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool), tc_fun(tc_fun(_1296085, _1296083), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool))))), tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1296085, _1296083), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)), tc_fun(tc_fun(_1296085, _1296083), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool))), tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1296085, _1296083), tc_fun(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1296085, _1296083), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)), tc_fun(tc_fun(_1296085, _1296083), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)))), tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool)), c_COMBS(tc_fun(_1296085, _1296083), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1296085, _1296083), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)), tc_fun(tc_fun(_1296085, _1296083), tc_fun(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)))), tc_fun(tc_prod(_1296083, _1296083), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool))), tc_fun(_1296085, _1296083)), c_Product__Type_OPair(tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool), tc_fun(tc_prod(_1296085, _1296085), tc_HOL_Obool)))), c_Relation_Oinv__image(_1296083, _1296085))))), c_Relation_Oinv__image(_1296083, _1296085))))], (28776 ^ _780461) ^ [_1296623, _1296625, _1296627, _1296629, _1296631, _1296633] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296623, tc_fun(_1296625, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1296623, tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_fun(_1296625, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296625, tc_fun(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_fun(_1296625, tc_HOL_Obool)), _1296623), c_COMBC(_1296625, tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296625, tc_prod(_1296623, _1296625)), tc_fun(_1296625, tc_fun(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_HOL_Obool)), _1296623), hAPP(c_COMBB(tc_prod(_1296623, _1296625), tc_fun(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_HOL_Obool), _1296625), c_member(tc_prod(_1296623, _1296625)))), c_Product__Type_OPair(_1296623, _1296625)))), _1296627)), hAPP(hAPP(c_COMBC(_1296623, tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_fun(_1296625, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296625, tc_fun(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_fun(_1296625, tc_HOL_Obool)), _1296623), c_COMBC(_1296625, tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1296625, tc_prod(_1296623, _1296625)), tc_fun(_1296625, tc_fun(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_HOL_Obool)), _1296623), hAPP(c_COMBB(tc_prod(_1296623, _1296625), tc_fun(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool), tc_HOL_Obool), _1296625), c_member(tc_prod(_1296623, _1296625)))), c_Product__Type_OPair(_1296623, _1296625)))), _1296629)), _1296631), _1296633)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1296623, _1296625)), hAPP(hAPP(c_Product__Type_OPair(_1296623, _1296625), _1296631), _1296633)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1296623, _1296625), tc_HOL_Obool)), _1296627), _1296629))))], (28782 ^ _780461) ^ [_1297280, _1297282, _1297284, _1297286, _1297288, _1297290] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1297280, _1297282)), hAPP(hAPP(c_Product__Type_OPair(_1297280, _1297282), _1297288), _1297290)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool)), _1297284), _1297286))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297280, tc_fun(_1297282, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1297280, tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_fun(_1297282, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297282, tc_fun(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_fun(_1297282, tc_HOL_Obool)), _1297280), c_COMBC(_1297282, tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297282, tc_prod(_1297280, _1297282)), tc_fun(_1297282, tc_fun(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_HOL_Obool)), _1297280), hAPP(c_COMBB(tc_prod(_1297280, _1297282), tc_fun(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_HOL_Obool), _1297282), c_member(tc_prod(_1297280, _1297282)))), c_Product__Type_OPair(_1297280, _1297282)))), _1297284)), hAPP(hAPP(c_COMBC(_1297280, tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_fun(_1297282, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297282, tc_fun(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_fun(_1297282, tc_HOL_Obool)), _1297280), c_COMBC(_1297282, tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297282, tc_prod(_1297280, _1297282)), tc_fun(_1297282, tc_fun(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_HOL_Obool)), _1297280), hAPP(c_COMBB(tc_prod(_1297280, _1297282), tc_fun(tc_fun(tc_prod(_1297280, _1297282), tc_HOL_Obool), tc_HOL_Obool), _1297282), c_member(tc_prod(_1297280, _1297282)))), c_Product__Type_OPair(_1297280, _1297282)))), _1297286)), _1297288), _1297290)))], (28788 ^ _780461) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (28790 ^ _780461) ^ [_1297961, _1297963, _1297965, _1297967, _1297969, _1297971] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1297961, tc_HOL_Obool), tc_fun(_1297961, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1297961, tc_HOL_Obool), tc_fun(_1297961, tc_HOL_Obool)), _1297963), _1297965)), c_Wellfounded_Omax__ext(_1297961, _1297967))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1297961, tc_HOL_Obool), tc_fun(_1297961, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1297961, tc_HOL_Obool), tc_fun(_1297961, tc_HOL_Obool)), _1297969), _1297971)), c_Wellfounded_Omax__ext(_1297961, _1297967))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1297961, tc_HOL_Obool), tc_fun(_1297961, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1297961, tc_HOL_Obool), tc_fun(_1297961, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297961, tc_HOL_Obool)), _1297963), _1297969)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1297961, tc_HOL_Obool)), _1297965), _1297971))), c_Wellfounded_Omax__ext(_1297961, _1297967))))], (28800 ^ _780461) ^ [_1298375, _1298377, _1298379, _1298381] : [c_Wellfounded_Omax__extp(_1298375, hAPP(hAPP(c_COMBC(_1298375, tc_fun(tc_prod(_1298375, _1298375), tc_HOL_Obool), tc_fun(_1298375, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1298375, tc_fun(tc_fun(tc_prod(_1298375, _1298375), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1298375, _1298375), tc_HOL_Obool), tc_fun(_1298375, tc_HOL_Obool)), _1298375), c_COMBC(_1298375, tc_fun(tc_prod(_1298375, _1298375), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1298375, tc_prod(_1298375, _1298375)), tc_fun(_1298375, tc_fun(tc_fun(tc_prod(_1298375, _1298375), tc_HOL_Obool), tc_HOL_Obool)), _1298375), hAPP(c_COMBB(tc_prod(_1298375, _1298375), tc_fun(tc_fun(tc_prod(_1298375, _1298375), tc_HOL_Obool), tc_HOL_Obool), _1298375), c_member(tc_prod(_1298375, _1298375)))), c_Product__Type_OPair(_1298375, _1298375)))), _1298377), _1298379, _1298381), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1298375, tc_HOL_Obool), tc_fun(_1298375, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1298375, tc_HOL_Obool), tc_fun(_1298375, tc_HOL_Obool)), _1298379), _1298381)), c_Wellfounded_Omax__ext(_1298375, _1298377))))], (28806 ^ _780461) ^ [_1298760, _1298762, _1298764, _1298766] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1298760, tc_HOL_Obool), tc_fun(_1298760, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1298760, tc_HOL_Obool), tc_fun(_1298760, tc_HOL_Obool)), _1298764), _1298766)), c_Wellfounded_Omax__ext(_1298760, _1298762))), -(c_Wellfounded_Omax__extp(_1298760, hAPP(hAPP(c_COMBC(_1298760, tc_fun(tc_prod(_1298760, _1298760), tc_HOL_Obool), tc_fun(_1298760, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1298760, tc_fun(tc_fun(tc_prod(_1298760, _1298760), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1298760, _1298760), tc_HOL_Obool), tc_fun(_1298760, tc_HOL_Obool)), _1298760), c_COMBC(_1298760, tc_fun(tc_prod(_1298760, _1298760), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1298760, tc_prod(_1298760, _1298760)), tc_fun(_1298760, tc_fun(tc_fun(tc_prod(_1298760, _1298760), tc_HOL_Obool), tc_HOL_Obool)), _1298760), hAPP(c_COMBB(tc_prod(_1298760, _1298760), tc_fun(tc_fun(tc_prod(_1298760, _1298760), tc_HOL_Obool), tc_HOL_Obool), _1298760), c_member(tc_prod(_1298760, _1298760)))), c_Product__Type_OPair(_1298760, _1298760)))), _1298762), _1298764, _1298766))], (28812 ^ _780461) ^ [_1299178, _1299180, _1299182, _1299184, _1299186, _1299188] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1299178, _1299178)), hAPP(hAPP(c_Product__Type_OPair(_1299178, _1299178), _1299180), _1299182)), hAPP(hAPP(c_Relation_Oinv__image(_1299184, _1299178), _1299186), _1299188))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1299184, _1299184)), hAPP(hAPP(c_Product__Type_OPair(_1299184, _1299184), hAPP(_1299188, _1299180)), hAPP(_1299188, _1299182))), _1299186)))], (28818 ^ _780461) ^ [_1299365, _1299367, _1299369, _1299371, _1299373, _1299375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1299371, _1299371)), hAPP(hAPP(c_Product__Type_OPair(_1299371, _1299371), hAPP(_1299375, _1299367)), hAPP(_1299375, _1299369))), _1299373)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1299365, _1299365)), hAPP(hAPP(c_Product__Type_OPair(_1299365, _1299365), _1299367), _1299369)), hAPP(hAPP(c_Relation_Oinv__image(_1299371, _1299365), _1299373), _1299375))))], (28824 ^ _780461) ^ [_1299558, _1299560, _1299562, _1299564, _1299566, _1299568] : [c_Hoare__Mirabelle_Ohoare__derivs(_1299558, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1299558), tc_HOL_Obool)), _1299560), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1299558), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1299558, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1299558)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1299558, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1299558))), hAPP(hAPP(c_COMBB(tc_fun(_1299558, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1299558, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1299558))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1299558)), _1299562)), c_Com_Ocom_OBODY)), _1299564)), _1299566)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1299558), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1299558, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1299558)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1299558, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1299558))), hAPP(hAPP(c_COMBB(tc_fun(_1299558, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1299558, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1299558))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1299558)), _1299562)), 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))), _1299564)), _1299566)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _1299568), _1299566)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1299558, _1299560, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1299558)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1299558), hAPP(_1299562, _1299568)), hAPP(c_Com_Ocom_OBODY, _1299568)), hAPP(_1299564, _1299568))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1299558), tc_HOL_Obool)))))], (28834 ^ _780461) ^ [_1300089, _1300091, _1300093, _1300095, _1300097] : [c_Hoare__Mirabelle_Ohoare__valids(_1300089, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1300089), tc_HOL_Obool)), _1300091), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1300089), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089))), hAPP(hAPP(c_COMBB(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1300089)), _1300093)), c_Com_Ocom_OBODY)), _1300095)), _1300097)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1300089), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089))), hAPP(hAPP(c_COMBB(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1300089)), _1300093)), 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))), _1300095)), _1300097)), -(c_Hoare__Mirabelle_Ohoare__valids(_1300089, _1300091, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1300089), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089))), hAPP(hAPP(c_COMBB(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1300089, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1300089))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1300089)), _1300093)), c_Com_Ocom_OBODY)), _1300095)), _1300097)))], (28840 ^ _780461) ^ [_1300610, _1300612, _1300614, _1300616, _1300618, _1300620] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1300610, tc_fun(_1300612, tc_HOL_Obool))), _1300614), _1300616), _1300618), _1300620)), -(hBOOL(hAPP(hAPP(_1300614, _1300618), _1300620))), -(hBOOL(hAPP(hAPP(_1300616, _1300618), _1300620)))], (28850 ^ _780461) ^ [_1300768, _1300770, _1300772, _1300774, _1300776, _1300778] : [28851 ^ _780461 : [(28852 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1300768, _1300770), _1300772))], (28854 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1300774, _1300770), _1300772))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1300776, tc_fun(_1300778, tc_HOL_Obool))), _1300774), _1300768), _1300770), _1300772)))], (28858 ^ _780461) ^ [_1300951, _1300953, _1300955, _1300957, _1300959, _1300961] : [_1300951 = hAPP(_1300953, _1300955), hBOOL(hAPP(hAPP(c_member(_1300957), _1300955), _1300959)), -(hBOOL(hAPP(hAPP(c_member(_1300961), _1300951), hAPP(c_Set_Oimage(_1300957, _1300961, _1300953), _1300959))))], (28868 ^ _780461) ^ [_1301144, _1301146, _1301148, _1301150, _1301152, _1301154] : [hBOOL(hAPP(hAPP(_1301144, _1301146), _1301148)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301150, tc_fun(_1301152, tc_HOL_Obool))), _1301144), _1301154), _1301146), _1301148)))], (28874 ^ _780461) ^ [_1301277, _1301279, _1301281, _1301283, _1301285, _1301287] : [hBOOL(hAPP(hAPP(_1301277, _1301279), _1301281)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301283, tc_fun(_1301285, tc_HOL_Obool))), _1301287), _1301277), _1301279), _1301281)))], (28880 ^ _780461) ^ [_1301410, _1301412, _1301414, _1301416, _1301418] : [-(hAPP(c_Set_Oimage(_1301410, _1301412, _1301414), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301410, tc_HOL_Obool)), _1301416), _1301418)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301412, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1301410, _1301412, _1301414), _1301416)), hAPP(c_Set_Oimage(_1301410, _1301412, _1301414), _1301418)))], (28882 ^ _780461) ^ [_1301484, _1301486, _1301488, _1301490, _1301492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301484, tc_HOL_Obool)), _1301486), _1301488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301490, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1301484, _1301490, _1301492), _1301486)), hAPP(c_Set_Oimage(_1301484, _1301490, _1301492), _1301488))))], (28888 ^ _780461) ^ [_1301659, _1301661, _1301663, _1301665, _1301667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301659, tc_HOL_Obool)), _1301661), hAPP(c_Set_Oimage(_1301663, _1301659, _1301665), _1301667))), 28892 ^ _780461 : [(28893 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301663, tc_HOL_Obool)), 28891 ^ [_1301659, _1301661, _1301663, _1301665, _1301667]), _1301667)))], (28895 ^ _780461) ^ [] : [-(_1301661 = hAPP(c_Set_Oimage(_1301663, _1301659, _1301665), 28891 ^ [_1301659, _1301661, _1301663, _1301665, _1301667]))]]], (28897 ^ _780461) ^ [_1301863, _1301865, _1301867, _1301869, _1301871] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301863, tc_HOL_Obool)), _1301865), hAPP(c_Set_Oimage(_1301867, _1301863, _1301869), _1301871)))), 28898 ^ _780461 : [(28899 ^ _780461) ^ [_1301943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301867, tc_HOL_Obool)), _1301943), _1301871)), _1301865 = hAPP(c_Set_Oimage(_1301867, _1301863, _1301869), _1301943)]]], (28907 ^ _780461) ^ [_1302108, _1302110, _1302112, _1302114, _1302116, _1302118] : [-(hAPP(c_Set_Oimage(_1302108, _1302110, _1302112), hAPP(c_Set_Oimage(_1302114, _1302108, _1302116), _1302118)) = hAPP(c_Set_Oimage(_1302114, _1302110, hAPP(hAPP(c_COMBB(_1302108, _1302110, _1302114), _1302112), _1302116)), _1302118))], (28909 ^ _780461) ^ [_1302196, _1302198, _1302200, _1302202, _1302204] : [hBOOL(hAPP(hAPP(c_member(_1302196), _1302198), hAPP(c_Set_Oimage(_1302200, _1302196, _1302202), _1302204))), 28913 ^ _780461 : [(28914 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1302200), 28912 ^ [_1302196, _1302198, _1302200, _1302202, _1302204]), _1302204)))], (28916 ^ _780461) ^ [] : [-(_1302198 = hAPP(_1302202, 28912 ^ [_1302196, _1302198, _1302200, _1302202, _1302204]))]]], (28918 ^ _780461) ^ [_1302380, _1302382, _1302384, _1302386, _1302388] : [-(hBOOL(hAPP(hAPP(c_member(_1302380), _1302382), hAPP(c_Set_Oimage(_1302384, _1302380, _1302386), _1302388)))), 28919 ^ _780461 : [(28920 ^ _780461) ^ [_1302450] : [hBOOL(hAPP(hAPP(c_member(_1302384), _1302450), _1302388)), _1302382 = hAPP(_1302386, _1302450)]]], (28928 ^ _780461) ^ [_1302598, _1302600, _1302602, _1302604, _1302606] : [hBOOL(hAPP(hAPP(c_member(_1302598), _1302600), _1302602)), -(hBOOL(hAPP(hAPP(c_member(_1302604), hAPP(_1302606, _1302600)), hAPP(c_Set_Oimage(_1302598, _1302604, _1302606), _1302602))))], (28934 ^ _780461) ^ [_1302729, _1302731, _1302733, _1302735, _1302737, _1302739] : [hBOOL(hAPP(hAPP(c_member(_1302729), _1302731), _1302733)), _1302735 = hAPP(_1302737, _1302731), -(hBOOL(hAPP(hAPP(c_member(_1302739), _1302735), hAPP(c_Set_Oimage(_1302729, _1302739, _1302737), _1302733))))], (28944 ^ _780461) ^ [_1302922, _1302924, _1302926, _1302928, _1302930] : [-(hAPP(c_Set_Oimage(_1302922, _1302924, _1302926), hAPP(hAPP(c_Set_Oinsert(_1302922), _1302928), _1302930)) = hAPP(hAPP(c_Set_Oinsert(_1302924), hAPP(_1302926, _1302928)), hAPP(c_Set_Oimage(_1302922, _1302924, _1302926), _1302930)))], (28946 ^ _780461) ^ [_1303007, _1303009, _1303011, _1303013] : [c_Orderings_Obot__class_Obot(tc_fun(_1303007, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1303009, _1303007, _1303011), _1303013), -(_1303013 = c_Orderings_Obot__class_Obot(tc_fun(_1303009, tc_HOL_Obool)))], (28952 ^ _780461) ^ [_1303118, _1303120, _1303122, _1303124] : [_1303124 = c_Orderings_Obot__class_Obot(tc_fun(_1303120, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_1303118, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_1303120, _1303118, _1303122), _1303124))], (28958 ^ _780461) ^ [_1303235, _1303237, _1303239] : [-(hAPP(c_Set_Oimage(_1303235, _1303237, _1303239), c_Orderings_Obot__class_Obot(tc_fun(_1303235, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1303237, tc_HOL_Obool)))], (28960 ^ _780461) ^ [_1303300, _1303302, _1303304, _1303306] : [hAPP(c_Set_Oimage(_1303300, _1303302, _1303304), _1303306) = c_Orderings_Obot__class_Obot(tc_fun(_1303302, tc_HOL_Obool)), -(_1303306 = c_Orderings_Obot__class_Obot(tc_fun(_1303300, tc_HOL_Obool)))], (28966 ^ _780461) ^ [_1303411, _1303413, _1303415, _1303417] : [_1303417 = c_Orderings_Obot__class_Obot(tc_fun(_1303411, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1303411, _1303413, _1303415), _1303417) = c_Orderings_Obot__class_Obot(tc_fun(_1303413, tc_HOL_Obool)))], (28972 ^ _780461) ^ [_1303528, _1303530, _1303532, _1303534, _1303536] : [hBOOL(hAPP(hAPP(c_member(_1303528), _1303530), _1303532)), -(hAPP(hAPP(c_Set_Oinsert(_1303534), hAPP(_1303536, _1303530)), hAPP(c_Set_Oimage(_1303528, _1303534, _1303536), _1303532)) = hAPP(c_Set_Oimage(_1303528, _1303534, _1303536), _1303532))], (28978 ^ _780461) ^ [_1303675, _1303677, _1303679, _1303681, _1303683] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1303675, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1303675, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1303677, _1303675, _1303679), _1303681)), hAPP(c_Set_Oimage(_1303677, _1303675, _1303679), _1303683))), hAPP(c_Set_Oimage(_1303677, _1303675, _1303679), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1303677, tc_HOL_Obool)), _1303681), _1303683)))))], (28980 ^ _780461) ^ [_1303774, _1303776, _1303778, _1303780] : [_1303774 = c_Orderings_Obot__class_Obot(tc_fun(_1303776, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1303776, _1303778, hAPP(c_COMBK(_1303778, _1303776), _1303780)), _1303774) = c_Orderings_Obot__class_Obot(tc_fun(_1303778, tc_HOL_Obool)))], (28986 ^ _780461) ^ [_1303895, _1303897, _1303899, _1303901] : [-(_1303895 = c_Orderings_Obot__class_Obot(tc_fun(_1303897, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1303897, _1303899, hAPP(c_COMBK(_1303899, _1303897), _1303901)), _1303895) = hAPP(hAPP(c_Set_Oinsert(_1303899), _1303901), c_Orderings_Obot__class_Obot(tc_fun(_1303899, tc_HOL_Obool))))], (28992 ^ _780461) ^ [_1303968, _1303970, _1303972, _1303974, _1303976] : [hBOOL(hAPP(hAPP(c_member(_1303968), _1303970), _1303972)), -(hAPP(c_Set_Oimage(_1303968, _1303974, hAPP(c_COMBK(_1303974, _1303968), _1303976)), _1303972) = hAPP(hAPP(c_Set_Oinsert(_1303974), _1303976), c_Orderings_Obot__class_Obot(tc_fun(_1303974, tc_HOL_Obool))))], (28998 ^ _780461) ^ [_1304117] : [-(c_Wellfounded_Omeasure(_1304117) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1304117), c_Wellfounded_Oless__than))], (29000 ^ _780461) ^ [_1304148, _1304150, _1304152, _1304154, _1304156] : [c_Hoare__Mirabelle_Ohoare__derivs(_1304148, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_1304148), tc_HOL_Obool)), _1304150), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1304148), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148))), hAPP(hAPP(c_COMBB(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1304148)), _1304152)), c_Com_Ocom_OBODY)), _1304154)), _1304156)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1304148), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148))), hAPP(hAPP(c_COMBB(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1304148)), _1304152)), 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))), _1304154)), _1304156)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1304148, _1304150, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_1304148), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148))), hAPP(hAPP(c_COMBB(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1304148, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1304148))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_1304148)), _1304152)), c_Com_Ocom_OBODY)), _1304154)), _1304156)))], (29006 ^ _780461) ^ [_1304684, _1304686] : [c_Relation_Oirrefl(_1304684, _1304686), 29009 ^ _780461 : [(29010 ^ _780461) ^ [_1304766] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1304684, _1304684)), hAPP(hAPP(c_Product__Type_OPair(_1304684, _1304684), _1304766), _1304766)), _1304686))]]], (29012 ^ _780461) ^ [_1304806, _1304808] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1304806, _1304806)), hAPP(hAPP(c_Product__Type_OPair(_1304806, _1304806), 29013 ^ [_1304806, _1304808]), 29013 ^ [_1304806, _1304808])), _1304808))), -(c_Relation_Oirrefl(_1304806, _1304808))], (29019 ^ _780461) ^ [_1304877, _1304879, _1304881, _1304883] : [-(hAPP(c_Relation_OField(_1304877), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1304877, _1304877)), hAPP(hAPP(c_Product__Type_OPair(_1304877, _1304877), _1304879), _1304881)), _1304883)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304877, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1304877), _1304879), hAPP(hAPP(c_Set_Oinsert(_1304877), _1304881), c_Orderings_Obot__class_Obot(tc_fun(_1304877, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1304877), _1304883)))], (29021 ^ _780461) ^ [_1304983, _1304985] : [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)), _1304983), 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)), _1304985), 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)), _1304983), _1304985)), c_Int_Ointrel)))], (29027 ^ _780461) ^ [_1305114, _1305116] : [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)), _1305114), _1305116)), 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)), _1305114), 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)), _1305116), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (29033 ^ _780461) ^ [_1305269, _1305271, _1305273] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1305269, hAPP(hAPP(c_COMBC(_1305269, tc_fun(tc_prod(_1305269, _1305269), tc_HOL_Obool), tc_fun(_1305269, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1305269, tc_fun(tc_fun(tc_prod(_1305269, _1305269), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1305269, _1305269), tc_HOL_Obool), tc_fun(_1305269, tc_HOL_Obool)), _1305269), c_COMBC(_1305269, tc_fun(tc_prod(_1305269, _1305269), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1305269, tc_prod(_1305269, _1305269)), tc_fun(_1305269, tc_fun(tc_fun(tc_prod(_1305269, _1305269), tc_HOL_Obool), tc_HOL_Obool)), _1305269), hAPP(c_COMBB(tc_prod(_1305269, _1305269), tc_fun(tc_fun(tc_prod(_1305269, _1305269), tc_HOL_Obool), tc_HOL_Obool), _1305269), c_member(tc_prod(_1305269, _1305269)))), c_Product__Type_OPair(_1305269, _1305269)))), _1305271)), _1305273)), -(hBOOL(hAPP(hAPP(c_member(_1305269), _1305273), c_Wellfounded_Oacc(_1305269, _1305271))))], (29039 ^ _780461) ^ [_1305610, _1305612, _1305614] : [hBOOL(hAPP(hAPP(c_member(_1305610), _1305614), c_Wellfounded_Oacc(_1305610, _1305612))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1305610, hAPP(hAPP(c_COMBC(_1305610, tc_fun(tc_prod(_1305610, _1305610), tc_HOL_Obool), tc_fun(_1305610, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1305610, tc_fun(tc_fun(tc_prod(_1305610, _1305610), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1305610, _1305610), tc_HOL_Obool), tc_fun(_1305610, tc_HOL_Obool)), _1305610), c_COMBC(_1305610, tc_fun(tc_prod(_1305610, _1305610), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1305610, tc_prod(_1305610, _1305610)), tc_fun(_1305610, tc_fun(tc_fun(tc_prod(_1305610, _1305610), tc_HOL_Obool), tc_HOL_Obool)), _1305610), hAPP(c_COMBB(tc_prod(_1305610, _1305610), tc_fun(tc_fun(tc_prod(_1305610, _1305610), tc_HOL_Obool), tc_HOL_Obool), _1305610), c_member(tc_prod(_1305610, _1305610)))), c_Product__Type_OPair(_1305610, _1305610)))), _1305612)), _1305614)))], (29045 ^ _780461) ^ [_1305957, _1305959, _1305961, _1305963, _1305965, _1305967, _1305969] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1305957, _1305959)), hAPP(hAPP(c_Product__Type_OPair(_1305957, _1305959), _1305961), _1305963)), _1305965)), -(hBOOL(hAPP(hAPP(c_member(_1305967), hAPP(hAPP(_1305969, _1305961), _1305963)), hAPP(c_Set_Oimage(tc_prod(_1305957, _1305959), _1305967, hAPP(c_Product__Type_Oprod_Oprod__case(_1305957, _1305959, _1305967), _1305969)), _1305965))))], (29051 ^ _780461) ^ [_1306142, _1306144, _1306146, _1306148, _1306150] : [-(hAPP(c_Relation_OImage(_1306142, _1306144, _1306146), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306142, tc_HOL_Obool)), _1306148), _1306150)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306144, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1306142, _1306144, _1306146), _1306148)), hAPP(c_Relation_OImage(_1306142, _1306144, _1306146), _1306150)))], (29053 ^ _780461) ^ [_1306216, _1306218] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1306216), _1306218) = 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)), _1306216)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306218))))], (29055 ^ _780461) ^ [_1306277, _1306279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1306277), _1306279)), -(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)), _1306277)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306279))))], (29061 ^ _780461) ^ [_1306382, _1306384] : [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)), _1306382)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1306382), _1306384)))], (29067 ^ _780461) ^ [_1306493] : [-(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)), _1306493)) = _1306493)], (29069 ^ _780461) ^ [_1306537, _1306539] : [_1306537 = _1306539, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306537) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306539))], (29075 ^ _780461) ^ [_1306622, _1306624] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306622) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306624), -(_1306622 = _1306624)], (29081 ^ _780461) ^ [_1306728, _1306730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1306728), _1306730)), -(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)), _1306728)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306730))))], (29087 ^ _780461) ^ [_1306833, _1306835] : [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)), _1306833)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306835))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1306833), _1306835)))], (29093 ^ _780461) ^ [_1306959, _1306961] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1306959), _1306961)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306959)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1306961))))], (29099 ^ _780461) ^ [_1307064, _1307066] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1307064)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1307066))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1307064), _1307066)))], (29105 ^ _780461) ^ [_1307175, _1307177, _1307179] : [-(hAPP(c_Relation_OImage(_1307175, _1307177, _1307179), c_Orderings_Obot__class_Obot(tc_fun(_1307175, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1307177, tc_HOL_Obool)))], (29107 ^ _780461) ^ [] : [-(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))))], (29109 ^ _780461) ^ [] : [-(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))))], (29111 ^ _780461) ^ [_1307255, _1307257, _1307259, _1307261, _1307263, _1307265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1307255, _1307257), tc_HOL_Obool)), _1307259), _1307261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307255, tc_HOL_Obool)), _1307263), _1307265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307257, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1307255, _1307257, _1307259), _1307263)), hAPP(c_Relation_OImage(_1307255, _1307257, _1307261), _1307265))))], (29121 ^ _780461) ^ [_1307494, _1307496, _1307498, _1307500, _1307502] : [-(hAPP(c_Relation_OImage(_1307494, _1307496, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1307494, _1307496), tc_HOL_Obool)), _1307498), _1307500)), _1307502) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307496, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1307494, _1307496, _1307498), _1307502)), hAPP(c_Relation_OImage(_1307494, _1307496, _1307500), _1307502)))], (29123 ^ _780461) ^ [_1307571, _1307573, _1307575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1307571, _1307571), tc_HOL_Obool)), _1307573), _1307575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307571, tc_HOL_Obool)), c_Wellfounded_Oacc(_1307571, _1307575)), c_Wellfounded_Oacc(_1307571, _1307573))))], (29129 ^ _780461) ^ [_1307708, _1307710, _1307712, _1307714, _1307716, _1307718] : [hBOOL(hAPP(hAPP(c_member(_1307708), _1307710), _1307712)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1307708, _1307714)), hAPP(hAPP(c_Product__Type_OPair(_1307708, _1307714), _1307710), _1307716)), _1307718)), -(hBOOL(hAPP(hAPP(c_member(_1307714), _1307716), hAPP(c_Relation_OImage(_1307708, _1307714, _1307718), _1307712))))], (29139 ^ _780461) ^ [_1307957, _1307959, _1307961, _1307963, _1307965] : [hBOOL(hAPP(hAPP(c_member(_1307957), _1307959), hAPP(c_Relation_OImage(_1307961, _1307957, _1307963), _1307965))), 29143 ^ _780461 : [(29144 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1307961), 29142 ^ [_1307957, _1307959, _1307961, _1307963, _1307965]), _1307965)))], (29146 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1307961, _1307957)), hAPP(hAPP(c_Product__Type_OPair(_1307961, _1307957), 29142 ^ [_1307957, _1307959, _1307961, _1307963, _1307965]), _1307959)), _1307963)))]]], (29148 ^ _780461) ^ [_1308173, _1308175, _1308177, _1308179, _1308181] : [-(hBOOL(hAPP(hAPP(c_member(_1308173), _1308175), hAPP(c_Relation_OImage(_1308177, _1308173, _1308179), _1308181)))), 29149 ^ _780461 : [(29150 ^ _780461) ^ [_1308259] : [hBOOL(hAPP(hAPP(c_member(_1308177), _1308259), _1308181)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1308177, _1308173)), hAPP(hAPP(c_Product__Type_OPair(_1308177, _1308173), _1308259), _1308175)), _1308179))]]], (29158 ^ _780461) ^ [_1308439] : [-(hAPP(c_Relation_OField(_1308439), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1308439, _1308439), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1308439, tc_HOL_Obool)))], (29160 ^ _780461) ^ [_1308480, _1308482, _1308484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1308480, _1308480), tc_HOL_Obool)), _1308482), _1308484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308480, tc_HOL_Obool)), hAPP(c_Relation_OField(_1308480), _1308482)), hAPP(c_Relation_OField(_1308480), _1308484))))], (29166 ^ _780461) ^ [_1308625, _1308627, _1308629] : [-(hAPP(c_Relation_OField(_1308625), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1308625, _1308625), tc_HOL_Obool)), _1308627), _1308629)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308625, tc_HOL_Obool)), hAPP(c_Relation_OField(_1308625), _1308627)), hAPP(c_Relation_OField(_1308625), _1308629)))], (29168 ^ _780461) ^ [_1308692, _1308694, _1308696, _1308698] : [hBOOL(hAPP(hAPP(c_member(_1308692), _1308694), c_Wellfounded_Oacc(_1308692, _1308696))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1308692, _1308692)), hAPP(hAPP(c_Product__Type_OPair(_1308692, _1308692), _1308698), _1308694)), _1308696)), -(hBOOL(hAPP(hAPP(c_member(_1308692), _1308698), c_Wellfounded_Oacc(_1308692, _1308696))))], (29188 ^ _780461) ^ [_1309178, _1309180, _1309182] : [29190 ^ _780461 : [(29191 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1309178, _1309178)), hAPP(hAPP(c_Product__Type_OPair(_1309178, _1309178), 29189 ^ [_1309178, _1309180, _1309182]), _1309180)), _1309182)))], (29193 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1309178), 29189 ^ [_1309178, _1309180, _1309182]), c_Wellfounded_Oacc(_1309178, _1309182)))]], -(hBOOL(hAPP(hAPP(c_member(_1309178), _1309180), c_Wellfounded_Oacc(_1309178, _1309182))))], (29178 ^ _780461) ^ [_1308925, _1308927, _1308929] : [hBOOL(hAPP(hAPP(c_member(_1308925), _1308927), c_Wellfounded_Oacc(_1308925, _1308929))), 29181 ^ _780461 : [(29182 ^ _780461) ^ [_1309039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1308925, _1308925)), hAPP(hAPP(c_Product__Type_OPair(_1308925, _1308925), _1309039), _1308927)), _1308929)), -(hBOOL(hAPP(hAPP(c_member(_1308925), _1309039), c_Wellfounded_Oacc(_1308925, _1308929))))]]], (29197 ^ _780461) ^ [_1309442, _1309444, _1309446, _1309448, _1309450] : [hBOOL(hAPP(hAPP(c_member(_1309442), _1309444), hAPP(c_Relation_OImage(_1309446, _1309442, _1309448), hAPP(hAPP(c_Set_Oinsert(_1309446), _1309450), c_Orderings_Obot__class_Obot(tc_fun(_1309446, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1309446, _1309442)), hAPP(hAPP(c_Product__Type_OPair(_1309446, _1309442), _1309450), _1309444)), _1309448)))], (29203 ^ _780461) ^ [_1309613, _1309615, _1309617, _1309619, _1309621] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1309617, _1309613)), hAPP(hAPP(c_Product__Type_OPair(_1309617, _1309613), _1309621), _1309615)), _1309619)), -(hBOOL(hAPP(hAPP(c_member(_1309613), _1309615), hAPP(c_Relation_OImage(_1309617, _1309613, _1309619), hAPP(hAPP(c_Set_Oinsert(_1309617), _1309621), c_Orderings_Obot__class_Obot(tc_fun(_1309617, tc_HOL_Obool)))))))], (29209 ^ _780461) ^ [_1309790, _1309792, _1309794] : [class_Rings_Oring__1(_1309790), -(hAPP(c_Int_Oring__1__class_Oof__int(_1309790), 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), _1309792), _1309794)), 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(_1309790), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1309790), _1309792)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1309790), _1309794)))], (29215 ^ _780461) ^ [] : [-(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))))))], (29217 ^ _780461) ^ [_1309967, _1309969, _1309971, _1309973] : [-(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), _1309967), _1309969)), 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), _1309971), _1309973)), 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), _1309967), _1309971)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1309969), _1309973))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1309967), _1309973)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1309969), _1309971)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (29219 ^ _780461) ^ [_1310113, _1310115, _1310117, _1310119] : [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), _1310113), _1310115)), 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), _1310117), _1310119)), 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), _1310113), _1310119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1310117), _1310115))))], (29225 ^ _780461) ^ [_1310306, _1310308, _1310310, _1310312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1310306), _1310312)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1310310), _1310308))), -(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), _1310306), _1310308)), 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), _1310310), _1310312)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (29231 ^ _780461) ^ [_1310505, _1310507] : [-(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), _1310505), _1310507)), 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), _1310507), _1310505)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (29233 ^ _780461) ^ [] : [-(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))))))], (29235 ^ _780461) ^ [_1310587] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1310587) = 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), _1310587), 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))))))], (29237 ^ _780461) ^ [_1310631, _1310633, _1310635, _1310637] : [-(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), _1310631), _1310633)), 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), _1310635), _1310637)), 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), _1310631), _1310635)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1310633), _1310637))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (29239 ^ _780461) ^ [_1310732, _1310734] : [-(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), _1310732), _1310734)), 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), _1310732), _1310734))], (29241 ^ _780461) ^ [_1310805, _1310807, _1310809, _1310811] : [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), _1310805), _1310807)), 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), _1310809), _1310811)), 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), _1310805), _1310811)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1310809), _1310807))))], (29247 ^ _780461) ^ [_1310998, _1311000, _1311002, _1311004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1310998), _1311004)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1311002), _1311000))), -(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), _1310998), _1311000)), 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), _1311002), _1311004)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (29253 ^ _780461) ^ [_1311197, _1311199] : [c_Nat__Transfer_Onat__set(_1311197), c_Nat__Transfer_Onat__set(_1311199), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311197), _1311199) = 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), _1311197)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311199))))], (29265 ^ _780461) ^ [_1311364] : [-(_1311364 = 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), 29262 ^ [_1311364]), 29263 ^ [_1311364])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (29267 ^ _780461) ^ [_1311415, _1311417] : [c_Nat__Transfer_Onat__set(_1311415), c_Nat__Transfer_Onat__set(_1311417), 29274 ^ _780461 : [(29275 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311415), _1311417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311415)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311417))))], (29281 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311415)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311415), _1311417)))]]], (29287 ^ _780461) ^ [_1311718, _1311720] : [c_Nat__Transfer_Onat__set(_1311718), c_Nat__Transfer_Onat__set(_1311720), 29294 ^ _780461 : [(29295 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311718), _1311720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311718)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311720))))], (29301 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311718)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311720))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311718), _1311720)))]]], (29307 ^ _780461) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (29309 ^ _780461) ^ [_1312039, _1312041] : [c_Nat__Transfer_Onat__set(_1312039), c_Nat__Transfer_Onat__set(_1312041), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1312039), _1312041)))], (29329 ^ _780461) ^ [_1312343] : [29331 ^ _780461 : [(29332 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29330 ^ [_1312343]), _1312343)))], (29334 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29330 ^ [_1312343]))]], -(c_Nat__Transfer_Onat__set(_1312343))], (29319 ^ _780461) ^ [_1312186] : [c_Nat__Transfer_Onat__set(_1312186), 29322 ^ _780461 : [(29323 ^ _780461) ^ [_1312252] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1312252), _1312186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1312252)))]]], (29338 ^ _780461) ^ [_1312491] : [-(c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1312491)))], (29340 ^ _780461) ^ [_1312516, _1312518] : [c_Nat__Transfer_Onat__set(_1312516), c_Nat__Transfer_Onat__set(_1312518), 29347 ^ _780461 : [(29348 ^ _780461) ^ [] : [_1312516 = _1312518, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1312516) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1312518))], (29354 ^ _780461) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1312516) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1312518), -(_1312516 = _1312518)]]], (29360 ^ _780461) ^ [_1312789, _1312791] : [c_Nat__Transfer_Onat__set(_1312789), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 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[hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1313150)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1313152))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1313150), _1313152)))]]], (29406 ^ _780461) ^ [_1313453, _1313455, _1313457, _1313459, _1313461] : [hBOOL(hAPP(hAPP(c_member(_1313453), _1313455), hAPP(c_Relation_OImage(_1313457, _1313453, _1313459), _1313461))), 29410 ^ _780461 : [(29411 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1313457, _1313453)), hAPP(hAPP(c_Product__Type_OPair(_1313457, _1313453), 29409 ^ [_1313453, _1313455, _1313457, _1313459, _1313461]), _1313455)), _1313459)))], (29413 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313457), 29409 ^ [_1313453, _1313455, _1313457, _1313459, _1313461]), _1313461)))]]], (29415 ^ _780461) ^ [_1313677, _1313679, _1313681, _1313683, _1313685] : [c_Equiv__Relations_Oequiv(_1313677, _1313679, _1313681), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313677, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1313677, _1313677, _1313681), hAPP(hAPP(c_Set_Oinsert(_1313677), _1313683), c_Orderings_Obot__class_Obot(tc_fun(_1313677, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1313677, _1313677, _1313681), hAPP(hAPP(c_Set_Oinsert(_1313677), _1313685), c_Orderings_Obot__class_Obot(tc_fun(_1313677, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1313677), _1313683), _1313679)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1313677, _1313677)), hAPP(hAPP(c_Product__Type_OPair(_1313677, _1313677), _1313685), _1313683)), _1313681)))], (29429 ^ _780461) ^ [_1314030] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1314030)), -(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))), _1314030)), c_FunDef_Omax__weak)))], (29435 ^ _780461) ^ [_1314125] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1314125)), -(_1314125 = 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))), _1314125)), c_FunDef_Omax__strict)))], (29445 ^ _780461) ^ [_1314235, _1314237] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1314235, _1314235)), _1314237)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1314235), hAPP(c_Relation_OField(_1314235), _1314237))))], (29451 ^ _780461) ^ [_1314344, _1314346, _1314348, _1314350] : [c_Equiv__Relations_Oequiv(_1314344, _1314346, _1314348), hBOOL(hAPP(hAPP(c_member(_1314344), _1314350), _1314346)), -(hBOOL(hAPP(hAPP(c_member(_1314344), _1314350), hAPP(c_Relation_OImage(_1314344, _1314344, _1314348), hAPP(hAPP(c_Set_Oinsert(_1314344), _1314350), c_Orderings_Obot__class_Obot(tc_fun(_1314344, tc_HOL_Obool)))))))], (29461 ^ _780461) ^ [_1314551, _1314553, _1314555, _1314557, _1314559] : [c_Equiv__Relations_Oequiv(_1314551, _1314553, _1314555), hBOOL(hAPP(hAPP(c_member(tc_prod(_1314551, _1314551)), hAPP(hAPP(c_Product__Type_OPair(_1314551, _1314551), _1314557), _1314559)), _1314555)), -(hAPP(c_Relation_OImage(_1314551, _1314551, _1314555), hAPP(hAPP(c_Set_Oinsert(_1314551), _1314557), c_Orderings_Obot__class_Obot(tc_fun(_1314551, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1314551, _1314551, _1314555), hAPP(hAPP(c_Set_Oinsert(_1314551), _1314559), c_Orderings_Obot__class_Obot(tc_fun(_1314551, tc_HOL_Obool)))))], (29471 ^ _780461) ^ [_1314812, _1314814, _1314816, _1314818, _1314820] : [c_Equiv__Relations_Oequiv(_1314812, _1314814, _1314816), 29474 ^ _780461 : [(29475 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1314812, _1314812)), hAPP(hAPP(c_Product__Type_OPair(_1314812, _1314812), _1314818), _1314820)), _1314816)), 29478 ^ _780461 : [(29479 ^ _780461) ^ [] : [-(hAPP(c_Relation_OImage(_1314812, _1314812, _1314816), hAPP(hAPP(c_Set_Oinsert(_1314812), _1314818), c_Orderings_Obot__class_Obot(tc_fun(_1314812, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1314812, _1314812, _1314816), hAPP(hAPP(c_Set_Oinsert(_1314812), _1314820), c_Orderings_Obot__class_Obot(tc_fun(_1314812, tc_HOL_Obool)))))], (29481 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1314812), _1314818), _1314814)))], (29483 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1314812), _1314820), _1314814)))]]], (29485 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1314812, _1314812)), hAPP(hAPP(c_Product__Type_OPair(_1314812, _1314812), _1314818), _1314820)), _1314816))), hAPP(c_Relation_OImage(_1314812, _1314812, _1314816), hAPP(hAPP(c_Set_Oinsert(_1314812), _1314818), c_Orderings_Obot__class_Obot(tc_fun(_1314812, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1314812, _1314812, _1314816), hAPP(hAPP(c_Set_Oinsert(_1314812), _1314820), c_Orderings_Obot__class_Obot(tc_fun(_1314812, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1314812), _1314818), _1314814)), hBOOL(hAPP(hAPP(c_member(_1314812), _1314820), _1314814))]]], (29499 ^ _780461) ^ [_1315412, _1315414, _1315416, _1315418, _1315420] : [hAPP(c_Relation_OImage(_1315412, _1315412, _1315414), hAPP(hAPP(c_Set_Oinsert(_1315412), _1315416), c_Orderings_Obot__class_Obot(tc_fun(_1315412, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1315412, _1315412, _1315414), hAPP(hAPP(c_Set_Oinsert(_1315412), _1315418), c_Orderings_Obot__class_Obot(tc_fun(_1315412, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1315412, _1315420, _1315414), hBOOL(hAPP(hAPP(c_member(_1315412), _1315418), _1315420)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1315412, _1315412)), hAPP(hAPP(c_Product__Type_OPair(_1315412, _1315412), _1315416), _1315418)), _1315414)))], (29513 ^ _780461) ^ [_1315745, _1315747, _1315749, _1315751, _1315753] : [c_Equiv__Relations_Oequiv(_1315745, _1315747, _1315749), hBOOL(hAPP(hAPP(c_member(_1315745), _1315751), _1315747)), hBOOL(hAPP(hAPP(c_member(_1315745), _1315753), _1315747)), 29524 ^ _780461 : [(29525 ^ _780461) ^ [] : [hAPP(c_Relation_OImage(_1315745, _1315745, _1315749), hAPP(hAPP(c_Set_Oinsert(_1315745), _1315751), c_Orderings_Obot__class_Obot(tc_fun(_1315745, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1315745, _1315745, _1315749), hAPP(hAPP(c_Set_Oinsert(_1315745), _1315753), c_Orderings_Obot__class_Obot(tc_fun(_1315745, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1315745, _1315745)), hAPP(hAPP(c_Product__Type_OPair(_1315745, _1315745), _1315751), _1315753)), _1315749)))], (29531 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1315745, _1315745)), hAPP(hAPP(c_Product__Type_OPair(_1315745, _1315745), _1315751), _1315753)), _1315749)), -(hAPP(c_Relation_OImage(_1315745, _1315745, _1315749), hAPP(hAPP(c_Set_Oinsert(_1315745), _1315751), c_Orderings_Obot__class_Obot(tc_fun(_1315745, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1315745, _1315745, _1315749), hAPP(hAPP(c_Set_Oinsert(_1315745), _1315753), c_Orderings_Obot__class_Obot(tc_fun(_1315745, tc_HOL_Obool)))))]]], (29537 ^ _780461) ^ [_1316293, _1316295, _1316297, _1316299, _1316301] : [c_Equiv__Relations_Oequiv(_1316293, _1316295, _1316297), hBOOL(hAPP(hAPP(c_member(tc_prod(_1316293, _1316293)), hAPP(hAPP(c_Product__Type_OPair(_1316293, _1316293), _1316299), _1316301)), _1316297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316293, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1316293, _1316293, _1316297), hAPP(hAPP(c_Set_Oinsert(_1316293), _1316299), c_Orderings_Obot__class_Obot(tc_fun(_1316293, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1316293, _1316293, _1316297), hAPP(hAPP(c_Set_Oinsert(_1316293), _1316301), c_Orderings_Obot__class_Obot(tc_fun(_1316293, tc_HOL_Obool)))))))], (29547 ^ _780461) ^ [_1316574, _1316576, _1316578] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1316574), _1316576)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1316574), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316574, tc_HOL_Obool)), _1316576), _1316578))))], (29553 ^ _780461) ^ [_1316691, _1316693, _1316695, _1316697] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1316691), _1316693)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1316695), hAPP(c_Set_Oimage(_1316691, _1316695, _1316697), _1316693))))], (29559 ^ _780461) ^ [_1316802, _1316804, _1316806] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1316802), _1316804)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1316802), hAPP(hAPP(c_Set_Oinsert(_1316802), _1316806), _1316804))))], (29565 ^ _780461) ^ [_1316913] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1316913), c_Orderings_Obot__class_Obot(tc_fun(_1316913, tc_HOL_Obool)))))], (29567 ^ _780461) ^ [_1316957] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1316957)), -(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)), _1316957))))], (29573 ^ _780461) ^ [_1317042] : [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)), _1317042))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1317042)))], (29579 ^ _780461) ^ [_1317133] : [c_Nat__Transfer_Onat__set(_1317133), 29582 ^ _780461 : [(29583 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1317133)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1317133))))], (29589 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1317133))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1317133)))]]], (29595 ^ _780461) ^ [_1317353, _1317355] : [class_Finite__Set_Ofinite(_1317353), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317353), _1317355)))], (29601 ^ _780461) ^ [_1317436, _1317438] : [class_Finite__Set_Ofinite(_1317436), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317436), _1317438)))], (29607 ^ _780461) ^ [_1317519] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317519), c_Orderings_Obot__class_Obot(tc_fun(_1317519, tc_HOL_Obool)))))], (29609 ^ _780461) ^ [_1317569, _1317571, _1317573] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317569), hAPP(hAPP(c_Set_Oinsert(_1317569), _1317571), _1317573))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317569), _1317573)))], (29615 ^ _780461) ^ [_1317676, _1317678, _1317680] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317676), _1317680)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317676), hAPP(hAPP(c_Set_Oinsert(_1317676), _1317678), _1317680))))], (29621 ^ _780461) ^ [_1317789, _1317791, _1317793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317789), _1317791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317789, tc_HOL_Obool)), _1317793), _1317791)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317789), _1317793)))], (29631 ^ _780461) ^ [_1317958, _1317960, _1317962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317958, tc_HOL_Obool)), _1317960), _1317962)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317958), _1317962)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317958), _1317960)))], (29641 ^ _780461) ^ [_1318145, _1318147, _1318149] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318145), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318145, tc_HOL_Obool)), _1318147), _1318149))), 29644 ^ _780461 : [(29645 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1318145), _1318147)))], (29647 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1318145), _1318149)))]]], (29649 ^ _780461) ^ [_1318292, _1318294, _1318296] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1318292), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318292, tc_HOL_Obool)), _1318294), _1318296)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318292), _1318294)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318292), _1318296))], (29659 ^ _780461) ^ [_1318473, _1318475, _1318477] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318473), _1318475)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318473), _1318477)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1318473), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318473, tc_HOL_Obool)), _1318475), _1318477))))], (29669 ^ _780461) ^ [_1318652, _1318654, _1318656] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318652), _1318654)), 29672 ^ _780461 : [(29673 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318652), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318652, tc_HOL_Obool)), _1318656), _1318654))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1318652), _1318656)))], (29679 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318652), _1318656)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1318652), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318652, tc_HOL_Obool)), _1318656), _1318654))))]]], (29685 ^ _780461) ^ [_1318930, _1318932, _1318934, _1318936, _1318938] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318930), _1318932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318934, tc_HOL_Obool)), _1318936), hAPP(c_Set_Oimage(_1318930, _1318934, _1318938), _1318932))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1318934), _1318936)))], (29695 ^ _780461) ^ [_1319142, _1319144, _1319146, _1319148] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1319142), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319142, tc_HOL_Obool)), _1319144), hAPP(hAPP(c_Set_Oinsert(_1319142), _1319146), _1319148)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1319142), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319142, tc_HOL_Obool)), _1319144), _1319148))))], (29701 ^ _780461) ^ [_1319295, _1319297, _1319299, _1319301] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1319295), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319295, tc_HOL_Obool)), _1319297), _1319301))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1319295), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1319295, tc_HOL_Obool)), _1319297), hAPP(hAPP(c_Set_Oinsert(_1319295), _1319299), _1319301)))))], (29707 ^ _780461) ^ [_1319472, _1319474, _1319476] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1319472, tc_HOL_Obool), tc_fun(_1319472, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1319472, tc_HOL_Obool), tc_fun(_1319472, tc_HOL_Obool)), _1319474), _1319476)), c_Wellfounded_Ofinite__psubset(_1319472))), 29710 ^ _780461 : [(29711 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1319472, tc_HOL_Obool)), _1319474), _1319476)))], (29713 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1319472), _1319476)))]]], (29715 ^ _780461) ^ [_1319667, _1319669, _1319671] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1319667, tc_HOL_Obool), tc_fun(_1319667, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1319667, tc_HOL_Obool), tc_fun(_1319667, tc_HOL_Obool)), _1319669), _1319671)), c_Wellfounded_Ofinite__psubset(_1319667)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1319667, tc_HOL_Obool)), _1319669), _1319671)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319667), _1319671))], (29725 ^ _780461) ^ [_1319896, _1319898, _1319900, _1319902, _1319904, _1319906, _1319908, _1319910, _1319912] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1319896), _1319898)), 29731 ^ _780461 : [(29732 ^ _780461) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1319900, _1319902, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1319900)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1319900), hAPP(_1319904, 29730 ^ [_1319896, _1319898, _1319900, _1319902, _1319904, _1319906, _1319908, _1319910, _1319912])), hAPP(_1319906, 29730 ^ [_1319896, _1319898, _1319900, _1319902, _1319904, _1319906, _1319908, _1319910, _1319912])), hAPP(_1319908, 29730 ^ [_1319896, _1319898, _1319900, _1319902, _1319904, _1319906, _1319908, _1319910, _1319912]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1319900), tc_HOL_Obool)))))], (29734 ^ _780461) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1319900, _1319902, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1319900)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1319900), hAPP(_1319910, 29730 ^ [_1319896, _1319898, _1319900, _1319902, _1319904, _1319906, _1319908, _1319910, _1319912])), hAPP(_1319906, 29730 ^ [_1319896, _1319898, _1319900, _1319902, _1319904, _1319906, _1319908, _1319910, _1319912])), hAPP(_1319912, 29730 ^ [_1319896, _1319898, _1319900, _1319902, _1319904, _1319906, _1319908, _1319910, _1319912]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1319900), tc_HOL_Obool))))]], c_Hoare__Mirabelle_Ohoare__derivs(_1319900, _1319902, hAPP(c_Set_Oimage(_1319896, tc_Hoare__Mirabelle_Otriple(_1319900), hAPP(hAPP(c_COMBS(_1319896, tc_fun(_1319900, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1319900)), hAPP(hAPP(c_COMBS(_1319896, tc_Com_Ocom, tc_fun(tc_fun(_1319900, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1319900))), hAPP(hAPP(c_COMBB(tc_fun(_1319900, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1319900, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1319900))), _1319896), c_Hoare__Mirabelle_Otriple_Otriple(_1319900)), _1319904)), _1319906)), _1319908)), _1319898)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1319900, _1319902, hAPP(c_Set_Oimage(_1319896, tc_Hoare__Mirabelle_Otriple(_1319900), hAPP(hAPP(c_COMBS(_1319896, tc_fun(_1319900, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1319900)), hAPP(hAPP(c_COMBS(_1319896, tc_Com_Ocom, tc_fun(tc_fun(_1319900, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1319900))), hAPP(hAPP(c_COMBB(tc_fun(_1319900, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1319900, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1319900))), _1319896), c_Hoare__Mirabelle_Otriple_Otriple(_1319900)), _1319910)), _1319906)), _1319912)), _1319898)))], (29742 ^ _780461) ^ [_1320785, _1320787, _1320789, _1320791, _1320793] : [c_Finite__Set_Ofolding__one(_1320785, _1320787, _1320789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320785), _1320791)), hBOOL(hAPP(hAPP(c_member(_1320785), _1320793), _1320791)), 29753 ^ _780461 : [(29754 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320785, tc_HOL_Obool)), _1320791), hAPP(hAPP(c_Set_Oinsert(_1320785), _1320793), c_Orderings_Obot__class_Obot(tc_fun(_1320785, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1320785, tc_HOL_Obool)), -(hAPP(_1320789, _1320791) = _1320793)], (29760 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320785, tc_HOL_Obool)), _1320791), hAPP(hAPP(c_Set_Oinsert(_1320785), _1320793), c_Orderings_Obot__class_Obot(tc_fun(_1320785, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1320785, tc_HOL_Obool))), -(hAPP(_1320789, _1320791) = hAPP(hAPP(_1320787, _1320793), hAPP(_1320789, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1320785, tc_HOL_Obool)), _1320791), hAPP(hAPP(c_Set_Oinsert(_1320785), _1320793), c_Orderings_Obot__class_Obot(tc_fun(_1320785, tc_HOL_Obool)))))))]]], (29766 ^ _780461) ^ [_1321307, _1321309, _1321311, _1321313, _1321315, _1321317, _1321319, _1321321] : [c_Finite__Set_Ofolding__image__simple(_1321307, _1321309, _1321311, _1321313, _1321315, _1321317), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321309), _1321319)), hBOOL(hAPP(hAPP(c_member(_1321309), _1321321), _1321319)), -(hAPP(_1321317, _1321319) = hAPP(hAPP(_1321311, hAPP(_1321315, _1321321)), hAPP(_1321317, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321309, tc_HOL_Obool)), _1321319), hAPP(hAPP(c_Set_Oinsert(_1321309), _1321321), c_Orderings_Obot__class_Obot(tc_fun(_1321309, tc_HOL_Obool)))))))], (29780 ^ _780461) ^ [_1321632, _1321634, _1321636, _1321638, _1321640, _1321642] : [c_Finite__Set_Ofolding__image__simple(_1321632, _1321634, _1321636, _1321638, _1321640, _1321642), -(hAPP(_1321642, c_Orderings_Obot__class_Obot(tc_fun(_1321634, tc_HOL_Obool))) = _1321638)], (29786 ^ _780461) ^ [_1321741, _1321743, _1321745, _1321747] : [c_Finite__Set_Ofolding__one(_1321741, _1321743, _1321745), -(hAPP(_1321745, hAPP(hAPP(c_Set_Oinsert(_1321741), _1321747), c_Orderings_Obot__class_Obot(tc_fun(_1321741, tc_HOL_Obool)))) = _1321747)], (29792 ^ _780461) ^ [_1321856, _1321858, _1321860, _1321862, _1321864, _1321866, _1321868, _1321870] : [c_Finite__Set_Ofolding__image__simple(_1321856, _1321858, _1321860, _1321862, _1321864, _1321866), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321858), _1321868)), -(hBOOL(hAPP(hAPP(c_member(_1321858), _1321870), _1321868))), -(hAPP(_1321866, hAPP(hAPP(c_Set_Oinsert(_1321858), _1321870), _1321868)) = hAPP(hAPP(_1321860, hAPP(_1321864, _1321870)), hAPP(_1321866, _1321868)))], (29806 ^ _780461) ^ [_1322100, _1322102, _1322104, _1322106, _1322108] : [c_Finite__Set_Ofolding__one(_1322100, _1322102, _1322104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322100), _1322106)), -(hBOOL(hAPP(hAPP(c_member(_1322100), _1322108), _1322106))), -(_1322106 = c_Orderings_Obot__class_Obot(tc_fun(_1322100, tc_HOL_Obool))), -(hAPP(_1322104, hAPP(hAPP(c_Set_Oinsert(_1322100), _1322108), _1322106)) = hAPP(hAPP(_1322102, _1322108), hAPP(_1322104, _1322106)))], (29824 ^ _780461) ^ [_1322345, _1322347, _1322349, _1322351, _1322353] : [c_Finite__Set_Ofolding__one(_1322345, _1322347, _1322349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322345), _1322351)), 29831 ^ _780461 : [(29832 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322345, tc_HOL_Obool)), _1322351), hAPP(hAPP(c_Set_Oinsert(_1322345), _1322353), c_Orderings_Obot__class_Obot(tc_fun(_1322345, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322345, tc_HOL_Obool)), -(hAPP(_1322349, hAPP(hAPP(c_Set_Oinsert(_1322345), _1322353), _1322351)) = _1322353)], (29838 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322345, tc_HOL_Obool)), _1322351), hAPP(hAPP(c_Set_Oinsert(_1322345), _1322353), c_Orderings_Obot__class_Obot(tc_fun(_1322345, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322345, tc_HOL_Obool))), -(hAPP(_1322349, hAPP(hAPP(c_Set_Oinsert(_1322345), _1322353), _1322351)) = hAPP(hAPP(_1322347, _1322353), hAPP(_1322349, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322345, tc_HOL_Obool)), _1322351), hAPP(hAPP(c_Set_Oinsert(_1322345), _1322353), c_Orderings_Obot__class_Obot(tc_fun(_1322345, tc_HOL_Obool)))))))]]], (29844 ^ _780461) ^ [_1322827, _1322829, _1322831, _1322833, _1322835, _1322837, _1322839, _1322841] : [c_Finite__Set_Ofolding__image__simple(_1322827, _1322829, _1322831, _1322833, _1322835, _1322837), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322829), _1322839)), -(hAPP(_1322837, hAPP(hAPP(c_Set_Oinsert(_1322829), _1322841), _1322839)) = hAPP(hAPP(_1322831, hAPP(_1322835, _1322841)), hAPP(_1322837, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322829, tc_HOL_Obool)), _1322839), hAPP(hAPP(c_Set_Oinsert(_1322829), _1322841), c_Orderings_Obot__class_Obot(tc_fun(_1322829, tc_HOL_Obool)))))))], (29865 ^ _780461) ^ [_1323289] : [29867 ^ _780461 : [(29868 ^ _780461) ^ [_1323365] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29866 ^ [_1323289, _1323365]), _1323289)))], (29870 ^ _780461) ^ [_1323399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 29866 ^ [_1323289, _1323399]), _1323399))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1323289)))], (29854 ^ _780461) ^ [_1323102] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1323102)), 29858 ^ _780461 : [(29859 ^ _780461) ^ [_1323182] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1323182), _1323102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1323182), 29857 ^ [_1323102])))]]], (29885 ^ _780461) ^ [_1323667] : [29887 ^ _780461 : [(29888 ^ _780461) ^ [_1323743] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29886 ^ [_1323667, _1323743]), _1323667)))], (29890 ^ _780461) ^ [_1323777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29886 ^ [_1323667, _1323777]), _1323777))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1323667)))], (29874 ^ _780461) ^ [_1323480] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1323480)), 29878 ^ _780461 : [(29879 ^ _780461) ^ [_1323560] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1323560), _1323480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1323560), 29877 ^ [_1323480])))]]], (29894 ^ _780461) ^ [_1323846, _1323848, _1323850, _1323852, _1323854] : [c_Equiv__Relations_Oequiv(_1323846, _1323848, _1323850), hBOOL(hAPP(hAPP(c_member(_1323846), _1323852), _1323848)), hBOOL(hAPP(hAPP(c_member(_1323846), _1323854), _1323848)), 29905 ^ _780461 : [(29906 ^ _780461) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1323846), hAPP(hAPP(c_Set_Oinsert(_1323846), _1323852), c_Orderings_Obot__class_Obot(tc_fun(_1323846, tc_HOL_Obool)))), _1323850) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1323846), hAPP(hAPP(c_Set_Oinsert(_1323846), _1323854), c_Orderings_Obot__class_Obot(tc_fun(_1323846, tc_HOL_Obool)))), _1323850), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1323846, _1323846)), hAPP(hAPP(c_Product__Type_OPair(_1323846, _1323846), _1323852), _1323854)), _1323850)))], (29912 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1323846, _1323846)), hAPP(hAPP(c_Product__Type_OPair(_1323846, _1323846), _1323852), _1323854)), _1323850)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1323846), hAPP(hAPP(c_Set_Oinsert(_1323846), _1323852), c_Orderings_Obot__class_Obot(tc_fun(_1323846, tc_HOL_Obool)))), _1323850) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1323846), hAPP(hAPP(c_Set_Oinsert(_1323846), _1323854), c_Orderings_Obot__class_Obot(tc_fun(_1323846, tc_HOL_Obool)))), _1323850))]]], (29918 ^ _780461) ^ [_1324400, _1324402, _1324404, _1324406, _1324408, _1324410] : [c_Equiv__Relations_Oequiv(_1324400, _1324402, _1324404), hBOOL(hAPP(hAPP(c_member(_1324400), _1324406), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324400, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1324400, _1324400, _1324404), hAPP(hAPP(c_Set_Oinsert(_1324400), _1324408), c_Orderings_Obot__class_Obot(tc_fun(_1324400, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1324400, _1324400, _1324404), hAPP(hAPP(c_Set_Oinsert(_1324400), _1324410), c_Orderings_Obot__class_Obot(tc_fun(_1324400, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1324400, _1324400)), hAPP(hAPP(c_Product__Type_OPair(_1324400, _1324400), _1324408), _1324410)), _1324404)))], (29928 ^ _780461) ^ [_1324701, _1324703, _1324705, _1324707] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324701, tc_HOL_Obool)), _1324703), _1324705), _1324707)), 29931 ^ _780461 : [(29932 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1324703, _1324707)))], (29934 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1324705, _1324707)))]]], (29936 ^ _780461) ^ [_1324846, _1324848, _1324850, _1324852] : [hBOOL(hAPP(_1324846, _1324848)), hBOOL(hAPP(_1324850, _1324848)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324852, tc_HOL_Obool)), _1324846), _1324850), _1324848)))], (29946 ^ _780461) ^ [_1325017, _1325019, _1325021, _1325023] : [hBOOL(hAPP(hAPP(c_member(_1325017), _1325019), _1325021)), hBOOL(hAPP(hAPP(c_member(_1325017), _1325019), _1325023)), -(hBOOL(hAPP(hAPP(c_member(_1325017), _1325019), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325017, tc_HOL_Obool)), _1325021), _1325023))))], (29956 ^ _780461) ^ [_1325218, _1325220, _1325222, _1325224] : [hBOOL(hAPP(hAPP(c_member(_1325218), _1325220), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325218, tc_HOL_Obool)), _1325222), _1325224))), 29959 ^ _780461 : [(29960 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325218), _1325220), _1325222)))], (29962 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325218), _1325220), _1325224)))]]], (29964 ^ _780461) ^ [_1325393, _1325395, _1325397] : [29965 ^ _780461 : [(29966 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1325393), _1325395))], (29968 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1325393), _1325397))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1325393), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325393, tc_HOL_Obool)), _1325395), _1325397))))], (29972 ^ _780461) ^ [_1325556, _1325558, _1325560, _1325562, _1325564] : [c_Equiv__Relations_Oequiv(_1325556, _1325558, _1325560), hBOOL(hAPP(hAPP(c_member(tc_fun(_1325556, tc_HOL_Obool)), _1325562), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1325556), _1325558), _1325560))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1325556, tc_HOL_Obool)), _1325564), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1325556), _1325558), _1325560))), -(_1325562 = _1325564), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325556, tc_HOL_Obool)), _1325562), _1325564) = c_Orderings_Obot__class_Obot(tc_fun(_1325556, tc_HOL_Obool)))], (29990 ^ _780461) ^ [_1325874, _1325876] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1325874), c_Orderings_Obot__class_Obot(tc_fun(_1325874, tc_HOL_Obool))), _1325876) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1325874, tc_HOL_Obool), tc_HOL_Obool)))], (29992 ^ _780461) ^ [_1325938, _1325940, _1325942] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1325938, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1325938), _1325940), _1325942), -(_1325940 = c_Orderings_Obot__class_Obot(tc_fun(_1325938, tc_HOL_Obool)))], (29998 ^ _780461) ^ [_1326055, _1326057, _1326059] : [_1326057 = c_Orderings_Obot__class_Obot(tc_fun(_1326055, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1326055, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1326055), _1326057), _1326059))], (30004 ^ _780461) ^ [_1326196, _1326198, _1326200] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1326196), _1326198), _1326200) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1326196, tc_HOL_Obool), tc_HOL_Obool)), -(_1326198 = c_Orderings_Obot__class_Obot(tc_fun(_1326196, tc_HOL_Obool)))], (30010 ^ _780461) ^ [_1326313, _1326315, _1326317] : [_1326315 = c_Orderings_Obot__class_Obot(tc_fun(_1326313, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1326313), _1326315), _1326317) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1326313, tc_HOL_Obool), tc_HOL_Obool)))], (30016 ^ _780461) ^ [_1326457, _1326459, _1326461, _1326463] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326457, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1326457, tc_fun(_1326457, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326457)), _1326459)), hAPP(hAPP(c_COMBC(_1326457, tc_fun(_1326457, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326457)), _1326461)), _1326463)), -(hBOOL(hAPP(hAPP(c_member(_1326457), _1326463), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326457, tc_HOL_Obool)), _1326459), _1326461))))], (30022 ^ _780461) ^ [_1326656, _1326658, _1326660, _1326662] : [hBOOL(hAPP(hAPP(c_member(_1326656), _1326662), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326656, tc_HOL_Obool)), _1326658), _1326660))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326656, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1326656, tc_fun(_1326656, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326656)), _1326658)), hAPP(hAPP(c_COMBC(_1326656, tc_fun(_1326656, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326656)), _1326660)), _1326662)))], (30028 ^ _780461) ^ [_1326861, _1326863, _1326865, _1326867] : [class_Lattices_Osemilattice__inf(_1326861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326861), _1326863), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1326861), _1326865), _1326867))), 30035 ^ _780461 : [(30036 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326861), _1326863), _1326865)))], (30038 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326861), _1326863), _1326867)))]]], (30040 ^ _780461) ^ [_1327084, _1327086, _1327088, _1327090, _1327092] : [class_Lattices_Osemilattice__inf(_1327084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327084), _1327086), _1327088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327084), _1327090), _1327092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327084), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1327084), _1327086), _1327090)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1327084), _1327088), _1327092))))], (30054 ^ _780461) ^ [_1327355, _1327357, _1327359, _1327361] : [class_Lattices_Osemilattice__inf(_1327355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327355), _1327357), _1327359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327355), _1327357), _1327361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327355), _1327357), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1327355), _1327359), _1327361))))], (30068 ^ _780461) ^ [_1327604, _1327606, _1327608, _1327610] : [class_Lattices_Osemilattice__inf(_1327604), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327604), _1327606), _1327608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327604), _1327606), _1327610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327604), _1327606), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1327604), _1327608), _1327610))))], (30082 ^ _780461) ^ [_1327853, _1327855, _1327857] : [class_Lattices_Osemilattice__inf(_1327853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327853), _1327855), _1327857)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1327853), _1327857), _1327855) = _1327855)], (30092 ^ _780461) ^ [_1328014, _1328016, _1328018] : [class_Lattices_Osemilattice__inf(_1328014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328014), _1328016), _1328018)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1328014), _1328016), _1328018) = _1328016)], (30102 ^ _780461) ^ [_1328175, _1328177, _1328179, _1328181] : [class_Lattices_Osemilattice__inf(_1328175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328175), _1328177), _1328179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328175), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1328175), _1328181), _1328177)), _1328179)))], (30112 ^ _780461) ^ [_1328354, _1328356, _1328358, _1328360] : [class_Lattices_Osemilattice__inf(_1328354), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328354), _1328356), _1328358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328354), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1328354), _1328356), _1328360)), _1328358)))], (30122 ^ _780461) ^ [_1328533, _1328535, _1328537, _1328539] : [class_Lattices_Osemilattice__inf(_1328533), 30125 ^ _780461 : [(30126 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328533), _1328535), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1328533), _1328537), _1328539))), 30129 ^ _780461 : [(30130 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328533), _1328535), _1328537)))], (30132 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328533), _1328535), _1328539)))]]], (30134 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328533), _1328535), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1328533), _1328537), _1328539)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328533), _1328535), _1328537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328533), _1328535), _1328539))]]], (30144 ^ _780461) ^ [_1328913, _1328915, _1328917] : [class_Lattices_Osemilattice__inf(_1328913), 30147 ^ _780461 : [(30148 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328913), _1328915), _1328917)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1328913), _1328915), _1328917) = _1328915)], (30154 ^ _780461) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1328913), _1328915), _1328917) = _1328915, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328913), _1328915), _1328917)))]]], (30160 ^ _780461) ^ [_1329169, _1329171, _1329173] : [class_Lattices_Osemilattice__inf(_1329169), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329169), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1329169), _1329171), _1329173)), _1329173)))], (30166 ^ _780461) ^ [_1329276, _1329278, _1329280] : [class_Lattices_Olattice(_1329276), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329276), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1329276), _1329278), _1329280)), _1329280)))], (30172 ^ _780461) ^ [_1329383, _1329385, _1329387] : [class_Lattices_Osemilattice__inf(_1329383), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329383), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1329383), _1329385), _1329387)), _1329385)))], (30178 ^ _780461) ^ [_1329490, _1329492, _1329494] : [class_Lattices_Olattice(_1329490), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1329490), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1329490), _1329492), _1329494)), _1329492)))], (30184 ^ _780461) ^ [_1329597, _1329599, _1329601, _1329603, _1329605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329597, tc_HOL_Obool)), _1329599), _1329601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329597, tc_HOL_Obool)), _1329603), _1329605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329597, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329597, tc_HOL_Obool)), _1329599), _1329603)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329597, tc_HOL_Obool)), _1329601), _1329605))))], (30194 ^ _780461) ^ [_1329842, _1329844, _1329846, _1329848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329842, tc_HOL_Obool)), _1329844), _1329846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329842, tc_HOL_Obool)), _1329844), _1329848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1329842, tc_HOL_Obool)), _1329844), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329842, tc_HOL_Obool)), _1329846), _1329848))))], (30204 ^ _780461) ^ [_1330061, _1330063, _1330065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330061, tc_HOL_Obool)), _1330063), _1330065)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330061, tc_HOL_Obool)), _1330065), _1330063) = _1330063)], (30210 ^ _780461) ^ [_1330182, _1330184, _1330186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330182, tc_HOL_Obool)), _1330184), _1330186)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330182, tc_HOL_Obool)), _1330184), _1330186) = _1330184)], (30216 ^ _780461) ^ [_1330303, _1330305, _1330307] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330303, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330303, tc_HOL_Obool)), _1330305), _1330307)), _1330307)))], (30218 ^ _780461) ^ [_1330351, _1330353, _1330355] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1330351, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330351, tc_HOL_Obool)), _1330353), _1330355)), _1330353)))], (30220 ^ _780461) ^ [_1330399, _1330401, _1330403, _1330405] : [class_Lattices_Osemilattice__inf(_1330399), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330399), _1330401), _1330403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330399), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1330399), _1330401), _1330405)), _1330403)))], (30230 ^ _780461) ^ [_1330578, _1330580, _1330582, _1330584] : [class_Lattices_Osemilattice__inf(_1330578), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330578), _1330580), _1330582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1330578), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1330578), _1330584), _1330580)), _1330582)))], (30240 ^ _780461) ^ [_1330757, _1330759] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330757, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1330757, tc_HOL_Obool))), _1330759) = c_Orderings_Obot__class_Obot(tc_fun(_1330757, tc_HOL_Obool)))], (30242 ^ _780461) ^ [_1330803, _1330805] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330803, tc_HOL_Obool)), _1330805), c_Orderings_Obot__class_Obot(tc_fun(_1330803, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1330803, tc_HOL_Obool)))], (30258 ^ _780461) ^ [_1331181, _1331183, _1331185] : [30260 ^ _780461 : [(30261 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331181), 30259 ^ [_1331181, _1331183, _1331185]), _1331183)))], (30264 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331181), 30262 ^ [_1331181, _1331183, _1331185]), _1331185)))], (30266 ^ _780461) ^ [] : [-(30259 ^ [_1331181, _1331183, _1331185] = 30262 ^ [_1331181, _1331183, _1331185])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331181, tc_HOL_Obool)), _1331183), _1331185) = c_Orderings_Obot__class_Obot(tc_fun(_1331181, tc_HOL_Obool)))], (30244 ^ _780461) ^ [_1330867, _1330869, _1330871] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330867, tc_HOL_Obool)), _1330869), _1330871) = c_Orderings_Obot__class_Obot(tc_fun(_1330867, tc_HOL_Obool)), 30247 ^ _780461 : [(30248 ^ _780461) ^ [_1330991] : [hBOOL(hAPP(hAPP(c_member(_1330867), _1330991), _1330869)), 30251 ^ _780461 : [(30252 ^ _780461) ^ [_1331081] : [hBOOL(hAPP(hAPP(c_member(_1330867), _1331081), _1330871)), _1330991 = _1331081]]]]], (30270 ^ _780461) ^ [_1331342, _1331344] : [class_Lattices_Obounded__lattice__bot(_1331342), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1331342), c_Orderings_Obot__class_Obot(_1331342)), _1331344) = c_Orderings_Obot__class_Obot(_1331342))], (30276 ^ _780461) ^ [_1331441, _1331443] : [class_Lattices_Obounded__lattice__bot(_1331441), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1331441), _1331443), c_Orderings_Obot__class_Obot(_1331441)) = c_Orderings_Obot__class_Obot(_1331441))], (30282 ^ _780461) ^ [_1331540, _1331542, _1331544, _1331546] : [hBOOL(hAPP(hAPP(c_member(_1331540), _1331542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331540, tc_HOL_Obool)), _1331544), _1331546))), -(hBOOL(hAPP(hAPP(c_member(_1331540), _1331542), _1331546)))], (30288 ^ _780461) ^ [_1331671, _1331673, _1331675, _1331677] : [hBOOL(hAPP(hAPP(c_member(_1331671), _1331673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331671, tc_HOL_Obool)), _1331675), _1331677))), -(hBOOL(hAPP(hAPP(c_member(_1331671), _1331673), _1331675)))], (30294 ^ _780461) ^ [_1331823, _1331825, _1331827, _1331829] : [hBOOL(hAPP(hAPP(c_member(_1331823), _1331825), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331823, tc_HOL_Obool)), _1331827), _1331829))), 30297 ^ _780461 : [(30298 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331823), _1331825), _1331827)))], (30300 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331823), _1331825), _1331829)))]]], (30302 ^ _780461) ^ [_1331990, _1331992, _1331994, _1331996] : [-(hBOOL(hAPP(hAPP(c_member(_1331990), _1331992), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331990, tc_HOL_Obool)), _1331994), _1331996)))), hBOOL(hAPP(hAPP(c_member(_1331990), _1331992), _1331994)), hBOOL(hAPP(hAPP(c_member(_1331990), _1331992), _1331996))], (30312 ^ _780461) ^ [_1332193, _1332195, _1332197, _1332199] : [class_Lattices_Odistrib__lattice(_1332193), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332193), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332193), _1332195), _1332197)), _1332199) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332193), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332193), _1332195), _1332199)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332193), _1332197), _1332199)))], (30318 ^ _780461) ^ [_1332352, _1332354, _1332356, _1332358] : [class_Lattices_Odistrib__lattice(_1332352), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332352), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332352), _1332354), _1332356)), _1332358) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332352), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332352), _1332354), _1332358)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332352), _1332356), _1332358)))], (30324 ^ _780461) ^ [_1332511, _1332513, _1332515, _1332517] : [class_Lattices_Odistrib__lattice(_1332511), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332511), _1332513), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332511), _1332515), _1332517)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332511), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332511), _1332513), _1332515)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332511), _1332513), _1332517)))], (30330 ^ _780461) ^ [_1332670, _1332672, _1332674, _1332676] : [class_Lattices_Odistrib__lattice(_1332670), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332670), _1332672), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332670), _1332674), _1332676)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332670), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332670), _1332672), _1332674)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332670), _1332672), _1332676)))], (30336 ^ _780461) ^ [_1332829, _1332831, _1332833] : [class_Lattices_Olattice(_1332829), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332829), _1332831), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332829), _1332831), _1332833)) = _1332831)], (30342 ^ _780461) ^ [_1332938, _1332940, _1332942] : [class_Lattices_Olattice(_1332938), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332938), _1332940), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1332938), _1332940), _1332942)) = _1332940)], (30348 ^ _780461) ^ [_1333047, _1333049, _1333051, _1333053] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333047, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333047, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333047, tc_HOL_Obool)), _1333049), _1333051)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333047, tc_HOL_Obool)), _1333051), _1333053))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333047, tc_HOL_Obool)), _1333053), _1333049)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333047, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333047, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333047, tc_HOL_Obool)), _1333049), _1333051)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333047, tc_HOL_Obool)), _1333051), _1333053))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333047, tc_HOL_Obool)), _1333053), _1333049)))], (30350 ^ _780461) ^ [_1333186, _1333188, _1333190, _1333192] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333186, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333186, tc_HOL_Obool)), _1333188), _1333190)), _1333192) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333186, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333186, tc_HOL_Obool)), _1333188), _1333192)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333186, tc_HOL_Obool)), _1333190), _1333192)))], (30352 ^ _780461) ^ [_1333270, _1333272, _1333274, _1333276] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333270, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333270, tc_HOL_Obool)), _1333272), _1333274)), _1333276) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333270, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333270, tc_HOL_Obool)), _1333272), _1333276)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333270, tc_HOL_Obool)), _1333274), _1333276)))], (30354 ^ _780461) ^ [_1333354, _1333356, _1333358, _1333360] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333354, tc_HOL_Obool)), _1333356), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333354, tc_HOL_Obool)), _1333358), _1333360)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333354, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333354, tc_HOL_Obool)), _1333356), _1333358)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333354, tc_HOL_Obool)), _1333356), _1333360)))], (30356 ^ _780461) ^ [_1333438, _1333440, _1333442, _1333444] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333438, tc_HOL_Obool)), _1333440), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333438, tc_HOL_Obool)), _1333442), _1333444)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333438, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333438, tc_HOL_Obool)), _1333440), _1333442)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333438, tc_HOL_Obool)), _1333440), _1333444)))], (30358 ^ _780461) ^ [_1333522, _1333524] : [class_Lattices_Olattice(_1333522), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1333522), _1333524), _1333524) = _1333524)], (30364 ^ _780461) ^ [_1333613, _1333615, _1333617, _1333619] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333613, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333613, tc_HOL_Obool)), _1333615), _1333617)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333613, tc_HOL_Obool)), _1333619), _1333617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333613, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333613, tc_HOL_Obool)), _1333615), _1333617)), _1333619))], (30366 ^ _780461) ^ [_1333697, _1333699, _1333701, _1333703] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333697, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333697, tc_HOL_Obool)), _1333699), _1333701)), _1333703) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333697, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333697, tc_HOL_Obool)), _1333699), _1333703)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333697, tc_HOL_Obool)), _1333701), _1333703)))], (30368 ^ _780461) ^ [_1333781, _1333783, _1333785, _1333787] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333781, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333781, tc_HOL_Obool)), _1333783), _1333785)), _1333787) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333781, tc_HOL_Obool)), _1333783), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333781, tc_HOL_Obool)), _1333785), _1333787)))], (30370 ^ _780461) ^ [_1333854, _1333856, _1333858, _1333860] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333854, tc_HOL_Obool)), _1333856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333854, tc_HOL_Obool)), _1333858), _1333860)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333854, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333854, tc_HOL_Obool)), _1333856), _1333858)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333854, tc_HOL_Obool)), _1333856), _1333860)))], (30372 ^ _780461) ^ [_1333938] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1333938) = c_Orderings_Oord__class_Omin(_1333938)), class_Lattices_Osemilattice__inf(_1333938), class_Orderings_Olinorder(_1333938)], (30382 ^ _780461) ^ [_1334067, _1334069, _1334071, _1334073, _1334075] : [class_Lattices_Olattice(_1334067), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334069, _1334067)), _1334071), _1334073), _1334075) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334067), hAPP(_1334071, _1334075)), hAPP(_1334073, _1334075)))], (30388 ^ _780461) ^ [_1334204, _1334206, _1334208, _1334210, _1334212] : [class_Lattices_Olattice(_1334204), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334206, _1334204)), _1334208), _1334210), _1334212) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334204), hAPP(_1334208, _1334212)), hAPP(_1334210, _1334212)))], (30394 ^ _780461) ^ [_1334341, _1334343, _1334345, _1334347] : [class_Lattices_Osemilattice__inf(_1334341), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334341), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334341), _1334343), _1334345)), _1334347) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334341), _1334343), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334341), _1334345), _1334347)))], (30400 ^ _780461) ^ [_1334484, _1334486, _1334488, _1334490] : [class_Lattices_Olattice(_1334484), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334484), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334484), _1334486), _1334488)), _1334490) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334484), _1334486), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334484), _1334488), _1334490)))], (30406 ^ _780461) ^ [_1334627, _1334629, _1334631, _1334633] : [class_Lattices_Osemilattice__inf(_1334627), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334627), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334627), _1334629), _1334631)), _1334633) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334627), _1334629), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334627), _1334631), _1334633)))], (30412 ^ _780461) ^ [_1334770, _1334772, _1334774, _1334776] : [class_Lattices_Osemilattice__inf(_1334770), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334770), _1334772), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334770), _1334774), _1334776)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334770), _1334774), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334770), _1334772), _1334776)))], (30418 ^ _780461) ^ [_1334913, _1334915, _1334917, _1334919] : [class_Lattices_Olattice(_1334913), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334913), _1334915), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334913), _1334917), _1334919)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334913), _1334917), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334913), _1334915), _1334919)))], (30424 ^ _780461) ^ [_1335056, _1335058, _1335060, _1335062] : [class_Lattices_Osemilattice__inf(_1335056), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335056), _1335058), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335056), _1335060), _1335062)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335056), _1335060), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335056), _1335058), _1335062)))], (30430 ^ _780461) ^ [_1335199, _1335201, _1335203] : [class_Lattices_Osemilattice__inf(_1335199), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335199), _1335201), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335199), _1335201), _1335203)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335199), _1335201), _1335203))], (30436 ^ _780461) ^ [_1335324, _1335326, _1335328] : [class_Lattices_Olattice(_1335324), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335324), _1335326), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335324), _1335326), _1335328)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335324), _1335326), _1335328))], (30442 ^ _780461) ^ [_1335449, _1335451, _1335453] : [class_Lattices_Osemilattice__inf(_1335449), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335449), _1335451), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335449), _1335451), _1335453)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335449), _1335451), _1335453))], (30448 ^ _780461) ^ [_1335574, _1335576, _1335578] : [class_Lattices_Osemilattice__inf(_1335574), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335574), _1335576), _1335578) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335574), _1335578), _1335576))], (30454 ^ _780461) ^ [_1335683, _1335685, _1335687] : [class_Lattices_Olattice(_1335683), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335683), _1335685), _1335687) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335683), _1335687), _1335685))], (30460 ^ _780461) ^ [_1335792, _1335794, _1335796] : [class_Lattices_Osemilattice__inf(_1335792), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335792), _1335794), _1335796) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335792), _1335796), _1335794))], (30466 ^ _780461) ^ [_1335901, _1335903] : [class_Lattices_Osemilattice__inf(_1335901), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335901), _1335903), _1335903) = _1335903)], (30472 ^ _780461) ^ [_1335992, _1335994] : [class_Lattices_Osemilattice__inf(_1335992), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335992), _1335994), _1335994) = _1335994)], (30478 ^ _780461) ^ [_1336083, _1336085, _1336087, _1336089] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336083, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336083, tc_HOL_Obool)), _1336085), _1336087)), _1336089) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336083, tc_HOL_Obool)), _1336085), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336083, tc_HOL_Obool)), _1336087), _1336089)))], (30480 ^ _780461) ^ [_1336156, _1336158, _1336160, _1336162] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336156, tc_HOL_Obool)), _1336158), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336156, tc_HOL_Obool)), _1336160), _1336162)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336156, tc_HOL_Obool)), _1336160), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336156, tc_HOL_Obool)), _1336158), _1336162)))], (30482 ^ _780461) ^ [_1336229, _1336231, _1336233] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336229, tc_HOL_Obool)), _1336231), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336229, tc_HOL_Obool)), _1336231), _1336233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336229, tc_HOL_Obool)), _1336231), _1336233))], (30484 ^ _780461) ^ [_1336289, _1336291, _1336293] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336289, tc_HOL_Obool)), _1336291), _1336293) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336289, tc_HOL_Obool)), _1336293), _1336291))], (30486 ^ _780461) ^ [_1336338, _1336340] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336338, tc_HOL_Obool)), _1336340), _1336340) = _1336340)], (30488 ^ _780461) ^ [_1336374, _1336376, _1336378, _1336380] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336374, tc_HOL_Obool)), _1336376), _1336378), _1336380)), -(hBOOL(hAPP(_1336378, _1336380)))], (30494 ^ _780461) ^ [_1336485, _1336487, _1336489, _1336491] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336485, tc_HOL_Obool)), _1336487), _1336489), _1336491)), -(hBOOL(hAPP(_1336487, _1336491)))], (30500 ^ _780461) ^ [_1336596, _1336598, _1336600, _1336602] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336596, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1336596), _1336598), _1336600)), hAPP(hAPP(c_Set_Oinsert(_1336596), _1336598), _1336602)) = hAPP(hAPP(c_Set_Oinsert(_1336596), _1336598), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336596, tc_HOL_Obool)), _1336600), _1336602)))], (30502 ^ _780461) ^ [_1336671, _1336673] : [c_Nat__Transfer_Onat__set(_1336671), c_Nat__Transfer_Onat__set(_1336673), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1336671), _1336673)))], (30512 ^ _780461) ^ [_1336806, _1336808, _1336810, _1336812] : [class_Lattices_Olattice(_1336806), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336806), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1336806), _1336808), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1336806), _1336810), _1336812))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1336806), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1336806), _1336808), _1336810)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1336806), _1336808), _1336812)))))], (30518 ^ _780461) ^ [_1336979, _1336981, _1336983, _1336985] : [class_Lattices_Olattice(_1336979), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1336979), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1336979), _1336981), _1336983)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1336979), _1336981), _1336985))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1336979), _1336981), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1336979), _1336983), _1336985)))))], (30524 ^ _780461) ^ [_1337152, _1337154] : [class_Lattices_Oboolean__algebra(_1337152), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1337152), hAPP(c_Groups_Ouminus__class_Ouminus(_1337152), _1337154)), _1337154) = c_Orderings_Obot__class_Obot(_1337152))], (30530 ^ _780461) ^ [_1337257, _1337259] : [class_Lattices_Oboolean__algebra(_1337257), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1337257), _1337259), hAPP(c_Groups_Ouminus__class_Ouminus(_1337257), _1337259)) = c_Orderings_Obot__class_Obot(_1337257))], (30536 ^ _780461) ^ [_1337362, _1337364, _1337366] : [class_Lattices_Oboolean__algebra(_1337362), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1337362), _1337364), _1337366) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1337362), _1337364), hAPP(c_Groups_Ouminus__class_Ouminus(_1337362), _1337366)))], (30542 ^ _780461) ^ [_1337481, _1337483, _1337485] : [class_Lattices_Oboolean__algebra(_1337481), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1337481), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1337481), _1337483), _1337485)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1337481), hAPP(c_Groups_Ouminus__class_Ouminus(_1337481), _1337483)), hAPP(c_Groups_Ouminus__class_Ouminus(_1337481), _1337485)))], (30548 ^ _780461) ^ [_1337620, _1337622, _1337624] : [class_Lattices_Oboolean__algebra(_1337620), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1337620), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1337620), _1337622), _1337624)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1337620), hAPP(c_Groups_Ouminus__class_Ouminus(_1337620), _1337622)), hAPP(c_Groups_Ouminus__class_Ouminus(_1337620), _1337624)))], (30554 ^ _780461) ^ [_1337759, _1337761, _1337763, _1337765] : [hBOOL(hAPP(hAPP(c_member(_1337759), _1337761), _1337763)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337759, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1337759), _1337761), _1337765)), _1337763) = hAPP(hAPP(c_Set_Oinsert(_1337759), _1337761), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337759, tc_HOL_Obool)), _1337765), _1337763)))], (30560 ^ _780461) ^ [_1337930, _1337932, _1337934, _1337936] : [hBOOL(hAPP(hAPP(c_member(_1337930), _1337932), _1337934)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337930, tc_HOL_Obool)), _1337934), hAPP(hAPP(c_Set_Oinsert(_1337930), _1337932), _1337936)) = hAPP(hAPP(c_Set_Oinsert(_1337930), _1337932), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337930, tc_HOL_Obool)), _1337934), _1337936)))], (30566 ^ _780461) ^ [_1338097, _1338099, _1338101, _1338103] : [-(hBOOL(hAPP(hAPP(c_member(_1338097), _1338099), _1338101))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338097, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1338097), _1338099), _1338103)), _1338101) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338097, tc_HOL_Obool)), _1338103), _1338101))], (30572 ^ _780461) ^ [_1338170, _1338172, _1338174, _1338176] : [-(hBOOL(hAPP(hAPP(c_member(_1338170), _1338172), _1338174))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338170, tc_HOL_Obool)), _1338174), hAPP(hAPP(c_Set_Oinsert(_1338170), _1338172), _1338176)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338170, tc_HOL_Obool)), _1338174), _1338176))], (30578 ^ _780461) ^ [_1338262, _1338264, _1338266, _1338268] : [hBOOL(hAPP(hAPP(c_member(_1338262), _1338264), _1338266)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338262, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1338262), _1338264), _1338268)), _1338266) = hAPP(hAPP(c_Set_Oinsert(_1338262), _1338264), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338262, tc_HOL_Obool)), _1338268), _1338266)))], (30584 ^ _780461) ^ [_1338427, _1338429, _1338431, _1338433] : [-(hBOOL(hAPP(hAPP(c_member(_1338427), _1338429), _1338431))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338427, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1338427), _1338429), _1338433)), _1338431) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338427, tc_HOL_Obool)), _1338433), _1338431))], (30590 ^ _780461) ^ [_1338521, _1338523, _1338525, _1338527] : [hBOOL(hAPP(hAPP(c_member(_1338521), _1338523), _1338525)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338521, tc_HOL_Obool)), _1338525), hAPP(hAPP(c_Set_Oinsert(_1338521), _1338523), _1338527)) = hAPP(hAPP(c_Set_Oinsert(_1338521), _1338523), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338521, tc_HOL_Obool)), _1338525), _1338527)))], (30596 ^ _780461) ^ [_1338686, _1338688, _1338690, _1338692] : [-(hBOOL(hAPP(hAPP(c_member(_1338686), _1338688), _1338690))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338686, tc_HOL_Obool)), _1338690), hAPP(hAPP(c_Set_Oinsert(_1338686), _1338688), _1338692)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338686, tc_HOL_Obool)), _1338690), _1338692))], (30602 ^ _780461) ^ [_1338765, _1338767, _1338769, _1338771, _1338773] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338765, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1338767, _1338765, _1338769), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338767, tc_HOL_Obool)), _1338771), _1338773))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338765, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1338767, _1338765, _1338769), _1338771)), hAPP(c_Set_Oimage(_1338767, _1338765, _1338769), _1338773)))))], (30604 ^ _780461) ^ [_1338849, _1338851, _1338853] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338849, tc_HOL_Obool)), _1338851), _1338853) = c_Orderings_Obot__class_Obot(tc_fun(_1338849, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1338849, tc_HOL_Obool)), _1338851), _1338853) = _1338851)], (30610 ^ _780461) ^ [_1338982, _1338984, _1338986] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338982, tc_HOL_Obool)), _1338984), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1338982, tc_HOL_Obool)), _1338986), _1338984)) = c_Orderings_Obot__class_Obot(tc_fun(_1338982, tc_HOL_Obool)))], (30612 ^ _780461) ^ [_1339057, _1339059, _1339061, _1339063] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339057, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339057, tc_HOL_Obool)), _1339059), _1339061)), _1339063) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339057, tc_HOL_Obool)), _1339059), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339057, tc_HOL_Obool)), _1339061), _1339063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339057, tc_HOL_Obool)), _1339063), _1339059)))], (30618 ^ _780461) ^ [_1339242, _1339244, _1339246, _1339248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339242, tc_HOL_Obool)), _1339248), _1339244)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339242, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339242, tc_HOL_Obool)), _1339244), _1339246)), _1339248) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339242, tc_HOL_Obool)), _1339244), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339242, tc_HOL_Obool)), _1339246), _1339248)))], (30624 ^ _780461) ^ [_1339433, _1339435, _1339437] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339433, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339433, tc_HOL_Obool)), _1339435), _1339437)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339433, tc_HOL_Obool)), _1339435), _1339437)) = _1339435)], (30626 ^ _780461) ^ [_1339493, _1339495, _1339497, _1339499] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339493, tc_HOL_Obool)), _1339495), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339493, tc_HOL_Obool)), _1339497), _1339499)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339493, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339493, tc_HOL_Obool)), _1339495), _1339497)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339493, tc_HOL_Obool)), _1339495), _1339499)))], (30628 ^ _780461) ^ [_1339577, _1339579, _1339581, _1339583] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339577, tc_HOL_Obool)), _1339579), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339577, tc_HOL_Obool)), _1339581), _1339583)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339577, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339577, tc_HOL_Obool)), _1339579), _1339581)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339577, tc_HOL_Obool)), _1339579), _1339583)))], (30630 ^ _780461) ^ [_1339661, _1339663] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1339661), _1339663) = 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)), _1339661)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1339663))))], (30632 ^ _780461) ^ [_1339707, _1339709] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339707, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1339707, tc_HOL_Obool)), _1339709)), _1339709) = c_Orderings_Obot__class_Obot(tc_fun(_1339707, tc_HOL_Obool)))], (30634 ^ _780461) ^ [_1339756, _1339758] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339756, tc_HOL_Obool)), _1339758), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1339756, tc_HOL_Obool)), _1339758)) = c_Orderings_Obot__class_Obot(tc_fun(_1339756, tc_HOL_Obool)))], (30636 ^ _780461) ^ [_1339805, _1339807, _1339809, _1339811, _1339813] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339805, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1339807, _1339805, _1339809), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339807, tc_HOL_Obool)), _1339811), _1339813))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339805, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1339807, _1339805, _1339809), _1339811)), hAPP(c_Relation_OImage(_1339807, _1339805, _1339809), _1339813)))))], (30638 ^ _780461) ^ [_1339889, _1339891, _1339893] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1339889, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339889, tc_HOL_Obool)), _1339891), _1339893)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339889, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1339889, tc_HOL_Obool)), _1339891)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1339889, tc_HOL_Obool)), _1339893)))], (30640 ^ _780461) ^ [_1339962, _1339964, _1339966] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1339962, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339962, tc_HOL_Obool)), _1339964), _1339966)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339962, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1339962, tc_HOL_Obool)), _1339964)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1339962, tc_HOL_Obool)), _1339966)))], (30642 ^ _780461) ^ [_1340035, _1340037, _1340039] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340035, tc_HOL_Obool)), _1340037), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1340035, tc_HOL_Obool)), _1340039)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340035, tc_HOL_Obool)), _1340037), _1340039))], (30644 ^ _780461) ^ [_1340092, _1340094, _1340096] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1340092, tc_HOL_Obool)), _1340094), _1340096) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340092, tc_HOL_Obool)), _1340094), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1340092, tc_HOL_Obool)), _1340096)))], (30646 ^ _780461) ^ [_1340149, _1340151] : [c_Nat__Transfer_Onat__set(_1340149), c_Nat__Transfer_Onat__set(_1340151), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1340149), _1340151) = 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), _1340149)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1340151))))], (30656 ^ _780461) ^ [_1340334, _1340336, _1340338] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340334, tc_HOL_Obool)), _1340336), _1340338) = c_Orderings_Obot__class_Obot(tc_fun(_1340334, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1340334, tc_HOL_Obool)), _1340336), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1340334, tc_HOL_Obool)), _1340338))))], (30662 ^ _780461) ^ [_1340477, _1340479, _1340481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1340477, tc_HOL_Obool)), _1340479), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1340477, tc_HOL_Obool)), _1340481))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340477, tc_HOL_Obool)), _1340479), _1340481) = c_Orderings_Obot__class_Obot(tc_fun(_1340477, tc_HOL_Obool)))], (30668 ^ _780461) ^ [_1340626, _1340628, _1340630, _1340632, _1340634, _1340636, _1340638, _1340640] : [c_Finite__Set_Ofolding__image__simple(_1340626, _1340628, _1340630, _1340632, _1340634, _1340636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340628), _1340638)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340628), _1340640)), -(hAPP(hAPP(_1340630, hAPP(_1340636, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340628, tc_HOL_Obool)), _1340638), _1340640))), hAPP(_1340636, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340628, tc_HOL_Obool)), _1340638), _1340640))) = hAPP(hAPP(_1340630, hAPP(_1340636, _1340638)), hAPP(_1340636, _1340640)))], (30682 ^ _780461) ^ [_1340959, _1340961, _1340963] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1340959), hAPP(hAPP(c_Set_Oinsert(_1340959), _1340961), c_Orderings_Obot__class_Obot(tc_fun(_1340959, tc_HOL_Obool)))), _1340963) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1340959, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1340959, _1340959, _1340963), hAPP(hAPP(c_Set_Oinsert(_1340959), _1340961), c_Orderings_Obot__class_Obot(tc_fun(_1340959, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1340959, tc_HOL_Obool), tc_HOL_Obool))))], (30684 ^ _780461) ^ [_1341046, _1341048, _1341050, _1341052, _1341054] : [c_Finite__Set_Ofolding__one(_1341046, _1341048, _1341050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341046), _1341052)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341046), _1341054)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341046, tc_HOL_Obool)), _1341052), _1341054) = c_Orderings_Obot__class_Obot(tc_fun(_1341046, tc_HOL_Obool))), -(hAPP(hAPP(_1341048, hAPP(_1341050, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341046, tc_HOL_Obool)), _1341052), _1341054))), hAPP(_1341050, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341046, tc_HOL_Obool)), _1341052), _1341054))) = hAPP(hAPP(_1341048, hAPP(_1341050, _1341052)), hAPP(_1341050, _1341054)))], (30702 ^ _780461) ^ [_1341402, _1341404, _1341406, _1341408, _1341410] : [c_Finite__Set_Ofolding__one(_1341402, _1341404, _1341406), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341402), _1341408)), -(_1341408 = c_Orderings_Obot__class_Obot(tc_fun(_1341402, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341402), _1341410)), -(_1341410 = c_Orderings_Obot__class_Obot(tc_fun(_1341402, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341402, tc_HOL_Obool)), _1341408), _1341410) = c_Orderings_Obot__class_Obot(tc_fun(_1341402, tc_HOL_Obool)), -(hAPP(_1341406, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341402, tc_HOL_Obool)), _1341408), _1341410)) = hAPP(hAPP(_1341404, hAPP(_1341406, _1341408)), hAPP(_1341406, _1341410)))], (30728 ^ _780461) ^ [_1341903, _1341905, _1341907, _1341909, _1341911, _1341913, _1341915, _1341917] : [c_Finite__Set_Ofolding__image__simple(_1341903, _1341905, _1341907, _1341909, _1341911, _1341913), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341905), _1341915)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341905), _1341917)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341905, tc_HOL_Obool)), _1341915), _1341917) = c_Orderings_Obot__class_Obot(tc_fun(_1341905, tc_HOL_Obool)), -(hAPP(_1341913, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341905, tc_HOL_Obool)), _1341915), _1341917)) = hAPP(hAPP(_1341907, hAPP(_1341913, _1341915)), hAPP(_1341913, _1341917)))], (30746 ^ _780461) ^ [_1342292, _1342294, _1342296, _1342298] : [hBOOL(hAPP(hAPP(c_member(_1342292), _1342294), _1342296)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1342292, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1342292, _1342292, _1342298), hAPP(hAPP(c_Set_Oinsert(_1342292), _1342294), c_Orderings_Obot__class_Obot(tc_fun(_1342292, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1342292), _1342296), _1342298))))], (30752 ^ _780461) ^ [_1342463, _1342465, _1342467, _1342469, _1342471, _1342473, _1342475] : [c_Equiv__Relations_Oequiv(_1342463, _1342465, _1342467), hBOOL(hAPP(hAPP(c_member(tc_fun(_1342463, tc_HOL_Obool)), _1342469), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1342463), _1342465), _1342467))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1342463, tc_HOL_Obool)), _1342471), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1342463), _1342465), _1342467))), hBOOL(hAPP(hAPP(c_member(_1342463), _1342473), _1342469)), hBOOL(hAPP(hAPP(c_member(_1342463), _1342475), _1342471)), 30771 ^ _780461 : [(30772 ^ _780461) ^ [] : [_1342469 = _1342471, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1342463, _1342463)), hAPP(hAPP(c_Product__Type_OPair(_1342463, _1342463), _1342473), _1342475)), _1342467)))], (30778 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1342463, _1342463)), hAPP(hAPP(c_Product__Type_OPair(_1342463, _1342463), _1342473), _1342475)), _1342467)), -(_1342469 = _1342471)]]], (30784 ^ _780461) ^ [_1343107, _1343109, _1343111, _1343113, _1343115, _1343117, _1343119] : [c_Equiv__Relations_Oequiv(_1343107, _1343109, _1343111), hBOOL(hAPP(hAPP(c_member(tc_fun(_1343107, tc_HOL_Obool)), _1343113), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1343107), _1343109), _1343111))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1343107, tc_HOL_Obool)), _1343115), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1343107), _1343109), _1343111))), hBOOL(hAPP(hAPP(c_member(_1343107), _1343117), _1343113)), hBOOL(hAPP(hAPP(c_member(_1343107), _1343119), _1343115)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1343107, _1343107)), hAPP(hAPP(c_Product__Type_OPair(_1343107, _1343107), _1343117), _1343119)), _1343111)), -(_1343113 = _1343115)], (30810 ^ _780461) ^ [_1343644, _1343646] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343644), _1343646)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343646, _1343644) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (30816 ^ _780461) ^ [_1343756, _1343758] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1343756), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343758))), 30819 ^ _780461 : [(30820 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343756), _1343758)))], (30822 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343758), _1343756))]]], (30824 ^ _780461) ^ [_1343901, _1343903] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1343901), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1343903)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343901), _1343903)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1343903), _1343901)))], (30834 ^ _780461) ^ [_1344088, _1344090] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1344088), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1344090))), 30837 ^ _780461 : [(30838 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344090), _1344088)))], (30840 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344088), _1344090))]]], (30842 ^ _780461) ^ [_1344233, _1344235] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1344233), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1344235)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344235), _1344233)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344233), _1344235)))], (30852 ^ _780461) ^ [_1344420, _1344422] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1344420), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344422))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344420), _1344422)))], (30858 ^ _780461) ^ [_1344521, _1344523] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344521), _1344523)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1344521), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1344523))))], (30864 ^ _780461) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (30866 ^ _780461) ^ [_1344673, _1344675, _1344677, _1344679, _1344681, _1344683] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1344673, tc_fun(_1344675, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1344673, tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_fun(_1344675, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344675, tc_fun(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_fun(_1344675, tc_HOL_Obool)), _1344673), c_COMBC(_1344675, tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344675, tc_prod(_1344673, _1344675)), tc_fun(_1344675, tc_fun(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_HOL_Obool)), _1344673), hAPP(c_COMBB(tc_prod(_1344673, _1344675), tc_fun(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_HOL_Obool), _1344675), c_member(tc_prod(_1344673, _1344675)))), c_Product__Type_OPair(_1344673, _1344675)))), _1344677)), hAPP(hAPP(c_COMBC(_1344673, tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_fun(_1344675, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344675, tc_fun(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_fun(_1344675, tc_HOL_Obool)), _1344673), c_COMBC(_1344675, tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1344675, tc_prod(_1344673, _1344675)), tc_fun(_1344675, tc_fun(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_HOL_Obool)), _1344673), hAPP(c_COMBB(tc_prod(_1344673, _1344675), tc_fun(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool), tc_HOL_Obool), _1344675), c_member(tc_prod(_1344673, _1344675)))), c_Product__Type_OPair(_1344673, _1344675)))), _1344679)), _1344681), _1344683)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1344673, _1344675)), hAPP(hAPP(c_Product__Type_OPair(_1344673, _1344675), _1344681), _1344683)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1344673, _1344675), tc_HOL_Obool)), _1344677), _1344679))))], (30872 ^ _780461) ^ [_1345330, _1345332, _1345334, _1345336, _1345338, _1345340] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1345330, _1345332)), hAPP(hAPP(c_Product__Type_OPair(_1345330, _1345332), _1345338), _1345340)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool)), _1345334), _1345336))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1345330, tc_fun(_1345332, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1345330, tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_fun(_1345332, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1345332, tc_fun(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_fun(_1345332, tc_HOL_Obool)), _1345330), c_COMBC(_1345332, tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1345332, tc_prod(_1345330, _1345332)), tc_fun(_1345332, tc_fun(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_HOL_Obool)), _1345330), hAPP(c_COMBB(tc_prod(_1345330, _1345332), tc_fun(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_HOL_Obool), _1345332), c_member(tc_prod(_1345330, _1345332)))), c_Product__Type_OPair(_1345330, _1345332)))), _1345334)), hAPP(hAPP(c_COMBC(_1345330, tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_fun(_1345332, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1345332, tc_fun(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_fun(_1345332, tc_HOL_Obool)), _1345330), c_COMBC(_1345332, tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1345332, tc_prod(_1345330, _1345332)), tc_fun(_1345332, tc_fun(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_HOL_Obool)), _1345330), hAPP(c_COMBB(tc_prod(_1345330, _1345332), tc_fun(tc_fun(tc_prod(_1345330, _1345332), tc_HOL_Obool), tc_HOL_Obool), _1345332), c_member(tc_prod(_1345330, _1345332)))), c_Product__Type_OPair(_1345330, _1345332)))), _1345336)), _1345338), _1345340)))], (30878 ^ _780461) ^ [_1346017, _1346019, _1346021, _1346023, _1346025] : [hBOOL(hAPP(hAPP(c_member(_1346017), _1346019), c_SetInterval_Oord_OgreaterThanLessThan(_1346017, _1346021, _1346023, _1346025))), 30881 ^ _780461 : [(30882 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1346021, _1346023), _1346019)))], (30884 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1346021, _1346019), _1346025)))]]], (30886 ^ _780461) ^ [_1346166, _1346168, _1346170, _1346172, _1346174] : [-(hBOOL(hAPP(hAPP(c_member(_1346166), _1346168), c_SetInterval_Oord_OgreaterThanLessThan(_1346166, _1346170, _1346172, _1346174)))), hBOOL(hAPP(hAPP(_1346170, _1346172), _1346168)), hBOOL(hAPP(hAPP(_1346170, _1346168), _1346174))], (30896 ^ _780461) ^ [_1346374, _1346376, _1346378, _1346380] : [hBOOL(hAPP(hAPP(c_member(_1346374), _1346376), c_SetInterval_Oord_OgreaterThan(_1346374, _1346378, _1346380))), -(hBOOL(hAPP(hAPP(_1346378, _1346380), _1346376)))], (30902 ^ _780461) ^ [_1346483, _1346485, _1346487, _1346489] : [hBOOL(hAPP(hAPP(_1346487, _1346489), _1346485)), -(hBOOL(hAPP(hAPP(c_member(_1346483), _1346485), c_SetInterval_Oord_OgreaterThan(_1346483, _1346487, _1346489))))], (30908 ^ _780461) ^ [_1346619, _1346621, _1346623, _1346625] : [hBOOL(hAPP(hAPP(c_member(_1346619), _1346621), c_SetInterval_Oord_OlessThan(_1346619, _1346623, _1346625))), -(hBOOL(hAPP(hAPP(_1346623, _1346621), _1346625)))], (30914 ^ _780461) ^ [_1346728, _1346730, _1346732, _1346734] : [hBOOL(hAPP(hAPP(_1346732, _1346730), _1346734)), -(hBOOL(hAPP(hAPP(c_member(_1346728), _1346730), c_SetInterval_Oord_OlessThan(_1346728, _1346732, _1346734))))], (30920 ^ _780461) ^ [_1346864, _1346866, _1346868, _1346870] : [hBOOL(hAPP(hAPP(c_member(_1346864), _1346866), c_SetInterval_Oord_OatMost(_1346864, _1346868, _1346870))), -(hBOOL(hAPP(hAPP(_1346868, _1346866), _1346870)))], (30926 ^ _780461) ^ [_1346973, _1346975, _1346977, _1346979] : [hBOOL(hAPP(hAPP(_1346977, _1346975), _1346979)), -(hBOOL(hAPP(hAPP(c_member(_1346973), _1346975), c_SetInterval_Oord_OatMost(_1346973, _1346977, _1346979))))], (30932 ^ _780461) ^ [_1347103, _1347105] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1347103), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347105))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347105), _1347103)))], (30938 ^ _780461) ^ [_1347204, _1347206] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347206), _1347204)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1347204), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1347206))))], (30944 ^ _780461) ^ [_1347311, _1347313, _1347315, _1347317] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1347311, tc_HOL_Obool)), _1347313), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1347311), _1347315), _1347317))), 30948 ^ _780461 : [(30949 ^ _780461) ^ [] : [-(_1347313 = hAPP(c_Relation_OImage(_1347311, _1347311, _1347317), hAPP(hAPP(c_Set_Oinsert(_1347311), 30947 ^ [_1347311, _1347313, _1347315, _1347317]), c_Orderings_Obot__class_Obot(tc_fun(_1347311, tc_HOL_Obool)))))], (30951 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347311), 30947 ^ [_1347311, _1347313, _1347315, _1347317]), _1347315)))]]], (30953 ^ _780461) ^ [_1347566, _1347568, _1347570, _1347572, _1347574, _1347576] : [hBOOL(hAPP(hAPP(c_member(_1347566), _1347568), c_SetInterval_Oord_OgreaterThanAtMost(_1347566, _1347570, _1347572, _1347574, _1347576))), 30956 ^ _780461 : [(30957 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1347572, _1347574), _1347568)))], (30959 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1347570, _1347568), _1347576)))]]], (30961 ^ _780461) ^ [_1347719, _1347721, _1347723, _1347725, _1347727, _1347729] : [-(hBOOL(hAPP(hAPP(c_member(_1347719), _1347721), c_SetInterval_Oord_OgreaterThanAtMost(_1347719, _1347723, _1347725, _1347727, _1347729)))), hBOOL(hAPP(hAPP(_1347725, _1347727), _1347721)), hBOOL(hAPP(hAPP(_1347723, _1347721), _1347729))], (30971 ^ _780461) ^ [_1347939, _1347941, _1347943, _1347945, _1347947, _1347949] : [hBOOL(hAPP(hAPP(c_member(_1347939), _1347941), c_SetInterval_Oord_OatLeastLessThan(_1347939, _1347943, _1347945, _1347947, _1347949))), 30974 ^ _780461 : [(30975 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1347943, _1347947), _1347941)))], (30977 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1347945, _1347941), _1347949)))]]], (30979 ^ _780461) ^ [_1348092, _1348094, _1348096, _1348098, _1348100, _1348102] : [-(hBOOL(hAPP(hAPP(c_member(_1348092), _1348094), c_SetInterval_Oord_OatLeastLessThan(_1348092, _1348096, _1348098, _1348100, _1348102)))), hBOOL(hAPP(hAPP(_1348096, _1348100), _1348094)), hBOOL(hAPP(hAPP(_1348098, _1348094), _1348102))], (30989 ^ _780461) ^ [_1348285, _1348287, _1348289, _1348291, _1348293, _1348295] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348285, tc_fun(_1348287, tc_HOL_Obool))), _1348289), _1348291), _1348293), _1348295)), 30992 ^ _780461 : [(30993 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1348289, _1348293), _1348295)))], (30995 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1348291, _1348293), _1348295)))]]], (30997 ^ _780461) ^ [_1348458, _1348460, _1348462, _1348464, _1348466, _1348468] : [hBOOL(hAPP(hAPP(_1348458, _1348460), _1348462)), hBOOL(hAPP(hAPP(_1348464, _1348460), _1348462)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348466, tc_fun(_1348468, tc_HOL_Obool))), _1348458), _1348464), _1348460), _1348462)))], (31007 ^ _780461) ^ [_1348661, _1348663, _1348665, _1348667, _1348669, _1348671] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348661, tc_fun(_1348663, tc_HOL_Obool))), _1348665), _1348667), _1348669), _1348671)), -(hBOOL(hAPP(hAPP(_1348667, _1348669), _1348671)))], (31013 ^ _780461) ^ [_1348794, _1348796, _1348798, _1348800, _1348802, _1348804] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348794, tc_fun(_1348796, tc_HOL_Obool))), _1348798), _1348800), _1348802), _1348804)), -(hBOOL(hAPP(hAPP(_1348798, _1348802), _1348804)))], (31019 ^ _780461) ^ [_1348927, _1348929] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1348927), _1348929)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1348929, _1348927) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (31025 ^ _780461) ^ [_1349026, _1349028] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349026), _1349028)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1349028, _1349026) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (31041 ^ _780461) ^ [_1349301, _1349303] : [31042 ^ _780461 : [(31043 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349301), _1349303)))], (31045 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349303), _1349301))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1349301, _1349303) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (31031 ^ _780461) ^ [_1349140, _1349142] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1349140, _1349142) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349140), _1349142)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349142), _1349140)))], (31059 ^ _780461) ^ [_1349625, _1349627] : [31060 ^ _780461 : [(31061 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349625), _1349627)))], (31063 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349627), _1349625))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1349625, _1349627) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (31049 ^ _780461) ^ [_1349464, _1349466] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1349464, _1349466) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349464), _1349466)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349466), _1349464)))], (31077 ^ _780461) ^ [_1349949, _1349951] : [31078 ^ _780461 : [(31079 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349949), _1349951)))], (31081 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349951), _1349949))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1349949, _1349951))], (31067 ^ _780461) ^ [_1349788, _1349790] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1349788, _1349790), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349788), _1349790)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1349790), _1349788)))], (31095 ^ _780461) ^ [_1350273, _1350275] : [31096 ^ _780461 : [(31097 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1350273), _1350275)))], (31099 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1350275), _1350273))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1350273, _1350275))], (31085 ^ _780461) ^ [_1350112, _1350114] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1350112, _1350114), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1350112), _1350114)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1350114), _1350112)))], (31103 ^ _780461) ^ [_1350442, _1350444, _1350446, _1350448] : [hBOOL(hAPP(hAPP(c_member(_1350442), _1350444), c_SetInterval_Oord_OatLeast(_1350442, _1350446, _1350448))), -(hBOOL(hAPP(hAPP(_1350446, _1350448), _1350444)))], (31109 ^ _780461) ^ [_1350551, _1350553, _1350555, _1350557] : [hBOOL(hAPP(hAPP(_1350555, _1350557), _1350553)), -(hBOOL(hAPP(hAPP(c_member(_1350551), _1350553), c_SetInterval_Oord_OatLeast(_1350551, _1350555, _1350557))))], (31115 ^ _780461) ^ [_1350690, _1350692, _1350694, _1350696, _1350698] : [hBOOL(hAPP(hAPP(c_member(_1350690), _1350692), c_SetInterval_Oord_OatLeastAtMost(_1350690, _1350694, _1350696, _1350698))), 31118 ^ _780461 : [(31119 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1350694, _1350696), _1350692)))], (31121 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1350694, _1350692), _1350698)))]]], (31123 ^ _780461) ^ [_1350839, _1350841, _1350843, _1350845, _1350847] : [-(hBOOL(hAPP(hAPP(c_member(_1350839), _1350841), c_SetInterval_Oord_OatLeastAtMost(_1350839, _1350843, _1350845, _1350847)))), hBOOL(hAPP(hAPP(_1350843, _1350845), _1350841)), hBOOL(hAPP(hAPP(_1350843, _1350841), _1350847))], (31133 ^ _780461) ^ [_1351026, _1351028, _1351030] : [class_Lattices_Olattice(_1351026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351026), _1351028)), hBOOL(hAPP(hAPP(c_member(_1351026), _1351030), _1351028)), 31144 ^ _780461 : [(31145 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351026, tc_HOL_Obool)), _1351028), hAPP(hAPP(c_Set_Oinsert(_1351026), _1351030), c_Orderings_Obot__class_Obot(tc_fun(_1351026, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1351026, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1351026, _1351028) = _1351030)], (31151 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351026, tc_HOL_Obool)), _1351028), hAPP(hAPP(c_Set_Oinsert(_1351026), _1351030), c_Orderings_Obot__class_Obot(tc_fun(_1351026, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1351026, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1351026, _1351028) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1351026), _1351030), c_Big__Operators_Olattice__class_OInf__fin(_1351026, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351026, tc_HOL_Obool)), _1351028), hAPP(hAPP(c_Set_Oinsert(_1351026), _1351030), c_Orderings_Obot__class_Obot(tc_fun(_1351026, tc_HOL_Obool)))))))]]], (31157 ^ _780461) ^ [_1351532, _1351534, _1351536] : [class_Lattices_Olattice(_1351532), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351532), _1351534)), hBOOL(hAPP(hAPP(c_member(_1351532), _1351536), _1351534)), 31168 ^ _780461 : [(31169 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351532, tc_HOL_Obool)), _1351534), hAPP(hAPP(c_Set_Oinsert(_1351532), _1351536), c_Orderings_Obot__class_Obot(tc_fun(_1351532, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1351532, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1351532, _1351534) = _1351536)], (31175 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351532, tc_HOL_Obool)), _1351534), hAPP(hAPP(c_Set_Oinsert(_1351532), _1351536), c_Orderings_Obot__class_Obot(tc_fun(_1351532, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1351532, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1351532, _1351534) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1351532), _1351536), c_Big__Operators_Olattice__class_OSup__fin(_1351532, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351532, tc_HOL_Obool)), _1351534), hAPP(hAPP(c_Set_Oinsert(_1351532), _1351536), c_Orderings_Obot__class_Obot(tc_fun(_1351532, tc_HOL_Obool)))))))]]], (31181 ^ _780461) ^ [_1352038, _1352040, _1352042] : [class_Orderings_Olinorder(_1352038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352038), _1352040)), hBOOL(hAPP(hAPP(c_member(_1352038), _1352042), _1352040)), 31192 ^ _780461 : [(31193 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352038, tc_HOL_Obool)), _1352040), hAPP(hAPP(c_Set_Oinsert(_1352038), _1352042), c_Orderings_Obot__class_Obot(tc_fun(_1352038, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1352038, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1352038, _1352040) = _1352042)], (31199 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352038, tc_HOL_Obool)), _1352040), hAPP(hAPP(c_Set_Oinsert(_1352038), _1352042), c_Orderings_Obot__class_Obot(tc_fun(_1352038, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1352038, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1352038, _1352040) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1352038), _1352042), c_Big__Operators_Olinorder__class_OMax(_1352038, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352038, tc_HOL_Obool)), _1352040), hAPP(hAPP(c_Set_Oinsert(_1352038), _1352042), c_Orderings_Obot__class_Obot(tc_fun(_1352038, tc_HOL_Obool)))))))]]], (31205 ^ _780461) ^ [_1352544, _1352546] : [class_Lattices_Olattice(_1352544), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352544), _1352546)), -(_1352546 = c_Orderings_Obot__class_Obot(tc_fun(_1352544, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352544), c_Big__Operators_Olattice__class_OInf__fin(_1352544, _1352546)), c_Big__Operators_Olattice__class_OSup__fin(_1352544, _1352546))))], (31219 ^ _780461) ^ [_1352730, _1352732] : [class_Orderings_Olinorder(_1352730), -(c_Big__Operators_Olinorder__class_OMax(_1352730, hAPP(hAPP(c_Set_Oinsert(_1352730), _1352732), c_Orderings_Obot__class_Obot(tc_fun(_1352730, tc_HOL_Obool)))) = _1352732)], (31225 ^ _780461) ^ [_1352837, _1352839] : [class_Lattices_Olattice(_1352837), -(c_Big__Operators_Olattice__class_OInf__fin(_1352837, hAPP(hAPP(c_Set_Oinsert(_1352837), _1352839), c_Orderings_Obot__class_Obot(tc_fun(_1352837, tc_HOL_Obool)))) = _1352839)], (31231 ^ _780461) ^ [_1352944, _1352946] : [class_Lattices_Olattice(_1352944), -(c_Big__Operators_Olattice__class_OSup__fin(_1352944, hAPP(hAPP(c_Set_Oinsert(_1352944), _1352946), c_Orderings_Obot__class_Obot(tc_fun(_1352944, tc_HOL_Obool)))) = _1352946)], (31237 ^ _780461) ^ [_1353051, _1353053, _1353055] : [class_Orderings_Olinorder(_1353051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353051), _1353053)), hBOOL(hAPP(hAPP(c_member(_1353051), _1353055), _1353053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1353051), _1353055), c_Big__Operators_Olinorder__class_OMax(_1353051, _1353053))))], (31251 ^ _780461) ^ [_1353278, _1353280] : [class_Orderings_Olinorder(_1353278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353278), _1353280)), -(_1353280 = c_Orderings_Obot__class_Obot(tc_fun(_1353278, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1353278), c_Big__Operators_Olinorder__class_OMax(_1353278, _1353280)), _1353280)))], (31265 ^ _780461) ^ [_1353458, _1353460, _1353462] : [class_Lattices_Olattice(_1353458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353458), _1353460)), hBOOL(hAPP(hAPP(c_member(_1353458), _1353462), _1353460)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1353458), _1353462), c_Big__Operators_Olattice__class_OInf__fin(_1353458, _1353460)) = _1353462)], (31279 ^ _780461) ^ [_1353687, _1353689, _1353691] : [class_Lattices_Olattice(_1353687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353687), _1353689)), hBOOL(hAPP(hAPP(c_member(_1353687), _1353691), _1353689)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1353687), _1353691), c_Big__Operators_Olattice__class_OSup__fin(_1353687, _1353689)) = c_Big__Operators_Olattice__class_OSup__fin(_1353687, _1353689))], (31293 ^ _780461) ^ [_1353922, _1353924, _1353926] : [class_Lattices_Olattice(_1353922), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353922), _1353924)), hBOOL(hAPP(hAPP(c_member(_1353922), _1353926), _1353924)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1353922), _1353926), c_Big__Operators_Olattice__class_OInf__fin(_1353922, _1353924)) = c_Big__Operators_Olattice__class_OInf__fin(_1353922, _1353924))], (31307 ^ _780461) ^ [_1354157, _1354159, _1354161] : [class_Lattices_Olattice(_1354157), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354157), _1354159)), hBOOL(hAPP(hAPP(c_member(_1354157), _1354161), _1354159)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1354157), _1354161), c_Big__Operators_Olattice__class_OSup__fin(_1354157, _1354159)) = _1354161)], (31321 ^ _780461) ^ [_1354386, _1354388, _1354390] : [class_Orderings_Olinorder(_1354386), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354386), _1354388)), hBOOL(hAPP(hAPP(c_member(_1354386), _1354390), _1354388)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1354386), _1354390), c_Big__Operators_Olinorder__class_OMax(_1354386, _1354388)) = c_Big__Operators_Olinorder__class_OMax(_1354386, _1354388))], (31335 ^ _780461) ^ [_1354621, _1354623] : [_1354621 = _1354623, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354621, _1354623) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1354621), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (31341 ^ _780461) ^ [_1354720] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354720, _1354720) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1354720), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (31343 ^ _780461) ^ [_1354772, _1354774, _1354776] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354772, _1354774) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1354776), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 31346 ^ _780461 : [(31347 ^ _780461) ^ [] : [-(_1354772 = _1354774)], (31349 ^ _780461) ^ [] : [-(_1354774 = _1354776)]]], (31351 ^ _780461) ^ [_1354895, _1354897, _1354899] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1354895, _1354897) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1354899), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1354895 = _1354897, _1354897 = _1354899], (31361 ^ _780461) ^ [_1355052, _1355054] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355054, _1355052) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355052), _1355054)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355054), _1355052)))], (31371 ^ _780461) ^ [_1355229, _1355231] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355229, _1355231) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355229), _1355231))], (31377 ^ _780461) ^ [_1355321, _1355323] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355321), _1355323))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355321, _1355323) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (31383 ^ _780461) ^ [_1355384, _1355386] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355384, _1355386), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355384), _1355386))], (31389 ^ _780461) ^ [_1355476, _1355478] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355476), _1355478))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1355476, _1355478))], (31395 ^ _780461) ^ [_1355524, _1355526, _1355528] : [class_Orderings_Olinorder(_1355524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1355524, tc_HOL_Obool)), _1355526), _1355528)), -(_1355526 = c_Orderings_Obot__class_Obot(tc_fun(_1355524, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355524), _1355528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355524), c_Big__Operators_Olinorder__class_OMax(_1355524, _1355526)), c_Big__Operators_Olinorder__class_OMax(_1355524, _1355528))))], (31413 ^ _780461) ^ [_1355830, _1355832, _1355834] : [class_Lattices_Olattice(_1355830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355830), _1355832)), -(_1355832 = c_Orderings_Obot__class_Obot(tc_fun(_1355830, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1355830, hAPP(hAPP(c_Set_Oinsert(_1355830), _1355834), _1355832)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1355830), _1355834), c_Big__Operators_Olattice__class_OSup__fin(_1355830, _1355832)))], (31427 ^ _780461) ^ [_1356038, _1356040, _1356042] : [class_Lattices_Olattice(_1356038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356038), _1356040)), -(_1356040 = c_Orderings_Obot__class_Obot(tc_fun(_1356038, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1356038, hAPP(hAPP(c_Set_Oinsert(_1356038), _1356042), _1356040)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1356038), _1356042), c_Big__Operators_Olattice__class_OInf__fin(_1356038, _1356040)))], (31441 ^ _780461) ^ [_1356246, _1356248, _1356250] : [class_Orderings_Olinorder(_1356246), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356246), _1356248)), -(_1356248 = c_Orderings_Obot__class_Obot(tc_fun(_1356246, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1356246, hAPP(hAPP(c_Set_Oinsert(_1356246), _1356250), _1356248)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1356246), _1356250), c_Big__Operators_Olinorder__class_OMax(_1356246, _1356248)))], (31455 ^ _780461) ^ [_1356454, _1356456, _1356458] : [class_Lattices_Olattice(_1356454), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356454), _1356456)), -(_1356458 = c_Orderings_Obot__class_Obot(tc_fun(_1356454, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1356454, tc_HOL_Obool)), _1356458), _1356456)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1356454), c_Big__Operators_Olattice__class_OSup__fin(_1356454, _1356458)), c_Big__Operators_Olattice__class_OSup__fin(_1356454, _1356456)) = c_Big__Operators_Olattice__class_OSup__fin(_1356454, _1356456))], (31473 ^ _780461) ^ [_1356768, _1356770, _1356772] : [class_Lattices_Olattice(_1356768), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356768), _1356770)), -(_1356772 = c_Orderings_Obot__class_Obot(tc_fun(_1356768, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1356768, tc_HOL_Obool)), _1356772), _1356770)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1356768), c_Big__Operators_Olattice__class_OInf__fin(_1356768, _1356772)), c_Big__Operators_Olattice__class_OInf__fin(_1356768, _1356770)) = c_Big__Operators_Olattice__class_OInf__fin(_1356768, _1356770))], (31491 ^ _780461) ^ [_1357082, _1357084, _1357086] : [class_Lattices_Olattice(_1357082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357082), _1357084)), -(_1357084 = c_Orderings_Obot__class_Obot(tc_fun(_1357082, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357082), _1357086)), -(_1357086 = c_Orderings_Obot__class_Obot(tc_fun(_1357082, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1357082, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1357082, tc_HOL_Obool)), _1357084), _1357086)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1357082), c_Big__Operators_Olattice__class_OSup__fin(_1357082, _1357084)), c_Big__Operators_Olattice__class_OSup__fin(_1357082, _1357086)))], (31513 ^ _780461) ^ [_1357431, _1357433, _1357435] : [class_Orderings_Olinorder(_1357431), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357431), _1357433)), -(_1357435 = c_Orderings_Obot__class_Obot(tc_fun(_1357431, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357431, tc_HOL_Obool)), _1357435), _1357433)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1357431), c_Big__Operators_Olinorder__class_OMax(_1357431, _1357435)), c_Big__Operators_Olinorder__class_OMax(_1357431, _1357433)) = c_Big__Operators_Olinorder__class_OMax(_1357431, _1357433))], (31531 ^ _780461) ^ [_1357745, _1357747, _1357749] : [class_Lattices_Olattice(_1357745), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357745), _1357747)), -(_1357747 = c_Orderings_Obot__class_Obot(tc_fun(_1357745, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357745), _1357749)), -(_1357749 = c_Orderings_Obot__class_Obot(tc_fun(_1357745, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1357745, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1357745, tc_HOL_Obool)), _1357747), _1357749)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1357745), c_Big__Operators_Olattice__class_OInf__fin(_1357745, _1357747)), c_Big__Operators_Olattice__class_OInf__fin(_1357745, _1357749)))], (31553 ^ _780461) ^ [_1358094, _1358096, _1358098] : [class_Orderings_Olinorder(_1358094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358094), _1358096)), -(_1358096 = c_Orderings_Obot__class_Obot(tc_fun(_1358094, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358094), _1358098)), -(_1358098 = c_Orderings_Obot__class_Obot(tc_fun(_1358094, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1358094, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1358094, tc_HOL_Obool)), _1358096), _1358098)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1358094), c_Big__Operators_Olinorder__class_OMax(_1358094, _1358096)), c_Big__Operators_Olinorder__class_OMax(_1358094, _1358098)))], (31575 ^ _780461) ^ [_1358464, _1358466, _1358468, _1358470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358464, _1358466)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358468, _1358470))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358464), _1358466)), 31582 ^ _780461 : [(31583 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358468), _1358464)))], (31585 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358466), _1358470)))]]], (31587 ^ _780461) ^ [_1358685, _1358687, _1358689, _1358691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358685, _1358687)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358689, _1358691)))), 31588 ^ _780461 : [(31589 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358685), _1358687)))], (31591 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358689), _1358685)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358687), _1358691))]]], (31599 ^ _780461) ^ [_1358938, _1358940, _1358942, _1358944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358938, _1358940)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358942, _1358944))), 31602 ^ _780461 : [(31621 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358942), _1358944)))], (31603 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358938), _1358940)), 31606 ^ _780461 : [(31607 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358942), _1358938)))], (31609 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358940), _1358944)))], (31611 ^ _780461) ^ [] : [31612 ^ _780461 : [(31613 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358942), _1358938)))], (31615 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358938), _1358942))]], 31616 ^ _780461 : [(31617 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358940), _1358944)))], (31619 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1358944), _1358940))]]]]]]], (31623 ^ _780461) ^ [_1359400, _1359402, _1359404, _1359406] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359400, _1359402)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359404, _1359406)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359404), _1359406)), 31626 ^ _780461 : [(31627 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359400), _1359402)))], (31629 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359404), _1359400)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359402), _1359406)), 31636 ^ _780461 : [(31637 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359404), _1359400)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359400), _1359404)))], (31643 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359402), _1359406)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1359406), _1359402)))]]]]], (31653 ^ _780461) ^ [_1359943, _1359945, _1359947] : [class_Lattices_Olattice(_1359943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359943), _1359945)), -(hBOOL(hAPP(hAPP(c_member(_1359943), _1359947), _1359945))), -(_1359945 = c_Orderings_Obot__class_Obot(tc_fun(_1359943, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1359943, hAPP(hAPP(c_Set_Oinsert(_1359943), _1359947), _1359945)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1359943), _1359947), c_Big__Operators_Olattice__class_OSup__fin(_1359943, _1359945)))], (31671 ^ _780461) ^ [_1360180, _1360182, _1360184] : [class_Lattices_Olattice(_1360180), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360180), _1360182)), -(hBOOL(hAPP(hAPP(c_member(_1360180), _1360184), _1360182))), -(_1360182 = c_Orderings_Obot__class_Obot(tc_fun(_1360180, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1360180, hAPP(hAPP(c_Set_Oinsert(_1360180), _1360184), _1360182)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1360180), _1360184), c_Big__Operators_Olattice__class_OInf__fin(_1360180, _1360182)))], (31689 ^ _780461) ^ [_1360417, _1360419, _1360421] : [class_Orderings_Olinorder(_1360417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360417), _1360419)), -(hBOOL(hAPP(hAPP(c_member(_1360417), _1360421), _1360419))), -(_1360419 = c_Orderings_Obot__class_Obot(tc_fun(_1360417, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1360417, hAPP(hAPP(c_Set_Oinsert(_1360417), _1360421), _1360419)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360417), _1360421), c_Big__Operators_Olinorder__class_OMax(_1360417, _1360419)))], (31707 ^ _780461) ^ [_1360654, _1360656, _1360658] : [class_Lattices_Olattice(_1360654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360654), _1360656)), 31714 ^ _780461 : [(31715 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360654, tc_HOL_Obool)), _1360656), hAPP(hAPP(c_Set_Oinsert(_1360654), _1360658), c_Orderings_Obot__class_Obot(tc_fun(_1360654, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1360654, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1360654, hAPP(hAPP(c_Set_Oinsert(_1360654), _1360658), _1360656)) = _1360658)], (31721 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360654, tc_HOL_Obool)), _1360656), hAPP(hAPP(c_Set_Oinsert(_1360654), _1360658), c_Orderings_Obot__class_Obot(tc_fun(_1360654, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1360654, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1360654, hAPP(hAPP(c_Set_Oinsert(_1360654), _1360658), _1360656)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1360654), _1360658), c_Big__Operators_Olattice__class_OSup__fin(_1360654, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1360654, tc_HOL_Obool)), _1360656), hAPP(hAPP(c_Set_Oinsert(_1360654), _1360658), c_Orderings_Obot__class_Obot(tc_fun(_1360654, tc_HOL_Obool)))))))]]], (31727 ^ _780461) ^ [_1361124, _1361126, _1361128] : [class_Lattices_Olattice(_1361124), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361124), _1361126)), 31734 ^ _780461 : [(31735 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361124, tc_HOL_Obool)), _1361126), hAPP(hAPP(c_Set_Oinsert(_1361124), _1361128), c_Orderings_Obot__class_Obot(tc_fun(_1361124, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1361124, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1361124, hAPP(hAPP(c_Set_Oinsert(_1361124), _1361128), _1361126)) = _1361128)], (31741 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361124, tc_HOL_Obool)), _1361126), hAPP(hAPP(c_Set_Oinsert(_1361124), _1361128), c_Orderings_Obot__class_Obot(tc_fun(_1361124, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1361124, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1361124, hAPP(hAPP(c_Set_Oinsert(_1361124), _1361128), _1361126)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1361124), _1361128), c_Big__Operators_Olattice__class_OInf__fin(_1361124, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361124, tc_HOL_Obool)), _1361126), hAPP(hAPP(c_Set_Oinsert(_1361124), _1361128), c_Orderings_Obot__class_Obot(tc_fun(_1361124, tc_HOL_Obool)))))))]]], (31747 ^ _780461) ^ [_1361594, _1361596, _1361598] : [class_Lattices_Olattice(_1361594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361594), _1361596)), -(_1361596 = c_Orderings_Obot__class_Obot(tc_fun(_1361594, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361594), _1361598)), -(_1361598 = c_Orderings_Obot__class_Obot(tc_fun(_1361594, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361594, tc_HOL_Obool)), _1361596), _1361598) = c_Orderings_Obot__class_Obot(tc_fun(_1361594, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1361594, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361594, tc_HOL_Obool)), _1361596), _1361598)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1361594), c_Big__Operators_Olattice__class_OSup__fin(_1361594, _1361596)), c_Big__Operators_Olattice__class_OSup__fin(_1361594, _1361598)))], (31773 ^ _780461) ^ [_1362071, _1362073, _1362075] : [class_Lattices_Olattice(_1362071), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362071), _1362073)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362071), _1362075)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1362071, tc_HOL_Obool)), _1362073), _1362075) = c_Orderings_Obot__class_Obot(tc_fun(_1362071, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1362071), c_Big__Operators_Olattice__class_OSup__fin(_1362071, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362071, tc_HOL_Obool)), _1362073), _1362075))), c_Big__Operators_Olattice__class_OSup__fin(_1362071, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1362071, tc_HOL_Obool)), _1362073), _1362075))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1362071), c_Big__Operators_Olattice__class_OSup__fin(_1362071, _1362073)), c_Big__Operators_Olattice__class_OSup__fin(_1362071, _1362075)))], (31791 ^ _780461) ^ [_1362419, _1362421, _1362423] : [class_Orderings_Olinorder(_1362419), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362419), _1362421)), 31798 ^ _780461 : [(31799 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1362419, tc_HOL_Obool)), _1362421), hAPP(hAPP(c_Set_Oinsert(_1362419), _1362423), c_Orderings_Obot__class_Obot(tc_fun(_1362419, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1362419, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1362419, hAPP(hAPP(c_Set_Oinsert(_1362419), _1362423), _1362421)) = _1362423)], (31805 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1362419, tc_HOL_Obool)), _1362421), hAPP(hAPP(c_Set_Oinsert(_1362419), _1362423), c_Orderings_Obot__class_Obot(tc_fun(_1362419, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1362419, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1362419, hAPP(hAPP(c_Set_Oinsert(_1362419), _1362423), _1362421)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1362419), _1362423), c_Big__Operators_Olinorder__class_OMax(_1362419, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1362419, tc_HOL_Obool)), _1362421), hAPP(hAPP(c_Set_Oinsert(_1362419), _1362423), c_Orderings_Obot__class_Obot(tc_fun(_1362419, tc_HOL_Obool)))))))]]], (31811 ^ _780461) ^ [_1362889, _1362891, _1362893] : [class_Lattices_Olattice(_1362889), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362889), _1362891)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1362889), _1362893)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1362889, tc_HOL_Obool)), _1362891), _1362893) = c_Orderings_Obot__class_Obot(tc_fun(_1362889, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1362889), c_Big__Operators_Olattice__class_OInf__fin(_1362889, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362889, tc_HOL_Obool)), _1362891), _1362893))), c_Big__Operators_Olattice__class_OInf__fin(_1362889, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1362889, tc_HOL_Obool)), _1362891), _1362893))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1362889), c_Big__Operators_Olattice__class_OInf__fin(_1362889, _1362891)), c_Big__Operators_Olattice__class_OInf__fin(_1362889, _1362893)))], (31829 ^ _780461) ^ [_1363237, _1363239, _1363241] : [class_Lattices_Olattice(_1363237), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363237), _1363239)), -(_1363239 = c_Orderings_Obot__class_Obot(tc_fun(_1363237, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363237), _1363241)), -(_1363241 = c_Orderings_Obot__class_Obot(tc_fun(_1363237, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1363237, tc_HOL_Obool)), _1363239), _1363241) = c_Orderings_Obot__class_Obot(tc_fun(_1363237, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1363237, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363237, tc_HOL_Obool)), _1363239), _1363241)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1363237), c_Big__Operators_Olattice__class_OInf__fin(_1363237, _1363239)), c_Big__Operators_Olattice__class_OInf__fin(_1363237, _1363241)))], (31855 ^ _780461) ^ [_1363714, _1363716, _1363718] : [class_Orderings_Olinorder(_1363714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363714), _1363716)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363714), _1363718)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1363714, tc_HOL_Obool)), _1363716), _1363718) = c_Orderings_Obot__class_Obot(tc_fun(_1363714, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363714), c_Big__Operators_Olinorder__class_OMax(_1363714, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363714, tc_HOL_Obool)), _1363716), _1363718))), c_Big__Operators_Olinorder__class_OMax(_1363714, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1363714, tc_HOL_Obool)), _1363716), _1363718))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1363714), c_Big__Operators_Olinorder__class_OMax(_1363714, _1363716)), c_Big__Operators_Olinorder__class_OMax(_1363714, _1363718)))], (31873 ^ _780461) ^ [_1364062, _1364064, _1364066] : [class_Orderings_Olinorder(_1364062), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364062), _1364064)), -(_1364064 = c_Orderings_Obot__class_Obot(tc_fun(_1364062, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364062), _1364066)), -(_1364066 = c_Orderings_Obot__class_Obot(tc_fun(_1364062, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364062, tc_HOL_Obool)), _1364064), _1364066) = c_Orderings_Obot__class_Obot(tc_fun(_1364062, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1364062, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364062, tc_HOL_Obool)), _1364064), _1364066)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364062), c_Big__Operators_Olinorder__class_OMax(_1364062, _1364064)), c_Big__Operators_Olinorder__class_OMax(_1364062, _1364066)))], (31899 ^ _780461) ^ [_1364539, _1364541] : [class_Orderings_Olinorder(_1364539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364539), _1364541)), -(_1364541 = c_Orderings_Obot__class_Obot(tc_fun(_1364539, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1364539), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1364539), 31912 ^ [_1364539, _1364541]), 31913 ^ [_1364539, _1364541])), hAPP(hAPP(c_Set_Oinsert(_1364539), 31912 ^ [_1364539, _1364541]), hAPP(hAPP(c_Set_Oinsert(_1364539), 31913 ^ [_1364539, _1364541]), c_Orderings_Obot__class_Obot(tc_fun(_1364539, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1364539), c_Big__Operators_Olinorder__class_OMax(_1364539, _1364541)), _1364541)))], (31919 ^ _780461) ^ [_1364983, _1364985] : [class_Lattices_Olattice(_1364983), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364983), _1364985)), -(_1364985 = c_Orderings_Obot__class_Obot(tc_fun(_1364983, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1364983), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1364983), 31932 ^ [_1364983, _1364985]), 31933 ^ [_1364983, _1364985])), hAPP(hAPP(c_Set_Oinsert(_1364983), 31932 ^ [_1364983, _1364985]), hAPP(hAPP(c_Set_Oinsert(_1364983), 31933 ^ [_1364983, _1364985]), c_Orderings_Obot__class_Obot(tc_fun(_1364983, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1364983), c_Big__Operators_Olattice__class_OInf__fin(_1364983, _1364985)), _1364985)))], (31939 ^ _780461) ^ [_1365427, _1365429] : [class_Lattices_Olattice(_1365427), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365427), _1365429)), -(_1365429 = c_Orderings_Obot__class_Obot(tc_fun(_1365427, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1365427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1365427), 31952 ^ [_1365427, _1365429]), 31953 ^ [_1365427, _1365429])), hAPP(hAPP(c_Set_Oinsert(_1365427), 31952 ^ [_1365427, _1365429]), hAPP(hAPP(c_Set_Oinsert(_1365427), 31953 ^ [_1365427, _1365429]), c_Orderings_Obot__class_Obot(tc_fun(_1365427, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1365427), c_Big__Operators_Olattice__class_OSup__fin(_1365427, _1365429)), _1365429)))], (31959 ^ _780461) ^ [_1365871, _1365873, _1365875] : [class_Orderings_Olinorder(_1365871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365871), _1365873)), hBOOL(hAPP(hAPP(c_member(_1365871), _1365875), _1365873)), 31970 ^ _780461 : [(31971 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365871, tc_HOL_Obool)), _1365873), hAPP(hAPP(c_Set_Oinsert(_1365871), _1365875), c_Orderings_Obot__class_Obot(tc_fun(_1365871, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365871, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1365871, _1365873) = _1365875)], (31977 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365871, tc_HOL_Obool)), _1365873), hAPP(hAPP(c_Set_Oinsert(_1365871), _1365875), c_Orderings_Obot__class_Obot(tc_fun(_1365871, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365871, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1365871, _1365873) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1365871), _1365875), c_Big__Operators_Olinorder__class_OMin(_1365871, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365871, tc_HOL_Obool)), _1365873), hAPP(hAPP(c_Set_Oinsert(_1365871), _1365875), c_Orderings_Obot__class_Obot(tc_fun(_1365871, tc_HOL_Obool)))))))]]], (31983 ^ _780461) ^ [_1366377, _1366379] : [class_Orderings_Olinorder(_1366377), -(c_Big__Operators_Olinorder__class_OMin(_1366377, hAPP(hAPP(c_Set_Oinsert(_1366377), _1366379), c_Orderings_Obot__class_Obot(tc_fun(_1366377, tc_HOL_Obool)))) = _1366379)], (31989 ^ _780461) ^ [_1366484, _1366486, _1366488] : [class_Orderings_Olinorder(_1366484), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366484), _1366486)), hBOOL(hAPP(hAPP(c_member(_1366484), _1366488), _1366486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366484), c_Big__Operators_Olinorder__class_OMin(_1366484, _1366486)), _1366488)))], (32003 ^ _780461) ^ [_1366711, _1366713] : [class_Orderings_Olinorder(_1366711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366711), _1366713)), -(_1366713 = c_Orderings_Obot__class_Obot(tc_fun(_1366711, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1366711), c_Big__Operators_Olinorder__class_OMin(_1366711, _1366713)), _1366713)))], (32017 ^ _780461) ^ [_1366891, _1366893, _1366895] : [class_Orderings_Olinorder(_1366891), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366891), _1366893)), hBOOL(hAPP(hAPP(c_member(_1366891), _1366895), _1366893)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1366891), _1366895), c_Big__Operators_Olinorder__class_OMin(_1366891, _1366893)) = c_Big__Operators_Olinorder__class_OMin(_1366891, _1366893))], (32031 ^ _780461) ^ [_1367126, _1367128, _1367130] : [class_Orderings_Olinorder(_1367126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1367126, tc_HOL_Obool)), _1367128), _1367130)), -(_1367128 = c_Orderings_Obot__class_Obot(tc_fun(_1367126, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367126), _1367130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367126), c_Big__Operators_Olinorder__class_OMin(_1367126, _1367130)), c_Big__Operators_Olinorder__class_OMin(_1367126, _1367128))))], (32049 ^ _780461) ^ [_1367432, _1367434, _1367436] : [class_Orderings_Olinorder(_1367432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367432), _1367434)), -(_1367434 = c_Orderings_Obot__class_Obot(tc_fun(_1367432, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1367432, hAPP(hAPP(c_Set_Oinsert(_1367432), _1367436), _1367434)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367432), _1367436), c_Big__Operators_Olinorder__class_OMin(_1367432, _1367434)))], (32063 ^ _780461) ^ [_1367640, _1367642, _1367644] : [class_Orderings_Olinorder(_1367640), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367640), _1367642)), -(_1367644 = c_Orderings_Obot__class_Obot(tc_fun(_1367640, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1367640, tc_HOL_Obool)), _1367644), _1367642)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367640), c_Big__Operators_Olinorder__class_OMin(_1367640, _1367644)), c_Big__Operators_Olinorder__class_OMin(_1367640, _1367642)) = c_Big__Operators_Olinorder__class_OMin(_1367640, _1367642))], (32081 ^ _780461) ^ [_1367954, _1367956, _1367958] : [class_Orderings_Olinorder(_1367954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367954), _1367956)), -(_1367956 = c_Orderings_Obot__class_Obot(tc_fun(_1367954, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367954), _1367958)), -(_1367958 = c_Orderings_Obot__class_Obot(tc_fun(_1367954, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1367954, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1367954, tc_HOL_Obool)), _1367956), _1367958)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367954), c_Big__Operators_Olinorder__class_OMin(_1367954, _1367956)), c_Big__Operators_Olinorder__class_OMin(_1367954, _1367958)))], (32103 ^ _780461) ^ [_1368303, _1368305, _1368307] : [class_Orderings_Olinorder(_1368303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368303), _1368305)), -(hBOOL(hAPP(hAPP(c_member(_1368303), _1368307), _1368305))), -(_1368305 = c_Orderings_Obot__class_Obot(tc_fun(_1368303, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1368303, hAPP(hAPP(c_Set_Oinsert(_1368303), _1368307), _1368305)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1368303), _1368307), c_Big__Operators_Olinorder__class_OMin(_1368303, _1368305)))], (32121 ^ _780461) ^ [_1368540, _1368542, _1368544] : [class_Orderings_Olinorder(_1368540), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368540), _1368542)), 32128 ^ _780461 : [(32129 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368540, tc_HOL_Obool)), _1368542), hAPP(hAPP(c_Set_Oinsert(_1368540), _1368544), c_Orderings_Obot__class_Obot(tc_fun(_1368540, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1368540, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1368540, hAPP(hAPP(c_Set_Oinsert(_1368540), _1368544), _1368542)) = _1368544)], (32135 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368540, tc_HOL_Obool)), _1368542), hAPP(hAPP(c_Set_Oinsert(_1368540), _1368544), c_Orderings_Obot__class_Obot(tc_fun(_1368540, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1368540, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1368540, hAPP(hAPP(c_Set_Oinsert(_1368540), _1368544), _1368542)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1368540), _1368544), c_Big__Operators_Olinorder__class_OMin(_1368540, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1368540, tc_HOL_Obool)), _1368542), hAPP(hAPP(c_Set_Oinsert(_1368540), _1368544), c_Orderings_Obot__class_Obot(tc_fun(_1368540, tc_HOL_Obool)))))))]]], (32141 ^ _780461) ^ [_1369010, _1369012, _1369014] : [class_Orderings_Olinorder(_1369010), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369010), _1369012)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369010), _1369014)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369010, tc_HOL_Obool)), _1369012), _1369014) = c_Orderings_Obot__class_Obot(tc_fun(_1369010, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1369010), c_Big__Operators_Olinorder__class_OMin(_1369010, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1369010, tc_HOL_Obool)), _1369012), _1369014))), c_Big__Operators_Olinorder__class_OMin(_1369010, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369010, tc_HOL_Obool)), _1369012), _1369014))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1369010), c_Big__Operators_Olinorder__class_OMin(_1369010, _1369012)), c_Big__Operators_Olinorder__class_OMin(_1369010, _1369014)))], (32159 ^ _780461) ^ [_1369358, _1369360, _1369362] : [class_Orderings_Olinorder(_1369358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369358), _1369360)), -(_1369360 = c_Orderings_Obot__class_Obot(tc_fun(_1369358, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369358), _1369362)), -(_1369362 = c_Orderings_Obot__class_Obot(tc_fun(_1369358, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369358, tc_HOL_Obool)), _1369360), _1369362) = c_Orderings_Obot__class_Obot(tc_fun(_1369358, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1369358, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1369358, tc_HOL_Obool)), _1369360), _1369362)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1369358), c_Big__Operators_Olinorder__class_OMin(_1369358, _1369360)), c_Big__Operators_Olinorder__class_OMin(_1369358, _1369362)))], (32185 ^ _780461) ^ [_1369835, _1369837] : [class_Groups_Olinordered__ab__group__add(_1369835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369835), _1369837)), -(_1369837 = c_Orderings_Obot__class_Obot(tc_fun(_1369835, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1369835), c_Big__Operators_Olinorder__class_OMax(_1369835, _1369837)) = c_Big__Operators_Olinorder__class_OMin(_1369835, hAPP(c_Set_Oimage(_1369835, _1369835, c_Groups_Ouminus__class_Ouminus(_1369835)), _1369837)))], (32199 ^ _780461) ^ [_1370035, _1370037] : [class_Groups_Olinordered__ab__group__add(_1370035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370035), _1370037)), -(_1370037 = c_Orderings_Obot__class_Obot(tc_fun(_1370035, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1370035), c_Big__Operators_Olinorder__class_OMin(_1370035, _1370037)) = c_Big__Operators_Olinorder__class_OMax(_1370035, hAPP(c_Set_Oimage(_1370035, _1370035, c_Groups_Ouminus__class_Ouminus(_1370035)), _1370037)))], (32213 ^ _780461) ^ [_1370235, _1370237] : [class_Orderings_Olinorder(_1370235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370235), _1370237)), -(_1370237 = c_Orderings_Obot__class_Obot(tc_fun(_1370235, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1370235), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1370235), 32226 ^ [_1370235, _1370237]), 32227 ^ [_1370235, _1370237])), hAPP(hAPP(c_Set_Oinsert(_1370235), 32226 ^ [_1370235, _1370237]), hAPP(hAPP(c_Set_Oinsert(_1370235), 32227 ^ [_1370235, _1370237]), c_Orderings_Obot__class_Obot(tc_fun(_1370235, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1370235), c_Big__Operators_Olinorder__class_OMin(_1370235, _1370237)), _1370237)))], (32233 ^ _780461) ^ [_1370679, _1370681, _1370683] : [class_Orderings_Olinorder(_1370679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370679), _1370681)), hBOOL(hAPP(hAPP(c_member(_1370679), _1370683), _1370681)), 32244 ^ _780461 : [(32245 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370679, tc_HOL_Obool)), _1370681), hAPP(hAPP(c_Set_Oinsert(_1370679), _1370683), c_Orderings_Obot__class_Obot(tc_fun(_1370679, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1370679, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1370679, c_Orderings_Oord__class_Omax(_1370679), _1370681) = _1370683)], (32251 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370679, tc_HOL_Obool)), _1370681), hAPP(hAPP(c_Set_Oinsert(_1370679), _1370683), c_Orderings_Obot__class_Obot(tc_fun(_1370679, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1370679, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1370679, c_Orderings_Oord__class_Omax(_1370679), _1370681) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1370679), _1370683), c_Big__Operators_Olattice_OSup__fin(_1370679, c_Orderings_Oord__class_Omax(_1370679), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1370679, tc_HOL_Obool)), _1370681), hAPP(hAPP(c_Set_Oinsert(_1370679), _1370683), c_Orderings_Obot__class_Obot(tc_fun(_1370679, tc_HOL_Obool)))))))]]], (32257 ^ _780461) ^ [_1371203, _1371205, _1371207] : [class_Orderings_Olinorder(_1371203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371203), _1371205)), hBOOL(hAPP(hAPP(c_member(_1371203), _1371207), _1371205)), 32268 ^ _780461 : [(32269 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371203, tc_HOL_Obool)), _1371205), hAPP(hAPP(c_Set_Oinsert(_1371203), _1371207), c_Orderings_Obot__class_Obot(tc_fun(_1371203, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371203, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1371203, c_Orderings_Oord__class_Omin(_1371203), _1371205) = _1371207)], (32275 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371203, tc_HOL_Obool)), _1371205), hAPP(hAPP(c_Set_Oinsert(_1371203), _1371207), c_Orderings_Obot__class_Obot(tc_fun(_1371203, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1371203, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1371203, c_Orderings_Oord__class_Omin(_1371203), _1371205) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371203), _1371207), c_Big__Operators_Olattice_OInf__fin(_1371203, c_Orderings_Oord__class_Omin(_1371203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371203, tc_HOL_Obool)), _1371205), hAPP(hAPP(c_Set_Oinsert(_1371203), _1371207), c_Orderings_Obot__class_Obot(tc_fun(_1371203, tc_HOL_Obool)))))))]]], (32281 ^ _780461) ^ [_1371727, _1371729] : [class_Orderings_Olinorder(_1371727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371727), _1371729)), -(_1371729 = c_Orderings_Obot__class_Obot(tc_fun(_1371727, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1371727), c_Big__Operators_Olattice_OInf__fin(_1371727, c_Orderings_Oord__class_Omin(_1371727), _1371729)), c_Big__Operators_Olattice_OSup__fin(_1371727, c_Orderings_Oord__class_Omax(_1371727), _1371729))))], (32295 ^ _780461) ^ [_1371925, _1371927, _1371929] : [class_Orderings_Olinorder(_1371925), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371925), _1371927)), hBOOL(hAPP(hAPP(c_member(_1371925), _1371929), _1371927)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1371925), _1371929), c_Big__Operators_Olattice_OInf__fin(_1371925, c_Orderings_Oord__class_Omin(_1371925), _1371927)) = c_Big__Operators_Olattice_OInf__fin(_1371925, c_Orderings_Oord__class_Omin(_1371925), _1371927))], (32309 ^ _780461) ^ [_1372172, _1372174, _1372176] : [class_Orderings_Olinorder(_1372172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372172), _1372174)), hBOOL(hAPP(hAPP(c_member(_1372172), _1372176), _1372174)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372172), _1372176), c_Big__Operators_Olattice_OSup__fin(_1372172, c_Orderings_Oord__class_Omax(_1372172), _1372174)) = c_Big__Operators_Olattice_OSup__fin(_1372172, c_Orderings_Oord__class_Omax(_1372172), _1372174))], (32323 ^ _780461) ^ [_1372419, _1372421] : [class_Orderings_Olinorder(_1372419), -(c_Big__Operators_Olattice_OInf__fin(_1372419, c_Orderings_Oord__class_Omin(_1372419), hAPP(hAPP(c_Set_Oinsert(_1372419), _1372421), c_Orderings_Obot__class_Obot(tc_fun(_1372419, tc_HOL_Obool)))) = _1372421)], (32329 ^ _780461) ^ [_1372532, _1372534] : [class_Orderings_Olinorder(_1372532), -(c_Big__Operators_Olattice_OSup__fin(_1372532, c_Orderings_Oord__class_Omax(_1372532), hAPP(hAPP(c_Set_Oinsert(_1372532), _1372534), c_Orderings_Obot__class_Obot(tc_fun(_1372532, tc_HOL_Obool)))) = _1372534)], (32335 ^ _780461) ^ [_1372645, _1372647, _1372649] : [class_Orderings_Olinorder(_1372645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372645), _1372647)), -(_1372647 = c_Orderings_Obot__class_Obot(tc_fun(_1372645, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1372645, c_Orderings_Oord__class_Omin(_1372645), hAPP(hAPP(c_Set_Oinsert(_1372645), _1372649), _1372647)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1372645), _1372649), c_Big__Operators_Olattice_OInf__fin(_1372645, c_Orderings_Oord__class_Omin(_1372645), _1372647)))], (32349 ^ _780461) ^ [_1372865, _1372867, _1372869] : [class_Orderings_Olinorder(_1372865), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372865), _1372867)), -(_1372867 = c_Orderings_Obot__class_Obot(tc_fun(_1372865, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1372865, c_Orderings_Oord__class_Omax(_1372865), hAPP(hAPP(c_Set_Oinsert(_1372865), _1372869), _1372867)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1372865), _1372869), c_Big__Operators_Olattice_OSup__fin(_1372865, c_Orderings_Oord__class_Omax(_1372865), _1372867)))], (32363 ^ _780461) ^ [_1373085, _1373087, _1373089] : [class_Orderings_Olinorder(_1373085), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373085), _1373087)), -(_1373089 = c_Orderings_Obot__class_Obot(tc_fun(_1373085, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373085, tc_HOL_Obool)), _1373089), _1373087)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1373085), c_Big__Operators_Olattice_OInf__fin(_1373085, c_Orderings_Oord__class_Omin(_1373085), _1373089)), c_Big__Operators_Olattice_OInf__fin(_1373085, c_Orderings_Oord__class_Omin(_1373085), _1373087)) = c_Big__Operators_Olattice_OInf__fin(_1373085, c_Orderings_Oord__class_Omin(_1373085), _1373087))], (32381 ^ _780461) ^ [_1373417, _1373419, _1373421] : [class_Orderings_Olinorder(_1373417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373417), _1373419)), -(_1373421 = c_Orderings_Obot__class_Obot(tc_fun(_1373417, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373417, tc_HOL_Obool)), _1373421), _1373419)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373417), c_Big__Operators_Olattice_OSup__fin(_1373417, c_Orderings_Oord__class_Omax(_1373417), _1373421)), c_Big__Operators_Olattice_OSup__fin(_1373417, c_Orderings_Oord__class_Omax(_1373417), _1373419)) = c_Big__Operators_Olattice_OSup__fin(_1373417, c_Orderings_Oord__class_Omax(_1373417), _1373419))], (32399 ^ _780461) ^ [_1373749, _1373751, _1373753] : [class_Orderings_Olinorder(_1373749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373749), _1373751)), hBOOL(hAPP(hAPP(c_member(_1373749), _1373753), _1373751)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1373749), _1373753), c_Big__Operators_Olattice_OSup__fin(_1373749, c_Orderings_Oord__class_Omax(_1373749), _1373751)) = _1373753)], (32413 ^ _780461) ^ [_1373984, _1373986, _1373988] : [class_Orderings_Olinorder(_1373984), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373984), _1373986)), hBOOL(hAPP(hAPP(c_member(_1373984), _1373988), _1373986)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1373984), _1373988), c_Big__Operators_Olattice_OInf__fin(_1373984, c_Orderings_Oord__class_Omin(_1373984), _1373986)) = _1373988)], (32427 ^ _780461) ^ [_1374219, _1374221, _1374223] : [class_Orderings_Olinorder(_1374219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374219), _1374221)), -(_1374221 = c_Orderings_Obot__class_Obot(tc_fun(_1374219, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374219), _1374223)), -(_1374223 = c_Orderings_Obot__class_Obot(tc_fun(_1374219, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1374219, c_Orderings_Oord__class_Omin(_1374219), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1374219, tc_HOL_Obool)), _1374221), _1374223)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1374219), c_Big__Operators_Olattice_OInf__fin(_1374219, c_Orderings_Oord__class_Omin(_1374219), _1374221)), c_Big__Operators_Olattice_OInf__fin(_1374219, c_Orderings_Oord__class_Omin(_1374219), _1374223)))], (32449 ^ _780461) ^ [_1374586, _1374588, _1374590] : [class_Orderings_Olinorder(_1374586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374586), _1374588)), -(_1374588 = c_Orderings_Obot__class_Obot(tc_fun(_1374586, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374586), _1374590)), -(_1374590 = c_Orderings_Obot__class_Obot(tc_fun(_1374586, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1374586, c_Orderings_Oord__class_Omax(_1374586), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1374586, tc_HOL_Obool)), _1374588), _1374590)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1374586), c_Big__Operators_Olattice_OSup__fin(_1374586, c_Orderings_Oord__class_Omax(_1374586), _1374588)), c_Big__Operators_Olattice_OSup__fin(_1374586, c_Orderings_Oord__class_Omax(_1374586), _1374590)))], (32471 ^ _780461) ^ [_1374953, _1374955, _1374957] : [class_Orderings_Olinorder(_1374953), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374953), _1374955)), -(hBOOL(hAPP(hAPP(c_member(_1374953), _1374957), _1374955))), -(_1374955 = c_Orderings_Obot__class_Obot(tc_fun(_1374953, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1374953, c_Orderings_Oord__class_Omin(_1374953), hAPP(hAPP(c_Set_Oinsert(_1374953), _1374957), _1374955)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1374953), _1374957), c_Big__Operators_Olattice_OInf__fin(_1374953, c_Orderings_Oord__class_Omin(_1374953), _1374955)))], (32489 ^ _780461) ^ [_1375202, _1375204, _1375206] : [class_Orderings_Olinorder(_1375202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375202), _1375204)), -(hBOOL(hAPP(hAPP(c_member(_1375202), _1375206), _1375204))), -(_1375204 = c_Orderings_Obot__class_Obot(tc_fun(_1375202, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1375202, c_Orderings_Oord__class_Omax(_1375202), hAPP(hAPP(c_Set_Oinsert(_1375202), _1375206), _1375204)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375202), _1375206), c_Big__Operators_Olattice_OSup__fin(_1375202, c_Orderings_Oord__class_Omax(_1375202), _1375204)))], (32507 ^ _780461) ^ [_1375451, _1375453, _1375455] : [class_Orderings_Olinorder(_1375451), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375451), _1375453)), 32514 ^ _780461 : [(32515 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375451, tc_HOL_Obool)), _1375453), hAPP(hAPP(c_Set_Oinsert(_1375451), _1375455), c_Orderings_Obot__class_Obot(tc_fun(_1375451, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1375451, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1375451, c_Orderings_Oord__class_Omin(_1375451), hAPP(hAPP(c_Set_Oinsert(_1375451), _1375455), _1375453)) = _1375455)], (32521 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375451, tc_HOL_Obool)), _1375453), hAPP(hAPP(c_Set_Oinsert(_1375451), _1375455), c_Orderings_Obot__class_Obot(tc_fun(_1375451, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1375451, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1375451, c_Orderings_Oord__class_Omin(_1375451), hAPP(hAPP(c_Set_Oinsert(_1375451), _1375455), _1375453)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1375451), _1375455), c_Big__Operators_Olattice_OInf__fin(_1375451, c_Orderings_Oord__class_Omin(_1375451), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375451, tc_HOL_Obool)), _1375453), hAPP(hAPP(c_Set_Oinsert(_1375451), _1375455), c_Orderings_Obot__class_Obot(tc_fun(_1375451, tc_HOL_Obool)))))))]]], (32527 ^ _780461) ^ [_1375939, _1375941, _1375943] : [class_Orderings_Olinorder(_1375939), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375939), _1375941)), 32534 ^ _780461 : [(32535 ^ _780461) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375939, tc_HOL_Obool)), _1375941), hAPP(hAPP(c_Set_Oinsert(_1375939), _1375943), c_Orderings_Obot__class_Obot(tc_fun(_1375939, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1375939, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1375939, c_Orderings_Oord__class_Omax(_1375939), hAPP(hAPP(c_Set_Oinsert(_1375939), _1375943), _1375941)) = _1375943)], (32541 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375939, tc_HOL_Obool)), _1375941), hAPP(hAPP(c_Set_Oinsert(_1375939), _1375943), c_Orderings_Obot__class_Obot(tc_fun(_1375939, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1375939, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1375939, c_Orderings_Oord__class_Omax(_1375939), hAPP(hAPP(c_Set_Oinsert(_1375939), _1375943), _1375941)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375939), _1375943), c_Big__Operators_Olattice_OSup__fin(_1375939, c_Orderings_Oord__class_Omax(_1375939), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1375939, tc_HOL_Obool)), _1375941), hAPP(hAPP(c_Set_Oinsert(_1375939), _1375943), c_Orderings_Obot__class_Obot(tc_fun(_1375939, tc_HOL_Obool)))))))]]], (32547 ^ _780461) ^ [_1376427, _1376429, _1376431] : [class_Orderings_Olinorder(_1376427), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376427), _1376429)), -(_1376429 = c_Orderings_Obot__class_Obot(tc_fun(_1376427, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376427), _1376431)), -(_1376431 = c_Orderings_Obot__class_Obot(tc_fun(_1376427, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376427, tc_HOL_Obool)), _1376429), _1376431) = c_Orderings_Obot__class_Obot(tc_fun(_1376427, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1376427, c_Orderings_Oord__class_Omin(_1376427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376427, tc_HOL_Obool)), _1376429), _1376431)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376427), c_Big__Operators_Olattice_OInf__fin(_1376427, c_Orderings_Oord__class_Omin(_1376427), _1376429)), c_Big__Operators_Olattice_OInf__fin(_1376427, c_Orderings_Oord__class_Omin(_1376427), _1376431)))], (32573 ^ _780461) ^ [_1376922, _1376924, _1376926] : [class_Orderings_Olinorder(_1376922), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376922), _1376924)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376922), _1376926)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376922, tc_HOL_Obool)), _1376924), _1376926) = c_Orderings_Obot__class_Obot(tc_fun(_1376922, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376922), c_Big__Operators_Olattice_OInf__fin(_1376922, c_Orderings_Oord__class_Omin(_1376922), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376922, tc_HOL_Obool)), _1376924), _1376926))), c_Big__Operators_Olattice_OInf__fin(_1376922, c_Orderings_Oord__class_Omin(_1376922), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376922, tc_HOL_Obool)), _1376924), _1376926))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376922), c_Big__Operators_Olattice_OInf__fin(_1376922, c_Orderings_Oord__class_Omin(_1376922), _1376924)), c_Big__Operators_Olattice_OInf__fin(_1376922, c_Orderings_Oord__class_Omin(_1376922), _1376926)))], (32591 ^ _780461) ^ [_1377294, _1377296, _1377298] : [class_Orderings_Olinorder(_1377294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377294), _1377296)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377294), _1377298)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377294, tc_HOL_Obool)), _1377296), _1377298) = c_Orderings_Obot__class_Obot(tc_fun(_1377294, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1377294), c_Big__Operators_Olattice_OSup__fin(_1377294, c_Orderings_Oord__class_Omax(_1377294), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377294, tc_HOL_Obool)), _1377296), _1377298))), c_Big__Operators_Olattice_OSup__fin(_1377294, c_Orderings_Oord__class_Omax(_1377294), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377294, tc_HOL_Obool)), _1377296), _1377298))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1377294), c_Big__Operators_Olattice_OSup__fin(_1377294, c_Orderings_Oord__class_Omax(_1377294), _1377296)), c_Big__Operators_Olattice_OSup__fin(_1377294, c_Orderings_Oord__class_Omax(_1377294), _1377298)))], (32609 ^ _780461) ^ [_1377666, _1377668, _1377670] : [class_Orderings_Olinorder(_1377666), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377666), _1377668)), -(_1377668 = c_Orderings_Obot__class_Obot(tc_fun(_1377666, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377666), _1377670)), -(_1377670 = c_Orderings_Obot__class_Obot(tc_fun(_1377666, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377666, tc_HOL_Obool)), _1377668), _1377670) = c_Orderings_Obot__class_Obot(tc_fun(_1377666, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1377666, c_Orderings_Oord__class_Omax(_1377666), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1377666, tc_HOL_Obool)), _1377668), _1377670)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1377666), c_Big__Operators_Olattice_OSup__fin(_1377666, c_Orderings_Oord__class_Omax(_1377666), _1377668)), c_Big__Operators_Olattice_OSup__fin(_1377666, c_Orderings_Oord__class_Omax(_1377666), _1377670)))], (32635 ^ _780461) ^ [_1378161, _1378163] : [class_Orderings_Olinorder(_1378161), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378161), _1378163)), -(_1378163 = c_Orderings_Obot__class_Obot(tc_fun(_1378161, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1378161), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1378161), 32648 ^ [_1378161, _1378163]), 32649 ^ [_1378161, _1378163])), hAPP(hAPP(c_Set_Oinsert(_1378161), 32648 ^ [_1378161, _1378163]), hAPP(hAPP(c_Set_Oinsert(_1378161), 32649 ^ [_1378161, _1378163]), c_Orderings_Obot__class_Obot(tc_fun(_1378161, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1378161), c_Big__Operators_Olattice_OSup__fin(_1378161, c_Orderings_Oord__class_Omax(_1378161), _1378163)), _1378163)))], (32655 ^ _780461) ^ [_1378611, _1378613] : [class_Orderings_Olinorder(_1378611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378611), _1378613)), -(_1378613 = c_Orderings_Obot__class_Obot(tc_fun(_1378611, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1378611), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1378611), 32668 ^ [_1378611, _1378613]), 32669 ^ [_1378611, _1378613])), hAPP(hAPP(c_Set_Oinsert(_1378611), 32668 ^ [_1378611, _1378613]), hAPP(hAPP(c_Set_Oinsert(_1378611), 32669 ^ [_1378611, _1378613]), c_Orderings_Obot__class_Obot(tc_fun(_1378611, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1378611), c_Big__Operators_Olattice_OInf__fin(_1378611, c_Orderings_Oord__class_Omin(_1378611), _1378613)), _1378613)))], (32675 ^ _780461) ^ [_1379061, _1379063, _1379065, _1379067] : [c_Finite__Set_Ofolding__one(_1379061, _1379063, _1379065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1379061), _1379067)), -(_1379067 = c_Orderings_Obot__class_Obot(tc_fun(_1379061, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1379061), hAPP(hAPP(_1379063, 32688 ^ [_1379061, _1379063, _1379065, _1379067]), 32689 ^ [_1379061, _1379063, _1379065, _1379067])), hAPP(hAPP(c_Set_Oinsert(_1379061), 32688 ^ [_1379061, _1379063, _1379065, _1379067]), hAPP(hAPP(c_Set_Oinsert(_1379061), 32689 ^ [_1379061, _1379063, _1379065, _1379067]), c_Orderings_Obot__class_Obot(tc_fun(_1379061, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1379061), hAPP(_1379065, _1379067)), _1379067)))], (32695 ^ _780461) ^ [_1379547, _1379549, _1379551] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1379547), _1379549)), hBOOL(hAPP(hAPP(c_member(_1379547), _1379551), _1379549)), -(hAPP(c_Finite__Set_Ocard(_1379547), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1379547, tc_HOL_Obool)), _1379549), hAPP(hAPP(c_Set_Oinsert(_1379547), _1379551), c_Orderings_Obot__class_Obot(tc_fun(_1379547, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1379547), _1379549)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (32705 ^ _780461) ^ [_1379782, _1379784, _1379786] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1379782), _1379784)), 32708 ^ _780461 : [(32709 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1379782), _1379786), _1379784)), -(hAPP(c_Finite__Set_Ocard(_1379782), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1379782, tc_HOL_Obool)), _1379784), hAPP(hAPP(c_Set_Oinsert(_1379782), _1379786), c_Orderings_Obot__class_Obot(tc_fun(_1379782, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1379782), _1379784)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (32715 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1379782), _1379786), _1379784))), -(hAPP(c_Finite__Set_Ocard(_1379782), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1379782, tc_HOL_Obool)), _1379784), hAPP(hAPP(c_Set_Oinsert(_1379782), _1379786), c_Orderings_Obot__class_Obot(tc_fun(_1379782, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1379782), _1379784))]]], (32721 ^ _780461) ^ [_1380146, _1380148, _1380150] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1380146), _1380148)), hBOOL(hAPP(hAPP(c_member(_1380146), _1380150), _1380148)), -(hAPP(c_Finite__Set_Ocard(_1380146), _1380148) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1380146), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1380146, tc_HOL_Obool)), _1380148), hAPP(hAPP(c_Set_Oinsert(_1380146), _1380150), c_Orderings_Obot__class_Obot(tc_fun(_1380146, tc_HOL_Obool)))))))], (32731 ^ _780461) ^ [_1380375] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1380375) = 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)), _1380375)))], (32733 ^ _780461) ^ [_1380407] : [c_Nat__Transfer_Onat__set(_1380407), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1380407) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1380407)))], (32739 ^ _780461) ^ [_1380498] : [-(hAPP(c_Finite__Set_Ocard(_1380498), c_Orderings_Obot__class_Obot(tc_fun(_1380498, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32741 ^ _780461) ^ [_1380527, _1380529] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380527), _1380529))), -(hAPP(c_Finite__Set_Ocard(_1380527), _1380529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32757 ^ _780461) ^ [_1380742, _1380744] : [32758 ^ _780461 : [(32759 ^ _780461) ^ [] : [_1380744 = c_Orderings_Obot__class_Obot(tc_fun(_1380742, tc_HOL_Obool))], (32761 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380742), _1380744)))]], -(hAPP(c_Finite__Set_Ocard(_1380742), _1380744) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32747 ^ _780461) ^ [_1380587, _1380589] : [hAPP(c_Finite__Set_Ocard(_1380587), _1380589) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1380589 = c_Orderings_Obot__class_Obot(tc_fun(_1380587, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1380587), _1380589))], (32765 ^ _780461) ^ [_1380886, _1380888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1380886), _1380888))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1380886), _1380888)))], (32771 ^ _780461) ^ [_1380985, _1380987, _1380989] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1380985), _1380987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1380985), _1380987)), hAPP(c_Finite__Set_Ocard(_1380985), hAPP(hAPP(c_Set_Oinsert(_1380985), _1380989), _1380987)))))], (32777 ^ _780461) ^ [_1381118, _1381120, _1381122] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381118), _1381120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1381118, tc_HOL_Obool)), _1381122), _1381120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1381118), _1381120)), hAPP(c_Finite__Set_Ocard(_1381118), _1381122))), -(_1381122 = _1381120)], (32791 ^ _780461) ^ [_1381363, _1381365, _1381367] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381363), _1381365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1381363, tc_HOL_Obool)), _1381367), _1381365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1381363), _1381367)), hAPP(c_Finite__Set_Ocard(_1381363), _1381365))))], (32801 ^ _780461) ^ [_1381554, _1381556, _1381558, _1381560] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381554), _1381556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1381558), hAPP(c_Set_Oimage(_1381554, _1381558, _1381560), _1381556))), hAPP(c_Finite__Set_Ocard(_1381554), _1381556))))], (32807 ^ _780461) ^ [_1381687, _1381689, _1381691] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381687), _1381689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1381687, tc_HOL_Obool)), _1381691), _1381689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1381687), _1381691)), hAPP(c_Finite__Set_Ocard(_1381687), _1381689))))], (32817 ^ _780461) ^ [_1381878, _1381880, _1381882] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1381878), _1381880)), 32820 ^ _780461 : [(32821 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1381878), _1381882), _1381880)), -(hAPP(c_Finite__Set_Ocard(_1381878), hAPP(hAPP(c_Set_Oinsert(_1381878), _1381882), _1381880)) = hAPP(c_Finite__Set_Ocard(_1381878), _1381880))], (32827 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381878), _1381882), _1381880))), -(hAPP(c_Finite__Set_Ocard(_1381878), hAPP(hAPP(c_Set_Oinsert(_1381878), _1381882), _1381880)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1381878), _1381880)))]]], (32833 ^ _780461) ^ [_1382172, _1382174, _1382176] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382172), _1382174)), -(hBOOL(hAPP(hAPP(c_member(_1382172), _1382176), _1382174))), -(hAPP(c_Finite__Set_Ocard(_1382172), hAPP(hAPP(c_Set_Oinsert(_1382172), _1382176), _1382174)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1382172), _1382174)))], (32843 ^ _780461) ^ [_1382345, _1382347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1382345), _1382347))), 32846 ^ _780461 : [(32847 ^ _780461) ^ [] : [_1382347 = c_Orderings_Obot__class_Obot(tc_fun(_1382345, tc_HOL_Obool))], (32849 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1382345), _1382347)))]]], (32851 ^ _780461) ^ [_1382486, _1382488] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1382486), _1382488)))), -(_1382488 = c_Orderings_Obot__class_Obot(tc_fun(_1382486, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382486), _1382488))], (32861 ^ _780461) ^ [_1382652, _1382654, _1382656] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382652), _1382654)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382652), _1382656)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1382652), _1382654)), hAPP(c_Finite__Set_Ocard(_1382652), _1382656)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1382652), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1382652, tc_HOL_Obool)), _1382654), _1382656))), hAPP(c_Finite__Set_Ocard(_1382652), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382652, tc_HOL_Obool)), _1382654), _1382656))))], (32871 ^ _780461) ^ [_1382909, _1382911, _1382913] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382909), _1382911)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382909), _1382913)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1382909), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1382909, tc_HOL_Obool)), _1382911), _1382913))), hAPP(c_Finite__Set_Ocard(_1382909), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382909, tc_HOL_Obool)), _1382911), _1382913))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1382909), _1382911)), hAPP(c_Finite__Set_Ocard(_1382909), _1382913)))], (32881 ^ _780461) ^ [_1383166, _1383168, _1383170] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1383166), _1383168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1383166, tc_HOL_Obool)), _1383168), _1383170)), -(hAPP(c_Finite__Set_Ocard(_1383166), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1383166, tc_HOL_Obool)), _1383170), _1383168)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1383166), _1383170)), hAPP(c_Finite__Set_Ocard(_1383166), _1383168)))], (32891 ^ _780461) ^ [_1383391, _1383393, _1383395] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1383391), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383391, tc_HOL_Obool)), _1383393), _1383395))), -(hAPP(c_Finite__Set_Ocard(_1383391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1383391, tc_HOL_Obool)), _1383393), _1383395)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1383391), _1383393)), hAPP(c_Finite__Set_Ocard(_1383391), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383391, tc_HOL_Obool)), _1383393), _1383395))))], (32897 ^ _780461) ^ [_1383586, _1383588, _1383590] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1383586), _1383588)), -(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(_1383586), _1383590)), hAPP(c_Finite__Set_Ocard(_1383586), _1383588))), hAPP(c_Finite__Set_Ocard(_1383586), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1383586, tc_HOL_Obool)), _1383590), _1383588)))))], (32903 ^ _780461) ^ [_1383747, _1383749, _1383751] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1383747), _1383749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1383747, tc_HOL_Obool)), _1383751), _1383749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1383747), _1383751)), hAPP(c_Finite__Set_Ocard(_1383747), _1383749))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1383747, tc_HOL_Obool)), _1383751), _1383749)))], (32917 ^ _780461) ^ [_1384012, _1384014, _1384016] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384012), _1384014)), -(hAPP(c_Finite__Set_Ocard(_1384012), hAPP(hAPP(c_Set_Oinsert(_1384012), _1384016), _1384014)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1384012), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384012, tc_HOL_Obool)), _1384014), hAPP(hAPP(c_Set_Oinsert(_1384012), _1384016), c_Orderings_Obot__class_Obot(tc_fun(_1384012, tc_HOL_Obool)))))))], (32923 ^ _780461) ^ [_1384189, _1384191, _1384193] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384189), _1384191)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384189), _1384193)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384189, tc_HOL_Obool)), _1384191), _1384193) = c_Orderings_Obot__class_Obot(tc_fun(_1384189, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1384189), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1384189, tc_HOL_Obool)), _1384191), _1384193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1384189), _1384191)), hAPP(c_Finite__Set_Ocard(_1384189), _1384193)))], (32937 ^ _780461) ^ [_1384488, _1384490, _1384492] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384488), _1384490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1384488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384488, tc_HOL_Obool)), _1384490), hAPP(hAPP(c_Set_Oinsert(_1384488), _1384492), c_Orderings_Obot__class_Obot(tc_fun(_1384488, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1384488), _1384490))))], (32943 ^ _780461) ^ [_1384653, _1384655, _1384657] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384653), _1384655)), -(hBOOL(hAPP(hAPP(c_member(_1384653), _1384657), _1384655))), -(hAPP(c_Finite__Set_Ocard(_1384653), hAPP(hAPP(c_Set_Oinsert(_1384653), _1384657), _1384655)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1384653), _1384655)))], (32953 ^ _780461) ^ [_1384811, _1384813, _1384815] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1384811), _1384813)), hBOOL(hAPP(hAPP(c_member(_1384811), _1384815), _1384813)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1384811), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1384811, tc_HOL_Obool)), _1384813), hAPP(hAPP(c_Set_Oinsert(_1384811), _1384815), c_Orderings_Obot__class_Obot(tc_fun(_1384811, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1384811), _1384813))], (32963 ^ _780461) ^ [_1385040, _1385042, _1385044, _1385046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1385040), _1385042)), hBOOL(hAPP(hAPP(c_member(_1385040), _1385044), _1385042)), hBOOL(hAPP(hAPP(c_member(_1385040), _1385046), _1385042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1385040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385040, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385040, tc_HOL_Obool)), _1385042), hAPP(hAPP(c_Set_Oinsert(_1385040), _1385044), c_Orderings_Obot__class_Obot(tc_fun(_1385040, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1385040), _1385046), c_Orderings_Obot__class_Obot(tc_fun(_1385040, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1385040), _1385042))))], (32977 ^ _780461) ^ [_1385395, _1385397, _1385399] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1385395), _1385397)), hBOOL(hAPP(hAPP(c_member(_1385395), _1385399), _1385397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1385395), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385395, tc_HOL_Obool)), _1385397), hAPP(hAPP(c_Set_Oinsert(_1385395), _1385399), c_Orderings_Obot__class_Obot(tc_fun(_1385395, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1385395), _1385397))))], (32987 ^ _780461) ^ [_1385628, _1385630, _1385632, _1385634] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1385628), _1385630)), hBOOL(hAPP(hAPP(c_member(_1385628), _1385632), _1385630)), -(hBOOL(hAPP(hAPP(c_member(_1385628), _1385632), _1385634))), -(hAPP(c_Finite__Set_Ocard(_1385628), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385628, tc_HOL_Obool)), _1385630), hAPP(hAPP(c_Set_Oinsert(_1385628), _1385632), _1385634))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1385628), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385628, tc_HOL_Obool)), _1385630), _1385634))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (33001 ^ _780461) ^ [_1385908, _1385910, _1385912] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1385908), _1385910)), -(hAPP(c_Finite__Set_Ocard(_1385908), hAPP(hAPP(c_Set_Oinsert(_1385908), _1385912), _1385910)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1385908), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385908, tc_HOL_Obool)), _1385910), hAPP(hAPP(c_Set_Oinsert(_1385908), _1385912), c_Orderings_Obot__class_Obot(tc_fun(_1385908, tc_HOL_Obool)))))))], (33007 ^ _780461) ^ [_1386085, _1386087, _1386089] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1386085), _1386087)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386085), _1386089)), 33017 ^ _780461 : [(33018 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1386085), 33016 ^ [_1386085, _1386087, _1386089]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386085, tc_HOL_Obool)), _1386087), _1386089))))], (33020 ^ _780461) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1386085), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386085, tc_HOL_Obool)), _1386087), _1386089)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1386085), _1386087)), hAPP(c_Finite__Set_Ocard(_1386085), _1386089)))], (33024 ^ _780461) ^ [_1386447, _1386449, _1386451] : [hAPP(c_Finite__Set_Ocard(_1386447), _1386449) = hAPP(c_Nat_OSuc, _1386451), 33029 ^ _780461 : [(33030 ^ _780461) ^ [] : [-(_1386449 = hAPP(hAPP(c_Set_Oinsert(_1386447), 33027 ^ [_1386447, _1386449, _1386451]), 33028 ^ [_1386447, _1386449, _1386451]))], (33032 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1386447), 33027 ^ [_1386447, _1386449, _1386451]), 33028 ^ [_1386447, _1386449, _1386451]))], (33034 ^ _780461) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1386447), 33028 ^ [_1386447, _1386449, _1386451]) = _1386451)], (33036 ^ _780461) ^ [] : [_1386451 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(33028 ^ [_1386447, _1386449, _1386451] = c_Orderings_Obot__class_Obot(tc_fun(_1386447, tc_HOL_Obool)))]]], (33042 ^ _780461) ^ [_1386865, _1386867, _1386869] : [-(hAPP(c_Finite__Set_Ocard(_1386865), _1386867) = hAPP(c_Nat_OSuc, _1386869)), 33043 ^ _780461 : [(33044 ^ _780461) ^ [_1386965, _1386967] : [_1386867 = hAPP(hAPP(c_Set_Oinsert(_1386865), _1386967), _1386965), -(hBOOL(hAPP(hAPP(c_member(_1386865), _1386967), _1386965))), hAPP(c_Finite__Set_Ocard(_1386865), _1386965) = _1386869, 33055 ^ _780461 : [(33056 ^ _780461) ^ [] : [-(_1386869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33058 ^ _780461) ^ [] : [_1386965 = c_Orderings_Obot__class_Obot(tc_fun(_1386865, tc_HOL_Obool))]]]]], (33062 ^ _780461) ^ [_1387287, _1387289, _1387291, _1387293] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1387287), _1387289)), c_Equiv__Relations_Oequiv(_1387287, _1387289, _1387291), 33072 ^ _780461 : [(33073 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1387287, tc_HOL_Obool)), 33071 ^ [_1387287, _1387289, _1387291, _1387293]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1387287), _1387289), _1387291))))], (33075 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1387293), hAPP(c_Finite__Set_Ocard(_1387287), 33071 ^ [_1387287, _1387289, _1387291, _1387293])))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1387293), hAPP(c_Finite__Set_Ocard(_1387287), _1387289))))], (33079 ^ _780461) ^ [_1387652, _1387654] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1387652, _1387654)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1387654), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1387652), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (33091 ^ _780461) ^ [_1387919, _1387921, _1387923, _1387925] : [33092 ^ _780461 : [(33093 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1387919), _1387921)))], (33095 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1387923), _1387925)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1387919, _1387923)), c_Sum__Type_OPlus(_1387919, _1387923, _1387921, _1387925)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33081 ^ _780461) ^ [_1387714, _1387716, _1387718, _1387720] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1387714, _1387718)), c_Sum__Type_OPlus(_1387714, _1387718, _1387716, _1387720)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1387714), _1387716)), hAPP(c_Finite__Set_Ocard(_1387718), _1387720))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387714), _1387716)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387718), _1387720))], (33099 ^ _780461) ^ [_1388019, _1388021, _1388023, _1388025, _1388027, _1388029] : [class_Groups_Ocomm__monoid__mult(_1388019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388021), _1388023)), 33106 ^ _780461 : [(33107 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1388021), _1388025), _1388023)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388021, _1388019), hAPP(hAPP(c_COMBC(_1388021, _1388019, _1388019), hAPP(hAPP(c_COMBS(_1388021, _1388019, tc_fun(_1388019, _1388019)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1388019, tc_fun(_1388019, _1388019)), _1388021), c_If(_1388019)), hAPP(hAPP(c_COMBC(_1388021, _1388021, tc_HOL_Obool), c_fequal), _1388025))), _1388027)), _1388029)), _1388023) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388019), hAPP(_1388027, _1388025)), hAPP(hAPP(c_Power_Opower__class_Opower(_1388019), _1388029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1388021), _1388023)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (33113 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1388021), _1388025), _1388023))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388021, _1388019), hAPP(hAPP(c_COMBC(_1388021, _1388019, _1388019), hAPP(hAPP(c_COMBS(_1388021, _1388019, tc_fun(_1388019, _1388019)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1388019, tc_fun(_1388019, _1388019)), _1388021), c_If(_1388019)), hAPP(hAPP(c_COMBC(_1388021, _1388021, tc_HOL_Obool), c_fequal), _1388025))), _1388027)), _1388029)), _1388023) = hAPP(hAPP(c_Power_Opower__class_Opower(_1388019), _1388029), hAPP(c_Finite__Set_Ocard(_1388021), _1388023)))]]], (33119 ^ _780461) ^ [_1388631, _1388633] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1388631, _1388633))))], (33121 ^ _780461) ^ [_1388662, _1388664, _1388666, _1388668, _1388670] : [hBOOL(hAPP(hAPP(c_member(_1388662), _1388664), _1388666)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_1388668, _1388662)), hAPP(c_Sum__Type_OInr(_1388662, _1388668), _1388664)), c_Sum__Type_OPlus(_1388668, _1388662, _1388670, _1388666))))], (33127 ^ _780461) ^ [_1388801, _1388803, _1388805, _1388807, _1388809] : [hBOOL(hAPP(hAPP(c_member(_1388801), _1388803), _1388805)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_1388801, _1388807)), hAPP(c_Sum__Type_OInl(_1388801, _1388807), _1388803)), c_Sum__Type_OPlus(_1388801, _1388807, _1388805, _1388809))))], (33133 ^ _780461) ^ [_1388940, _1388942, _1388944, _1388946] : [class_Fields_Olinordered__field(_1388940), -(hAPP(c_Groups_Oabs__class_Oabs(_1388940), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388942, _1388940), _1388944), _1388946)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1388942, _1388940), hAPP(hAPP(c_COMBB(_1388940, _1388940, _1388942), c_Groups_Oabs__class_Oabs(_1388940)), _1388944)), _1388946))], (33139 ^ _780461) ^ [_1389089, _1389091, _1389093, _1389095, _1389097] : [class_Groups_Ocomm__monoid__mult(_1389089), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389091, _1389089), hAPP(hAPP(c_COMBS(_1389091, _1389089, _1389089), hAPP(hAPP(c_COMBB(_1389089, tc_fun(_1389089, _1389089), _1389091), c_Groups_Otimes__class_Otimes(_1389089)), _1389093)), _1389095)), _1389097) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389089), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389091, _1389089), _1389093), _1389097)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389091, _1389089), _1389095), _1389097)))], (33145 ^ _780461) ^ [_1389290, _1389292, _1389294] : [class_Groups_Ocomm__monoid__mult(_1389290), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389292, _1389290), hAPP(c_COMBK(_1389290, _1389292), c_Groups_Oone__class_Oone(_1389290))), _1389294) = c_Groups_Oone__class_Oone(_1389290))], (33151 ^ _780461) ^ [_1389405, _1389407, _1389409] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389405, tc_Nat_Onat), _1389407), _1389409) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389405, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1389405), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1389407)), _1389409)))], (33153 ^ _780461) ^ [_1389463, _1389465, _1389467] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389463, tc_Nat_Onat), _1389465), _1389467)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389463, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1389463), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1389465)), _1389467))], (33155 ^ _780461) ^ [_1389521, _1389523, _1389525, _1389527] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1389521), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389523, tc_Nat_Onat), _1389525), _1389527)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389523, _1389521), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1389521, _1389523), c_Nat_Osemiring__1__class_Oof__nat(_1389521)), _1389525)), _1389527)), class_Groups_Ocomm__monoid__mult(_1389521), class_Rings_Osemiring__1(_1389521)], (33165 ^ _780461) ^ [_1389724, _1389726, _1389728, _1389730] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1389724), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389726, tc_Int_Oint), _1389728), _1389730)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389726, _1389724), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1389724, _1389726), c_Int_Oring__1__class_Oof__int(_1389724)), _1389728)), _1389730)), class_Groups_Ocomm__monoid__mult(_1389724), class_Rings_Oring__1(_1389724)], (33175 ^ _780461) ^ [_1389927, _1389929, _1389931] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1389927), _1389929), _1389931) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1389927), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1389927, tc_Int_Oint), _1389929), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1389931))), class_Groups_Ocomm__monoid__add(_1389927), class_Groups_Ocomm__monoid__mult(_1389927)], (33185 ^ _780461) ^ [_1390118, _1390120, _1390122, _1390124] : [class_Rings_Ocomm__semiring__1(_1390118), class_Rings_Ono__zero__divisors(_1390118), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390120), _1390122)), 33196 ^ _780461 : [(33197 ^ _780461) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390120, _1390118), _1390124), _1390122) = c_Groups_Ozero__class_Ozero(_1390118), 33201 ^ _780461 : [(33202 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390120), 33200 ^ [_1390118, _1390120, _1390122, _1390124]), _1390122)))], (33204 ^ _780461) ^ [] : [-(hAPP(_1390124, 33200 ^ [_1390118, _1390120, _1390122, _1390124]) = c_Groups_Ozero__class_Ozero(_1390118))]]], (33206 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390120, _1390118), _1390124), _1390122) = c_Groups_Ozero__class_Ozero(_1390118)), 33207 ^ _780461 : [(33208 ^ _780461) ^ [_1390496] : [hBOOL(hAPP(hAPP(c_member(_1390120), _1390496), _1390122)), hAPP(_1390124, _1390496) = c_Groups_Ozero__class_Ozero(_1390118)]]]]], (33216 ^ _780461) ^ [_1390651, _1390653, _1390655, _1390657] : [class_Rings_Ocomm__semiring__1(_1390651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390653), _1390655)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390653, _1390651), _1390657), _1390655) = c_Groups_Ozero__class_Ozero(_1390651)), 33225 ^ _780461 : [(33226 ^ _780461) ^ [_1390832] : [hBOOL(hAPP(hAPP(c_member(_1390653), _1390832), _1390655)), hAPP(_1390657, _1390832) = c_Groups_Ozero__class_Ozero(_1390651)]]], (33234 ^ _780461) ^ [_1390981, _1390983, _1390985] : [class_Groups_Ocomm__monoid__mult(_1390981), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390983, _1390981), _1390985), c_Orderings_Obot__class_Obot(tc_fun(_1390983, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1390981))], (33240 ^ _780461) ^ [_1391090, _1391092, _1391094] : [class_Groups_Ocomm__monoid__mult(_1391090), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391092, _1391090), _1391094), c_Orderings_Obot__class_Obot(tc_fun(_1391092, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1391090))], (33246 ^ _780461) ^ [_1391199, _1391201, _1391203, _1391205] : [class_Groups_Ocomm__monoid__mult(_1391199), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391201), _1391203))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391201, _1391199), _1391205), _1391203) = c_Groups_Oone__class_Oone(_1391199))], (33256 ^ _780461) ^ [_1391323, _1391325, _1391327, _1391329] : [class_Groups_Ocomm__monoid__mult(_1391323), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391325), _1391327))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391325, _1391323), _1391329), _1391327) = c_Groups_Oone__class_Oone(_1391323))], (33266 ^ _780461) ^ [_1391447, _1391449, _1391451] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391447), _1391449)), 33269 ^ _780461 : [(33280 ^ _780461) ^ [] : [33282 ^ _780461 : [(33283 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391447), 33281 ^ [_1391447, _1391449, _1391451]), _1391449)))], (33285 ^ _780461) ^ [] : [hAPP(_1391451, 33281 ^ [_1391447, _1391449, _1391451]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391447, tc_Nat_Onat), _1391451), _1391449) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (33270 ^ _780461) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1391447, tc_Nat_Onat), _1391451), _1391449) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 33273 ^ _780461 : [(33274 ^ _780461) ^ [_1391609] : [hBOOL(hAPP(hAPP(c_member(_1391447), _1391609), _1391449)), -(hAPP(_1391451, _1391609) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (33289 ^ _780461) ^ [_1391888, _1391890, _1391892, _1391894] : [c_Sum__Type_OPlus(_1391888, _1391890, _1391892, _1391894) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1391888, _1391890), tc_HOL_Obool)), 33292 ^ _780461 : [(33293 ^ _780461) ^ [] : [-(_1391892 = c_Orderings_Obot__class_Obot(tc_fun(_1391888, tc_HOL_Obool)))], (33295 ^ _780461) ^ [] : [-(_1391894 = c_Orderings_Obot__class_Obot(tc_fun(_1391890, tc_HOL_Obool)))]]], (33297 ^ _780461) ^ [_1392037, _1392039, _1392041, _1392043] : [-(c_Sum__Type_OPlus(_1392037, _1392039, _1392041, _1392043) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1392037, _1392039), tc_HOL_Obool))), _1392041 = c_Orderings_Obot__class_Obot(tc_fun(_1392037, tc_HOL_Obool)), _1392043 = c_Orderings_Obot__class_Obot(tc_fun(_1392039, tc_HOL_Obool))], (33307 ^ _780461) ^ [_1392243, _1392245, _1392247, _1392249] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1392243, _1392245)), c_Sum__Type_OPlus(_1392243, _1392245, _1392247, _1392249))), 33310 ^ _780461 : [(33311 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1392243), _1392247)))], (33313 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1392245), _1392249)))]]], (33315 ^ _780461) ^ [_1392386, _1392388, _1392390, _1392392] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1392386, _1392388)), c_Sum__Type_OPlus(_1392386, _1392388, _1392390, _1392392)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392386), _1392390)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392388), _1392392))], (33325 ^ _780461) ^ [_1392565, _1392567, _1392569, _1392571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1392565), _1392567)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392569), _1392571)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1392565, _1392569)), c_Sum__Type_OPlus(_1392565, _1392569, _1392567, _1392571))))], (33335 ^ _780461) ^ [_1392742, _1392744, _1392746, _1392748] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1392742, _1392744)), c_Sum__Type_OPlus(_1392742, _1392744, _1392746, _1392748))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1392742), _1392746)))], (33341 ^ _780461) ^ [_1392855, _1392857, _1392859, _1392861] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1392855, _1392857)), c_Sum__Type_OPlus(_1392855, _1392857, _1392859, _1392861))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1392857), _1392861)))], (33347 ^ _780461) ^ [_1392968, _1392970, _1392972] : [class_Groups_Ocomm__monoid__add(_1392968), class_Groups_Ocomm__monoid__mult(_1392968), c_Nat__Transfer_Onat__set(_1392970), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1392968), _1392972), _1392970) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1392968), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1392968, tc_Nat_Onat), _1392972), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1392970)))], (33361 ^ _780461) ^ [_1393213, _1393215, _1393217, _1393219, _1393221] : [class_Groups_Ocomm__monoid__mult(_1393213), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393215), _1393217)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393215, _1393213), hAPP(hAPP(c_COMBS(_1393215, _1393213, _1393213), hAPP(hAPP(c_COMBB(_1393213, tc_fun(_1393213, _1393213), _1393215), c_Groups_Otimes__class_Otimes(_1393213)), _1393219)), _1393221)), _1393217) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393213), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393215, _1393213), _1393219), _1393217)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393215, _1393213), _1393221), _1393217)))], (33371 ^ _780461) ^ [_1393480, _1393482, _1393484, _1393486, _1393488] : [class_Fields_Ofield__inverse__zero(_1393480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393482), _1393484)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393482, _1393480), hAPP(hAPP(c_COMBS(_1393482, _1393480, _1393480), hAPP(hAPP(c_COMBB(_1393480, tc_fun(_1393480, _1393480), _1393482), c_Rings_Oinverse__class_Odivide(_1393480)), _1393486)), _1393488)), _1393484) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393480), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393482, _1393480), _1393486), _1393484)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393482, _1393480), _1393488), _1393484)))], (33381 ^ _780461) ^ [_1393747, _1393749, _1393751, _1393753, _1393755] : [class_Rings_Ocomm__semiring__1(_1393747), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393749), _1393751)), hBOOL(hAPP(hAPP(c_member(_1393749), _1393753), _1393751)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1393747), hAPP(_1393755, _1393753)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1393749, _1393747), _1393755), _1393751))))], (33395 ^ _780461) ^ [_1394004, _1394006, _1394008] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1394004), _1394006)), 33398 ^ _780461 : [(33409 ^ _780461) ^ [] : [33411 ^ _780461 : [(33412 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1394004), 33410 ^ [_1394004, _1394006, _1394008]), _1394006)))], (33414 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1394008, 33410 ^ [_1394004, _1394006, _1394008])))]], -(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(_1394004, tc_Nat_Onat), _1394008), _1394006))))], (33399 ^ _780461) ^ [] : [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(_1394004, tc_Nat_Onat), _1394008), _1394006))), 33402 ^ _780461 : [(33403 ^ _780461) ^ [_1394172] : [hBOOL(hAPP(hAPP(c_member(_1394004), _1394172), _1394006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1394008, _1394172))))]]]]], (33418 ^ _780461) ^ [_1394440, _1394442, _1394444, _1394446, _1394448] : [class_Groups_Ocomm__monoid__mult(_1394440), class_Rings_Odvd(_1394440), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394442), _1394444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394442, tc_HOL_Obool)), _1394446), _1394444)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1394440), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394442, _1394440), _1394448), _1394446)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1394442, _1394440), _1394448), _1394444))))], (33436 ^ _780461) ^ [_1394773, _1394775, _1394777] : [class_Orderings_Oorder(_1394773), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394773), _1394775), _1394777)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1394773, _1394777, _1394775) = c_Orderings_Obot__class_Obot(tc_fun(_1394773, tc_HOL_Obool)))], (33446 ^ _780461) ^ [_1394936, _1394938, _1394940] : [class_Groups_Oordered__ab__group__add(_1394936), -(hAPP(c_Set_Oimage(_1394936, _1394936, c_Groups_Ouminus__class_Ouminus(_1394936)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1394936, _1394938, _1394940)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1394936, hAPP(c_Groups_Ouminus__class_Ouminus(_1394936), _1394940), hAPP(c_Groups_Ouminus__class_Ouminus(_1394936), _1394938)))], (33452 ^ _780461) ^ [_1395067, _1395069, _1395071, _1395073, _1395075] : [class_Groups_Ocomm__monoid__mult(_1395067), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395069), _1395071)), 33459 ^ _780461 : [(33460 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1395069), _1395073), _1395071)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395069, _1395067), hAPP(hAPP(c_COMBC(_1395069, _1395067, _1395067), hAPP(hAPP(c_COMBS(_1395069, _1395067, tc_fun(_1395067, _1395067)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1395067, tc_fun(_1395067, _1395067)), _1395069), c_If(_1395067)), hAPP(hAPP(c_COMBC(_1395069, _1395069, tc_HOL_Obool), c_fequal), _1395073))), _1395075)), c_Groups_Oone__class_Oone(_1395067))), _1395071) = hAPP(_1395075, _1395073))], (33466 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395069), _1395073), _1395071))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395069, _1395067), hAPP(hAPP(c_COMBC(_1395069, _1395067, _1395067), hAPP(hAPP(c_COMBS(_1395069, _1395067, tc_fun(_1395067, _1395067)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1395067, tc_fun(_1395067, _1395067)), _1395069), c_If(_1395067)), hAPP(hAPP(c_COMBC(_1395069, _1395069, tc_HOL_Obool), c_fequal), _1395073))), _1395075)), c_Groups_Oone__class_Oone(_1395067))), _1395071) = c_Groups_Oone__class_Oone(_1395067))]]], (33472 ^ _780461) ^ [_1395605, _1395607, _1395609, _1395611, _1395613] : [class_Groups_Ocomm__monoid__mult(_1395605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395607), _1395609)), 33479 ^ _780461 : [(33480 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1395607), _1395611), _1395609)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395607, _1395605), hAPP(hAPP(c_COMBC(_1395607, _1395605, _1395605), hAPP(hAPP(c_COMBS(_1395607, _1395605, tc_fun(_1395605, _1395605)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1395605, tc_fun(_1395605, _1395605)), _1395607), c_If(_1395605)), hAPP(c_fequal, _1395611))), _1395613)), c_Groups_Oone__class_Oone(_1395605))), _1395609) = hAPP(_1395613, _1395611))], (33486 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1395607), _1395611), _1395609))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1395607, _1395605), hAPP(hAPP(c_COMBC(_1395607, _1395605, _1395605), hAPP(hAPP(c_COMBS(_1395607, _1395605, tc_fun(_1395605, _1395605)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1395605, tc_fun(_1395605, _1395605)), _1395607), c_If(_1395605)), hAPP(c_fequal, _1395611))), _1395613)), c_Groups_Oone__class_Oone(_1395605))), _1395609) = c_Groups_Oone__class_Oone(_1395605))]]], (33492 ^ _780461) ^ [_1396115, _1396117, _1396119, _1396121] : [class_Groups_Ocomm__monoid__mult(_1396115), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396117), _1396119)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396117, _1396115), hAPP(c_COMBK(_1396115, _1396117), _1396121)), _1396119) = hAPP(hAPP(c_Power_Opower__class_Opower(_1396115), _1396121), hAPP(c_Finite__Set_Ocard(_1396117), _1396119)))], (33502 ^ _780461) ^ [_1396314, _1396316, _1396318, _1396320, _1396322] : [class_Groups_Ocomm__monoid__mult(_1396314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396316), _1396318)), -(hBOOL(hAPP(hAPP(c_member(_1396316), _1396320), _1396318))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396316, _1396314), _1396322), hAPP(hAPP(c_Set_Oinsert(_1396316), _1396320), _1396318)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396314), hAPP(_1396322, _1396320)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396316, _1396314), _1396322), _1396318)))], (33516 ^ _780461) ^ [_1396564, _1396566, _1396568, _1396570, _1396572] : [class_Groups_Ocomm__monoid__mult(_1396564), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396566), _1396568)), -(hBOOL(hAPP(hAPP(c_member(_1396566), _1396570), _1396568))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396566, _1396564), _1396572), hAPP(hAPP(c_Set_Oinsert(_1396566), _1396570), _1396568)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396564), hAPP(_1396572, _1396570)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396566, _1396564), _1396572), _1396568)))], (33530 ^ _780461) ^ [_1396814, _1396816, _1396818, _1396820, _1396822] : [class_Groups_Ocomm__monoid__mult(_1396814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396816), _1396818)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396816), _1396820)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396814), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396816, _1396814), _1396822), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396816, tc_HOL_Obool)), _1396818), _1396820))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396816, _1396814), _1396822), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396816, tc_HOL_Obool)), _1396818), _1396820))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396814), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396816, _1396814), _1396822), _1396818)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1396816, _1396814), _1396822), _1396820)))], (33544 ^ _780461) ^ [_1397175, _1397177, _1397179, _1397181, _1397183] : [class_Groups_Ocomm__monoid__mult(_1397175), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397177), _1397179)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397177), _1397181)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397175), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397177, _1397175), _1397183), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397177, tc_HOL_Obool)), _1397179), _1397181))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397177, _1397175), _1397183), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397177, tc_HOL_Obool)), _1397179), _1397181))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397175), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397177, _1397175), _1397183), _1397179)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397177, _1397175), _1397183), _1397181)))], (33558 ^ _780461) ^ [_1397536, _1397538, _1397540, _1397542] : [-(c_Sum__Type_OPlus(_1397536, _1397538, _1397540, _1397542) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(_1397536, _1397538), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1397536, tc_sum(_1397536, _1397538), c_Sum__Type_OInl(_1397536, _1397538)), _1397540)), hAPP(c_Set_Oimage(_1397538, tc_sum(_1397536, _1397538), c_Sum__Type_OInr(_1397538, _1397536)), _1397542)))], (33560 ^ _780461) ^ [_1397610, _1397612, _1397614, _1397616, _1397618] : [class_Orderings_Olinorder(_1397610), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397610, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1397610, _1397612, _1397614)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1397610, _1397616, _1397618)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1397610, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1397610), _1397612), _1397616), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1397610), _1397614), _1397618)))], (33566 ^ _780461) ^ [_1397769, _1397771, _1397773, _1397775, _1397777] : [class_Groups_Ocomm__monoid__mult(_1397769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397771), _1397773)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397771, _1397769), _1397775), hAPP(hAPP(c_Set_Oinsert(_1397771), _1397777), _1397773)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397769), hAPP(_1397775, _1397777)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397771, _1397769), _1397775), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1397771, tc_HOL_Obool)), _1397773), hAPP(hAPP(c_Set_Oinsert(_1397771), _1397777), c_Orderings_Obot__class_Obot(tc_fun(_1397771, tc_HOL_Obool)))))))], (33576 ^ _780461) ^ [_1398038, _1398040, _1398042, _1398044, _1398046] : [class_Groups_Ocomm__monoid__mult(_1398038), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398040), _1398042)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398040), _1398044)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398040, tc_HOL_Obool)), _1398042), _1398044) = c_Orderings_Obot__class_Obot(tc_fun(_1398040, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398040, _1398038), _1398046), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398040, tc_HOL_Obool)), _1398042), _1398044)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398038), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398040, _1398038), _1398046), _1398042)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398040, _1398038), _1398046), _1398044)))], (33594 ^ _780461) ^ [_1398433, _1398435, _1398437, _1398439, _1398441] : [class_Groups_Ocomm__monoid__mult(_1398433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398435), _1398437)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398435), _1398439)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398435, tc_HOL_Obool)), _1398437), _1398439) = c_Orderings_Obot__class_Obot(tc_fun(_1398435, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398435, _1398433), _1398441), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398435, tc_HOL_Obool)), _1398437), _1398439)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398433), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398435, _1398433), _1398441), _1398437)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1398435, _1398433), _1398441), _1398439)))], (33612 ^ _780461) ^ [_1398828, _1398830, _1398832, _1398834] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398828), _1398830)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398832), _1398834)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1398828, _1398832)), c_Sum__Type_OPlus(_1398828, _1398832, _1398830, _1398834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1398828), _1398830)), hAPP(c_Finite__Set_Ocard(_1398832), _1398834)))], (33622 ^ _780461) ^ [_1399039, _1399041, _1399043, _1399045, _1399047] : [class_Groups_Ocomm__monoid__mult(_1399039), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399041), _1399043)), hBOOL(hAPP(hAPP(c_member(_1399041), _1399045), _1399043)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399041, _1399039), _1399047), _1399043) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399039), hAPP(_1399047, _1399045)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399041, _1399039), _1399047), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399041, tc_HOL_Obool)), _1399043), hAPP(hAPP(c_Set_Oinsert(_1399041), _1399045), c_Orderings_Obot__class_Obot(tc_fun(_1399041, tc_HOL_Obool)))))))], (33636 ^ _780461) ^ [_1399364, _1399366, _1399368, _1399370, _1399372] : [class_Fields_Ofield(_1399364), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399366), _1399368)), -(hAPP(_1399370, _1399372) = c_Groups_Ozero__class_Ozero(_1399364)), 33647 ^ _780461 : [(33648 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1399366), _1399372), _1399368)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399366, _1399364), _1399370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399366, tc_HOL_Obool)), _1399368), hAPP(hAPP(c_Set_Oinsert(_1399366), _1399372), c_Orderings_Obot__class_Obot(tc_fun(_1399366, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399364), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399366, _1399364), _1399370), _1399368)), hAPP(_1399370, _1399372)))], (33654 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399366), _1399372), _1399368))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399366, _1399364), _1399370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1399366, tc_HOL_Obool)), _1399368), hAPP(hAPP(c_Set_Oinsert(_1399366), _1399372), c_Orderings_Obot__class_Obot(tc_fun(_1399366, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399366, _1399364), _1399370), _1399368))]]], (33660 ^ _780461) ^ [_1399905, _1399907, _1399909, _1399911, _1399913] : [class_Fields_Ofield(_1399905), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399907), _1399909)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399907), _1399911)), 33674 ^ _780461 : [(33675 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1399907), 33673 ^ [_1399905, _1399907, _1399909, _1399911, _1399913]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399907, tc_HOL_Obool)), _1399909), _1399911))))], (33677 ^ _780461) ^ [] : [-(hAPP(_1399913, 33673 ^ [_1399905, _1399907, _1399909, _1399911, _1399913]) = c_Groups_Ozero__class_Ozero(_1399905))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399907, _1399905), _1399913), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399907, tc_HOL_Obool)), _1399909), _1399911)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399905), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399905), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399907, _1399905), _1399913), _1399909)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399907, _1399905), _1399913), _1399911))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1399907, _1399905), _1399913), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399907, tc_HOL_Obool)), _1399909), _1399911))))], (33681 ^ _780461) ^ [_1400401, _1400403, _1400405, _1400407, _1400409] : [class_Groups_Ocomm__monoid__mult(_1400401), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400403), _1400405)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400403), _1400407)), 33695 ^ _780461 : [(33696 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1400403), 33694 ^ [_1400401, _1400403, _1400405, _1400407, _1400409]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400403, tc_HOL_Obool)), _1400405), _1400407))))], (33698 ^ _780461) ^ [] : [hAPP(_1400409, 33694 ^ [_1400401, _1400403, _1400405, _1400407, _1400409]) = c_Groups_Oone__class_Oone(_1400401)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400403, _1400401), _1400409), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400403, tc_HOL_Obool)), _1400405), _1400407)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400401), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400403, _1400401), _1400409), _1400405)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400403, _1400401), _1400409), _1400407)))], (33702 ^ _780461) ^ [_1400896, _1400898, _1400900, _1400902, _1400904] : [class_Groups_Ocomm__monoid__mult(_1400896), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400898), _1400900)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400898), _1400902)), 33716 ^ _780461 : [(33717 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1400898), 33715 ^ [_1400896, _1400898, _1400900, _1400902, _1400904]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400898, tc_HOL_Obool)), _1400900), _1400902))))], (33719 ^ _780461) ^ [] : [hAPP(_1400904, 33715 ^ [_1400896, _1400898, _1400900, _1400902, _1400904]) = c_Groups_Oone__class_Oone(_1400896)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400898, _1400896), _1400904), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400898, tc_HOL_Obool)), _1400900), _1400902)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400896), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400898, _1400896), _1400904), _1400900)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1400898, _1400896), _1400904), _1400902)))], (33723 ^ _780461) ^ [_1401391, _1401393] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1401391, _1401393))))], (33725 ^ _780461) ^ [_1401422, _1401424] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1401422, _1401424)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401424), hAPP(c_Nat_OSuc, _1401422)))], (33727 ^ _780461) ^ [_1401463, _1401465, _1401467] : [33729 ^ _780461 : [(33730 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401463), 33728 ^ [_1401463, _1401465, _1401467]), _1401465)))], (33732 ^ _780461) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1401467, 33728 ^ [_1401463, _1401465, _1401467]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401463, tc_Int_Oint), _1401467), _1401465) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1401463, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1401463), c_Int_Onat), _1401467)), _1401465)))], (33736 ^ _780461) ^ [_1401693, _1401695, _1401697] : [class_Orderings_Olinorder(_1401693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401693), _1401695), _1401697)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1401693, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1401693, _1401695, _1401697)), hAPP(hAPP(c_Set_Oinsert(_1401693), _1401697), c_Orderings_Obot__class_Obot(tc_fun(_1401693, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1401693, _1401695, _1401697))], (33746 ^ _780461) ^ [_1401902, _1401904, _1401906] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401902), _1401904), _1401906) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401902, tc_fun(tc_fun(_1401902, tc_HOL_Obool), tc_HOL_Obool)), _1401904), hAPP(hAPP(c_COMBC(_1401902, tc_fun(tc_fun(_1401902, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1401902, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401902, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1401902, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1401902, tc_HOL_Obool), tc_HOL_Obool)), _1401902), c_Set_Oinsert(tc_fun(_1401902, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1401902, tc_HOL_Obool), tc_fun(_1401902, tc_HOL_Obool), _1401902), c_Relation_OImage(_1401902, _1401902, _1401906)), hAPP(hAPP(c_COMBC(_1401902, tc_fun(_1401902, tc_HOL_Obool), tc_fun(_1401902, tc_HOL_Obool)), c_Set_Oinsert(_1401902)), c_Orderings_Obot__class_Obot(tc_fun(_1401902, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1401902, tc_HOL_Obool), tc_HOL_Obool)))))], (33748 ^ _780461) ^ [_1402058, _1402060] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1402058, _1402060))))], (33750 ^ _780461) ^ [_1402089, _1402091] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1402089, _1402091))))], (33752 ^ _780461) ^ [_1402120, _1402122, _1402124, _1402126, _1402128, _1402130] : [hBOOL(hAPP(hAPP(c_member(_1402120), _1402122), _1402124)), hBOOL(hAPP(hAPP(_1402126, _1402122), _1402128)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402120, tc_fun(_1402130, tc_HOL_Obool)), _1402124), _1402126), _1402128)))], (33762 ^ _780461) ^ [_1402317, _1402319, _1402321, _1402323] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1402317), _1402319)), 33765 ^ _780461 : [(33776 ^ _780461) ^ [] : [33778 ^ _780461 : [(33779 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1402317), 33777 ^ [_1402317, _1402319, _1402321, _1402323]), _1402319)))], (33781 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1402321), hAPP(_1402323, 33777 ^ [_1402317, _1402319, _1402321, _1402323])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1402321), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402317, tc_fun(_1402321, tc_HOL_Obool)), _1402319), _1402323))))], (33766 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1402321), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402317, tc_fun(_1402321, tc_HOL_Obool)), _1402319), _1402323))), 33769 ^ _780461 : [(33770 ^ _780461) ^ [_1402501] : [hBOOL(hAPP(hAPP(c_member(_1402317), _1402501), _1402319)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1402321), hAPP(_1402323, _1402501))))]]]]], (33785 ^ _780461) ^ [_1402816, _1402818, _1402820, _1402822, _1402824] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402816, tc_fun(_1402818, tc_HOL_Obool)), _1402820), _1402822), _1402824)), 33789 ^ _780461 : [(33790 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1402816), 33788 ^ [_1402816, _1402818, _1402820, _1402822, _1402824]), _1402820)))], (33792 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1402822, 33788 ^ [_1402816, _1402818, _1402820, _1402822, _1402824]), _1402824)))]]], (33794 ^ _780461) ^ [_1403004, _1403006, _1403008, _1403010, _1403012] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403004, tc_fun(_1403006, tc_HOL_Obool)), _1403008), _1403010), _1403012))), 33795 ^ _780461 : [(33796 ^ _780461) ^ [_1403076] : [hBOOL(hAPP(hAPP(c_member(_1403004), _1403076), _1403008)), hBOOL(hAPP(hAPP(_1403010, _1403076), _1403012))]]], (33804 ^ _780461) ^ [_1403228, _1403230, _1403232, _1403234, _1403236, _1403238] : [-(hAPP(c_Relation_OImage(_1403228, _1403230, _1403232), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403234, tc_fun(_1403228, tc_HOL_Obool)), _1403236), _1403238)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403234, tc_fun(_1403230, tc_HOL_Obool)), _1403236), hAPP(hAPP(c_COMBB(tc_fun(_1403228, tc_HOL_Obool), tc_fun(_1403230, tc_HOL_Obool), _1403234), c_Relation_OImage(_1403228, _1403230, _1403232)), _1403238)))], (33806 ^ _780461) ^ [_1403312, _1403314, _1403316] : [class_Orderings_Oorder(_1403312), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403312), _1403314), _1403316)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1403312, _1403316, _1403314) = c_Orderings_Obot__class_Obot(tc_fun(_1403312, tc_HOL_Obool)))], (33816 ^ _780461) ^ [_1403475, _1403477, _1403479] : [class_Orderings_Oorder(_1403475), 33819 ^ _780461 : [(33820 ^ _780461) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1403475, _1403477, _1403479) = c_Orderings_Obot__class_Obot(tc_fun(_1403475, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403475), _1403477), _1403479))], (33826 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403475), _1403477), _1403479))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1403475, _1403477, _1403479) = c_Orderings_Obot__class_Obot(tc_fun(_1403475, tc_HOL_Obool)))]]], (33832 ^ _780461) ^ [_1403694, _1403696, _1403698] : [class_Orderings_Oorder(_1403694), 33835 ^ _780461 : [(33836 ^ _780461) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1403694, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1403694, _1403696, _1403698), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403694), _1403696), _1403698))], (33842 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1403694), _1403696), _1403698))), -(c_Orderings_Obot__class_Obot(tc_fun(_1403694, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1403694, _1403696, _1403698))]]], (33848 ^ _780461) ^ [_1403913, _1403915, _1403917, _1403919] : [class_Orderings_Olinorder(_1403913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403913), _1403915), _1403917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1403913), _1403917), _1403919)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403913, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1403913, _1403915, _1403917)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1403913, _1403917, _1403919)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1403913, _1403915, _1403919))], (33862 ^ _780461) ^ [_1404178, _1404180, _1404182, _1404184] : [class_Orderings_Oorder(_1404178), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404178, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1404178, _1404180, _1404182)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1404178, _1404182, _1404184)) = c_Orderings_Obot__class_Obot(tc_fun(_1404178, tc_HOL_Obool)))], (33868 ^ _780461) ^ [_1404305, _1404307] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1404305, _1404307)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1404307), _1404305))], (33870 ^ _780461) ^ [_1404343, _1404345, _1404347, _1404349] : [-(hAPP(c_Relation_OImage(_1404343, _1404345, _1404347), _1404349) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404343, tc_fun(_1404345, tc_HOL_Obool)), _1404349), hAPP(hAPP(c_COMBB(tc_fun(_1404343, tc_HOL_Obool), tc_fun(_1404345, tc_HOL_Obool), _1404343), c_Relation_OImage(_1404343, _1404345, _1404347)), hAPP(hAPP(c_COMBC(_1404343, tc_fun(_1404343, tc_HOL_Obool), tc_fun(_1404343, tc_HOL_Obool)), c_Set_Oinsert(_1404343)), c_Orderings_Obot__class_Obot(tc_fun(_1404343, tc_HOL_Obool))))))], (33872 ^ _780461) ^ [_1404434, _1404436, _1404438, _1404440, _1404442] : [class_Orderings_Olinorder(_1404434), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404434, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1404434, _1404436, _1404438)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1404434, _1404440, _1404442)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1404434, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1404434), _1404436), _1404440), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1404434), _1404438), _1404442)))], (33878 ^ _780461) ^ [_1404593, _1404595, _1404597, _1404599] : [class_Orderings_Oorder(_1404593), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404593, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1404593, _1404595, _1404597)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1404593, _1404597, _1404599)) = c_Orderings_Obot__class_Obot(tc_fun(_1404593, tc_HOL_Obool)))], (33884 ^ _780461) ^ [_1404720, _1404722] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1404720, _1404722)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1404722), _1404720)))], (33886 ^ _780461) ^ [_1404761, _1404763, _1404765, _1404767] : [class_Orderings_Olinorder(_1404761), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404761), _1404763), _1404765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1404761), _1404765), _1404767)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404761, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1404761, _1404763, _1404765)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1404761, _1404765, _1404767)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1404761, _1404763, _1404767))], (33900 ^ _780461) ^ [_1405026, _1405028, _1405030, _1405032, _1405034, _1405036] : [hBOOL(hAPP(hAPP(c_member(_1405026), _1405028), _1405030)), hBOOL(hAPP(hAPP(c_member(_1405032), _1405034), hAPP(_1405036, _1405028))), -(hBOOL(hAPP(hAPP(c_member(_1405032), _1405034), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405026, tc_fun(_1405032, tc_HOL_Obool)), _1405030), _1405036))))], (33910 ^ _780461) ^ [_1405243, _1405245, _1405247, _1405249] : [-(hAPP(c_Set_Oimage(_1405243, _1405245, _1405247), _1405249) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405243, tc_fun(_1405245, tc_HOL_Obool)), _1405249), hAPP(hAPP(c_COMBC(_1405243, tc_fun(_1405245, tc_HOL_Obool), tc_fun(_1405245, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1405245, tc_fun(tc_fun(_1405245, tc_HOL_Obool), tc_fun(_1405245, tc_HOL_Obool)), _1405243), c_Set_Oinsert(_1405245)), _1405247)), c_Orderings_Obot__class_Obot(tc_fun(_1405245, tc_HOL_Obool)))))], (33912 ^ _780461) ^ [_1405333, _1405335, _1405337, _1405339, _1405341, _1405343] : [c_Equiv__Relations_Oequiv(_1405333, _1405335, _1405337), c_Equiv__Relations_Ocongruent(_1405333, tc_fun(_1405339, tc_HOL_Obool), _1405337, _1405341), hBOOL(hAPP(hAPP(c_member(_1405333), _1405343), _1405335)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405333, tc_fun(_1405339, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1405333, _1405333, _1405337), hAPP(hAPP(c_Set_Oinsert(_1405333), _1405343), c_Orderings_Obot__class_Obot(tc_fun(_1405333, tc_HOL_Obool))))), _1405341) = hAPP(_1405341, _1405343))], (33943 ^ _780461) ^ [_1406094, _1406096, _1406098, _1406100, _1406102] : [33945 ^ _780461 : [(33946 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406096), 33944 ^ [_1406094, _1406096, _1406098, _1406100, _1406102]), _1406098)))], (33949 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406094), 33947 ^ [_1406094, _1406096, _1406098, _1406100, _1406102]), hAPP(_1406100, 33944 ^ [_1406094, _1406096, _1406098, _1406100, _1406102]))))], (33951 ^ _780461) ^ [] : [hBOOL(hAPP(_1406102, 33947 ^ [_1406094, _1406096, _1406098, _1406100, _1406102]))]], 33952 ^ _780461 : [(33953 ^ _780461) ^ [_1406404] : [hBOOL(hAPP(hAPP(c_member(_1406094), _1406404), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406096, tc_fun(_1406094, tc_HOL_Obool)), _1406098), _1406100))), -(hBOOL(hAPP(_1406102, _1406404)))]]], (33926 ^ _780461) ^ [_1405658, _1405660, _1405662, _1405664, _1405666] : [33928 ^ _780461 : [(33929 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405658), 33927 ^ [_1405658, _1405660, _1405662, _1405664, _1405666]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405660, tc_fun(_1405658, tc_HOL_Obool)), _1405662), _1405664))))], (33931 ^ _780461) ^ [] : [hBOOL(hAPP(_1405666, 33927 ^ [_1405658, _1405660, _1405662, _1405664, _1405666]))]], 33932 ^ _780461 : [(33933 ^ _780461) ^ [_1405880] : [hBOOL(hAPP(hAPP(c_member(_1405660), _1405880), _1405662)), 33936 ^ _780461 : [(33937 ^ _780461) ^ [_1405977] : [hBOOL(hAPP(hAPP(c_member(_1405658), _1405977), hAPP(_1405664, _1405880))), -(hBOOL(hAPP(_1405666, _1405977)))]]]]], (33969 ^ _780461) ^ [_1406936, _1406938, _1406940, _1406942] : [33971 ^ _780461 : [(33972 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1406936, _1406936)), 33970 ^ [_1406936, _1406938, _1406940, _1406942]), _1406940)))], (33974 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1406936, _1406936, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1406936, tc_fun(_1406936, _1406938), tc_fun(_1406936, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1406938, tc_HOL_Obool), tc_fun(tc_fun(_1406936, _1406938), tc_fun(_1406936, tc_HOL_Obool)), _1406936), c_COMBB(_1406938, tc_HOL_Obool, _1406936)), hAPP(hAPP(c_COMBB(_1406938, tc_fun(_1406938, tc_HOL_Obool), _1406936), c_fequal), _1406942))), _1406942)), 33970 ^ [_1406936, _1406938, _1406940, _1406942]))]], -(c_Equiv__Relations_Ocongruent(_1406936, _1406938, _1406940, _1406942))], (33959 ^ _780461) ^ [_1406560, _1406562, _1406564, _1406566] : [c_Equiv__Relations_Ocongruent(_1406560, _1406562, _1406564, _1406566), 33962 ^ _780461 : [(33963 ^ _780461) ^ [_1406705] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1406560, _1406560)), _1406705), _1406564)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1406560, _1406560, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1406560, tc_fun(_1406560, _1406562), tc_fun(_1406560, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1406562, tc_HOL_Obool), tc_fun(tc_fun(_1406560, _1406562), tc_fun(_1406560, tc_HOL_Obool)), _1406560), c_COMBB(_1406562, tc_HOL_Obool, _1406560)), hAPP(hAPP(c_COMBB(_1406562, tc_fun(_1406562, tc_HOL_Obool), _1406560), c_fequal), _1406566))), _1406566)), _1406705)))]]], (33978 ^ _780461) ^ [_1407311, _1407313, _1407315, _1407317, _1407319, _1407321] : [class_Complete__Lattice_Ocomplete__lattice(_1407311), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407313, _1407311), _1407315), hAPP(hAPP(c_COMBB(tc_fun(_1407317, _1407311), _1407311, _1407313), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407317, _1407311), _1407319)), _1407321)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407317, _1407311), _1407319), hAPP(hAPP(c_COMBB(tc_fun(_1407313, _1407311), _1407311, _1407317), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407313, _1407311), _1407315)), hAPP(c_COMBC(_1407313, _1407317, _1407311), _1407321))))], (33984 ^ _780461) ^ [_1407520, _1407522, _1407524, _1407526, _1407528, _1407530] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407520, tc_fun(_1407522, tc_HOL_Obool)), _1407524), hAPP(hAPP(c_COMBC(_1407520, tc_fun(_1407526, tc_fun(_1407522, tc_HOL_Obool)), tc_fun(_1407522, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407526, tc_HOL_Obool), tc_fun(tc_fun(_1407526, tc_fun(_1407522, tc_HOL_Obool)), tc_fun(_1407522, tc_HOL_Obool)), _1407520), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407526, tc_fun(_1407522, tc_HOL_Obool))), _1407528)), _1407530)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407526, tc_fun(_1407522, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407520, tc_fun(_1407526, tc_HOL_Obool)), _1407524), _1407528)), _1407530))], (33986 ^ _780461) ^ [_1407639, _1407641, _1407643, _1407645, _1407647, _1407649] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407639, tc_fun(_1407641, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407643, tc_fun(_1407639, tc_HOL_Obool)), _1407645), _1407647)), _1407649) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407643, tc_fun(_1407641, tc_HOL_Obool)), _1407645), hAPP(hAPP(c_COMBC(_1407643, tc_fun(_1407639, tc_fun(_1407641, tc_HOL_Obool)), tc_fun(_1407641, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407639, tc_HOL_Obool), tc_fun(tc_fun(_1407639, tc_fun(_1407641, tc_HOL_Obool)), tc_fun(_1407641, tc_HOL_Obool)), _1407643), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407639, tc_fun(_1407641, tc_HOL_Obool))), _1407647)), _1407649)))], (33988 ^ _780461) ^ [_1407758, _1407760, _1407762, _1407764, _1407766, _1407768] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407758, tc_fun(_1407760, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407762, tc_fun(_1407758, tc_HOL_Obool)), _1407764), _1407766)), _1407768) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407762, tc_fun(_1407760, tc_HOL_Obool)), _1407764), hAPP(hAPP(c_COMBC(_1407762, tc_fun(_1407758, tc_fun(_1407760, tc_HOL_Obool)), tc_fun(_1407760, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407758, tc_HOL_Obool), tc_fun(tc_fun(_1407758, tc_fun(_1407760, tc_HOL_Obool)), tc_fun(_1407760, tc_HOL_Obool)), _1407762), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407758, tc_fun(_1407760, tc_HOL_Obool))), _1407766)), _1407768)))], (33990 ^ _780461) ^ [_1407877, _1407879, _1407881, _1407883, _1407885, _1407887] : [c_Equiv__Relations_Ocongruent(_1407877, _1407879, _1407881, _1407883), hBOOL(hAPP(hAPP(c_member(tc_prod(_1407877, _1407877)), hAPP(hAPP(c_Product__Type_OPair(_1407877, _1407877), _1407885), _1407887)), _1407881)), -(hAPP(_1407883, _1407885) = hAPP(_1407883, _1407887))], (34000 ^ _780461) ^ [_1408076, _1408078, _1408080, _1408082, _1408084] : [class_Complete__Lattice_Ocomplete__lattice(_1408076), 34003 ^ _780461 : [(34014 ^ _780461) ^ [] : [34016 ^ _780461 : [(34017 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1408078), 34015 ^ [_1408076, _1408078, _1408080, _1408082, _1408084]), _1408080)))], (34019 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408076), hAPP(_1408082, 34015 ^ [_1408076, _1408078, _1408080, _1408082, _1408084])), _1408084))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408076), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408078, _1408076), _1408080), _1408082)), _1408084)))], (34004 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408076), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408078, _1408076), _1408080), _1408082)), _1408084)), 34007 ^ _780461 : [(34008 ^ _780461) ^ [_1408257] : [hBOOL(hAPP(hAPP(c_member(_1408078), _1408257), _1408080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408076), hAPP(_1408082, _1408257)), _1408084)))]]]]], (34023 ^ _780461) ^ [_1408570, _1408572, _1408574, _1408576, _1408578] : [class_Complete__Lattice_Ocomplete__lattice(_1408570), class_Orderings_Olinorder(_1408570), 34030 ^ _780461 : [(34031 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408570), _1408572), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408574, _1408570), _1408576), _1408578))), 34035 ^ _780461 : [(34036 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1408574), 34034 ^ [_1408570, _1408572, _1408574, _1408576, _1408578]), _1408576)))], (34038 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408570), _1408572), hAPP(_1408578, 34034 ^ [_1408570, _1408572, _1408574, _1408576, _1408578]))))]]], (34040 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408570), _1408572), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408574, _1408570), _1408576), _1408578)))), 34041 ^ _780461 : [(34042 ^ _780461) ^ [_1408918] : [hBOOL(hAPP(hAPP(c_member(_1408574), _1408918), _1408576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408570), _1408572), hAPP(_1408578, _1408918)))]]]]], (34050 ^ _780461) ^ [_1409112, _1409114, _1409116, _1409118, _1409120] : [hBOOL(hAPP(hAPP(c_member(_1409112), _1409114), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409116, tc_fun(_1409112, tc_HOL_Obool)), _1409118), _1409120))), 34054 ^ _780461 : [(34055 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409116), 34053 ^ [_1409112, _1409114, _1409116, _1409118, _1409120]), _1409118)))], (34057 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409112), _1409114), hAPP(_1409120, 34053 ^ [_1409112, _1409114, _1409116, _1409118, _1409120]))))]]], (34059 ^ _780461) ^ [_1409320, _1409322, _1409324, _1409326, _1409328] : [-(hBOOL(hAPP(hAPP(c_member(_1409320), _1409322), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409324, tc_fun(_1409320, tc_HOL_Obool)), _1409326), _1409328)))), 34060 ^ _780461 : [(34061 ^ _780461) ^ [_1409402] : [hBOOL(hAPP(hAPP(c_member(_1409324), _1409402), _1409326)), hBOOL(hAPP(hAPP(c_member(_1409320), _1409322), hAPP(_1409328, _1409402)))]]], (34069 ^ _780461) ^ [_1409569, _1409571, _1409573, _1409575] : [class_Complete__Lattice_Ocomplete__lattice(_1409569), -(_1409571 = c_Orderings_Obot__class_Obot(tc_fun(_1409573, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409573, _1409569), _1409571), hAPP(c_COMBK(_1409569, _1409573), _1409575)) = _1409575)], (34089 ^ _780461) ^ [_1409953, _1409955, _1409957, _1409959] : [34091 ^ _780461 : [(34092 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409953), 34090 ^ [_1409953, _1409955, _1409957, _1409959]), _1409957)))], (34094 ^ _780461) ^ [] : [hAPP(_1409959, 34090 ^ [_1409953, _1409955, _1409957, _1409959]) = c_Orderings_Obot__class_Obot(tc_fun(_1409955, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409953, tc_fun(_1409955, tc_HOL_Obool)), _1409957), _1409959) = c_Orderings_Obot__class_Obot(tc_fun(_1409955, tc_HOL_Obool)))], (34079 ^ _780461) ^ [_1409724, _1409726, _1409728, _1409730] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409724, tc_fun(_1409726, tc_HOL_Obool)), _1409728), _1409730) = c_Orderings_Obot__class_Obot(tc_fun(_1409726, tc_HOL_Obool)), 34082 ^ _780461 : [(34083 ^ _780461) ^ [_1409840] : [hBOOL(hAPP(hAPP(c_member(_1409724), _1409840), _1409728)), -(hAPP(_1409730, _1409840) = c_Orderings_Obot__class_Obot(tc_fun(_1409726, tc_HOL_Obool)))]]], (34098 ^ _780461) ^ [_1410198, _1410200, _1410202, _1410204] : [_1410198 = c_Orderings_Obot__class_Obot(tc_fun(_1410200, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410200, tc_fun(_1410202, tc_HOL_Obool)), _1410198), hAPP(c_COMBK(tc_fun(_1410202, tc_HOL_Obool), _1410200), _1410204)) = c_Orderings_Obot__class_Obot(tc_fun(_1410202, tc_HOL_Obool)))], (34104 ^ _780461) ^ [_1410335, _1410337, _1410339, _1410341] : [-(_1410335 = c_Orderings_Obot__class_Obot(tc_fun(_1410337, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410337, tc_fun(_1410339, tc_HOL_Obool)), _1410335), hAPP(c_COMBK(tc_fun(_1410339, tc_HOL_Obool), _1410337), _1410341)) = _1410341)], (34110 ^ _780461) ^ [_1410403, _1410405, _1410407] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410403, tc_fun(_1410405, tc_HOL_Obool)), _1410407), hAPP(c_COMBK(tc_fun(_1410405, tc_HOL_Obool), _1410403), c_Orderings_Obot__class_Obot(tc_fun(_1410405, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1410405, tc_HOL_Obool)))], (34122 ^ _780461) ^ [_1410711, _1410713, _1410715, _1410717] : [34124 ^ _780461 : [(34125 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1410713), 34123 ^ [_1410711, _1410713, _1410715, _1410717]), _1410715)))], (34127 ^ _780461) ^ [] : [hAPP(_1410717, 34123 ^ [_1410711, _1410713, _1410715, _1410717]) = c_Orderings_Obot__class_Obot(tc_fun(_1410711, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1410711, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410713, tc_fun(_1410711, tc_HOL_Obool)), _1410715), _1410717))], (34112 ^ _780461) ^ [_1410482, _1410484, _1410486, _1410488] : [c_Orderings_Obot__class_Obot(tc_fun(_1410482, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410484, tc_fun(_1410482, tc_HOL_Obool)), _1410486), _1410488), 34115 ^ _780461 : [(34116 ^ _780461) ^ [_1410598] : [hBOOL(hAPP(hAPP(c_member(_1410484), _1410598), _1410486)), -(hAPP(_1410488, _1410598) = c_Orderings_Obot__class_Obot(tc_fun(_1410482, tc_HOL_Obool)))]]], (34141 ^ _780461) ^ [_1411223, _1411225, _1411227, _1411229, _1411231] : [34143 ^ _780461 : [(34144 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411225), 34142 ^ [_1411223, _1411225, _1411227, _1411229, _1411231]), _1411227)))], (34146 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1411223, tc_HOL_Obool)), hAPP(_1411229, 34142 ^ [_1411223, _1411225, _1411227, _1411229, _1411231])), _1411231))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1411223, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411225, tc_fun(_1411223, tc_HOL_Obool)), _1411227), _1411229)), _1411231)))], (34131 ^ _780461) ^ [_1410965, _1410967, _1410969, _1410971, _1410973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410965, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410967, tc_fun(_1410965, tc_HOL_Obool)), _1410969), _1410971)), _1410973)), 34134 ^ _780461 : [(34135 ^ _780461) ^ [_1411098] : [hBOOL(hAPP(hAPP(c_member(_1410967), _1411098), _1410969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410965, tc_HOL_Obool)), hAPP(_1410971, _1411098)), _1410973)))]]], (34150 ^ _780461) ^ [_1411486, _1411488, _1411490, _1411492, _1411494, _1411496] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411486, tc_fun(_1411488, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1411490, _1411486, _1411492), _1411494)), _1411496) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411490, tc_fun(_1411488, tc_HOL_Obool)), _1411494), hAPP(hAPP(c_COMBB(_1411486, tc_fun(_1411488, tc_HOL_Obool), _1411490), _1411496), _1411492)))], (34152 ^ _780461) ^ [_1411563, _1411565, _1411567, _1411569, _1411571, _1411573] : [-(hAPP(c_Set_Oimage(_1411563, _1411565, _1411567), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411569, tc_fun(_1411563, tc_HOL_Obool)), _1411571), _1411573)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411569, tc_fun(_1411565, tc_HOL_Obool)), _1411571), hAPP(hAPP(c_COMBB(tc_fun(_1411563, tc_HOL_Obool), tc_fun(_1411565, tc_HOL_Obool), _1411569), c_Set_Oimage(_1411563, _1411565, _1411567)), _1411573)))], (34154 ^ _780461) ^ [_1411647, _1411649, _1411651, _1411653, _1411655, _1411657] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411647, tc_fun(_1411649, tc_HOL_Obool)), _1411651), hAPP(hAPP(c_COMBB(_1411653, tc_fun(_1411649, tc_HOL_Obool), _1411647), _1411655), _1411657)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411653, tc_fun(_1411649, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1411647, _1411653, _1411657), _1411651)), _1411655))], (34156 ^ _780461) ^ [_1411724, _1411726, _1411728, _1411730, _1411732] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411724, tc_fun(_1411726, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411724, tc_HOL_Obool)), _1411728), _1411730)), _1411732) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411726, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411724, tc_fun(_1411726, tc_HOL_Obool)), _1411728), _1411732)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411724, tc_fun(_1411726, tc_HOL_Obool)), _1411730), _1411732)))], (34158 ^ _780461) ^ [_1411813, _1411815, _1411817, _1411819, _1411821] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411813, tc_fun(_1411815, tc_HOL_Obool)), _1411817), hAPP(hAPP(c_COMBS(_1411813, tc_fun(_1411815, tc_HOL_Obool), tc_fun(_1411815, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411815, tc_HOL_Obool), tc_fun(tc_fun(_1411815, tc_HOL_Obool), tc_fun(_1411815, tc_HOL_Obool)), _1411813), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411815, tc_HOL_Obool))), _1411819)), _1411821)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411815, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411813, tc_fun(_1411815, tc_HOL_Obool)), _1411817), _1411819)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411813, tc_fun(_1411815, tc_HOL_Obool)), _1411817), _1411821)))], (34160 ^ _780461) ^ [_1411934, _1411936, _1411938, _1411940, _1411942, _1411944, _1411946] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411934, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411936, tc_fun(_1411934, tc_HOL_Obool)), _1411938), _1411940)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411942, tc_fun(_1411934, tc_HOL_Obool)), _1411944), _1411946)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411936, tc_fun(_1411934, tc_HOL_Obool)), _1411938), hAPP(hAPP(c_COMBB(tc_fun(_1411942, tc_fun(_1411934, tc_HOL_Obool)), tc_fun(_1411934, tc_HOL_Obool), _1411936), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411942, tc_fun(_1411934, tc_HOL_Obool)), _1411944)), hAPP(hAPP(c_COMBC(_1411936, tc_fun(_1411942, tc_fun(_1411934, tc_HOL_Obool)), tc_fun(_1411942, tc_fun(_1411934, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1411934, tc_HOL_Obool), tc_fun(_1411934, tc_HOL_Obool)), tc_fun(tc_fun(_1411942, tc_fun(_1411934, tc_HOL_Obool)), tc_fun(_1411942, tc_fun(_1411934, tc_HOL_Obool))), _1411936), c_COMBB(tc_fun(_1411934, tc_HOL_Obool), tc_fun(_1411934, tc_HOL_Obool), _1411942)), hAPP(hAPP(c_COMBB(tc_fun(_1411934, tc_HOL_Obool), tc_fun(tc_fun(_1411934, tc_HOL_Obool), tc_fun(_1411934, tc_HOL_Obool)), _1411936), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411934, tc_HOL_Obool))), _1411940))), _1411946))))], (34162 ^ _780461) ^ [_1412137, _1412139, _1412141, _1412143, _1412145] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412137, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412139, tc_fun(_1412137, tc_HOL_Obool)), _1412141), _1412143)), _1412145) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412139, tc_fun(_1412137, tc_HOL_Obool)), _1412141), hAPP(hAPP(c_COMBC(_1412139, tc_fun(_1412137, tc_HOL_Obool), tc_fun(_1412137, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412137, tc_HOL_Obool), tc_fun(tc_fun(_1412137, tc_HOL_Obool), tc_fun(_1412137, tc_HOL_Obool)), _1412139), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412137, tc_HOL_Obool))), _1412143)), _1412145)))], (34164 ^ _780461) ^ [_1412246, _1412248, _1412250, _1412252, _1412254] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412246, tc_HOL_Obool)), _1412248), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412250, tc_fun(_1412246, tc_HOL_Obool)), _1412252), _1412254)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412250, tc_fun(_1412246, tc_HOL_Obool)), _1412252), hAPP(hAPP(c_COMBB(tc_fun(_1412246, tc_HOL_Obool), tc_fun(_1412246, tc_HOL_Obool), _1412250), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412246, tc_HOL_Obool)), _1412248)), _1412254)))], (34166 ^ _780461) ^ [_1412336, _1412338, _1412340, _1412342, _1412344] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412336, tc_HOL_Obool)), _1412338), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412340, tc_fun(_1412336, tc_HOL_Obool)), _1412342), _1412344)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412340, tc_fun(_1412336, tc_HOL_Obool)), _1412342), hAPP(hAPP(c_COMBB(tc_fun(_1412336, tc_HOL_Obool), tc_fun(_1412336, tc_HOL_Obool), _1412340), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412336, tc_HOL_Obool)), _1412338)), _1412344)))], (34168 ^ _780461) ^ [_1412426, _1412428, _1412430, _1412432, _1412434] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412426, tc_fun(_1412428, tc_HOL_Obool)), _1412430), hAPP(hAPP(c_COMBC(_1412426, tc_fun(_1412428, tc_HOL_Obool), tc_fun(_1412428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412428, tc_HOL_Obool), tc_fun(tc_fun(_1412428, tc_HOL_Obool), tc_fun(_1412428, tc_HOL_Obool)), _1412426), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412428, tc_HOL_Obool))), _1412432)), _1412434)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412428, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412426, tc_fun(_1412428, tc_HOL_Obool)), _1412430), _1412432)), _1412434))], (34170 ^ _780461) ^ [_1412535, _1412537, _1412539, _1412541, _1412543] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412535, tc_fun(_1412537, tc_HOL_Obool)), _1412539), hAPP(hAPP(c_COMBB(tc_fun(_1412537, tc_HOL_Obool), tc_fun(_1412537, tc_HOL_Obool), _1412535), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412537, tc_HOL_Obool)), _1412541)), _1412543)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412537, tc_HOL_Obool)), _1412541), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412535, tc_fun(_1412537, tc_HOL_Obool)), _1412539), _1412543)))], (34172 ^ _780461) ^ [_1412625, _1412627, _1412629, _1412631, _1412633, _1412635] : [class_Complete__Lattice_Ocomplete__lattice(_1412625), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412627, tc_fun(_1412629, _1412625)), _1412631), _1412633), _1412635) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412627, _1412625), _1412631), hAPP(hAPP(c_COMBC(_1412627, _1412629, _1412625), _1412633), _1412635)))], (34178 ^ _780461) ^ [_1412776, _1412778, _1412780, _1412782, _1412784] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1412776, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412778, tc_fun(_1412776, tc_HOL_Obool)), _1412780), _1412782)), _1412784) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412778, tc_fun(_1412776, tc_HOL_Obool)), _1412780), hAPP(hAPP(c_COMBC(_1412778, tc_fun(_1412776, tc_HOL_Obool), tc_fun(_1412776, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412776, tc_HOL_Obool), tc_fun(tc_fun(_1412776, tc_HOL_Obool), tc_fun(_1412776, tc_HOL_Obool)), _1412778), c_Groups_Ominus__class_Ominus(tc_fun(_1412776, tc_HOL_Obool))), _1412782)), _1412784)))], (34180 ^ _780461) ^ [_1412885, _1412887, _1412889, _1412891, _1412893] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412885, tc_fun(_1412887, tc_HOL_Obool)), _1412889), hAPP(hAPP(c_COMBC(_1412885, tc_fun(_1412887, tc_HOL_Obool), tc_fun(_1412887, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412887, tc_HOL_Obool), tc_fun(tc_fun(_1412887, tc_HOL_Obool), tc_fun(_1412887, tc_HOL_Obool)), _1412885), c_Groups_Ominus__class_Ominus(tc_fun(_1412887, tc_HOL_Obool))), _1412891)), _1412893)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1412887, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412885, tc_fun(_1412887, tc_HOL_Obool)), _1412889), _1412891)), _1412893))], (34182 ^ _780461) ^ [_1412994, _1412996, _1412998, _1413000, _1413002] : [class_Complete__Lattice_Ocomplete__lattice(_1412994), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412996, tc_HOL_Obool)), _1412998), _1413000)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412994), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412996, _1412994), _1412998), _1413002)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412996, _1412994), _1413000), _1413002))))], (34192 ^ _780461) ^ [_1413203, _1413205, _1413207, _1413209, _1413211] : [class_Complete__Lattice_Ocomplete__lattice(_1413203), hBOOL(hAPP(hAPP(c_member(_1413205), _1413207), _1413209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413203), hAPP(_1413211, _1413207)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413205, _1413203), _1413209), _1413211))))], (34202 ^ _780461) ^ [_1413394, _1413396, _1413398, _1413400, _1413402, _1413404] : [hBOOL(hAPP(hAPP(c_member(_1413394), _1413396), _1413398)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413394, tc_fun(_1413400, tc_HOL_Obool)), _1413398), hAPP(hAPP(c_COMBB(tc_fun(_1413400, tc_HOL_Obool), tc_fun(_1413400, tc_HOL_Obool), _1413394), hAPP(c_Set_Oinsert(_1413400), _1413402)), _1413404)) = hAPP(hAPP(c_Set_Oinsert(_1413400), _1413402), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413394, tc_fun(_1413400, tc_HOL_Obool)), _1413398), _1413404)))], (34208 ^ _780461) ^ [_1413599, _1413601, _1413603, _1413605, _1413607] : [hBOOL(hAPP(hAPP(c_member(_1413599), _1413601), _1413603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413605, tc_HOL_Obool)), hAPP(_1413607, _1413601)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413599, tc_fun(_1413605, tc_HOL_Obool)), _1413603), _1413607))))], (34214 ^ _780461) ^ [_1413746, _1413748, _1413750, _1413752, _1413754] : [hBOOL(hAPP(hAPP(c_member(_1413746), _1413748), _1413750)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413752, tc_HOL_Obool)), hAPP(_1413754, _1413748)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413746, tc_fun(_1413752, tc_HOL_Obool)), _1413750), _1413754)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413746, tc_fun(_1413752, tc_HOL_Obool)), _1413750), _1413754))], (34220 ^ _780461) ^ [_1413937, _1413939, _1413941, _1413943, _1413945] : [_1413937 = c_Orderings_Obot__class_Obot(tc_fun(_1413939, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1413941), _1413943), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413939, tc_fun(_1413941, tc_HOL_Obool)), _1413937), _1413945)) = hAPP(hAPP(c_Set_Oinsert(_1413941), _1413943), c_Orderings_Obot__class_Obot(tc_fun(_1413941, tc_HOL_Obool))))], (34226 ^ _780461) ^ [_1414090, _1414092, _1414094, _1414096, _1414098] : [-(_1414090 = c_Orderings_Obot__class_Obot(tc_fun(_1414092, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1414094), _1414096), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414092, tc_fun(_1414094, tc_HOL_Obool)), _1414090), _1414098)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414092, tc_fun(_1414094, tc_HOL_Obool)), _1414090), hAPP(hAPP(c_COMBB(tc_fun(_1414094, tc_HOL_Obool), tc_fun(_1414094, tc_HOL_Obool), _1414092), hAPP(c_Set_Oinsert(_1414094), _1414096)), _1414098)))], (34232 ^ _780461) ^ [_1414192, _1414194] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414192, tc_fun(_1414192, tc_HOL_Obool)), _1414194), hAPP(hAPP(c_COMBC(_1414192, tc_fun(_1414192, tc_HOL_Obool), tc_fun(_1414192, tc_HOL_Obool)), c_Set_Oinsert(_1414192)), c_Orderings_Obot__class_Obot(tc_fun(_1414192, tc_HOL_Obool)))) = _1414194)], (34234 ^ _780461) ^ [_1414270, _1414272, _1414274, _1414276, _1414278] : [_1414270 = c_Orderings_Obot__class_Obot(tc_fun(_1414272, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414272, tc_fun(_1414274, tc_HOL_Obool)), _1414270), hAPP(hAPP(c_COMBB(tc_fun(_1414274, tc_HOL_Obool), tc_fun(_1414274, tc_HOL_Obool), _1414272), hAPP(c_Set_Oinsert(_1414274), _1414276)), _1414278)) = c_Orderings_Obot__class_Obot(tc_fun(_1414274, tc_HOL_Obool)))], (34240 ^ _780461) ^ [_1414433, _1414435, _1414437, _1414439, _1414441] : [-(_1414433 = c_Orderings_Obot__class_Obot(tc_fun(_1414435, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414435, tc_fun(_1414437, tc_HOL_Obool)), _1414433), hAPP(hAPP(c_COMBB(tc_fun(_1414437, tc_HOL_Obool), tc_fun(_1414437, tc_HOL_Obool), _1414435), hAPP(c_Set_Oinsert(_1414437), _1414439)), _1414441)) = hAPP(hAPP(c_Set_Oinsert(_1414437), _1414439), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414435, tc_fun(_1414437, tc_HOL_Obool)), _1414433), _1414441)))], (34246 ^ _780461) ^ [_1414553, _1414555, _1414557, _1414559, _1414561] : [_1414553 = c_Orderings_Obot__class_Obot(tc_fun(_1414555, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414555, tc_fun(_1414557, tc_HOL_Obool)), _1414553), hAPP(hAPP(c_COMBB(tc_fun(_1414557, tc_HOL_Obool), tc_fun(_1414557, tc_HOL_Obool), _1414555), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414557, tc_HOL_Obool)), _1414559)), _1414561)) = c_Orderings_Obot__class_Obot(tc_fun(_1414557, tc_HOL_Obool)))], (34252 ^ _780461) ^ [_1414722, _1414724, _1414726, _1414728, _1414730] : [-(_1414722 = c_Orderings_Obot__class_Obot(tc_fun(_1414724, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414724, tc_fun(_1414726, tc_HOL_Obool)), _1414722), hAPP(hAPP(c_COMBB(tc_fun(_1414726, tc_HOL_Obool), tc_fun(_1414726, tc_HOL_Obool), _1414724), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414726, tc_HOL_Obool)), _1414728)), _1414730)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414726, tc_HOL_Obool)), _1414728), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414724, tc_fun(_1414726, tc_HOL_Obool)), _1414722), _1414730)))], (34258 ^ _780461) ^ [_1414848, _1414850, _1414852, _1414854, _1414856] : [_1414848 = c_Orderings_Obot__class_Obot(tc_fun(_1414850, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414850, tc_fun(_1414852, tc_HOL_Obool)), _1414848), hAPP(hAPP(c_COMBC(_1414850, tc_fun(_1414852, tc_HOL_Obool), tc_fun(_1414852, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414852, tc_HOL_Obool), tc_fun(tc_fun(_1414852, tc_HOL_Obool), tc_fun(_1414852, tc_HOL_Obool)), _1414850), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414852, tc_HOL_Obool))), _1414854)), _1414856)) = c_Orderings_Obot__class_Obot(tc_fun(_1414852, tc_HOL_Obool)))], (34264 ^ _780461) ^ [_1415055, _1415057, _1415059, _1415061, _1415063] : [-(_1415055 = c_Orderings_Obot__class_Obot(tc_fun(_1415057, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415057, tc_fun(_1415059, tc_HOL_Obool)), _1415055), hAPP(hAPP(c_COMBC(_1415057, tc_fun(_1415059, tc_HOL_Obool), tc_fun(_1415059, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1415059, tc_HOL_Obool), tc_fun(tc_fun(_1415059, tc_HOL_Obool), tc_fun(_1415059, tc_HOL_Obool)), _1415057), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415059, tc_HOL_Obool))), _1415061)), _1415063)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415059, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415057, tc_fun(_1415059, tc_HOL_Obool)), _1415055), _1415061)), _1415063))], (34270 ^ _780461) ^ [_1415200, _1415202, _1415204, _1415206, _1415208] : [_1415200 = c_Orderings_Obot__class_Obot(tc_fun(_1415202, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415204, tc_HOL_Obool)), _1415206), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415202, tc_fun(_1415204, tc_HOL_Obool)), _1415200), _1415208)) = _1415206)], (34276 ^ _780461) ^ [_1415333, _1415335, _1415337, _1415339, _1415341] : [-(_1415333 = c_Orderings_Obot__class_Obot(tc_fun(_1415335, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415337, tc_HOL_Obool)), _1415339), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415335, tc_fun(_1415337, tc_HOL_Obool)), _1415333), _1415341)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415335, tc_fun(_1415337, tc_HOL_Obool)), _1415333), hAPP(hAPP(c_COMBB(tc_fun(_1415337, tc_HOL_Obool), tc_fun(_1415337, tc_HOL_Obool), _1415335), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415337, tc_HOL_Obool)), _1415339)), _1415341)))], (34282 ^ _780461) ^ [_1415459, _1415461, _1415463, _1415465, _1415467] : [_1415459 = c_Orderings_Obot__class_Obot(tc_fun(_1415461, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415463, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415461, tc_fun(_1415463, tc_HOL_Obool)), _1415459), _1415465)), _1415467) = _1415467)], (34288 ^ _780461) ^ [_1415592, _1415594, _1415596, _1415598, _1415600] : [-(_1415592 = c_Orderings_Obot__class_Obot(tc_fun(_1415594, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415596, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415594, tc_fun(_1415596, tc_HOL_Obool)), _1415592), _1415598)), _1415600) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415594, tc_fun(_1415596, tc_HOL_Obool)), _1415592), hAPP(hAPP(c_COMBC(_1415594, tc_fun(_1415596, tc_HOL_Obool), tc_fun(_1415596, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1415596, tc_HOL_Obool), tc_fun(tc_fun(_1415596, tc_HOL_Obool), tc_fun(_1415596, tc_HOL_Obool)), _1415594), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415596, tc_HOL_Obool))), _1415598)), _1415600)))], (34294 ^ _780461) ^ [_1415719, _1415721, _1415723, _1415725, _1415727] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415719, tc_fun(_1415721, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1415719), _1415723), _1415725)), _1415727) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415721, tc_HOL_Obool)), hAPP(_1415727, _1415723)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415719, tc_fun(_1415721, tc_HOL_Obool)), _1415725), _1415727)))], (34296 ^ _780461) ^ [_1415796, _1415798, _1415800, _1415802, _1415804, _1415806, _1415808, _1415810, _1415812] : [c_Equiv__Relations_Oequiv(_1415796, _1415798, _1415800), c_Equiv__Relations_Oequiv(_1415802, _1415804, _1415806), c_Equiv__Relations_Ocongruent2(_1415796, _1415802, tc_fun(_1415808, tc_HOL_Obool), _1415800, _1415806, _1415810), hBOOL(hAPP(hAPP(c_member(_1415802), _1415812), _1415804)), -(c_Equiv__Relations_Ocongruent(_1415796, tc_fun(_1415808, tc_HOL_Obool), _1415800, hAPP(hAPP(c_COMBB(tc_fun(_1415802, tc_fun(_1415808, tc_HOL_Obool)), tc_fun(_1415808, tc_HOL_Obool), _1415796), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415802, tc_fun(_1415808, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1415802, _1415802, _1415806), hAPP(hAPP(c_Set_Oinsert(_1415802), _1415812), c_Orderings_Obot__class_Obot(tc_fun(_1415802, tc_HOL_Obool)))))), _1415810)))], (34314 ^ _780461) ^ [_1416223] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1416223) = 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, _1416223)), 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))))))))], (34316 ^ _780461) ^ [_1416261, _1416263, _1416265, _1416267, _1416269, _1416271, _1416273, _1416275, _1416277, _1416279] : [c_Equiv__Relations_Oequiv(_1416261, _1416263, _1416265), c_Equiv__Relations_Oequiv(_1416267, _1416269, _1416271), c_Equiv__Relations_Ocongruent2(_1416261, _1416267, tc_fun(_1416273, tc_HOL_Obool), _1416265, _1416271, _1416275), hBOOL(hAPP(hAPP(c_member(_1416261), _1416277), _1416263)), hBOOL(hAPP(hAPP(c_member(_1416267), _1416279), _1416269)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416261, tc_fun(_1416273, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1416261, _1416261, _1416265), hAPP(hAPP(c_Set_Oinsert(_1416261), _1416277), c_Orderings_Obot__class_Obot(tc_fun(_1416261, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1416267, tc_fun(_1416273, tc_HOL_Obool)), tc_fun(_1416273, tc_HOL_Obool), _1416261), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416267, tc_fun(_1416273, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1416267, _1416267, _1416271), hAPP(hAPP(c_Set_Oinsert(_1416267), _1416279), c_Orderings_Obot__class_Obot(tc_fun(_1416267, tc_HOL_Obool)))))), _1416275)) = hAPP(hAPP(_1416275, _1416277), _1416279))], (34338 ^ _780461) ^ [_1416844, _1416846, _1416848, _1416850, _1416852, _1416854, _1416856, _1416858] : [hBOOL(hAPP(hAPP(c_member(_1416844), _1416846), _1416848)), hBOOL(hAPP(hAPP(hAPP(_1416850, _1416846), _1416852), _1416854)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416844, tc_fun(_1416856, tc_fun(_1416858, tc_HOL_Obool))), _1416848), _1416850), _1416852), _1416854)))], (34348 ^ _780461) ^ [_1417082, _1417084] : [hAPP(c_Int_ORep__Integ, _1417082) = hAPP(c_Int_ORep__Integ, _1417084), -(_1417082 = _1417084)], (34354 ^ _780461) ^ [_1417167, _1417169] : [_1417167 = _1417169, -(hAPP(c_Int_ORep__Integ, _1417167) = hAPP(c_Int_ORep__Integ, _1417169))], (34360 ^ _780461) ^ [_1417258] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1417258)) = _1417258)], (34362 ^ _780461) ^ [_1417287, _1417289, _1417291, _1417293, _1417295, _1417297, _1417299, _1417301, _1417303, _1417305] : [c_Equiv__Relations_Ocongruent2(_1417287, _1417289, _1417291, _1417293, _1417295, _1417297), hBOOL(hAPP(hAPP(c_member(tc_prod(_1417287, _1417287)), hAPP(hAPP(c_Product__Type_OPair(_1417287, _1417287), _1417299), _1417301)), _1417293)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1417289, _1417289)), hAPP(hAPP(c_Product__Type_OPair(_1417289, _1417289), _1417303), _1417305)), _1417295)), -(hAPP(hAPP(_1417297, _1417299), _1417303) = hAPP(hAPP(_1417297, _1417301), _1417305))], (34376 ^ _780461) ^ [_1417624] : [-(hAPP(c_Int_Onat, _1417624) = 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, _1417624)), 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)))))))], (34378 ^ _780461) ^ [_1417662, _1417664, _1417666, _1417668, _1417670, _1417672, _1417674, _1417676] : [c_Equiv__Relations_Oequiv(_1417662, _1417664, _1417666), c_Equiv__Relations_Ocongruent2(_1417662, _1417668, _1417670, _1417666, _1417672, _1417674), hBOOL(hAPP(hAPP(c_member(_1417662), _1417676), _1417664)), -(c_Equiv__Relations_Ocongruent(_1417668, _1417670, _1417672, hAPP(_1417674, _1417676)))], (34392 ^ _780461) ^ [_1417913, _1417915, _1417917, _1417919, _1417921, _1417923, _1417925] : [c_Equiv__Relations_Oequiv(_1417913, _1417915, _1417917), c_Equiv__Relations_Ocongruent(_1417913, tc_fun(_1417919, tc_HOL_Obool), _1417917, _1417921), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417913, tc_fun(_1417919, tc_HOL_Obool)), _1417923), _1417921) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417913, tc_fun(_1417919, tc_HOL_Obool)), _1417925), _1417921), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417913, tc_HOL_Obool)), _1417923), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417913), _1417915), _1417917))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417913, tc_HOL_Obool)), _1417925), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417913), _1417915), _1417917))), 34414 ^ _780461 : [(34415 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417913), 34413 ^ [_1417913, _1417915, _1417917, _1417919, _1417921, _1417923, _1417925]), _1417915)))], (34418 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417913), 34416 ^ [_1417913, _1417915, _1417917, _1417919, _1417921, _1417923, _1417925]), _1417915)))], (34420 ^ _780461) ^ [] : [-(hAPP(_1417921, 34413 ^ [_1417913, _1417915, _1417917, _1417919, _1417921, _1417923, _1417925]) = hAPP(_1417921, 34416 ^ [_1417913, _1417915, _1417917, _1417919, _1417921, _1417923, _1417925]))], (34422 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1417913, _1417913)), hAPP(hAPP(c_Product__Type_OPair(_1417913, _1417913), 34413 ^ [_1417913, _1417915, _1417917, _1417919, _1417921, _1417923, _1417925]), 34416 ^ [_1417913, _1417915, _1417917, _1417919, _1417921, _1417923, _1417925])), _1417917))]], -(_1417923 = _1417925)], (34426 ^ _780461) ^ [_1418883, _1418885, _1418887, _1418889, _1418891, _1418893, _1418895, _1418897, _1418899, _1418901, _1418903] : [c_Equiv__Relations_Oequiv(_1418883, _1418885, _1418887), c_Equiv__Relations_Oequiv(_1418889, _1418891, _1418893), c_Equiv__Relations_Ocongruent2(_1418883, _1418889, tc_fun(_1418895, tc_HOL_Obool), _1418887, _1418893, _1418897), hBOOL(hAPP(hAPP(c_member(tc_fun(_1418883, tc_HOL_Obool)), _1418899), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1418883), _1418885), _1418887))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1418889, tc_HOL_Obool)), _1418901), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1418889), _1418891), _1418893))), 34448 ^ _780461 : [(34449 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418883), 34447 ^ [_1418883, _1418885, _1418887, _1418889, _1418891, _1418893, _1418895, _1418897, _1418899, _1418901, _1418903]), _1418885)))], (34452 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418889), 34450 ^ [_1418883, _1418885, _1418887, _1418889, _1418891, _1418893, _1418895, _1418897, _1418899, _1418901, _1418903]), _1418891)))], (34454 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1418895, tc_HOL_Obool)), hAPP(hAPP(_1418897, 34447 ^ [_1418883, _1418885, _1418887, _1418889, _1418891, _1418893, _1418895, _1418897, _1418899, _1418901, _1418903]), 34450 ^ [_1418883, _1418885, _1418887, _1418889, _1418891, _1418893, _1418895, _1418897, _1418899, _1418901, _1418903])), _1418903))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1418895, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418883, tc_fun(_1418895, tc_HOL_Obool)), _1418899), hAPP(hAPP(c_COMBB(tc_fun(_1418889, tc_fun(_1418895, tc_HOL_Obool)), tc_fun(_1418895, tc_HOL_Obool), _1418883), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418889, tc_fun(_1418895, tc_HOL_Obool)), _1418901)), _1418897))), _1418903)))], (34458 ^ _780461) ^ [_1419885, _1419887, _1419889, _1419891, _1419893, _1419895, _1419897] : [c_Equiv__Relations_Oequiv(_1419885, _1419887, _1419889), c_Equiv__Relations_Ocongruent(_1419885, tc_fun(_1419891, tc_HOL_Obool), _1419889, _1419893), hBOOL(hAPP(hAPP(c_member(tc_fun(_1419885, tc_HOL_Obool)), _1419895), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1419885), _1419887), _1419889))), 34472 ^ _780461 : [(34473 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419885), 34471 ^ [_1419885, _1419887, _1419889, _1419891, _1419893, _1419895, _1419897]), _1419887)))], (34475 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1419891, tc_HOL_Obool)), hAPP(_1419893, 34471 ^ [_1419885, _1419887, _1419889, _1419891, _1419893, _1419895, _1419897])), _1419897))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1419891, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419885, tc_fun(_1419891, tc_HOL_Obool)), _1419895), _1419893)), _1419897)))], (34479 ^ _780461) ^ [_1420426, _1420428, _1420430, _1420432, _1420434, _1420436, _1420438] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420426, tc_fun(_1420428, tc_fun(_1420430, tc_HOL_Obool))), _1420432), _1420434), _1420436), _1420438)), 34483 ^ _780461 : [(34484 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1420426), 34482 ^ [_1420426, _1420428, _1420430, _1420432, _1420434, _1420436, _1420438]), _1420432)))], (34486 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1420434, 34482 ^ [_1420426, _1420428, _1420430, _1420432, _1420434, _1420436, _1420438]), _1420436), _1420438)))]]], (34488 ^ _780461) ^ [_1420644, _1420646, _1420648, _1420650, _1420652, _1420654, _1420656] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420644, tc_fun(_1420646, tc_fun(_1420648, tc_HOL_Obool))), _1420650), _1420652), _1420654), _1420656))), 34489 ^ _780461 : [(34490 ^ _780461) ^ [_1420729] : [hBOOL(hAPP(hAPP(c_member(_1420644), _1420729), _1420650)), hBOOL(hAPP(hAPP(hAPP(_1420652, _1420729), _1420654), _1420656))]]], (34498 ^ _780461) ^ [_1420897, _1420899] : [-(c_Relation_OId__on(_1420897, _1420899) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420897, tc_fun(tc_prod(_1420897, _1420897), tc_HOL_Obool)), _1420899), hAPP(hAPP(c_COMBC(_1420897, tc_fun(tc_prod(_1420897, _1420897), tc_HOL_Obool), tc_fun(tc_prod(_1420897, _1420897), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1420897, _1420897), tc_fun(tc_fun(tc_prod(_1420897, _1420897), tc_HOL_Obool), tc_fun(tc_prod(_1420897, _1420897), tc_HOL_Obool)), _1420897), c_Set_Oinsert(tc_prod(_1420897, _1420897))), hAPP(hAPP(c_COMBS(_1420897, _1420897, tc_prod(_1420897, _1420897)), c_Product__Type_OPair(_1420897, _1420897)), c_COMBI(_1420897)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1420897, _1420897), tc_HOL_Obool)))))], (34516 ^ _780461) ^ [_1421658, _1421660, _1421662] : [-(c_Relation_Orefl__on(_1421658, _1421660, _1421662)), 34520 ^ _780461 : [(34521 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1421658, _1421658)), 34519 ^ [_1421658, _1421660, _1421662]), _1421662)))], (34523 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1421658, _1421658, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1421658, tc_fun(_1421658, tc_HOL_Obool), tc_fun(_1421658, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1421658, tc_HOL_Obool), tc_fun(_1421658, tc_HOL_Obool)), _1421658), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1421658)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1421658), c_fconj), hAPP(hAPP(c_COMBC(_1421658, tc_fun(_1421658, tc_HOL_Obool), tc_HOL_Obool), c_member(_1421658)), _1421660)))), hAPP(hAPP(c_COMBC(_1421658, tc_fun(_1421658, tc_HOL_Obool), tc_HOL_Obool), c_member(_1421658)), _1421660))), 34519 ^ [_1421658, _1421660, _1421662]))]], 34525 ^ _780461 : [(34526 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1421658), 34524 ^ [_1421658, _1421660, _1421662]), _1421660)))], (34528 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1421658, _1421658)), hAPP(hAPP(c_Product__Type_OPair(_1421658, _1421658), 34524 ^ [_1421658, _1421660, _1421662]), 34524 ^ [_1421658, _1421660, _1421662])), _1421662))]]], (34500 ^ _780461) ^ [_1421039, _1421041, _1421043] : [c_Relation_Orefl__on(_1421039, _1421041, _1421043), 34503 ^ _780461 : [(34504 ^ _780461) ^ [_1421250] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1421039, _1421039)), _1421250), _1421043)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1421039, _1421039, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1421039, tc_fun(_1421039, tc_HOL_Obool), tc_fun(_1421039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1421039, tc_HOL_Obool), tc_fun(_1421039, tc_HOL_Obool)), _1421039), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1421039)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1421039), c_fconj), hAPP(hAPP(c_COMBC(_1421039, tc_fun(_1421039, tc_HOL_Obool), tc_HOL_Obool), c_member(_1421039)), _1421041)))), hAPP(hAPP(c_COMBC(_1421039, tc_fun(_1421039, tc_HOL_Obool), tc_HOL_Obool), c_member(_1421039)), _1421041))), _1421250)))], (34510 ^ _780461) ^ [_1421523] : [hBOOL(hAPP(hAPP(c_member(_1421039), _1421523), _1421041)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1421039, _1421039)), hAPP(hAPP(c_Product__Type_OPair(_1421039, _1421039), _1421523), _1421523)), _1421043)))]]], (34532 ^ _780461) ^ [_1422299, _1422301, _1422303, _1422305, _1422307] : [class_Groups_Ocomm__monoid__mult(_1422299), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422301), _1422303)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422301), _1422305)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1422301, tc_HOL_Obool)), _1422303), _1422305) = c_Orderings_Obot__class_Obot(tc_fun(_1422301, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1422299, _1422301, c_Groups_Otimes__class_Otimes(_1422299)), _1422307), c_Groups_Oone__class_Oone(_1422299)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1422301, tc_HOL_Obool)), _1422303), _1422305)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422299), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1422299, _1422301, c_Groups_Otimes__class_Otimes(_1422299)), _1422307), c_Groups_Oone__class_Oone(_1422299)), _1422303)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1422299, _1422301, c_Groups_Otimes__class_Otimes(_1422299)), _1422307), c_Groups_Oone__class_Oone(_1422299)), _1422305)))], (34550 ^ _780461) ^ [_1422742, _1422744, _1422746, _1422748, _1422750] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1422742, _1422744, _1422746), _1422748), _1422750), c_Orderings_Obot__class_Obot(tc_fun(_1422744, tc_HOL_Obool))) = _1422750)], (34552 ^ _780461) ^ [_1422791, _1422793] : [-(c_Relation_Orefl__on(_1422791, _1422793, c_Relation_OId__on(_1422791, _1422793)))], (34554 ^ _780461) ^ [_1422820, _1422822] : [-(c_Relation_OId__on(_1422820, _1422822) = hAPP(c_Product__Type_Oprod_Oprod__case(_1422820, _1422820, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1422820, tc_HOL_Obool, tc_fun(_1422820, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1422820, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1422820, tc_HOL_Obool)), _1422820), c_COMBC(_1422820, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1422820, tc_HOL_Obool), tc_fun(_1422820, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1422820), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1422820), c_fconj)), c_fequal))), _1422822)))], (34556 ^ _780461) ^ [_1422914, _1422916, _1422918, _1422920, _1422922, _1422924, _1422926] : [c_Finite__Set_Ofolding__image__simple(_1422914, _1422916, _1422918, _1422920, _1422922, _1422924), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422916), _1422926)), -(hAPP(_1422924, _1422926) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1422914, _1422916, _1422918), _1422922), _1422920), _1422926))], (34566 ^ _780461) ^ [_1423111] : [-(c_Relation_Orefl__on(_1423111, c_Orderings_Obot__class_Obot(tc_fun(_1423111, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1423111, _1423111), tc_HOL_Obool))))], (34568 ^ _780461) ^ [_1423148, _1423150, _1423152, _1423154, _1423156] : [c_Relation_Orefl__on(_1423148, _1423150, _1423152), c_Relation_Orefl__on(_1423148, _1423154, _1423156), -(c_Relation_Orefl__on(_1423148, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423148, tc_HOL_Obool)), _1423150), _1423154), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1423148, _1423148), tc_HOL_Obool)), _1423152), _1423156)))], (34578 ^ _780461) ^ [_1423345, _1423347, _1423349, _1423351, _1423353] : [c_Relation_Orefl__on(_1423345, _1423347, _1423349), c_Relation_Orefl__on(_1423345, _1423351, _1423353), -(c_Relation_Orefl__on(_1423345, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423345, tc_HOL_Obool)), _1423347), _1423351), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1423345, _1423345), tc_HOL_Obool)), _1423349), _1423353)))], (34588 ^ _780461) ^ [_1423542] : [-(c_Relation_OId__on(_1423542, c_Orderings_Obot__class_Obot(tc_fun(_1423542, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1423542, _1423542), tc_HOL_Obool)))], (34590 ^ _780461) ^ [_1423581, _1423583, _1423585] : [-(hAPP(c_Relation_OImage(_1423581, _1423581, c_Relation_OId__on(_1423581, _1423583)), _1423585) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423581, tc_HOL_Obool)), _1423583), _1423585))], (34592 ^ _780461) ^ [_1423629, _1423631, _1423633, _1423635, _1423637] : [class_Groups_Ocomm__monoid__mult(_1423629), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423631), _1423633)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1423629, _1423631, c_Groups_Otimes__class_Otimes(_1423629)), hAPP(hAPP(c_COMBS(_1423631, _1423629, _1423629), hAPP(hAPP(c_COMBB(_1423629, tc_fun(_1423629, _1423629), _1423631), c_Groups_Otimes__class_Otimes(_1423629)), _1423635)), _1423637)), c_Groups_Oone__class_Oone(_1423629)), _1423633) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423629), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1423629, _1423631, c_Groups_Otimes__class_Otimes(_1423629)), _1423635), c_Groups_Oone__class_Oone(_1423629)), _1423633)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1423629, _1423631, c_Groups_Otimes__class_Otimes(_1423629)), _1423637), c_Groups_Oone__class_Oone(_1423629)), _1423633)))], (34602 ^ _780461) ^ [_1423944, _1423946, _1423948, _1423950, _1423952] : [c_Relation_Orefl__on(_1423944, _1423946, _1423948), hBOOL(hAPP(hAPP(c_member(tc_prod(_1423944, _1423944)), hAPP(hAPP(c_Product__Type_OPair(_1423944, _1423944), _1423950), _1423952)), _1423948)), -(hBOOL(hAPP(hAPP(c_member(_1423944), _1423952), _1423946)))], (34612 ^ _780461) ^ [_1424139, _1424141, _1424143, _1424145, _1424147] : [c_Relation_Orefl__on(_1424139, _1424141, _1424143), hBOOL(hAPP(hAPP(c_member(tc_prod(_1424139, _1424139)), hAPP(hAPP(c_Product__Type_OPair(_1424139, _1424139), _1424145), _1424147)), _1424143)), -(hBOOL(hAPP(hAPP(c_member(_1424139), _1424145), _1424141)))], (34622 ^ _780461) ^ [_1424334, _1424336, _1424338, _1424340] : [c_Relation_Orefl__on(_1424334, _1424336, _1424338), hBOOL(hAPP(hAPP(c_member(_1424334), _1424340), _1424336)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1424334, _1424334)), hAPP(hAPP(c_Product__Type_OPair(_1424334, _1424334), _1424340), _1424340)), _1424338)))], (34632 ^ _780461) ^ [_1424525, _1424527, _1424529, _1424531, _1424533, _1424535] : [class_Groups_Oab__semigroup__mult(_1424525), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424527), _1424529)), -(hBOOL(hAPP(hAPP(c_member(_1424527), _1424531), _1424529))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1424525, _1424527, c_Groups_Otimes__class_Otimes(_1424525)), _1424533), _1424535), hAPP(hAPP(c_Set_Oinsert(_1424527), _1424531), _1424529)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424525), hAPP(_1424533, _1424531)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1424525, _1424527, c_Groups_Otimes__class_Otimes(_1424525)), _1424533), _1424535), _1424529)))], (34646 ^ _780461) ^ [_1424803, _1424805, _1424807, _1424809] : [class_Groups_Ocomm__monoid__mult(_1424803), 34649 ^ _780461 : [(34650 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1424805), _1424807)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1424805, _1424803), _1424809), _1424807) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1424803, _1424805, c_Groups_Otimes__class_Otimes(_1424803)), _1424809), c_Groups_Oone__class_Oone(_1424803)), _1424807))], (34656 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1424805), _1424807))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1424805, _1424803), _1424809), _1424807) = c_Groups_Oone__class_Oone(_1424803))]]], (34662 ^ _780461) ^ [_1425075, _1425077, _1425079, _1425081] : [class_Groups_Ocomm__monoid__mult(_1425075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425077), _1425079)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1425077, _1425075), _1425081), _1425079) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1425075, _1425077, c_Groups_Otimes__class_Otimes(_1425075)), _1425081), c_Groups_Oone__class_Oone(_1425075)), _1425079))], (34672 ^ _780461) ^ [_1425291, _1425293, _1425295, _1425297] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1425291, _1425291)), hAPP(hAPP(c_Product__Type_OPair(_1425291, _1425291), _1425293), _1425295)), c_Relation_OId__on(_1425291, _1425297))), 34675 ^ _780461 : [(34676 ^ _780461) ^ [] : [-(_1425293 = _1425295)], (34678 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425291), _1425293), _1425297)))]]], (34680 ^ _780461) ^ [_1425452, _1425454, _1425456, _1425458] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1425452, _1425452)), hAPP(hAPP(c_Product__Type_OPair(_1425452, _1425452), _1425454), _1425456)), c_Relation_OId__on(_1425452, _1425458)))), _1425454 = _1425456, hBOOL(hAPP(hAPP(c_member(_1425452), _1425454), _1425458))], (34690 ^ _780461) ^ [_1425649, _1425651, _1425653, _1425655] : [_1425649 = _1425651, hBOOL(hAPP(hAPP(c_member(_1425653), _1425649), _1425655)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1425653, _1425653)), hAPP(hAPP(c_Product__Type_OPair(_1425653, _1425653), _1425649), _1425651)), c_Relation_OId__on(_1425653, _1425655))))], (34700 ^ _780461) ^ [_1425844, _1425846, _1425848, _1425850, _1425852] : [class_Groups_Ocomm__monoid__mult(_1425844), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425846), _1425848)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425846), _1425850)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425844), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1425844, _1425846, c_Groups_Otimes__class_Otimes(_1425844)), _1425852), c_Groups_Oone__class_Oone(_1425844)), _1425848)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1425844, _1425846, c_Groups_Otimes__class_Otimes(_1425844)), _1425852), c_Groups_Oone__class_Oone(_1425844)), _1425850)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425844), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1425844, _1425846, c_Groups_Otimes__class_Otimes(_1425844)), _1425852), c_Groups_Oone__class_Oone(_1425844)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1425846, tc_HOL_Obool)), _1425848), _1425850))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1425844, _1425846, c_Groups_Otimes__class_Otimes(_1425844)), _1425852), c_Groups_Oone__class_Oone(_1425844)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425846, tc_HOL_Obool)), _1425848), _1425850))))], (34714 ^ _780461) ^ [_1426269, _1426271, _1426273, _1426275] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426269), _1426271)), -(hAPP(c_Set_Oimage(_1426269, _1426273, _1426275), _1426271) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1426273, tc_HOL_Obool), _1426269, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426273, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1426269, tc_fun(_1426273, tc_HOL_Obool), tc_fun(_1426273, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1426273, tc_fun(tc_fun(_1426273, tc_HOL_Obool), tc_fun(_1426273, tc_HOL_Obool)), _1426269), c_Set_Oinsert(_1426273)), _1426275)), c_Orderings_Obot__class_Obot(tc_fun(_1426273, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1426273, tc_HOL_Obool))), _1426271))], (34720 ^ _780461) ^ [_1426508, _1426510] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426508), _1426510)), -(hAPP(c_Finite__Set_Ocard(_1426508), _1426510) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1426508, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1426508), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1426510))], (34726 ^ _780461) ^ [_1426650, _1426652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426650), _1426652)), -(hAPP(c_Finite__Set_Ocard(_1426650), _1426652) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1426650, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1426650), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1426652))], (34732 ^ _780461) ^ [_1426777, _1426779] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1426777), _1426779))), -(hAPP(c_Finite__Set_Ocard(_1426777), _1426779) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34738 ^ _780461) ^ [_1426824, _1426826, _1426828, _1426830, _1426832, _1426834, _1426836] : [c_Big__Operators_Ocomm__monoid__big(_1426824, _1426826, _1426828, _1426830, _1426832), 34741 ^ _780461 : [(34742 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426826), _1426834)), -(hAPP(hAPP(_1426832, _1426836), _1426834) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1426824, _1426826, _1426828), _1426836), _1426830), _1426834))], (34748 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1426826), _1426834))), -(hAPP(hAPP(_1426832, _1426836), _1426834) = _1426830)]]], (34754 ^ _780461) ^ [_1427092, _1427094, _1427096, _1427098, _1427100] : [class_Groups_Ocomm__monoid__mult(_1427092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427094), _1427096)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427094), _1427098)), 34768 ^ _780461 : [(34769 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1427094), 34767 ^ [_1427092, _1427094, _1427096, _1427098, _1427100]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427094, tc_HOL_Obool)), _1427096), _1427098))))], (34771 ^ _780461) ^ [] : [hAPP(_1427100, 34767 ^ [_1427092, _1427094, _1427096, _1427098, _1427100]) = c_Groups_Oone__class_Oone(_1427092)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1427092, _1427094, c_Groups_Otimes__class_Otimes(_1427092)), _1427100), c_Groups_Oone__class_Oone(_1427092)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427094, tc_HOL_Obool)), _1427096), _1427098)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427092), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1427092, _1427094, c_Groups_Otimes__class_Otimes(_1427092)), _1427100), c_Groups_Oone__class_Oone(_1427092)), _1427096)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1427092, _1427094, c_Groups_Otimes__class_Otimes(_1427092)), _1427100), c_Groups_Oone__class_Oone(_1427092)), _1427098)))], (34775 ^ _780461) ^ [_1427635, _1427637, _1427639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1427635, _1427635)), _1427637), c_Relation_OId__on(_1427635, _1427639))), 34779 ^ _780461 : [(34780 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1427635), 34778 ^ [_1427635, _1427637, _1427639]), _1427639)))], (34782 ^ _780461) ^ [] : [-(_1427637 = hAPP(hAPP(c_Product__Type_OPair(_1427635, _1427635), 34778 ^ [_1427635, _1427637, _1427639]), 34778 ^ [_1427635, _1427637, _1427639]))]]], (34784 ^ _780461) ^ [_1427834, _1427836, _1427838, _1427840, _1427842, _1427844, _1427846] : [c_Big__Operators_Ocomm__monoid__big(_1427834, _1427836, _1427838, _1427840, _1427842), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1427836), _1427844))), -(hAPP(hAPP(_1427842, _1427846), _1427844) = _1427840)], (34794 ^ _780461) ^ [_1427962, _1427964, _1427966] : [class_Orderings_Olinorder(_1427962), hAPP(_1427964, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1427962), 34799 ^ [_1427962, _1427964, _1427966]), 34800 ^ [_1427962, _1427964, _1427966])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1427962), hAPP(_1427964, 34799 ^ [_1427962, _1427964, _1427966])), hAPP(_1427964, 34800 ^ [_1427962, _1427964, _1427966])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427962), _1427966)), -(_1427966 = c_Orderings_Obot__class_Obot(tc_fun(_1427962, tc_HOL_Obool))), -(hAPP(_1427964, c_Big__Operators_Olattice_OSup__fin(_1427962, c_Orderings_Oord__class_Omax(_1427962), _1427966)) = c_Big__Operators_Olattice_OSup__fin(_1427962, c_Orderings_Oord__class_Omax(_1427962), hAPP(c_Set_Oimage(_1427962, _1427962, _1427964), _1427966)))], (34814 ^ _780461) ^ [_1428377, _1428379, _1428381] : [class_Orderings_Olinorder(_1428377), hAPP(_1428379, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1428377), 34819 ^ [_1428377, _1428379, _1428381]), 34820 ^ [_1428377, _1428379, _1428381])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1428377), hAPP(_1428379, 34819 ^ [_1428377, _1428379, _1428381])), hAPP(_1428379, 34820 ^ [_1428377, _1428379, _1428381])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428377), _1428381)), -(_1428381 = c_Orderings_Obot__class_Obot(tc_fun(_1428377, tc_HOL_Obool))), -(hAPP(_1428379, c_Big__Operators_Olattice_OInf__fin(_1428377, c_Orderings_Oord__class_Omin(_1428377), _1428381)) = c_Big__Operators_Olattice_OInf__fin(_1428377, c_Orderings_Oord__class_Omin(_1428377), hAPP(c_Set_Oimage(_1428377, _1428377, _1428379), _1428381)))], (34834 ^ _780461) ^ [_1428792, _1428794, _1428796] : [class_Orderings_Olinorder(_1428792), hAPP(_1428794, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1428792), 34839 ^ [_1428792, _1428794, _1428796]), 34840 ^ [_1428792, _1428794, _1428796])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1428792), hAPP(_1428794, 34839 ^ [_1428792, _1428794, _1428796])), hAPP(_1428794, 34840 ^ [_1428792, _1428794, _1428796])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428792), _1428796)), -(_1428796 = c_Orderings_Obot__class_Obot(tc_fun(_1428792, tc_HOL_Obool))), -(hAPP(_1428794, c_Big__Operators_Olinorder__class_OMax(_1428792, _1428796)) = c_Big__Operators_Olinorder__class_OMax(_1428792, hAPP(c_Set_Oimage(_1428792, _1428792, _1428794), _1428796)))], (34854 ^ _780461) ^ [_1429195, _1429197, _1429199] : [class_Orderings_Olinorder(_1429195), hAPP(_1429197, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1429195), 34859 ^ [_1429195, _1429197, _1429199]), 34860 ^ [_1429195, _1429197, _1429199])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1429195), hAPP(_1429197, 34859 ^ [_1429195, _1429197, _1429199])), hAPP(_1429197, 34860 ^ [_1429195, _1429197, _1429199])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429195), _1429199)), -(_1429199 = c_Orderings_Obot__class_Obot(tc_fun(_1429195, tc_HOL_Obool))), -(hAPP(_1429197, c_Big__Operators_Olinorder__class_OMin(_1429195, _1429199)) = c_Big__Operators_Olinorder__class_OMin(_1429195, hAPP(c_Set_Oimage(_1429195, _1429195, _1429197), _1429199)))], (34874 ^ _780461) ^ [_1429598, _1429600, _1429602] : [class_Lattices_Olattice(_1429598), hAPP(_1429600, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1429598), 34879 ^ [_1429598, _1429600, _1429602]), 34880 ^ [_1429598, _1429600, _1429602])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1429598), hAPP(_1429600, 34879 ^ [_1429598, _1429600, _1429602])), hAPP(_1429600, 34880 ^ [_1429598, _1429600, _1429602])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429598), _1429602)), -(_1429602 = c_Orderings_Obot__class_Obot(tc_fun(_1429598, tc_HOL_Obool))), -(hAPP(_1429600, c_Big__Operators_Olattice__class_OInf__fin(_1429598, _1429602)) = c_Big__Operators_Olattice__class_OInf__fin(_1429598, hAPP(c_Set_Oimage(_1429598, _1429598, _1429600), _1429602)))], (34894 ^ _780461) ^ [_1430001, _1430003, _1430005] : [class_Lattices_Olattice(_1430001), hAPP(_1430003, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1430001), 34899 ^ [_1430001, _1430003, _1430005]), 34900 ^ [_1430001, _1430003, _1430005])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1430001), hAPP(_1430003, 34899 ^ [_1430001, _1430003, _1430005])), hAPP(_1430003, 34900 ^ [_1430001, _1430003, _1430005])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430001), _1430005)), -(_1430005 = c_Orderings_Obot__class_Obot(tc_fun(_1430001, tc_HOL_Obool))), -(hAPP(_1430003, c_Big__Operators_Olattice__class_OSup__fin(_1430001, _1430005)) = c_Big__Operators_Olattice__class_OSup__fin(_1430001, hAPP(c_Set_Oimage(_1430001, _1430001, _1430003), _1430005)))], (34914 ^ _780461) ^ [_1430404, _1430406, _1430408, _1430410, _1430412] : [class_Groups_Ocomm__monoid__mult(_1430404), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430406), _1430408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430406, tc_HOL_Obool)), _1430410), _1430408)), 34928 ^ _780461 : [(34929 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1430406), 34927 ^ [_1430404, _1430406, _1430408, _1430410, _1430412]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430406, tc_HOL_Obool)), _1430408), _1430410))))], (34931 ^ _780461) ^ [] : [hAPP(_1430412, 34927 ^ [_1430404, _1430406, _1430408, _1430410, _1430412]) = c_Groups_Oone__class_Oone(_1430404)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1430406, _1430404), _1430412), _1430408) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1430406, _1430404), _1430412), _1430410))], (34935 ^ _780461) ^ [_1430855, _1430857, _1430859, _1430861, _1430863] : [class_Groups_Ocomm__monoid__mult(_1430855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430857), _1430859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430857, tc_HOL_Obool)), _1430861), _1430859)), 34949 ^ _780461 : [(34950 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1430857), 34948 ^ [_1430855, _1430857, _1430859, _1430861, _1430863]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430857, tc_HOL_Obool)), _1430859), _1430861))))], (34952 ^ _780461) ^ [] : [hAPP(_1430863, 34948 ^ [_1430855, _1430857, _1430859, _1430861, _1430863]) = c_Groups_Oone__class_Oone(_1430855)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1430857, _1430855), _1430863), _1430861) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1430857, _1430855), _1430863), _1430859))], (34956 ^ _780461) ^ [_1431306, _1431308] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1431306), _1431308)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1431306, tc_HOL_Obool)), hAPP(c_Set_OPow(_1431306), _1431308)) = 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(_1431306), _1431308)))], (34962 ^ _780461) ^ [_1431433, _1431435, _1431437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1431433, tc_HOL_Obool)), _1431435), _1431437)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1431433, tc_HOL_Obool)), _1431435), hAPP(c_Set_OPow(_1431433), _1431437))))], (34968 ^ _780461) ^ [_1431562, _1431564] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1431562, tc_HOL_Obool)), _1431564), hAPP(c_Set_OPow(_1431562), _1431564))))], (34970 ^ _780461) ^ [_1431617, _1431619] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1431617, tc_HOL_Obool)), hAPP(c_Set_OPow(_1431617), _1431619))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1431617), _1431619)))], (34976 ^ _780461) ^ [_1431722, _1431724] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1431722), _1431724)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1431722, tc_HOL_Obool)), hAPP(c_Set_OPow(_1431722), _1431724))))], (34982 ^ _780461) ^ [_1431833, _1431835, _1431837, _1431839, _1431841] : [hAPP(c_Set_Oimage(_1431833, _1431835, _1431837), _1431839) = _1431841, -(hAPP(c_Set_Oimage(tc_fun(_1431833, tc_HOL_Obool), tc_fun(_1431835, tc_HOL_Obool), c_Set_Oimage(_1431833, _1431835, _1431837)), hAPP(c_Set_OPow(_1431833), _1431839)) = hAPP(c_Set_OPow(_1431835), _1431841))], (34988 ^ _780461) ^ [_1431984, _1431986, _1431988] : [-(hAPP(c_Set_OPow(_1431984), hAPP(hAPP(c_Set_Oinsert(_1431984), _1431986), _1431988)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1431984, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1431984), _1431988)), hAPP(c_Set_Oimage(tc_fun(_1431984, tc_HOL_Obool), tc_fun(_1431984, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1431984), _1431986)), hAPP(c_Set_OPow(_1431984), _1431988))))], (34990 ^ _780461) ^ [_1432078, _1432080] : [hAPP(c_Set_OPow(_1432078), _1432080) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1432078, tc_HOL_Obool), tc_HOL_Obool))], (34992 ^ _780461) ^ [_1432116, _1432118, _1432120] : [-(hAPP(c_Set_OPow(_1432116), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432116, tc_HOL_Obool)), _1432118), _1432120)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1432116, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1432116), _1432118)), hAPP(c_Set_OPow(_1432116), _1432120)))], (34994 ^ _780461) ^ [_1432183, _1432185] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1432183, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1432183, tc_HOL_Obool))), hAPP(c_Set_OPow(_1432183), _1432185))))], (34996 ^ _780461) ^ [_1432228, _1432230, _1432232] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1432228, tc_HOL_Obool)), _1432230), hAPP(c_Set_OPow(_1432228), _1432232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432228, tc_HOL_Obool)), _1432230), _1432232)))], (35002 ^ _780461) ^ [_1432375, _1432377, _1432379] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1432375, tc_HOL_Obool)), _1432377), hAPP(c_Set_OPow(_1432375), _1432379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432375, tc_HOL_Obool)), _1432377), _1432379)))], (35008 ^ _780461) ^ [_1432500, _1432502, _1432504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432500, tc_HOL_Obool)), _1432502), _1432504)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1432500, tc_HOL_Obool)), _1432502), hAPP(c_Set_OPow(_1432500), _1432504))))], (35014 ^ _780461) ^ [_1432631, _1432633, _1432635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432631, tc_HOL_Obool)), _1432633), _1432635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1432631, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1432631), _1432633)), hAPP(c_Set_OPow(_1432631), _1432635))))], (35020 ^ _780461) ^ [_1432776, _1432778, _1432780] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1432776, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1432776, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1432776), _1432778)), hAPP(c_Set_OPow(_1432776), _1432780))), hAPP(c_Set_OPow(_1432776), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1432776, tc_HOL_Obool)), _1432778), _1432780)))))], (35022 ^ _780461) ^ [_1432856, _1432858, _1432860, _1432862, _1432864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432856, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1432858, _1432856, _1432860), _1432862)), _1432864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1432856, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1432858, tc_HOL_Obool), tc_fun(_1432856, tc_HOL_Obool), c_Set_Oimage(_1432858, _1432856, _1432860)), hAPP(c_Set_OPow(_1432858), _1432862))), hAPP(c_Set_OPow(_1432856), _1432864))))], (35028 ^ _780461) ^ [_1433053] : [-(hAPP(c_Set_OPow(_1433053), c_Orderings_Obot__class_Obot(tc_fun(_1433053, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1433053, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1433053, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1433053, tc_HOL_Obool), tc_HOL_Obool))))], (35030 ^ _780461) ^ [_1433128, _1433130, _1433132] : [hBOOL(hAPP(c_Predicate_OPowp(_1433128, hAPP(hAPP(c_COMBC(_1433128, tc_fun(_1433128, tc_HOL_Obool), tc_HOL_Obool), c_member(_1433128)), _1433130)), _1433132)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1433128, tc_HOL_Obool)), _1433132), hAPP(c_Set_OPow(_1433128), _1433130))))], (35036 ^ _780461) ^ [_1433273, _1433275, _1433277] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1433273, tc_HOL_Obool)), _1433277), hAPP(c_Set_OPow(_1433273), _1433275))), -(hBOOL(hAPP(c_Predicate_OPowp(_1433273, hAPP(hAPP(c_COMBC(_1433273, tc_fun(_1433273, tc_HOL_Obool), tc_HOL_Obool), c_member(_1433273)), _1433275)), _1433277)))], (35042 ^ _780461) ^ [_1433424, _1433426, _1433428, _1433430] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1433424, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433426, tc_fun(tc_fun(_1433424, tc_HOL_Obool), tc_HOL_Obool)), _1433428), hAPP(hAPP(c_COMBB(tc_fun(_1433424, tc_HOL_Obool), tc_fun(tc_fun(_1433424, tc_HOL_Obool), tc_HOL_Obool), _1433426), c_Set_OPow(_1433424)), _1433430))), hAPP(c_Set_OPow(_1433424), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433426, tc_fun(_1433424, tc_HOL_Obool)), _1433428), _1433430)))))], (35044 ^ _780461) ^ [_1433519, _1433521, _1433523] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1433519), _1433521)), c_Fun_Oinj__on(_1433519, tc_fun(tc_fun(_1433519, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1433519, tc_fun(tc_prod(_1433519, _1433519), tc_HOL_Obool), tc_fun(tc_fun(_1433519, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1433519, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1433519, _1433519), tc_HOL_Obool), tc_fun(tc_fun(_1433519, tc_HOL_Obool), tc_HOL_Obool)), _1433519), c_Equiv__Relations_Oquotient(_1433519)), hAPP(hAPP(c_COMBC(_1433519, tc_fun(_1433519, tc_HOL_Obool), tc_fun(_1433519, tc_HOL_Obool)), c_Set_Oinsert(_1433519)), c_Orderings_Obot__class_Obot(tc_fun(_1433519, tc_HOL_Obool))))), _1433523), _1433521), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1433519, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1433519), _1433521), _1433523)) = hAPP(c_Finite__Set_Ocard(_1433519), _1433521))], (35054 ^ _780461) ^ [_1433868, _1433870, _1433872] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1433868), _1433870)), hBOOL(hAPP(_1433872, _1433870)), 35065 ^ _780461 : [(35066 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1433868), 35064 ^ [_1433868, _1433870, _1433872])))], (35068 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1433868), 35063 ^ [_1433868, _1433870, _1433872]), 35064 ^ [_1433868, _1433870, _1433872])))], (35070 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1433872, 35064 ^ [_1433868, _1433870, _1433872])))], (35072 ^ _780461) ^ [] : [hBOOL(hAPP(_1433872, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1433868, tc_HOL_Obool)), 35064 ^ [_1433868, _1433870, _1433872]), hAPP(hAPP(c_Set_Oinsert(_1433868), 35063 ^ [_1433868, _1433870, _1433872]), c_Orderings_Obot__class_Obot(tc_fun(_1433868, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1433872, c_Orderings_Obot__class_Obot(tc_fun(_1433868, tc_HOL_Obool)))))], (35076 ^ _780461) ^ [_1434393, _1434395, _1434397, _1434399] : [class_Orderings_Olinorder(_1434393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434393), _1434395), _1434397)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434393), _1434397), _1434399)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434393, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1434393, _1434395, _1434397)), c_SetInterval_Oord__class_OatLeastAtMost(_1434393, _1434397, _1434399)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1434393, _1434395, _1434399))], (35090 ^ _780461) ^ [_1434658, _1434660] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434658, _1434660))))], (35092 ^ _780461) ^ [_1434689, _1434691] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1434689, _1434691))))], (35094 ^ _780461) ^ [_1434720, _1434722, _1434724] : [-(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)), _1434720)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434722, _1434724)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1434722), _1434720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1434724), _1434720)))], (35096 ^ _780461) ^ [_1434777, _1434779] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434777, _1434779)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1434777), hAPP(c_Nat_OSuc, _1434779)))], (35098 ^ _780461) ^ [_1434819, _1434821] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434819, _1434821) = 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), _1434819), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1434821))))], (35100 ^ _780461) ^ [_1434861, _1434863, _1434865, _1434867] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1434861), hAPP(c_Set_Oimage(_1434863, _1434861, _1434865), _1434867))), c_Fun_Oinj__on(_1434863, _1434861, _1434865, _1434867), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1434863), _1434867)))], (35110 ^ _780461) ^ [_1435032, _1435034, _1435036, _1435038] : [c_Fun_Oinj__on(_1435032, _1435034, _1435036, _1435038), -(hAPP(c_Finite__Set_Ocard(_1435034), hAPP(c_Set_Oimage(_1435032, _1435034, _1435036), _1435038)) = hAPP(c_Finite__Set_Ocard(_1435032), _1435038))], (35116 ^ _780461) ^ [_1435151, _1435153] : [c_Nat__Transfer_Ois__nat(_1435151), c_Nat__Transfer_Ois__nat(_1435153), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1435151, _1435153) = 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, _1435151), hAPP(c_Int_Onat, _1435153))))], (35126 ^ _780461) ^ [_1435310, _1435312] : [c_Nat__Transfer_Ois__nat(_1435310), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1435310, _1435312)))], (35132 ^ _780461) ^ [_1435391, _1435393, _1435395] : [class_Orderings_Oorder(_1435391), 35135 ^ _780461 : [(35136 ^ _780461) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1435391, _1435393, _1435395) = c_Orderings_Obot__class_Obot(tc_fun(_1435391, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435391), _1435393), _1435395))], (35142 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435391), _1435393), _1435395))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1435391, _1435393, _1435395) = c_Orderings_Obot__class_Obot(tc_fun(_1435391, tc_HOL_Obool)))]]], (35148 ^ _780461) ^ [_1435610, _1435612, _1435614] : [class_Orderings_Oorder(_1435610), 35151 ^ _780461 : [(35152 ^ _780461) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1435610, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1435610, _1435612, _1435614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435610), _1435612), _1435614))], (35158 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435610), _1435612), _1435614))), -(c_Orderings_Obot__class_Obot(tc_fun(_1435610, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1435610, _1435612, _1435614))]]], (35164 ^ _780461) ^ [_1435829, _1435831, _1435833] : [class_Orderings_Oorder(_1435829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435829), _1435831), _1435833)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1435829, _1435833, _1435831) = c_Orderings_Obot__class_Obot(tc_fun(_1435829, tc_HOL_Obool)))], (35174 ^ _780461) ^ [_1435992, _1435994, _1435996, _1435998, _1436000] : [class_Orderings_Oorder(_1435992), 35177 ^ _780461 : [(35178 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1435992, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1435992, _1435994, _1435996)), c_SetInterval_Oord__class_OatLeastAtMost(_1435992, _1435998, _1436000))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435992), _1435994), _1435996)), 35185 ^ _780461 : [(35186 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435992), _1435998), _1435994)))], (35188 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435992), _1435996), _1436000)))]]], (35190 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1435992, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1435992, _1435994, _1435996)), c_SetInterval_Oord__class_OatLeastAtMost(_1435992, _1435998, _1436000)))), 35191 ^ _780461 : [(35192 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435992), _1435994), _1435996)))], (35194 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435992), _1435998), _1435994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435992), _1435996), _1436000))]]]]], (35202 ^ _780461) ^ [_1436495, _1436497, _1436499] : [class_Orderings_Oorder(_1436495), _1436497 = _1436499, -(c_SetInterval_Oord__class_OatLeastAtMost(_1436495, _1436497, _1436499) = hAPP(hAPP(c_Set_Oinsert(_1436495), _1436497), c_Orderings_Obot__class_Obot(tc_fun(_1436495, tc_HOL_Obool))))], (35212 ^ _780461) ^ [_1436660, _1436662, _1436664, _1436666] : [class_Orderings_Oorder(_1436660), 35215 ^ _780461 : [(35216 ^ _780461) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1436660, _1436662, _1436664) = hAPP(hAPP(c_Set_Oinsert(_1436660), _1436666), c_Orderings_Obot__class_Obot(tc_fun(_1436660, tc_HOL_Obool))), 35219 ^ _780461 : [(35220 ^ _780461) ^ [] : [-(_1436662 = _1436664)], (35222 ^ _780461) ^ [] : [-(_1436664 = _1436666)]]], (35224 ^ _780461) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1436660, _1436662, _1436664) = hAPP(hAPP(c_Set_Oinsert(_1436660), _1436666), c_Orderings_Obot__class_Obot(tc_fun(_1436660, tc_HOL_Obool)))), _1436662 = _1436664, _1436664 = _1436666]]], (35234 ^ _780461) ^ [_1437004, _1437006] : [class_Orderings_Oorder(_1437004), -(c_SetInterval_Oord__class_OatLeastAtMost(_1437004, _1437006, _1437006) = hAPP(hAPP(c_Set_Oinsert(_1437004), _1437006), c_Orderings_Obot__class_Obot(tc_fun(_1437004, tc_HOL_Obool))))], (35240 ^ _780461) ^ [_1437113, _1437115, _1437117] : [class_Groups_Oordered__ab__group__add(_1437113), -(hAPP(c_Set_Oimage(_1437113, _1437113, c_Groups_Ouminus__class_Ouminus(_1437113)), c_SetInterval_Oord__class_OatLeastAtMost(_1437113, _1437115, _1437117)) = c_SetInterval_Oord__class_OatLeastAtMost(_1437113, hAPP(c_Groups_Ouminus__class_Ouminus(_1437113), _1437117), hAPP(c_Groups_Ouminus__class_Ouminus(_1437113), _1437115)))], (35246 ^ _780461) ^ [_1437244, _1437246] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1437244), _1437246) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1437244, _1437246))], (35248 ^ _780461) ^ [_1437280, _1437282, _1437284] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1437280), _1437282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437280, tc_HOL_Obool)), _1437282), hAPP(c_Set_Oimage(_1437280, _1437280, _1437284), _1437282))), -(c_Fun_Oinj__on(_1437280, _1437280, _1437284, _1437282))], (35258 ^ _780461) ^ [_1437459, _1437461, _1437463] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1437459), _1437461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437459, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1437459, _1437459, _1437463), _1437461)), _1437461)), c_Fun_Oinj__on(_1437459, _1437459, _1437463, _1437461), -(hAPP(c_Set_Oimage(_1437459, _1437459, _1437463), _1437461) = _1437461)], (35272 ^ _780461) ^ [_1437706, _1437708, _1437710, _1437712] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1437706), _1437708)), 35275 ^ _780461 : [(35276 ^ _780461) ^ [] : [c_Fun_Oinj__on(_1437706, _1437710, _1437712, _1437708), -(hAPP(c_Finite__Set_Ocard(_1437710), hAPP(c_Set_Oimage(_1437706, _1437710, _1437712), _1437708)) = hAPP(c_Finite__Set_Ocard(_1437706), _1437708))], (35282 ^ _780461) ^ [] : [hAPP(c_Finite__Set_Ocard(_1437710), hAPP(c_Set_Oimage(_1437706, _1437710, _1437712), _1437708)) = hAPP(c_Finite__Set_Ocard(_1437706), _1437708), -(c_Fun_Oinj__on(_1437706, _1437710, _1437712, _1437708))]]], (35288 ^ _780461) ^ [_1437990, _1437992, _1437994, _1437996] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1437990), _1437992)), hAPP(c_Finite__Set_Ocard(_1437994), hAPP(c_Set_Oimage(_1437990, _1437994, _1437996), _1437992)) = hAPP(c_Finite__Set_Ocard(_1437990), _1437992), -(c_Fun_Oinj__on(_1437990, _1437994, _1437996, _1437992))], (35298 ^ _780461) ^ [_1438173, _1438175, _1438177, _1438179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1438173), hAPP(c_Set_Oimage(_1438175, _1438173, _1438177), _1438179))), hAPP(c_Finite__Set_Ocard(_1438175), _1438179))), c_Fun_Oinj__on(_1438175, _1438173, _1438177, _1438179)], (35304 ^ _780461) ^ [_1438303, _1438305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1438303)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1438303, _1438305)))], (35310 ^ _780461) ^ [_1438390, _1438392] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1438390, _1438392)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1438392)), _1438390))], (35312 ^ _780461) ^ [_1438431, _1438433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1438431), hAPP(c_Nat_OSuc, _1438433))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1438431, hAPP(c_Nat_OSuc, _1438433)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1438433)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1438431, _1438433)))], (35318 ^ _780461) ^ [_1438564, _1438566] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1438564), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1438566) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1438564, _1438566))], (35320 ^ _780461) ^ [_1438603, _1438605, _1438607, _1438609, _1438611, _1438613] : [c_Fun_Oinj__on(_1438603, _1438605, _1438607, _1438609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438605, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1438603, _1438605, _1438607), _1438609)), _1438611)), c_Fun_Oinj__on(_1438605, _1438603, _1438613, _1438611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1438603, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1438605, _1438603, _1438613), _1438611)), _1438609)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438603), _1438609)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1438605), _1438611)), -(hAPP(c_Finite__Set_Ocard(_1438603), _1438609) = hAPP(c_Finite__Set_Ocard(_1438605), _1438611))], (35346 ^ _780461) ^ [_1439100, _1439102, _1439104, _1439106, _1439108] : [class_Orderings_Olinorder(_1439100), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1439100, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1439100, _1439102, _1439104)), c_SetInterval_Oord__class_OatLeastAtMost(_1439100, _1439106, _1439108)) = c_SetInterval_Oord__class_OatLeastAtMost(_1439100, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1439100), _1439102), _1439106), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1439100), _1439104), _1439108)))], (35352 ^ _780461) ^ [_1439259, _1439261, _1439263, _1439265, _1439267] : [class_Orderings_Oorder(_1439259), 35355 ^ _780461 : [(35356 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1439259, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1439259, _1439261, _1439263)), c_SetInterval_Oord__class_OatLeastAtMost(_1439259, _1439265, _1439267))), 35359 ^ _780461 : [(35374 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439259), _1439265), _1439267)))], (35360 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439259), _1439261), _1439263)), 35363 ^ _780461 : [(35364 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439259), _1439265), _1439261)))], (35366 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439259), _1439263), _1439267)))], (35368 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439259), _1439265), _1439261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439259), _1439263), _1439267)))]]]]], (35376 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1439259, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1439259, _1439261, _1439263)), c_SetInterval_Oord__class_OatLeastAtMost(_1439259, _1439265, _1439267)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439259), _1439265), _1439267)), 35379 ^ _780461 : [(35380 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439259), _1439261), _1439263)))], (35382 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439259), _1439265), _1439261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439259), _1439263), _1439267)), 35389 ^ _780461 : [(35390 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439259), _1439265), _1439261))], (35392 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439259), _1439263), _1439267))]]]]]]], (35398 ^ _780461) ^ [_1440030, _1440032, _1440034, _1440036] : [class_Orderings_Olinorder(_1440030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440030), _1440032), _1440034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440030), _1440034), _1440036)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440030, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1440030, _1440032, _1440034)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1440030, _1440034, _1440036)) = c_SetInterval_Oord__class_OatLeastAtMost(_1440030, _1440032, _1440036))], (35412 ^ _780461) ^ [_1440295, _1440297, _1440299, _1440301] : [class_Orderings_Oorder(_1440295), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440295, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1440295, _1440297, _1440299)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1440295, _1440299, _1440301)) = c_Orderings_Obot__class_Obot(tc_fun(_1440295, tc_HOL_Obool)))], (35418 ^ _780461) ^ [_1440422, _1440424, _1440426, _1440428] : [class_Orderings_Oorder(_1440422), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440422, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1440422, _1440424, _1440426)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1440422, _1440426, _1440428)) = c_Orderings_Obot__class_Obot(tc_fun(_1440422, tc_HOL_Obool)))], (35424 ^ _780461) ^ [_1440549, _1440551, _1440553, _1440555] : [class_Orderings_Oorder(_1440549), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440549, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1440549, _1440551, _1440553)), c_SetInterval_Oord__class_OatLeastAtMost(_1440549, _1440553, _1440555)) = c_Orderings_Obot__class_Obot(tc_fun(_1440549, tc_HOL_Obool)))], (35430 ^ _780461) ^ [_1440685, _1440687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440685), _1440687)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1440687, _1440685) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (35436 ^ _780461) ^ [_1440774, _1440776] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440774), _1440776))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1440776, _1440774) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1440776), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1440776), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1440774)))], (35442 ^ _780461) ^ [_1440837, _1440839, _1440841, _1440843] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1440837), _1440839)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440841), _1440843)), 35449 ^ _780461 : [(35460 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1440837), _1440839)), hAPP(c_Finite__Set_Ocard(_1440841), _1440843))), 35464 ^ _780461 : [(35465 ^ _780461) ^ [] : [-(c_Fun_Oinj__on(_1440837, _1440841, 35463 ^ [_1440837, _1440839, _1440841, _1440843], _1440839))], (35467 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1440841, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1440837, _1440841, 35463 ^ [_1440837, _1440839, _1440841, _1440843]), _1440839)), _1440843)))]]], (35450 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1440837), _1440839)), hAPP(c_Finite__Set_Ocard(_1440841), _1440843)))), 35451 ^ _780461 : [(35452 ^ _780461) ^ [_1441048] : [c_Fun_Oinj__on(_1440837, _1440841, _1441048, _1440839), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1440841, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1440837, _1440841, _1441048), _1440839)), _1440843))]]]]], (35469 ^ _780461) ^ [_1441364, _1441366, _1441368, _1441370, _1441372] : [c_Fun_Oinj__on(_1441364, _1441366, _1441368, _1441370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1441366, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1441364, _1441366, _1441368), _1441370)), _1441372)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441366), _1441372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1441364), _1441370)), hAPP(c_Finite__Set_Ocard(_1441366), _1441372))))], (35483 ^ _780461) ^ [_1441639, _1441641, _1441643, _1441645] : [c_Fun_Oinj__on(_1441639, tc_fun(tc_fun(_1441639, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1441639, tc_fun(tc_prod(_1441639, _1441639), tc_HOL_Obool), tc_fun(tc_fun(_1441639, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441639, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1441639, _1441639), tc_HOL_Obool), tc_fun(tc_fun(_1441639, tc_HOL_Obool), tc_HOL_Obool)), _1441639), c_Equiv__Relations_Oquotient(_1441639)), hAPP(hAPP(c_COMBC(_1441639, tc_fun(_1441639, tc_HOL_Obool), tc_fun(_1441639, tc_HOL_Obool)), c_Set_Oinsert(_1441639)), c_Orderings_Obot__class_Obot(tc_fun(_1441639, tc_HOL_Obool))))), _1441641), _1441643), hBOOL(hAPP(hAPP(c_member(_1441639), _1441645), _1441643)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1441639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1441639, tc_HOL_Obool)), _1441643), hAPP(hAPP(c_Set_Oinsert(_1441639), _1441645), c_Orderings_Obot__class_Obot(tc_fun(_1441639, tc_HOL_Obool))))), _1441641) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1441639, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1441639), _1441643), _1441641)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1441639), hAPP(hAPP(c_Set_Oinsert(_1441639), _1441645), c_Orderings_Obot__class_Obot(tc_fun(_1441639, tc_HOL_Obool)))), _1441641)))], (35493 ^ _780461) ^ [_1442106, _1442108] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1442106, _1442108)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1442108), _1442106)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35495 ^ _780461) ^ [_1442153, _1442155, _1442157] : [class_Orderings_Olinorder(_1442153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442153), _1442155), _1442157)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442153, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1442153), _1442155), c_Orderings_Obot__class_Obot(tc_fun(_1442153, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1442153, _1442155, _1442157)) = c_SetInterval_Oord__class_OatLeastAtMost(_1442153, _1442155, _1442157))], (35505 ^ _780461) ^ [_1442386, _1442388, _1442390, _1442392, _1442394] : [c_Fun_Oinj__on(_1442386, _1442388, _1442390, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442386, tc_HOL_Obool)), _1442392), _1442394)), 35508 ^ _780461 : [(35509 ^ _780461) ^ [] : [-(c_Fun_Oinj__on(_1442386, _1442388, _1442390, _1442392))], (35511 ^ _780461) ^ [] : [-(c_Fun_Oinj__on(_1442386, _1442388, _1442390, _1442394))], (35513 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442388, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1442386, _1442388, _1442390), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1442386, tc_HOL_Obool)), _1442392), _1442394))), hAPP(c_Set_Oimage(_1442386, _1442388, _1442390), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1442386, tc_HOL_Obool)), _1442394), _1442392))) = c_Orderings_Obot__class_Obot(tc_fun(_1442388, tc_HOL_Obool)))]]], (35515 ^ _780461) ^ [_1442653, _1442655, _1442657, _1442659, _1442661] : [-(c_Fun_Oinj__on(_1442653, _1442655, _1442657, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442653, tc_HOL_Obool)), _1442659), _1442661))), c_Fun_Oinj__on(_1442653, _1442655, _1442657, _1442659), c_Fun_Oinj__on(_1442653, _1442655, _1442657, _1442661), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442655, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1442653, _1442655, _1442657), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1442653, tc_HOL_Obool)), _1442659), _1442661))), hAPP(c_Set_Oimage(_1442653, _1442655, _1442657), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1442653, tc_HOL_Obool)), _1442661), _1442659))) = c_Orderings_Obot__class_Obot(tc_fun(_1442655, tc_HOL_Obool))], (35529 ^ _780461) ^ [_1443016, _1443018, _1443020, _1443022, _1443024] : [c_Fun_Oinj__on(_1443016, _1443018, _1443020, hAPP(hAPP(c_Set_Oinsert(_1443016), _1443022), _1443024)), 35532 ^ _780461 : [(35533 ^ _780461) ^ [] : [-(c_Fun_Oinj__on(_1443016, _1443018, _1443020, _1443024))], (35535 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1443018), hAPP(_1443020, _1443022)), hAPP(c_Set_Oimage(_1443016, _1443018, _1443020), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443016, tc_HOL_Obool)), _1443024), hAPP(hAPP(c_Set_Oinsert(_1443016), _1443022), c_Orderings_Obot__class_Obot(tc_fun(_1443016, tc_HOL_Obool)))))))]]], (35537 ^ _780461) ^ [_1443235, _1443237, _1443239, _1443241, _1443243] : [-(c_Fun_Oinj__on(_1443235, _1443237, _1443239, hAPP(hAPP(c_Set_Oinsert(_1443235), _1443241), _1443243))), c_Fun_Oinj__on(_1443235, _1443237, _1443239, _1443243), -(hBOOL(hAPP(hAPP(c_member(_1443237), hAPP(_1443239, _1443241)), hAPP(c_Set_Oimage(_1443235, _1443237, _1443239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443235, tc_HOL_Obool)), _1443243), hAPP(hAPP(c_Set_Oinsert(_1443235), _1443241), c_Orderings_Obot__class_Obot(tc_fun(_1443235, tc_HOL_Obool))))))))], (35547 ^ _780461) ^ [_1443487, _1443489] : [class_Groups_Oordered__ab__group__add(_1443487), -(c_Fun_Oinj__on(_1443487, _1443487, c_Groups_Ouminus__class_Ouminus(_1443487), _1443489))], (35553 ^ _780461) ^ [_1443570, _1443572, _1443574] : [-(c_Fun_Oinj__on(_1443570, _1443572, _1443574, c_Orderings_Obot__class_Obot(tc_fun(_1443570, tc_HOL_Obool))))], (35555 ^ _780461) ^ [_1443604, _1443606, _1443608] : [-(c_Fun_Oinj__on(_1443604, tc_sum(_1443604, _1443606), c_Sum__Type_OInl(_1443604, _1443606), _1443608))], (35557 ^ _780461) ^ [_1443639, _1443641, _1443643] : [-(c_Fun_Oinj__on(_1443639, tc_sum(_1443641, _1443639), c_Sum__Type_OInr(_1443639, _1443641), _1443643))], (35559 ^ _780461) ^ [_1443674] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1443674))], (35561 ^ _780461) ^ [_1443699, _1443701] : [-(c_Fun_Oinj__on(_1443699, tc_Option_Ooption(_1443699), c_Option_Ooption_OSome(_1443699), _1443701))], (35563 ^ _780461) ^ [_1443730, _1443732] : [-(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)), _1443730), _1443732))], (35565 ^ _780461) ^ [_1443760, _1443762, _1443764] : [-(c_Fun_Oinj__on(tc_prod(_1443760, _1443762), tc_prod(_1443762, _1443760), hAPP(c_Product__Type_Oprod_Oprod__case(_1443760, _1443762, tc_prod(_1443762, _1443760)), hAPP(c_COMBC(_1443762, _1443760, tc_prod(_1443762, _1443760)), c_Product__Type_OPair(_1443762, _1443760))), _1443764))], (35585 ^ _780461) ^ [_1444224, _1444226, _1444228, _1444230] : [35587 ^ _780461 : [(35588 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444224), 35586 ^ [_1444224, _1444226, _1444228, _1444230]), _1444230)))], (35591 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444224), 35589 ^ [_1444224, _1444226, _1444228, _1444230]), _1444230)))], (35593 ^ _780461) ^ [] : [-(hAPP(_1444228, 35586 ^ [_1444224, _1444226, _1444228, _1444230]) = hAPP(_1444228, 35589 ^ [_1444224, _1444226, _1444228, _1444230]))], (35595 ^ _780461) ^ [] : [35586 ^ [_1444224, _1444226, _1444228, _1444230] = 35589 ^ [_1444224, _1444226, _1444228, _1444230]]], -(c_Fun_Oinj__on(_1444224, _1444226, _1444228, _1444230))], (35567 ^ _780461) ^ [_1443839, _1443841, _1443843, _1443845] : [c_Fun_Oinj__on(_1443839, _1443841, _1443843, _1443845), 35570 ^ _780461 : [(35571 ^ _780461) ^ [_1443947] : [hBOOL(hAPP(hAPP(c_member(_1443839), _1443947), _1443845)), 35574 ^ _780461 : [(35575 ^ _780461) ^ [_1444049] : [hBOOL(hAPP(hAPP(c_member(_1443839), _1444049), _1443845)), hAPP(_1443843, _1443947) = hAPP(_1443843, _1444049), -(_1443947 = _1444049)]]]]], (35599 ^ _780461) ^ [_1444616, _1444618] : [-(hAPP(c_Set_Oimage(_1444616, _1444616, c_COMBI(_1444616)), _1444618) = _1444618)], (35601 ^ _780461) ^ [_1444650, _1444652] : [-(c_Fun_Oinj__on(_1444650, _1444650, c_COMBI(_1444650), _1444652))], (35603 ^ _780461) ^ [_1444679, _1444681, _1444683, _1444685, _1444687, _1444689] : [c_Fun_Oinj__on(_1444679, _1444681, _1444683, _1444685), hAPP(_1444683, _1444687) = hAPP(_1444683, _1444689), hBOOL(hAPP(hAPP(c_member(_1444679), _1444687), _1444685)), hBOOL(hAPP(hAPP(c_member(_1444679), _1444689), _1444685)), -(_1444687 = _1444689)], (35621 ^ _780461) ^ [_1444988, _1444990, _1444992, _1444994, _1444996, _1444998] : [c_Fun_Oinj__on(_1444988, _1444990, _1444992, _1444994), hBOOL(hAPP(hAPP(c_member(_1444988), _1444996), _1444994)), hBOOL(hAPP(hAPP(c_member(_1444988), _1444998), _1444994)), 35632 ^ _780461 : [(35633 ^ _780461) ^ [] : [hAPP(_1444992, _1444996) = hAPP(_1444992, _1444998), -(_1444996 = _1444998)], (35639 ^ _780461) ^ [] : [_1444996 = _1444998, -(hAPP(_1444992, _1444996) = hAPP(_1444992, _1444998))]]], (35645 ^ _780461) ^ [_1445389, _1445391, _1445393, _1445395, _1445397, _1445399] : [c_Fun_Oinj__on(_1445389, _1445391, _1445393, _1445395), -(_1445397 = _1445399), hBOOL(hAPP(hAPP(c_member(_1445389), _1445397), _1445395)), hBOOL(hAPP(hAPP(c_member(_1445389), _1445399), _1445395)), hAPP(_1445393, _1445397) = hAPP(_1445393, _1445399)], (35663 ^ _780461) ^ [_1445702, _1445704, _1445706, _1445708, _1445710] : [c_Fun_Oinj__on(_1445702, _1445704, _1445706, _1445708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1445702, tc_HOL_Obool)), _1445710), _1445708)), -(c_Fun_Oinj__on(_1445702, _1445704, _1445706, _1445710))], (35673 ^ _780461) ^ [_1445871, _1445873, _1445875, _1445877, _1445879] : [c_Fun_Oinj__on(_1445871, _1445873, _1445875, _1445877), c_Fun_Oinj__on(_1445871, _1445873, _1445875, _1445879), -(c_Fun_Oinj__on(_1445871, _1445873, _1445875, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445871, tc_HOL_Obool)), _1445877), _1445879)))], (35683 ^ _780461) ^ [_1446046, _1446048, _1446050, _1446052, _1446054] : [c_Fun_Oinj__on(_1446046, _1446048, _1446050, _1446052), -(c_Fun_Oinj__on(_1446046, _1446048, _1446050, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1446046, tc_HOL_Obool)), _1446052), _1446054)))], (35689 ^ _780461) ^ [_1446175, _1446177, _1446179] : [hAPP(c_Set_Oimage(_1446177, tc_fun(_1446177, tc_HOL_Obool), _1446175), _1446179) = hAPP(c_Set_OPow(_1446177), _1446179)], (35691 ^ _780461) ^ [_1446217, _1446219, _1446221, _1446223, _1446225] : [c_Fun_Oinj__on(_1446217, _1446219, _1446221, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1446217, tc_HOL_Obool)), _1446223), _1446225)), 35694 ^ _780461 : [(35695 ^ _780461) ^ [] : [hAPP(c_Set_Oimage(_1446217, _1446219, _1446221), _1446223) = hAPP(c_Set_Oimage(_1446217, _1446219, _1446221), _1446225), -(_1446223 = _1446225)], (35701 ^ _780461) ^ [] : [_1446223 = _1446225, -(hAPP(c_Set_Oimage(_1446217, _1446219, _1446221), _1446223) = hAPP(c_Set_Oimage(_1446217, _1446219, _1446221), _1446225))]]], (35707 ^ _780461) ^ [_1446510, _1446512, _1446514, _1446516, _1446518] : [c_Fun_Oinj__on(_1446510, _1446512, _1446514, _1446516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1446510, tc_HOL_Obool)), _1446518), _1446516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1446512, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1446510, _1446512, _1446514), _1446518)), hAPP(c_Set_Oimage(_1446510, _1446512, _1446514), _1446516))))], (35717 ^ _780461) ^ [_1446723, _1446725, _1446727, _1446729, _1446731, _1446733] : [c_Fun_Oinj__on(_1446723, _1446725, _1446727, _1446729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446723, tc_HOL_Obool)), _1446731), _1446729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1446723, tc_HOL_Obool)), _1446733), _1446729)), -(hAPP(c_Set_Oimage(_1446723, _1446725, _1446727), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446723, tc_HOL_Obool)), _1446731), _1446733)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1446725, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1446723, _1446725, _1446727), _1446731)), hAPP(c_Set_Oimage(_1446723, _1446725, _1446727), _1446733)))], (35731 ^ _780461) ^ [_1447058, _1447060, _1447062, _1447064, _1447066, _1447068] : [c_Fun_Oinj__on(_1447058, _1447060, _1447062, _1447064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447058, tc_HOL_Obool)), _1447066), _1447064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447058, tc_HOL_Obool)), _1447068), _1447064)), -(hAPP(c_Set_Oimage(_1447058, _1447060, _1447062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1447058, tc_HOL_Obool)), _1447066), _1447068)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1447060, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1447058, _1447060, _1447062), _1447066)), hAPP(c_Set_Oimage(_1447058, _1447060, _1447062), _1447068)))], (35745 ^ _780461) ^ [_1447392, _1447394, _1447396, _1447398] : [-(_1447392 = c_Orderings_Obot__class_Obot(tc_fun(_1447394, tc_HOL_Obool))), 35748 ^ _780461 : [(35760 ^ _780461) ^ [] : [35761 ^ _780461 : [(35762 ^ _780461) ^ [_1447725] : [hAPP(c_Set_Oimage(_1447396, _1447394, _1447725), _1447398) = _1447392]], 35764 ^ _780461 : [(35765 ^ _780461) ^ [] : [-(c_Fun_Oinj__on(_1447394, _1447396, 35763 ^ [_1447392, _1447394, _1447396, _1447398], _1447392))], (35767 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447396, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1447394, _1447396, 35763 ^ [_1447392, _1447394, _1447396, _1447398]), _1447392)), _1447398)))]]], (35749 ^ _780461) ^ [] : [-(hAPP(c_Set_Oimage(_1447396, _1447394, 35756 ^ [_1447392, _1447394, _1447396, _1447398]), _1447398) = _1447392), 35750 ^ _780461 : [(35751 ^ _780461) ^ [_1447533] : [c_Fun_Oinj__on(_1447394, _1447396, _1447533, _1447392), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447396, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1447394, _1447396, _1447533), _1447392)), _1447398))]]]]], (35769 ^ _780461) ^ [_1447865, _1447867] : [35777 ^ _780461 : [(35778 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35776 ^ [_1447865, _1447867]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1447865))))], (35780 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1447867, 35776 ^ [_1447865, _1447867])))]], 35770 ^ _780461 : [(35771 ^ _780461) ^ [_1447934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1447934), _1447865)), hBOOL(hAPP(_1447867, _1447934))]]], (35782 ^ _780461) ^ [_1448095, _1448097] : [35790 ^ _780461 : [(35791 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35789 ^ [_1448095, _1448097]), _1448095)))], (35793 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1448097, 35789 ^ [_1448095, _1448097])))]], 35783 ^ _780461 : [(35784 ^ _780461) ^ [_1448164] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1448164), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1448095))), hBOOL(hAPP(_1448097, _1448164))]]], (35795 ^ _780461) ^ [_1448350, _1448352] : [35797 ^ _780461 : [(35798 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35796 ^ [_1448350, _1448352]), _1448350)))], (35800 ^ _780461) ^ [] : [hBOOL(hAPP(_1448352, 35796 ^ [_1448350, _1448352]))]], 35801 ^ _780461 : [(35802 ^ _780461) ^ [_1448501] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1448501), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1448350))), -(hBOOL(hAPP(_1448352, _1448501)))]]], (35808 ^ _780461) ^ [_1448604, _1448606] : [35810 ^ _780461 : [(35811 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35809 ^ [_1448604, _1448606]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1448604))))], (35813 ^ _780461) ^ [] : [hBOOL(hAPP(_1448606, 35809 ^ [_1448604, _1448606]))]], 35814 ^ _780461 : [(35815 ^ _780461) ^ [_1448759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1448759), _1448604)), -(hBOOL(hAPP(_1448606, _1448759)))]]], (35821 ^ _780461) ^ [_1448860, _1448862, _1448864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1448860)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1448862), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1448864)), 35828 ^ _780461 : [(35829 ^ _780461) ^ [_1449068] : [35831 ^ _780461 : [(35832 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35830 ^ [_1448860, _1448862, _1448864, _1449068]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1448860))))], (35835 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35833 ^ [_1448860, _1448862, _1448864, _1449068]), _1448864)))], (35837 ^ _780461) ^ [] : [-(_1449068 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35833 ^ [_1448860, _1448862, _1448864, _1449068]), 35830 ^ [_1448860, _1448862, _1448864, _1449068]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448862), _1449068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448862), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1449068), _1448860))))]]], (35845 ^ _780461) ^ [_1449344, _1449346, _1449348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449344)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449346), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1449348)), 35852 ^ _780461 : [(35853 ^ _780461) ^ [_1449552] : [35855 ^ _780461 : [(35856 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35854 ^ [_1449344, _1449346, _1449348, _1449552]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1449344))))], (35859 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35857 ^ [_1449344, _1449346, _1449348, _1449552]), _1449348)))], (35861 ^ _780461) ^ [] : [-(_1449552 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35857 ^ [_1449344, _1449346, _1449348, _1449552]), 35854 ^ [_1449344, _1449346, _1449348, _1449552]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1449552), _1449346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449552), _1449344)), _1449346)))]]], (35869 ^ _780461) ^ [_1449828, _1449830, _1449832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449828)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1449830), _1449832)), 35876 ^ _780461 : [(35877 ^ _780461) ^ [_1450018] : [35879 ^ _780461 : [(35880 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35878 ^ [_1449828, _1449830, _1449832, _1450018]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1449828))))], (35883 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35881 ^ [_1449828, _1449830, _1449832, _1450018]), _1449832)))], (35885 ^ _780461) ^ [] : [-(_1450018 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35881 ^ [_1449828, _1449830, _1449832, _1450018]), 35878 ^ [_1449828, _1449830, _1449832, _1450018]))]], -(_1450018 = _1449830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1450018), _1449828) = _1449830]]], (35893 ^ _780461) ^ [_1450278, _1450280, _1450282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450278)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450280), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1450282)), 35903 ^ _780461 : [(35904 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35902 ^ [_1450278, _1450280, _1450282]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1450278))))], (35907 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35905 ^ [_1450278, _1450280, _1450282]), _1450282)))], (35909 ^ _780461) ^ [] : [-(_1450280 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35905 ^ [_1450278, _1450280, _1450282]), 35902 ^ [_1450278, _1450280, _1450282]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450280), _1450278) = _1450280)], (35913 ^ _780461) ^ [_1450617, _1450619, _1450621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450617)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1450619), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1450621)), 35923 ^ _780461 : [(35924 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35922 ^ [_1450617, _1450619, _1450621]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1450617))))], (35927 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35925 ^ [_1450617, _1450619, _1450621]), _1450621)))], (35929 ^ _780461) ^ [] : [-(_1450619 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35925 ^ [_1450617, _1450619, _1450621]), 35922 ^ [_1450617, _1450619, _1450621]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1450619), _1450617) = _1450619)], (35933 ^ _780461) ^ [_1450956, _1450958, _1450960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450956)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1450958), _1450960)), 35940 ^ _780461 : [(35941 ^ _780461) ^ [_1451152] : [35943 ^ _780461 : [(35944 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35942 ^ [_1450956, _1450958, _1450960, _1451152]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1450956))))], (35947 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35945 ^ [_1450956, _1450958, _1450960, _1451152]), _1450960)))], (35949 ^ _780461) ^ [] : [-(_1451152 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35945 ^ [_1450956, _1450958, _1450960, _1451152]), 35942 ^ [_1450956, _1450958, _1450960, _1451152]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451152), _1450958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451152), _1450956)), _1450958)))]]], (35957 ^ _780461) ^ [_1451428, _1451430, _1451432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451428)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1451430), _1451432)), 35964 ^ _780461 : [(35965 ^ _780461) ^ [_1451618] : [35967 ^ _780461 : [(35968 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35966 ^ [_1451428, _1451430, _1451432, _1451618]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1451428))))], (35971 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35969 ^ [_1451428, _1451430, _1451432, _1451618]), _1451432)))], (35973 ^ _780461) ^ [] : [-(_1451618 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35969 ^ [_1451428, _1451430, _1451432, _1451618]), 35966 ^ [_1451428, _1451430, _1451432, _1451618]))]], -(_1451618 = _1451430), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1451618), _1451428) = _1451430]]], (35981 ^ _780461) ^ [_1451878, _1451880, _1451882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451878)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1451880), _1451882)), 35988 ^ _780461 : [(35989 ^ _780461) ^ [_1452074] : [35991 ^ _780461 : [(35992 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35990 ^ [_1451878, _1451880, _1451882, _1452074]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1451878))))], (35995 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35993 ^ [_1451878, _1451880, _1451882, _1452074]), _1451882)))], (35997 ^ _780461) ^ [] : [-(_1452074 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35993 ^ [_1451878, _1451880, _1451882, _1452074]), 35990 ^ [_1451878, _1451880, _1451882, _1452074]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451880), _1452074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451880), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1452074), _1451878))))]]], (36005 ^ _780461) ^ [_1452350, _1452352, _1452354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452350)), 36008 ^ _780461 : [(36009 ^ _780461) ^ [_1452484] : [36011 ^ _780461 : [(36012 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36010 ^ [_1452350, _1452352, _1452354, _1452484]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1452350))))], (36015 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36013 ^ [_1452350, _1452352, _1452354, _1452484]), _1452352)))], (36017 ^ _780461) ^ [] : [-(_1452484 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36013 ^ [_1452350, _1452352, _1452354, _1452484]), 36010 ^ [_1452350, _1452352, _1452354, _1452484]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1452354), _1452484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1452354), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1452484), _1452350))))]]], (36025 ^ _780461) ^ [_1452758, _1452760, _1452762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452758)), 36028 ^ _780461 : [(36029 ^ _780461) ^ [_1452892] : [36031 ^ _780461 : [(36032 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36030 ^ [_1452758, _1452760, _1452762, _1452892]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1452758))))], (36035 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36033 ^ [_1452758, _1452760, _1452762, _1452892]), _1452760)))], (36037 ^ _780461) ^ [] : [-(_1452892 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36033 ^ [_1452758, _1452760, _1452762, _1452892]), 36030 ^ [_1452758, _1452760, _1452762, _1452892]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1452892), _1452762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1452892), _1452758)), _1452762)))]]], (36045 ^ _780461) ^ [_1453166, _1453168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1453166)), 36054 ^ _780461 : [(36055 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1453168, 36050 ^ [_1453166, _1453168])))], (36057 ^ _780461) ^ [] : [hBOOL(hAPP(_1453168, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36050 ^ [_1453166, _1453168]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 36051 ^ [_1453166, _1453168]), _1453166))))]], 36058 ^ _780461 : [(36059 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1453168, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36050 ^ [_1453166, _1453168]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 36051 ^ [_1453166, _1453168]), _1453166)))))], (36061 ^ _780461) ^ [] : [hBOOL(hAPP(_1453168, 36050 ^ [_1453166, _1453168]))]], 36062 ^ _780461 : [(36063 ^ _780461) ^ [] : [36064 ^ _780461 : [(36065 ^ _780461) ^ [_1453598] : [hBOOL(hAPP(_1453168, _1453598))]], 36067 ^ _780461 : [(36068 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36066 ^ [_1453166, _1453168]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1453166))))], (36070 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1453168, 36066 ^ [_1453166, _1453168])))]]], (36072 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1453168, 36079 ^ [_1453166, _1453168]))), 36073 ^ _780461 : [(36074 ^ _780461) ^ [_1453713] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1453713), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1453166))), hBOOL(hAPP(_1453168, _1453713))]]]]], (36083 ^ _780461) ^ [_1453860, _1453862, _1453864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1453860)), 36086 ^ _780461 : [(36087 ^ _780461) ^ [_1453994] : [36089 ^ _780461 : [(36090 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36088 ^ [_1453860, _1453862, _1453864, _1453994]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1453860))))], (36093 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36091 ^ [_1453860, _1453862, _1453864, _1453994]), _1453862)))], (36095 ^ _780461) ^ [] : [-(_1453994 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36091 ^ [_1453860, _1453862, _1453864, _1453994]), 36088 ^ [_1453860, _1453862, _1453864, _1453994]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453864), _1453994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1453994), _1453860))))]]], (36103 ^ _780461) ^ [_1454268, _1454270, _1454272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1454268)), 36106 ^ _780461 : [(36107 ^ _780461) ^ [_1454402] : [36109 ^ _780461 : [(36110 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36108 ^ [_1454268, _1454270, _1454272, _1454402]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1454268))))], (36113 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36111 ^ [_1454268, _1454270, _1454272, _1454402]), _1454270)))], (36115 ^ _780461) ^ [] : [-(_1454402 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36111 ^ [_1454268, _1454270, _1454272, _1454402]), 36108 ^ [_1454268, _1454270, _1454272, _1454402]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1454402), _1454272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1454402), _1454268)), _1454272)))]]], (36123 ^ _780461) ^ [_1454688, _1454690, _1454692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1454688), _1454690)), -(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)), _1454688)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1454692), _1454690)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1454692), _1454688)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1454690), _1454688)))], (36129 ^ _780461) ^ [_1454840, _1454842, _1454844] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1454840), _1454842))), 36132 ^ _780461 : [(36133 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1454844), _1454842)), -(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)), _1454840)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1454844), _1454842)) = 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))))], (36139 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1454844), _1454842))), -(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)), _1454840)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1454844), _1454842)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (36145 ^ _780461) ^ [_1455109, _1455111, _1455113, _1455115] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1455109), _1455111)), 36148 ^ _780461 : [(36149 ^ _780461) ^ [_1455263] : [36151 ^ _780461 : [(36152 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36150 ^ [_1455109, _1455111, _1455113, _1455115, _1455263]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1455111))))], (36155 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36153 ^ [_1455109, _1455111, _1455113, _1455115, _1455263]), _1455113)))], (36157 ^ _780461) ^ [] : [-(_1455263 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36153 ^ [_1455109, _1455111, _1455113, _1455115, _1455263]), 36150 ^ [_1455109, _1455111, _1455113, _1455115, _1455263]))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1455109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1455263), _1455115))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1455109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1455263), _1455111)), _1455115))))]]], (36165 ^ _780461) ^ [_1455573, _1455575] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1455573), _1455575))))], (36167 ^ _780461) ^ [_1455606, _1455608, _1455610, _1455612, _1455614] : [class_Orderings_Olinorder(_1455606), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1455606, _1455608), _1455610) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1455606, _1455612), _1455614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455606), _1455608), _1455610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455606), _1455612), _1455614)), -(_1455610 = _1455614)], (36185 ^ _780461) ^ [_1455913, _1455915, _1455917, _1455919, _1455921] : [class_Orderings_Olinorder(_1455913), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1455913, _1455915), _1455917) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1455913, _1455919), _1455921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455913), _1455915), _1455917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455913), _1455919), _1455921)), -(_1455915 = _1455919)], (36203 ^ _780461) ^ [_1456220, _1456222, _1456224, _1456226, _1456228] : [class_Orderings_Olinorder(_1456220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456220), _1456222), _1456224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456220), _1456226), _1456228)), 36214 ^ _780461 : [(36215 ^ _780461) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456220, _1456222), _1456224) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456220, _1456226), _1456228), 36218 ^ _780461 : [(36219 ^ _780461) ^ [] : [-(_1456222 = _1456226)], (36221 ^ _780461) ^ [] : [-(_1456224 = _1456228)]]], (36223 ^ _780461) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456220, _1456222), _1456224) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1456220, _1456226), _1456228)), _1456222 = _1456226, _1456224 = _1456228]]], (36233 ^ _780461) ^ [_1456716, _1456718] : [36235 ^ _780461 : [(36236 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 36234 ^ [_1456716, _1456718]), _1456716)))], (36238 ^ _780461) ^ [] : [hBOOL(hAPP(_1456718, 36234 ^ [_1456716, _1456718]))]], 36239 ^ _780461 : [(36240 ^ _780461) ^ [_1456866] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1456866), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1456716))), -(hBOOL(hAPP(_1456718, _1456866)))]]], (36246 ^ _780461) ^ [_1456967, _1456969] : [36248 ^ _780461 : [(36249 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 36247 ^ [_1456967, _1456969]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1456967))))], (36251 ^ _780461) ^ [] : [hBOOL(hAPP(_1456969, 36247 ^ [_1456967, _1456969]))]], 36252 ^ _780461 : [(36253 ^ _780461) ^ [_1457120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1457120), _1456967)), -(hBOOL(hAPP(_1456969, _1457120)))]]], (36259 ^ _780461) ^ [_1457236, _1457238] : [36267 ^ _780461 : [(36268 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 36266 ^ [_1457236, _1457238]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457236))))], (36270 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1457238, 36266 ^ [_1457236, _1457238])))]], 36260 ^ _780461 : [(36261 ^ _780461) ^ [_1457304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1457304), _1457236)), hBOOL(hAPP(_1457238, _1457304))]]], (36272 ^ _780461) ^ [_1457464, _1457466] : [36280 ^ _780461 : [(36281 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 36279 ^ [_1457464, _1457466]), _1457464)))], (36283 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1457466, 36279 ^ [_1457464, _1457466])))]], 36273 ^ _780461 : [(36274 ^ _780461) ^ [_1457532] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1457532), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457464))), hBOOL(hAPP(_1457466, _1457532))]]], (36285 ^ _780461) ^ [_1457701, _1457703] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1457701), hAPP(c_Nat_OSuc, _1457703)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1457701, _1457703))], (36287 ^ _780461) ^ [_1457739] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1457739), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (36289 ^ _780461) ^ [_1457768, _1457770] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1457768), _1457770)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1457770), _1457768))], (36291 ^ _780461) ^ [_1457808, _1457810] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1457808), _1457810)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1457808)), hAPP(c_Nat_OSuc, _1457810)))], (36293 ^ _780461) ^ [_1457854, _1457856, _1457858] : [class_Orderings_Oorder(_1457854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457854), _1457856), _1457858)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1457854, _1457858), _1457856) = c_Orderings_Obot__class_Obot(tc_fun(_1457854, tc_HOL_Obool)))], (36303 ^ _780461) ^ [_1458021, _1458023, _1458025] : [class_Orderings_Oorder(_1458021), 36306 ^ _780461 : [(36307 ^ _780461) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1458021, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458021, _1458023), _1458025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458021), _1458023), _1458025))], (36313 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458021), _1458023), _1458025))), -(c_Orderings_Obot__class_Obot(tc_fun(_1458021, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458021, _1458023), _1458025))]]], (36319 ^ _780461) ^ [_1458246, _1458248, _1458250] : [class_Orderings_Oorder(_1458246), 36322 ^ _780461 : [(36323 ^ _780461) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458246, _1458248), _1458250) = c_Orderings_Obot__class_Obot(tc_fun(_1458246, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458246), _1458248), _1458250))], (36329 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458246), _1458248), _1458250))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458246, _1458248), _1458250) = c_Orderings_Obot__class_Obot(tc_fun(_1458246, tc_HOL_Obool)))]]], (36335 ^ _780461) ^ [_1458471, _1458473, _1458475, _1458477, _1458479] : [class_Orderings_Olinorder(_1458471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458471, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458471, _1458473), _1458475)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458471, _1458477), _1458479))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458471), _1458475), _1458473))), 36346 ^ _780461 : [(36347 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458471), _1458477), _1458473)))], (36349 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458471), _1458475), _1458479)))]]], (36351 ^ _780461) ^ [_1458752, _1458754, _1458756, _1458758] : [class_Orderings_Olinorder(_1458752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458752), _1458754), _1458756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458752), _1458756), _1458758)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458752, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458752, _1458754), _1458756)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458752, _1458756), _1458758)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1458752, _1458754), _1458758))], (36365 ^ _780461) ^ [_1459029, _1459031, _1459033, _1459035] : [class_Orderings_Olinorder(_1459029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459029), _1459031), _1459033)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1459029, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459029, _1459031), _1459035)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459029, _1459031), _1459033)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459029, _1459033), _1459035))], (36375 ^ _780461) ^ [_1459236, _1459238, _1459240, _1459242] : [class_Orderings_Oorder(_1459236), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459236, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459236, _1459238), _1459240)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459236, _1459240), _1459242)) = c_Orderings_Obot__class_Obot(tc_fun(_1459236, tc_HOL_Obool)))], (36381 ^ _780461) ^ [_1459371, _1459373] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1459371)), _1459373) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1459371, _1459373))], (36383 ^ _780461) ^ [_1459409, _1459411, _1459413] : [-(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)), _1459409)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459411), _1459413)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1459411), _1459409)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1459413), _1459409)))], (36385 ^ _780461) ^ [_1459470] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459470), hAPP(c_Nat_OSuc, _1459470)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1459470), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (36387 ^ _780461) ^ [_1459508, _1459510, _1459512, _1459514] : [class_Orderings_Olinorder(_1459508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459508), _1459510), _1459512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459508), _1459512), _1459514)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459508, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459508, _1459510), _1459512)), c_SetInterval_Oord__class_OatLeastAtMost(_1459508, _1459512, _1459514)) = c_SetInterval_Oord__class_OatLeastAtMost(_1459508, _1459510, _1459514))], (36401 ^ _780461) ^ [_1459777, _1459779, _1459781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1459777), _1459779)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1459779), _1459781)) = 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, _1459777), _1459779)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1459779), _1459781))))], (36407 ^ _780461) ^ [_1459938, _1459940, _1459942, _1459944] : [class_Orderings_Oorder(_1459938), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459938, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1459938, _1459940), _1459942)), c_SetInterval_Oord__class_OatLeastAtMost(_1459938, _1459942, _1459944)) = c_Orderings_Obot__class_Obot(tc_fun(_1459938, tc_HOL_Obool)))], (36413 ^ _780461) ^ [_1460069, _1460071, _1460073, _1460075, _1460077] : [class_Orderings_Olinorder(_1460069), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460069, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460069, _1460071), _1460073)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460069, _1460075), _1460077)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460069, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1460069), _1460071), _1460075)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1460069), _1460073), _1460077)))], (36419 ^ _780461) ^ [_1460240, _1460242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1460240), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1460242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1460242), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1460240))))), -(_1460240 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1460242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1460242), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1460240))))], (36425 ^ _780461) ^ [_1460387, _1460389, _1460391, _1460393] : [class_Orderings_Oorder(_1460387), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460387, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1460387, _1460389, _1460391)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460387, _1460391), _1460393)) = c_Orderings_Obot__class_Obot(tc_fun(_1460387, tc_HOL_Obool)))], (36431 ^ _780461) ^ [_1460518, _1460520, _1460522] : [class_Groups_Oordered__ab__group__add(_1460518), -(hAPP(c_Set_Oimage(_1460518, _1460518, c_Groups_Ouminus__class_Ouminus(_1460518)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1460518, _1460520, _1460522)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460518, hAPP(c_Groups_Ouminus__class_Ouminus(_1460518), _1460522)), hAPP(c_Groups_Ouminus__class_Ouminus(_1460518), _1460520)))], (36437 ^ _780461) ^ [_1460653, _1460655, _1460657] : [class_Groups_Oordered__ab__group__add(_1460653), -(hAPP(c_Set_Oimage(_1460653, _1460653, c_Groups_Ouminus__class_Ouminus(_1460653)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460653, _1460655), _1460657)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1460653, hAPP(c_Groups_Ouminus__class_Ouminus(_1460653), _1460657), hAPP(c_Groups_Ouminus__class_Ouminus(_1460653), _1460655)))], (36443 ^ _780461) ^ [_1460797, _1460799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1460797), _1460799)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1460797), hAPP(c_Nat_OSuc, _1460799)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1460799), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1460797), _1460799)))], (36449 ^ _780461) ^ [_1460920, _1460922] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1460920), _1460922))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1460920), hAPP(c_Nat_OSuc, _1460922)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (36455 ^ _780461) ^ [_1460972, _1460974, _1460976, _1460978] : [class_Orderings_Olinorder(_1460972), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460972), _1460974), _1460976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460972), _1460976), _1460978)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1460972, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1460972, _1460974, _1460976)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1460972, _1460976), _1460978)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1460972, _1460974, _1460978))], (36469 ^ _780461) ^ [_1461241, _1461243, _1461245] : [class_Orderings_Olinorder(_1461241), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1461241), _1461243), _1461245)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461241, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1461241, _1461243), _1461245)), hAPP(hAPP(c_Set_Oinsert(_1461241), _1461245), c_Orderings_Obot__class_Obot(tc_fun(_1461241, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1461241, _1461243, _1461245))], (36479 ^ _780461) ^ [_1461454, _1461456, _1461458] : [class_Orderings_Olinorder(_1461454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1461454), _1461456), _1461458)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461454, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1461454), _1461456), c_Orderings_Obot__class_Obot(tc_fun(_1461454, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1461454, _1461456, _1461458)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1461454, _1461456), _1461458))], (36489 ^ _780461) ^ [_1461667, _1461669, _1461671, _1461673] : [class_Orderings_Olinorder(_1461667), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1461667), _1461669), _1461671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1461667), _1461671), _1461673)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461667, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1461667, _1461669, _1461671)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1461667, _1461671, _1461673)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1461667, _1461669), _1461673))], (36503 ^ _780461) ^ [_1461936, _1461938, _1461940, _1461942] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461936), _1461938)), 36506 ^ _780461 : [(36507 ^ _780461) ^ [_1462094] : [36509 ^ _780461 : [(36510 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36508 ^ [_1461936, _1461938, _1461940, _1461942, _1462094]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1461938))))], (36513 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36511 ^ [_1461936, _1461938, _1461940, _1461942, _1462094]), _1461940)))], (36515 ^ _780461) ^ [] : [-(_1462094 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36511 ^ [_1461936, _1461938, _1461940, _1461942, _1462094]), 36508 ^ [_1461936, _1461938, _1461940, _1461942, _1462094]))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1462094), _1461942)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1461936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1462094), _1461938)), _1461942)))]]], (36523 ^ _780461) ^ [_1462408, _1462410, _1462412, _1462414] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462408), _1462410)), 36526 ^ _780461 : [(36527 ^ _780461) ^ [_1462566] : [36529 ^ _780461 : [(36530 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36528 ^ [_1462408, _1462410, _1462412, _1462414, _1462566]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1462410))))], (36533 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36531 ^ [_1462408, _1462410, _1462412, _1462414, _1462566]), _1462412)))], (36535 ^ _780461) ^ [] : [-(_1462566 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36531 ^ [_1462408, _1462410, _1462412, _1462414, _1462566]), 36528 ^ [_1462408, _1462410, _1462412, _1462414, _1462566]))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462408), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1462566), _1462414)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462408), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1462566), _1462410)), _1462414)))]]], (36543 ^ _780461) ^ [_1462880, _1462882, _1462884, _1462886] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462880), _1462882)), 36546 ^ _780461 : [(36547 ^ _780461) ^ [_1463034] : [36549 ^ _780461 : [(36550 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36548 ^ [_1462880, _1462882, _1462884, _1462886, _1463034]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1462882))))], (36553 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36551 ^ [_1462880, _1462882, _1462884, _1462886, _1463034]), _1462884)))], (36555 ^ _780461) ^ [] : [-(_1463034 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36551 ^ [_1462880, _1462882, _1462884, _1462886, _1463034]), 36548 ^ [_1462880, _1462882, _1462884, _1462886, _1463034]))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1463034), _1462886))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1462880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1463034), _1462882)), _1462886))))]]], (36563 ^ _780461) ^ [_1463344, _1463346] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1463344), _1463346))))], (36565 ^ _780461) ^ [_1463377] : [-(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)), _1463377))))], (36567 ^ _780461) ^ [_1463405, _1463407] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1463405), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1463407), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1463405, _1463407))], (36569 ^ _780461) ^ [_1463446, _1463448] : [-(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)), _1463446)), 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), _1463448), _1463446))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1463446), _1463448))], (36571 ^ _780461) ^ [_1463496] : [-(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)), _1463496)) = hAPP(c_Int_Onat, _1463496))], (36573 ^ _780461) ^ [_1463528, _1463530] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1463528), _1463530)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1463530), _1463528)))], (36575 ^ _780461) ^ [_1463571, _1463573] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1463571), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1463573) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1463571, _1463573))], (36577 ^ _780461) ^ [_1463612] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1463612) = 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), _1463612))))], (36579 ^ _780461) ^ [_1463669, _1463671, _1463673, _1463675, _1463677, _1463679] : [hBOOL(hAPP(hAPP(c_member(_1463669), _1463671), _1463673)), -(hAPP(c_Set_Oimage(_1463669, _1463675, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1463669, _1463675), _1463677), _1463671), _1463679)), _1463673) = hAPP(hAPP(c_Set_Oinsert(_1463675), _1463679), hAPP(c_Set_Oimage(_1463669, _1463675, _1463677), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463669, tc_HOL_Obool)), _1463673), hAPP(hAPP(c_Set_Oinsert(_1463669), _1463671), c_Orderings_Obot__class_Obot(tc_fun(_1463669, tc_HOL_Obool)))))))], (36585 ^ _780461) ^ [_1463878, _1463880, _1463882, _1463884, _1463886, _1463888] : [-(hBOOL(hAPP(hAPP(c_member(_1463878), _1463880), _1463882))), -(hAPP(c_Set_Oimage(_1463878, _1463884, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1463878, _1463884), _1463886), _1463880), _1463888)), _1463882) = hAPP(c_Set_Oimage(_1463878, _1463884, _1463886), _1463882))], (36591 ^ _780461) ^ [_1463957, _1463959, _1463961, _1463963, _1463965, _1463967] : [c_Fun_Oinj__on(_1463957, _1463959, _1463961, _1463963), hBOOL(hAPP(hAPP(c_member(_1463959), _1463965), hAPP(c_Set_Oimage(_1463957, _1463959, _1463961), _1463963))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1463957, tc_HOL_Obool)), _1463963), _1463967)), -(hBOOL(hAPP(hAPP(c_member(_1463957), hAPP(c_Fun_Othe__inv__into(_1463957, _1463959, _1463963, _1463961), _1463965)), _1463967)))], (36605 ^ _780461) ^ [_1464244, _1464246, _1464248, _1464250] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1464244, _1464246), _1464248), _1464250), hAPP(_1464248, _1464250)) = _1464248)], (36607 ^ _780461) ^ [_1464288] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1464288))))], (36609 ^ _780461) ^ [_1464316, _1464318, _1464320] : [class_Orderings_Olinorder(_1464316), 36612 ^ _780461 : [(36613 ^ _780461) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1464316), _1464318) = hAPP(c_SetInterval_Oord__class_OatMost(_1464316), _1464320), -(_1464318 = _1464320)], (36619 ^ _780461) ^ [] : [_1464318 = _1464320, -(hAPP(c_SetInterval_Oord__class_OatMost(_1464316), _1464318) = hAPP(c_SetInterval_Oord__class_OatMost(_1464316), _1464320))]]], (36625 ^ _780461) ^ [_1464578, _1464580, _1464582, _1464584, _1464586, _1464588] : [_1464578 = _1464580, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1464582, _1464584), _1464586), _1464580), _1464588), _1464578) = _1464588)], (36631 ^ _780461) ^ [_1464687, _1464689, _1464691, _1464693, _1464695, _1464697] : [-(_1464687 = _1464689), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1464691, _1464693), _1464695), _1464689), _1464697), _1464687) = hAPP(_1464695, _1464687))], (36637 ^ _780461) ^ [_1464775, _1464777, _1464779, _1464781, _1464783] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1464775, _1464777), _1464779), _1464781), _1464783) = _1464779, -(hAPP(_1464779, _1464781) = _1464783)], (36643 ^ _780461) ^ [_1464884, _1464886, _1464888, _1464890, _1464892] : [hAPP(_1464888, _1464890) = _1464892, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1464884, _1464886), _1464888), _1464890), _1464892) = _1464888)], (36649 ^ _780461) ^ [_1464999, _1465001, _1465003, _1465005, _1465007, _1465009] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1464999, _1465001), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1464999, _1465001), _1465003), _1465005), _1465007)), _1465005), _1465009) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1464999, _1465001), _1465003), _1465005), _1465009))], (36651 ^ _780461) ^ [_1465068, _1465070, _1465072, _1465074, _1465076] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465068, _1465070), _1465072), _1465074), _1465076), _1465074) = _1465076)], (36653 ^ _780461) ^ [_1465135, _1465137, _1465139, _1465141, _1465143, _1465145] : [_1465135 = _1465137, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465139, _1465141), _1465143), _1465137), _1465145), _1465135) = _1465145)], (36659 ^ _780461) ^ [_1465244, _1465246, _1465248, _1465250, _1465252, _1465254] : [-(_1465244 = _1465246), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465248, _1465250), _1465252), _1465246), _1465254), _1465244) = hAPP(_1465252, _1465244))], (36665 ^ _780461) ^ [_1465304, _1465306, _1465308, _1465310, _1465312, _1465314, _1465316] : [-(_1465304 = _1465306), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465308, _1465310), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465308, _1465310), _1465312), _1465304), _1465314)), _1465306), _1465316) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465308, _1465310), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465308, _1465310), _1465312), _1465306), _1465316)), _1465304), _1465314))], (36671 ^ _780461) ^ [_1465394, _1465396, _1465398, _1465400, _1465402, _1465404] : [-(_1465394 = _1465396), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465398, _1465400), _1465402), _1465396), _1465404), _1465394) = hAPP(_1465402, _1465394))], (36677 ^ _780461) ^ [_1465456, _1465458, _1465460, _1465462, _1465464] : [hAPP(_1465456, _1465458) = _1465460, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1465462, _1465464), _1465456), _1465458), _1465460) = _1465456)], (36683 ^ _780461) ^ [_1465569] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1465569) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1465569))], (36685 ^ _780461) ^ [_1465599] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1465599)) = hAPP(c_Nat_OSuc, _1465599))], (36687 ^ _780461) ^ [_1465631] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1465631)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1465631)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1465631)))], (36689 ^ _780461) ^ [_1465672, _1465674, _1465676] : [class_Orderings_Oord(_1465672), 36692 ^ _780461 : [(36693 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1465672), _1465674), hAPP(c_SetInterval_Oord__class_OatMost(_1465672), _1465676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1465672), _1465674), _1465676)))], (36699 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1465672), _1465674), _1465676)), -(hBOOL(hAPP(hAPP(c_member(_1465672), _1465674), hAPP(c_SetInterval_Oord__class_OatMost(_1465672), _1465676))))]]], (36705 ^ _780461) ^ [_1465940, _1465942, _1465944] : [class_Orderings_Oorder(_1465940), 36708 ^ _780461 : [(36709 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465940, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1465940), _1465942)), hAPP(c_SetInterval_Oord__class_OatMost(_1465940), _1465944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1465940), _1465942), _1465944)))], (36715 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1465940), _1465942), _1465944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465940, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1465940), _1465942)), hAPP(c_SetInterval_Oord__class_OatMost(_1465940), _1465944))))]]], (36721 ^ _780461) ^ [_1466232, _1466234, _1466236, _1466238] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1466232, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1466234)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1466232, tc_HOL_Obool), tc_Nat_Onat), _1466236), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1466238))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1466232, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1466238, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1466234), _1466238))), _1466236))], (36723 ^ _780461) ^ [_1466314, _1466316, _1466318, _1466320, _1466322, _1466324] : [c_Fun_Oinj__on(_1466314, _1466316, _1466318, _1466320), hAPP(_1466318, _1466322) = _1466324, hBOOL(hAPP(hAPP(c_member(_1466314), _1466322), _1466320)), -(hAPP(c_Fun_Othe__inv__into(_1466314, _1466316, _1466320, _1466318), _1466324) = _1466322)], (36737 ^ _780461) ^ [_1466559, _1466561, _1466563, _1466565, _1466567] : [c_Fun_Oinj__on(_1466559, _1466561, _1466563, _1466565), hBOOL(hAPP(hAPP(c_member(_1466559), _1466567), _1466565)), -(hAPP(c_Fun_Othe__inv__into(_1466559, _1466561, _1466565, _1466563), hAPP(_1466563, _1466567)) = _1466567)], (36747 ^ _780461) ^ [_1466740, _1466742, _1466744, _1466746] : [c_Fun_Oinj__on(_1466740, _1466742, _1466744, _1466746), -(c_Fun_Oinj__on(_1466742, _1466740, c_Fun_Othe__inv__into(_1466740, _1466742, _1466746, _1466744), hAPP(c_Set_Oimage(_1466740, _1466742, _1466744), _1466746)))], (36753 ^ _780461) ^ [_1466853, _1466855, _1466857, _1466859] : [c_Fun_Oinj__on(_1466853, _1466855, _1466857, _1466859), -(hAPP(c_Set_Oimage(_1466855, _1466853, c_Fun_Othe__inv__into(_1466853, _1466855, _1466859, _1466857)), hAPP(c_Set_Oimage(_1466853, _1466855, _1466857), _1466859)) = _1466859)], (36759 ^ _780461) ^ [_1466976, _1466978, _1466980, _1466982, _1466984, _1466986] : [c_Fun_Oinj__on(_1466976, _1466978, _1466980, _1466982), -(hBOOL(hAPP(hAPP(c_member(_1466978), _1466984), hAPP(c_Set_Oimage(_1466976, _1466978, _1466980), _1466982)))), -(c_Fun_Oinj__on(_1466976, _1466978, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1466976, _1466978), _1466980), _1466986), _1466984), _1466982))], (36769 ^ _780461) ^ [_1467136, _1467138, _1467140, _1467142, _1467144] : [-(hAPP(c_Fun_Othe__inv__into(_1467136, _1467138, _1467140, _1467142), _1467144) = c_HOL_OThe(_1467136, hAPP(hAPP(c_COMBS(_1467136, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1467136), c_fconj), hAPP(hAPP(c_COMBC(_1467136, tc_fun(_1467136, tc_HOL_Obool), tc_HOL_Obool), c_member(_1467136)), _1467140))), hAPP(hAPP(c_COMBC(_1467136, _1467138, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1467138, tc_fun(_1467138, tc_HOL_Obool), _1467136), c_fequal), _1467142)), _1467144))))], (36771 ^ _780461) ^ [] : [-(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))))], (36773 ^ _780461) ^ [_1467254, _1467256, _1467258, _1467260] : [class_Orderings_Olinorder(_1467254), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467254, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1467254), _1467256)), c_SetInterval_Oord__class_OatLeastAtMost(_1467254, _1467258, _1467260)) = c_SetInterval_Oord__class_OatLeastAtMost(_1467254, _1467258, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1467254), _1467256), _1467260)))], (36779 ^ _780461) ^ [_1467397, _1467399, _1467401, _1467403] : [class_Orderings_Olinorder(_1467397), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467397, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1467397, _1467399, _1467401)), hAPP(c_SetInterval_Oord__class_OatMost(_1467397), _1467403)) = c_SetInterval_Oord__class_OatLeastAtMost(_1467397, _1467399, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1467397), _1467401), _1467403)))], (36785 ^ _780461) ^ [_1467540, _1467542, _1467544] : [class_Orderings_Olinorder(_1467540), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1467540), _1467542), _1467544)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1467540, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1467540), _1467542)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1467540, _1467542, _1467544)) = hAPP(c_SetInterval_Oord__class_OatMost(_1467540), _1467544))], (36795 ^ _780461) ^ [_1467735, _1467737, _1467739] : [class_Orderings_Oorder(_1467735), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467735, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1467735), _1467737)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1467735, _1467737, _1467739)) = c_Orderings_Obot__class_Obot(tc_fun(_1467735, tc_HOL_Obool)))], (36801 ^ _780461) ^ [_1467862, _1467864, _1467866] : [class_Orderings_Oorder(_1467862), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467862, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1467862), _1467864)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1467862, _1467864, _1467866)) = c_Orderings_Obot__class_Obot(tc_fun(_1467862, tc_HOL_Obool)))], (36807 ^ _780461) ^ [_1467989, _1467991, _1467993, _1467995, _1467997] : [c_Fun_Oinj__on(_1467989, _1467991, _1467993, _1467995), hBOOL(hAPP(hAPP(c_member(_1467991), _1467997), hAPP(c_Set_Oimage(_1467989, _1467991, _1467993), _1467995))), -(hAPP(_1467993, hAPP(c_Fun_Othe__inv__into(_1467989, _1467991, _1467995, _1467993), _1467997)) = _1467997)], (36817 ^ _780461) ^ [_1468184, _1468186, _1468188] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1468184, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1468186)), _1468188) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468184, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1468184, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1468186)), _1468188)), hAPP(_1468188, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36819 ^ _780461) ^ [_1468277, _1468279, _1468281, _1468283, _1468285] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1468277, tc_Option_Ooption(_1468279)), _1468281), _1468283), hAPP(c_Option_Ooption_OSome(_1468279), _1468285)) = hAPP(c_COMBK(tc_Option_Ooption(_1468279), _1468277), c_Option_Ooption_ONone(_1468279))], (36821 ^ _780461) ^ [_1468337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468337)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1468337) = 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, _1468337))))], (36827 ^ _780461) ^ [_1468436, _1468438, _1468440, _1468442, _1468444, _1468446] : [-(hBOOL(hAPP(hAPP(c_member(_1468436), _1468438), _1468440))), -(hAPP(c_Set_Oimage(_1468436, tc_Option_Ooption(_1468442), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1468436, tc_Option_Ooption(_1468442)), _1468444), _1468438), hAPP(c_Option_Ooption_OSome(_1468442), _1468446))), _1468440) = hAPP(c_Set_Oimage(_1468436, tc_Option_Ooption(_1468442), _1468444), _1468440))], (36833 ^ _780461) ^ [_1468524] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1468524))))], (36835 ^ _780461) ^ [_1468552] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1468552)) = _1468552)], (36837 ^ _780461) ^ [_1468581, _1468583, _1468585] : [class_Orderings_Olinorder(_1468581), 36840 ^ _780461 : [(36841 ^ _780461) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1468581), _1468583) = hAPP(c_SetInterval_Oord__class_OlessThan(_1468581), _1468585), -(_1468583 = _1468585)], (36847 ^ _780461) ^ [] : [_1468583 = _1468585, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1468581), _1468583) = hAPP(c_SetInterval_Oord__class_OlessThan(_1468581), _1468585))]]], (36853 ^ _780461) ^ [_1468822] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1468822) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1468822))], (36855 ^ _780461) ^ [] : [-(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)))], (36857 ^ _780461) ^ [_1468869] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1468869)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1468869), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1468869)))], (36859 ^ _780461) ^ [_1468907] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1468907)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1468907))], (36861 ^ _780461) ^ [_1468939, _1468941, _1468943] : [class_Orderings_Oord(_1468939), 36864 ^ _780461 : [(36865 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1468939), _1468941), hAPP(c_SetInterval_Oord__class_OlessThan(_1468939), _1468943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1468939), _1468941), _1468943)))], (36871 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1468939), _1468941), _1468943)), -(hBOOL(hAPP(hAPP(c_member(_1468939), _1468941), hAPP(c_SetInterval_Oord__class_OlessThan(_1468939), _1468943))))]]], (36877 ^ _780461) ^ [_1469207, _1469209, _1469211] : [class_Orderings_Olinorder(_1469207), 36880 ^ _780461 : [(36881 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469207, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1469207), _1469209)), hAPP(c_SetInterval_Oord__class_OlessThan(_1469207), _1469211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469207), _1469209), _1469211)))], (36887 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1469207), _1469209), _1469211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469207, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1469207), _1469209)), hAPP(c_SetInterval_Oord__class_OlessThan(_1469207), _1469211))))]]], (36893 ^ _780461) ^ [_1469499, _1469501, _1469503] : [class_Orderings_Olinorder(_1469499), 36896 ^ _780461 : [(36897 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1469499, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1469499), _1469501)), hAPP(c_SetInterval_Oord__class_OlessThan(_1469499), _1469503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1469499), _1469501), _1469503)))], (36903 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1469499), _1469501), _1469503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1469499, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1469499), _1469501)), hAPP(c_SetInterval_Oord__class_OlessThan(_1469499), _1469503))))]]], (36909 ^ _780461) ^ [_1469791, _1469793, _1469795, _1469797, _1469799, _1469801, _1469803] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1469791, tc_Option_Ooption(_1469793)), _1469795), _1469797), hAPP(c_Option_Ooption_OSome(_1469793), _1469799)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1469791, tc_Option_Ooption(_1469793)), _1469801), _1469797), hAPP(c_Option_Ooption_OSome(_1469793), _1469803)), -(_1469799 = _1469803)], (36915 ^ _780461) ^ [_1469954, _1469956, _1469958, _1469960, _1469962] : [hAPP(_1469954, _1469956) = hAPP(c_Option_Ooption_OSome(_1469958), _1469960), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1469962, tc_Option_Ooption(_1469958)), _1469954), _1469956), hAPP(c_Option_Ooption_OSome(_1469958), _1469960)) = _1469954)], (36921 ^ _780461) ^ [_1470121, _1470123, _1470125, _1470127, _1470129, _1470131, _1470133] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1470121, tc_Option_Ooption(_1470123)), _1470125), _1470127), hAPP(c_Option_Ooption_OSome(_1470123), _1470129)), _1470131) = hAPP(c_Option_Ooption_OSome(_1470123), _1470133), 36926 ^ _780461 : [(36927 ^ _780461) ^ [] : [-(_1470131 = _1470127)], (36929 ^ _780461) ^ [] : [-(_1470129 = _1470133)]], 36930 ^ _780461 : [(36931 ^ _780461) ^ [] : [_1470131 = _1470127], (36933 ^ _780461) ^ [] : [-(hAPP(_1470125, _1470131) = hAPP(c_Option_Ooption_OSome(_1470123), _1470133))]]], (36935 ^ _780461) ^ [_1470399, _1470401, _1470403, _1470405, _1470407, _1470409, _1470411] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1470399, tc_Option_Ooption(_1470401)), _1470403), _1470405), hAPP(c_Option_Ooption_OSome(_1470401), _1470407)), _1470409) = hAPP(c_Option_Ooption_OSome(_1470401), _1470411)), 36936 ^ _780461 : [(36937 ^ _780461) ^ [] : [_1470409 = _1470405, _1470407 = _1470411], (36943 ^ _780461) ^ [] : [-(_1470409 = _1470405), hAPP(_1470403, _1470409) = hAPP(c_Option_Ooption_OSome(_1470401), _1470411)]]], (36951 ^ _780461) ^ [_1470716, _1470718] : [class_Orderings_Oorder(_1470716), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470716, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1470716), _1470718), c_Orderings_Obot__class_Obot(tc_fun(_1470716, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1470716), _1470718)) = hAPP(hAPP(c_Set_Oinsert(_1470716), _1470718), c_Orderings_Obot__class_Obot(tc_fun(_1470716, tc_HOL_Obool))))], (36957 ^ _780461) ^ [_1470875, _1470877, _1470879] : [class_Orderings_Olinorder(_1470875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1470875), _1470877), _1470879)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470875, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1470875), _1470877)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1470875, _1470877), _1470879)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1470875), _1470879))], (36967 ^ _780461) ^ [_1471074, _1471076, _1471078] : [class_Orderings_Oorder(_1471074), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471074, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1471074), _1471076)), c_SetInterval_Oord__class_OatLeastAtMost(_1471074, _1471076, _1471078)) = c_Orderings_Obot__class_Obot(tc_fun(_1471074, tc_HOL_Obool)))], (36973 ^ _780461) ^ [_1471201, _1471203, _1471205] : [class_Orderings_Oorder(_1471201), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471201, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1471201), _1471203)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1471201, _1471203), _1471205)) = c_Orderings_Obot__class_Obot(tc_fun(_1471201, tc_HOL_Obool)))], (36979 ^ _780461) ^ [_1471332, _1471334, _1471336, _1471338] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1471332, tc_Option_Ooption(_1471334)), hAPP(c_COMBK(tc_Option_Ooption(_1471334), _1471332), c_Option_Ooption_ONone(_1471334))), _1471336), c_Option_Ooption_ONone(_1471334)), _1471338) = c_Option_Ooption_ONone(_1471334))], (36981 ^ _780461) ^ [_1471392] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1471392)) = 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), _1471392))))], (36983 ^ _780461) ^ [_1471430, _1471432] : [class_Orderings_Olinorder(_1471430), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471430, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1471430), _1471432)), hAPP(hAPP(c_Set_Oinsert(_1471430), _1471432), c_Orderings_Obot__class_Obot(tc_fun(_1471430, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1471430), _1471432))], (36989 ^ _780461) ^ [_1471573, _1471575, _1471577] : [class_Orderings_Olinorder(_1471573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1471573), _1471575), _1471577)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471573, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1471573), _1471575)), c_SetInterval_Oord__class_OatLeastAtMost(_1471573, _1471575, _1471577)) = hAPP(c_SetInterval_Oord__class_OatMost(_1471573), _1471577))], (36999 ^ _780461) ^ [_1471768, _1471770, _1471772] : [class_Orderings_Olinorder(_1471768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1471768), _1471770), _1471772)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1471768, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1471768), _1471770)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1471768, _1471770, _1471772)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1471768), _1471772))], (37009 ^ _780461) ^ [_1471963, _1471965, _1471967] : [-(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), _1471963)), 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))), _1471965))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1471967))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1471967)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1471963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1471963), 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), _1471967), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1471965)))))], (37011 ^ _780461) ^ [_1472050, _1472052, _1472054, _1472056, _1472058] : [hAPP(_1472050, _1472052) = c_Option_Ooption_ONone(_1472054), -(c_Map_Oran(_1472056, _1472054, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472056, tc_Option_Ooption(_1472054)), _1472050), _1472052), hAPP(c_Option_Ooption_OSome(_1472054), _1472058))) = hAPP(hAPP(c_Set_Oinsert(_1472054), _1472058), c_Map_Oran(_1472056, _1472054, _1472050)))], (37017 ^ _780461) ^ [_1472231, _1472233, _1472235, _1472237, _1472239] : [hBOOL(hAPP(hAPP(c_member(_1472231), _1472233), _1472235)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472231, tc_Option_Ooption(_1472237)), c_Map_Orestrict__map(_1472231, _1472237, _1472239, _1472235)), _1472233), c_Option_Ooption_ONone(_1472237)) = c_Map_Orestrict__map(_1472231, _1472237, _1472239, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472231, tc_HOL_Obool)), _1472235), hAPP(hAPP(c_Set_Oinsert(_1472231), _1472233), c_Orderings_Obot__class_Obot(tc_fun(_1472231, tc_HOL_Obool))))))], (37023 ^ _780461) ^ [_1472422, _1472424, _1472426, _1472428, _1472430] : [-(hBOOL(hAPP(hAPP(c_member(_1472422), _1472424), _1472426))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1472422, tc_Option_Ooption(_1472428)), c_Map_Orestrict__map(_1472422, _1472428, _1472430, _1472426)), _1472424), c_Option_Ooption_ONone(_1472428)) = c_Map_Orestrict__map(_1472422, _1472428, _1472430, _1472426))], (37029 ^ _780461) ^ [_1472499, _1472501, _1472503, _1472505] : [class_Groups_Oordered__ab__group__add__abs(_1472499), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472499), hAPP(c_Groups_Oabs__class_Oabs(_1472499), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472501, _1472499), _1472503), _1472505))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472501, _1472499), hAPP(hAPP(c_COMBB(_1472499, _1472499, _1472501), c_Groups_Oabs__class_Oabs(_1472499)), _1472503)), _1472505))))], (37035 ^ _780461) ^ [_1472662, _1472664, _1472666, _1472668] : [class_Groups_Oordered__ab__group__add__abs(_1472662), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472662), c_Groups_Ozero__class_Ozero(_1472662)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472664, _1472662), hAPP(hAPP(c_COMBB(_1472662, _1472662, _1472664), c_Groups_Oabs__class_Oabs(_1472662)), _1472666)), _1472668))))], (37041 ^ _780461) ^ [_1472801, _1472803, _1472805, _1472807, _1472809] : [hBOOL(hAPP(hAPP(c_member(_1472801), _1472803), _1472805)), -(hAPP(c_Map_Orestrict__map(_1472801, _1472807, _1472809, _1472805), _1472803) = hAPP(_1472809, _1472803))], (37047 ^ _780461) ^ [_1472920, _1472922, _1472924, _1472926, _1472928] : [-(c_Map_Orestrict__map(_1472920, _1472922, c_Map_Orestrict__map(_1472920, _1472922, _1472924, _1472926), _1472928) = c_Map_Orestrict__map(_1472920, _1472922, _1472924, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1472920, tc_HOL_Obool)), _1472926), _1472928)))], (37049 ^ _780461) ^ [_1472977, _1472979, _1472981, _1472983] : [class_Groups_Oordered__ab__group__add__abs(_1472977), -(hAPP(c_Groups_Oabs__class_Oabs(_1472977), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472979, _1472977), hAPP(hAPP(c_COMBB(_1472977, _1472977, _1472979), c_Groups_Oabs__class_Oabs(_1472977)), _1472981)), _1472983)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472979, _1472977), hAPP(hAPP(c_COMBB(_1472977, _1472977, _1472979), c_Groups_Oabs__class_Oabs(_1472977)), _1472981)), _1472983))], (37055 ^ _780461) ^ [_1473150, _1473152, _1473154, _1473156, _1473158] : [class_Fields_Ofield(_1473150), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1473150), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473152, _1473150), _1473154), _1473156)), _1473158) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473152, _1473150), hAPP(hAPP(c_COMBC(_1473152, _1473150, _1473150), hAPP(hAPP(c_COMBB(_1473150, tc_fun(_1473150, _1473150), _1473152), c_Rings_Oinverse__class_Odivide(_1473150)), _1473154)), _1473158)), _1473156))], (37061 ^ _780461) ^ [_1473333, _1473335, _1473337, _1473339] : [class_Groups_Oab__group__add(_1473333), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473335, _1473333), hAPP(hAPP(c_COMBB(_1473333, _1473333, _1473335), c_Groups_Ouminus__class_Ouminus(_1473333)), _1473337)), _1473339) = hAPP(c_Groups_Ouminus__class_Ouminus(_1473333), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473335, _1473333), _1473337), _1473339)))], (37067 ^ _780461) ^ [_1473482, _1473484, _1473486] : [class_Groups_Ocomm__monoid__add(_1473482), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473484, _1473482), hAPP(c_COMBK(_1473482, _1473484), c_Groups_Ozero__class_Ozero(_1473482))), _1473486) = c_Groups_Ozero__class_Ozero(_1473482))], (37073 ^ _780461) ^ [_1473597, _1473599, _1473601, _1473603] : [class_Rings_Osemiring__1(_1473597), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1473597), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473599, tc_Nat_Onat), _1473601), _1473603)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473599, _1473597), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1473597, _1473599), c_Nat_Osemiring__1__class_Oof__nat(_1473597)), _1473601)), _1473603))], (37079 ^ _780461) ^ [_1473746, _1473748, _1473750, _1473752] : [class_Rings_Oring__1(_1473746), -(hAPP(c_Int_Oring__1__class_Oof__int(_1473746), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473748, tc_Int_Oint), _1473750), _1473752)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473748, _1473746), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1473746, _1473748), c_Int_Oring__1__class_Oof__int(_1473746)), _1473750)), _1473752))], (37085 ^ _780461) ^ [_1473895, _1473897, _1473899, _1473901, _1473903, _1473905] : [class_Groups_Ocomm__monoid__add(_1473895), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473897, _1473895), hAPP(hAPP(c_COMBC(_1473897, tc_fun(_1473899, tc_HOL_Obool), _1473895), hAPP(hAPP(c_COMBB(tc_fun(_1473899, _1473895), tc_fun(tc_fun(_1473899, tc_HOL_Obool), _1473895), _1473897), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473899, _1473895)), _1473901)), _1473903)), _1473905) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473899, _1473895), hAPP(hAPP(c_COMBC(_1473899, tc_fun(_1473897, tc_HOL_Obool), _1473895), hAPP(hAPP(c_COMBB(tc_fun(_1473897, _1473895), tc_fun(tc_fun(_1473897, tc_HOL_Obool), _1473895), _1473899), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473897, _1473895)), hAPP(c_COMBC(_1473897, _1473899, _1473895), _1473901))), _1473905)), _1473903))], (37091 ^ _780461) ^ [_1474168, _1474170, _1474172, _1474174, _1474176, _1474178, _1474180] : [class_Rings_Osemiring__0(_1474168), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1474168), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474170, _1474168), _1474172), _1474174)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474176, _1474168), _1474178), _1474180)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474170, _1474168), hAPP(hAPP(c_COMBC(_1474170, tc_fun(_1474176, tc_HOL_Obool), _1474168), hAPP(hAPP(c_COMBB(tc_fun(_1474176, _1474168), tc_fun(tc_fun(_1474176, tc_HOL_Obool), _1474168), _1474170), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474176, _1474168)), hAPP(hAPP(c_COMBC(_1474170, tc_fun(_1474176, _1474168), tc_fun(_1474176, _1474168)), hAPP(hAPP(c_COMBB(tc_fun(_1474168, _1474168), tc_fun(tc_fun(_1474176, _1474168), tc_fun(_1474176, _1474168)), _1474170), c_COMBB(_1474168, _1474168, _1474176)), hAPP(hAPP(c_COMBB(_1474168, tc_fun(_1474168, _1474168), _1474170), c_Groups_Otimes__class_Otimes(_1474168)), _1474172))), _1474178))), _1474180)), _1474174))], (37097 ^ _780461) ^ [_1474507, _1474509, _1474511, _1474513, _1474515] : [class_Rings_Osemiring__0(_1474507), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1474507), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474509, _1474507), _1474511), _1474513)), _1474515) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474509, _1474507), hAPP(hAPP(c_COMBC(_1474509, _1474507, _1474507), hAPP(hAPP(c_COMBB(_1474507, tc_fun(_1474507, _1474507), _1474509), c_Groups_Otimes__class_Otimes(_1474507)), _1474511)), _1474515)), _1474513))], (37103 ^ _780461) ^ [_1474690, _1474692, _1474694, _1474696, _1474698] : [class_Rings_Osemiring__0(_1474690), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1474690), _1474692), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474694, _1474690), _1474696), _1474698)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474694, _1474690), hAPP(hAPP(c_COMBB(_1474690, _1474690, _1474694), hAPP(c_Groups_Otimes__class_Otimes(_1474690), _1474692)), _1474696)), _1474698))], (37109 ^ _780461) ^ [_1474853, _1474855, _1474857, _1474859, _1474861] : [class_Groups_Ocomm__monoid__add(_1474853), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474855, _1474853), hAPP(hAPP(c_COMBS(_1474855, _1474853, _1474853), hAPP(hAPP(c_COMBB(_1474853, tc_fun(_1474853, _1474853), _1474855), c_Groups_Oplus__class_Oplus(_1474853)), _1474857)), _1474859)), _1474861) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1474853), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474855, _1474853), _1474857), _1474861)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474855, _1474853), _1474859), _1474861)))], (37115 ^ _780461) ^ [_1475054, _1475056, _1475058, _1475060] : [class_Groups_Ocomm__monoid__add(_1475054), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1475056), _1475058))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475056, _1475054), _1475060), _1475058) = c_Groups_Ozero__class_Ozero(_1475054))], (37125 ^ _780461) ^ [_1475178, _1475180, _1475182, _1475184] : [class_Groups_Ocomm__monoid__add(_1475178), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1475180), _1475182))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475180, _1475178), _1475184), _1475182) = c_Groups_Ozero__class_Ozero(_1475178))], (37135 ^ _780461) ^ [_1475302, _1475304, _1475306] : [class_Groups_Ocomm__monoid__add(_1475302), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475304, _1475302), _1475306), c_Orderings_Obot__class_Obot(tc_fun(_1475304, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1475302))], (37141 ^ _780461) ^ [_1475411, _1475413, _1475415] : [class_Groups_Ocomm__monoid__add(_1475411), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475413, _1475411), _1475415), c_Orderings_Obot__class_Obot(tc_fun(_1475413, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1475411))], (37147 ^ _780461) ^ [_1475520, _1475522, _1475524, _1475526, _1475528] : [class_Groups_Oab__group__add(_1475520), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475522, _1475520), hAPP(hAPP(c_COMBS(_1475522, _1475520, _1475520), hAPP(hAPP(c_COMBB(_1475520, tc_fun(_1475520, _1475520), _1475522), c_Groups_Ominus__class_Ominus(_1475520)), _1475524)), _1475526)), _1475528) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1475520), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475522, _1475520), _1475524), _1475528)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475522, _1475520), _1475526), _1475528)))], (37153 ^ _780461) ^ [_1475721, _1475723, _1475725, _1475727] : [-(hAPP(c_Map_Orestrict__map(_1475721, _1475723, hAPP(c_COMBK(tc_Option_Ooption(_1475723), _1475721), c_Option_Ooption_ONone(_1475723)), _1475725), _1475727) = c_Option_Ooption_ONone(_1475723))], (37155 ^ _780461) ^ [_1475770, _1475772, _1475774, _1475776, _1475778] : [class_Groups_Ocomm__monoid__add(_1475770), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475772), _1475774)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475772, _1475770), hAPP(hAPP(c_COMBS(_1475772, _1475770, _1475770), hAPP(hAPP(c_COMBB(_1475770, tc_fun(_1475770, _1475770), _1475772), c_Groups_Oplus__class_Oplus(_1475770)), _1475776)), _1475778)), _1475774) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1475770), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475772, _1475770), _1475776), _1475774)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475772, _1475770), _1475778), _1475774)))], (37165 ^ _780461) ^ [_1476037, _1476039, _1476041, _1476043] : [class_Groups_Ocomm__monoid__add(_1476037), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476037), _1476039), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1476041)), hAPP(c_Nat_OSuc, _1476043))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476037), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1476037, tc_Nat_Onat), _1476039), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1476041), _1476043)))], (37171 ^ _780461) ^ [_1476208, _1476210, _1476212, _1476214, _1476216] : [class_Groups_Ocomm__monoid__add(_1476208), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476208), _1476210), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1476212), _1476214)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1476216), _1476214))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476208), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1476208, tc_Nat_Onat), _1476210), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1476214))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1476212), _1476216)))], (37177 ^ _780461) ^ [_1476399, _1476401, _1476403, _1476405] : [class_Groups_Ocomm__monoid__add(_1476399), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476399), _1476401), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1476403), hAPP(c_Nat_OSuc, _1476405))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476399), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1476399, tc_Nat_Onat), _1476401), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1476403, _1476405)))], (37183 ^ _780461) ^ [_1476562, _1476564, _1476566, _1476568, _1476570] : [class_Groups_Ocomm__monoid__add(_1476562), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476562), _1476564), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1476566), _1476568), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1476570), _1476568))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476562), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1476562, tc_Nat_Onat), _1476564), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1476568))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1476566, _1476570)))], (37189 ^ _780461) ^ [_1476741, _1476743, _1476745, _1476747, _1476749] : [-(hBOOL(hAPP(hAPP(c_member(_1476741), _1476743), _1476745))), -(hAPP(c_Map_Orestrict__map(_1476741, _1476747, _1476749, _1476745), _1476743) = c_Option_Ooption_ONone(_1476747))], (37195 ^ _780461) ^ [_1476800, _1476802, _1476804, _1476806, _1476808] : [-(c_Map_Orestrict__map(_1476800, _1476802, _1476804, hAPP(hAPP(c_Set_Oinsert(_1476800), _1476806), _1476808)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1476800, tc_Option_Ooption(_1476802)), c_Map_Orestrict__map(_1476800, _1476802, _1476804, _1476808)), _1476806), hAPP(_1476804, _1476806)))], (37197 ^ _780461) ^ [_1476866, _1476868, _1476870, _1476872, _1476874] : [class_Groups_Ocomm__monoid__add(_1476866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1476868), _1476870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1476870), _1476872)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1476866), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476866), _1476874), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1476868), _1476870))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476866), _1476874), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1476870), _1476872))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1476866), _1476874), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1476868), _1476872)))], (37211 ^ _780461) ^ [_1477189, _1477191, _1477193, _1477195, _1477197] : [class_Groups_Oab__group__add(_1477189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1477191), _1477193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1477193), _1477195)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1477189), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1477189), _1477197), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1477191), _1477195))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1477189), _1477197), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1477191), _1477193))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1477189), _1477197), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1477193), _1477195)))], (37225 ^ _780461) ^ [_1477512, _1477514, _1477516, _1477518, _1477520] : [class_Groups_Ocomm__monoid__add(_1477512), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477514), _1477516)), 37232 ^ _780461 : [(37233 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1477514), _1477518), _1477516)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477514, _1477512), hAPP(hAPP(c_COMBC(_1477514, _1477512, _1477512), hAPP(hAPP(c_COMBS(_1477514, _1477512, tc_fun(_1477512, _1477512)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1477512, tc_fun(_1477512, _1477512)), _1477514), c_If(_1477512)), hAPP(c_fequal, _1477518))), _1477520)), c_Groups_Ozero__class_Ozero(_1477512))), _1477516) = hAPP(_1477520, _1477518))], (37239 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477514), _1477518), _1477516))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477514, _1477512), hAPP(hAPP(c_COMBC(_1477514, _1477512, _1477512), hAPP(hAPP(c_COMBS(_1477514, _1477512, tc_fun(_1477512, _1477512)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1477512, tc_fun(_1477512, _1477512)), _1477514), c_If(_1477512)), hAPP(c_fequal, _1477518))), _1477520)), c_Groups_Ozero__class_Ozero(_1477512))), _1477516) = c_Groups_Ozero__class_Ozero(_1477512))]]], (37245 ^ _780461) ^ [_1478022, _1478024, _1478026, _1478028, _1478030] : [class_Groups_Ocomm__monoid__add(_1478022), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478024), _1478026)), 37252 ^ _780461 : [(37253 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1478024), _1478028), _1478026)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478024, _1478022), hAPP(hAPP(c_COMBC(_1478024, _1478022, _1478022), hAPP(hAPP(c_COMBS(_1478024, _1478022, tc_fun(_1478022, _1478022)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1478022, tc_fun(_1478022, _1478022)), _1478024), c_If(_1478022)), hAPP(hAPP(c_COMBC(_1478024, _1478024, tc_HOL_Obool), c_fequal), _1478028))), _1478030)), c_Groups_Ozero__class_Ozero(_1478022))), _1478026) = hAPP(_1478030, _1478028))], (37259 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478024), _1478028), _1478026))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478024, _1478022), hAPP(hAPP(c_COMBC(_1478024, _1478022, _1478022), hAPP(hAPP(c_COMBS(_1478024, _1478022, tc_fun(_1478022, _1478022)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1478022, tc_fun(_1478022, _1478022)), _1478024), c_If(_1478022)), hAPP(hAPP(c_COMBC(_1478024, _1478024, tc_HOL_Obool), c_fequal), _1478028))), _1478030)), c_Groups_Ozero__class_Ozero(_1478022))), _1478026) = c_Groups_Ozero__class_Ozero(_1478022))]]], (37265 ^ _780461) ^ [_1478578, _1478580, _1478582, _1478584, _1478586] : [hBOOL(hAPP(hAPP(c_member(_1478578), _1478580), _1478582)), -(hAPP(c_Map_Orestrict__map(_1478578, _1478584, _1478586, _1478582), _1478580) = hAPP(_1478586, _1478580))], (37271 ^ _780461) ^ [_1478691, _1478693, _1478695, _1478697, _1478699] : [-(hBOOL(hAPP(hAPP(c_member(_1478691), _1478693), _1478695))), -(hAPP(c_Map_Orestrict__map(_1478691, _1478697, _1478699, _1478695), _1478693) = c_Option_Ooption_ONone(_1478697))], (37277 ^ _780461) ^ [_1478752, _1478754, _1478756, _1478758] : [-(hAPP(c_Map_Orestrict__map(_1478752, _1478754, _1478756, c_Orderings_Obot__class_Obot(tc_fun(_1478752, tc_HOL_Obool))), _1478758) = c_Option_Ooption_ONone(_1478754))], (37279 ^ _780461) ^ [_1478796, _1478798, _1478800, _1478802] : [class_Rings_Osemiring__1(_1478796), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1478798, _1478796), hAPP(c_COMBK(_1478796, _1478798), _1478800)), _1478802) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1478796), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1478796), hAPP(c_Finite__Set_Ocard(_1478798), _1478802))), _1478800))], (37285 ^ _780461) ^ [_1478941, _1478943, _1478945] : [class_Groups_Ocomm__monoid__add(_1478941), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1478941), _1478943), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1478945))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478941), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1478941), _1478943), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1478945))), hAPP(_1478943, _1478945)))], (37291 ^ _780461) ^ [_1479094, _1479096, _1479098] : [class_Groups_Ocomm__monoid__add(_1479094), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1479094), _1479096), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1479098))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1479094), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1479094), _1479096), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1479098))), hAPP(_1479096, hAPP(c_Nat_OSuc, _1479098))))], (37297 ^ _780461) ^ [_1479253, _1479255, _1479257, _1479259, _1479261] : [class_Groups_Ocomm__monoid__add(_1479253), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479255), _1479257)), -(hBOOL(hAPP(hAPP(c_member(_1479255), _1479259), _1479257))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479255, _1479253), _1479261), hAPP(hAPP(c_Set_Oinsert(_1479255), _1479259), _1479257)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1479253), hAPP(_1479261, _1479259)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479255, _1479253), _1479261), _1479257)))], (37311 ^ _780461) ^ [_1479503, _1479505, _1479507, _1479509, _1479511] : [class_Groups_Ocomm__monoid__add(_1479503), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479505), _1479507)), -(hBOOL(hAPP(hAPP(c_member(_1479505), _1479509), _1479507))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479505, _1479503), _1479511), hAPP(hAPP(c_Set_Oinsert(_1479505), _1479509), _1479507)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1479503), hAPP(_1479511, _1479509)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479505, _1479503), _1479511), _1479507)))], (37325 ^ _780461) ^ [_1479753, _1479755, _1479757, _1479759, _1479761] : [class_Groups_Ocomm__monoid__add(_1479753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479755), _1479757)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479755), _1479759)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1479753), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479755, _1479753), _1479761), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479755, tc_HOL_Obool)), _1479757), _1479759))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479755, _1479753), _1479761), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479755, tc_HOL_Obool)), _1479757), _1479759))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1479753), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479755, _1479753), _1479761), _1479757)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1479755, _1479753), _1479761), _1479759)))], (37339 ^ _780461) ^ [_1480114, _1480116, _1480118, _1480120, _1480122] : [class_Groups_Oab__group__add(_1480114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480116), _1480118)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480116, tc_HOL_Obool)), _1480120), _1480118)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480116, _1480114), _1480122), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1480116, tc_HOL_Obool)), _1480118), _1480120)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1480114), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480116, _1480114), _1480122), _1480118)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480116, _1480114), _1480122), _1480120)))], (37353 ^ _780461) ^ [_1480431, _1480433, _1480435, _1480437] : [class_Groups_Ocomm__monoid__add(_1480431), 37356 ^ _780461 : [(37357 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1480433), _1480435)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480433, _1480431), _1480437), _1480435) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1480431, _1480433, c_Groups_Oplus__class_Oplus(_1480431)), _1480437), c_Groups_Ozero__class_Ozero(_1480431)), _1480435))], (37363 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1480433), _1480435))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480433, _1480431), _1480437), _1480435) = c_Groups_Ozero__class_Ozero(_1480431))]]], (37369 ^ _780461) ^ [_1480703, _1480705, _1480707, _1480709] : [class_Groups_Ocomm__monoid__add(_1480703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480705), _1480707)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1480705, _1480703), _1480709), _1480707) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1480703, _1480705, c_Groups_Oplus__class_Oplus(_1480703)), _1480709), c_Groups_Ozero__class_Ozero(_1480703)), _1480707))], (37379 ^ _780461) ^ [_1480898, _1480900, _1480902] : [class_Groups_Ocomm__monoid__add(_1480898), hAPP(_1480900, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1480898), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1480898), _1480900), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1480902)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1480898), _1480900), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1480902)))], (37389 ^ _780461) ^ [_1481087, _1481089, _1481091, _1481093] : [class_Groups_Ocomm__monoid__add(_1481087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1481089), _1481091)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1481087), _1481093), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1481089), _1481091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1481087), hAPP(_1481093, _1481089)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1481087), _1481093), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1481089)), _1481091))))], (37399 ^ _780461) ^ [_1481320, _1481322, _1481324, _1481326] : [class_Groups_Ocomm__monoid__add(_1481320), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1481322), _1481324)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1481320), _1481326), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1481322, _1481324)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1481320), hAPP(_1481326, _1481322)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1481320), _1481326), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1481322), _1481324))))], (37409 ^ _780461) ^ [_1481545, _1481547, _1481549, _1481551, _1481553] : [class_Groups_Ocomm__monoid__add(_1481545), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481547), _1481549)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481547, _1481545), _1481551), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481547, tc_HOL_Obool)), _1481549), _1481553)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481547, _1481545), hAPP(hAPP(c_COMBC(_1481547, _1481545, _1481545), hAPP(hAPP(c_COMBS(_1481547, _1481545, tc_fun(_1481545, _1481545)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1481545, tc_fun(_1481545, _1481545)), _1481547), c_If(_1481545)), hAPP(hAPP(c_COMBC(_1481547, tc_fun(_1481547, tc_HOL_Obool), tc_HOL_Obool), c_member(_1481547)), _1481553))), _1481551)), c_Groups_Ozero__class_Ozero(_1481545))), _1481549))], (37419 ^ _780461) ^ [_1481866, _1481868, _1481870, _1481872, _1481874] : [hAPP(_1481866, _1481868) = hAPP(c_Option_Ooption_OSome(_1481870), _1481872), -(hBOOL(hAPP(hAPP(c_member(_1481870), _1481872), c_Map_Oran(_1481874, _1481870, _1481866))))], (37425 ^ _780461) ^ [_1481987, _1481989, _1481991, _1481993, _1481995] : [class_Groups_Ocomm__monoid__add(_1481987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481989), _1481991)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481989, _1481987), _1481993), hAPP(hAPP(c_Set_Oinsert(_1481989), _1481995), _1481991)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1481987), hAPP(_1481993, _1481995)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481989, _1481987), _1481993), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1481989, tc_HOL_Obool)), _1481991), hAPP(hAPP(c_Set_Oinsert(_1481989), _1481995), c_Orderings_Obot__class_Obot(tc_fun(_1481989, tc_HOL_Obool)))))))], (37435 ^ _780461) ^ [_1482256, _1482258, _1482260, _1482262, _1482264] : [class_Groups_Ocomm__monoid__add(_1482256), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482258), _1482260)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482258), _1482262)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482258, tc_HOL_Obool)), _1482260), _1482262) = c_Orderings_Obot__class_Obot(tc_fun(_1482258, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482258, _1482256), _1482264), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482258, tc_HOL_Obool)), _1482260), _1482262)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1482256), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482258, _1482256), _1482264), _1482260)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482258, _1482256), _1482264), _1482262)))], (37453 ^ _780461) ^ [_1482651, _1482653, _1482655, _1482657, _1482659] : [class_Groups_Oab__group__add(_1482651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482653), _1482655)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482653), _1482657)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482653, _1482651), _1482659), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482653, tc_HOL_Obool)), _1482655), _1482657)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1482651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1482651), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482653, _1482651), _1482659), _1482655)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482653, _1482651), _1482659), _1482657))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482653, _1482651), _1482659), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482653, tc_HOL_Obool)), _1482655), _1482657))))], (37467 ^ _780461) ^ [_1483012, _1483014, _1483016, _1483018] : [class_Groups_Ocomm__monoid__add(_1483012), 37470 ^ _780461 : [(37471 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1483014), _1483016)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483012), _1483018), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1483016), hAPP(c_Nat_OSuc, _1483014))) = c_Groups_Ozero__class_Ozero(_1483012))], (37477 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1483014), _1483016))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483012), _1483018), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1483016), hAPP(c_Nat_OSuc, _1483014))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1483012), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483012), _1483018), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1483016), _1483014))), hAPP(_1483018, _1483014)))]]], (37483 ^ _780461) ^ [_1483342, _1483344, _1483346, _1483348] : [class_Groups_Ocomm__monoid__add(_1483342), 37486 ^ _780461 : [(37487 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1483344)), _1483346)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483342), _1483348), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483346, hAPP(c_Nat_OSuc, _1483344))) = c_Groups_Ozero__class_Ozero(_1483342))], (37493 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1483344)), _1483346))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483342), _1483348), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483346, hAPP(c_Nat_OSuc, _1483344))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1483342), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483342), _1483348), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483346, _1483344))), hAPP(_1483348, hAPP(c_Nat_OSuc, _1483344))))]]], (37499 ^ _780461) ^ [_1483678, _1483680, _1483682, _1483684] : [class_Groups_Ocomm__monoid__add(_1483678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1483680), _1483682)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483678), _1483684), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483680, _1483682)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1483678), hAPP(_1483684, _1483680)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483678), _1483684), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1483680, _1483682))))], (37509 ^ _780461) ^ [_1483897, _1483899, _1483901, _1483903, _1483905] : [class_Groups_Ocomm__monoid__add(_1483897), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1483899), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1483901), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483897), _1483903), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483899, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1483901), _1483905))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1483897), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483897), _1483903), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1483899, _1483901))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1483897), _1483903), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1483901), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1483901), _1483905)))))], (37519 ^ _780461) ^ [_1484188, _1484190, _1484192, _1484194, _1484196, _1484198] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1484188, tc_Option_Ooption(_1484190)), c_Map_Orestrict__map(_1484188, _1484190, _1484192, _1484194)), _1484196), _1484198) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1484188, tc_Option_Ooption(_1484190)), c_Map_Orestrict__map(_1484188, _1484190, _1484192, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1484188, tc_HOL_Obool)), _1484194), hAPP(hAPP(c_Set_Oinsert(_1484188), _1484196), c_Orderings_Obot__class_Obot(tc_fun(_1484188, tc_HOL_Obool)))))), _1484196), _1484198))], (37521 ^ _780461) ^ [_1484283, _1484285] : [-(c_Map_Oran(_1484283, _1484285, hAPP(c_COMBK(tc_Option_Ooption(_1484285), _1484283), c_Option_Ooption_ONone(_1484285))) = c_Orderings_Obot__class_Obot(tc_fun(_1484285, tc_HOL_Obool)))], (37523 ^ _780461) ^ [_1484327, _1484329, _1484331, _1484333, _1484335] : [class_Groups_Ocomm__monoid__add(_1484327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1484329), _1484331)), hBOOL(hAPP(hAPP(c_member(_1484329), _1484333), _1484331)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484329, _1484327), _1484335), _1484331) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1484327), hAPP(_1484335, _1484333)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484329, _1484327), _1484335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1484329, tc_HOL_Obool)), _1484331), hAPP(hAPP(c_Set_Oinsert(_1484329), _1484333), c_Orderings_Obot__class_Obot(tc_fun(_1484329, tc_HOL_Obool)))))))], (37537 ^ _780461) ^ [_1484652, _1484654, _1484656, _1484658, _1484660] : [class_Groups_Ocomm__monoid__add(_1484652), hBOOL(hAPP(c_Finite__Set_Ofinite(_1484654), _1484656)), hBOOL(hAPP(hAPP(c_member(_1484654), _1484658), _1484656)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484654, _1484652), _1484660), _1484656) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1484652), hAPP(_1484660, _1484658)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484654, _1484652), _1484660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1484654, tc_HOL_Obool)), _1484656), hAPP(hAPP(c_Set_Oinsert(_1484654), _1484658), c_Orderings_Obot__class_Obot(tc_fun(_1484654, tc_HOL_Obool)))))))], (37551 ^ _780461) ^ [_1484977, _1484979, _1484981, _1484983, _1484985] : [class_Groups_Oab__group__add(_1484977), hBOOL(hAPP(c_Finite__Set_Ofinite(_1484979), _1484981)), 37558 ^ _780461 : [(37559 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1484979), _1484983), _1484981)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484979, _1484977), _1484985), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1484979, tc_HOL_Obool)), _1484981), hAPP(hAPP(c_Set_Oinsert(_1484979), _1484983), c_Orderings_Obot__class_Obot(tc_fun(_1484979, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1484977), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484979, _1484977), _1484985), _1484981)), hAPP(_1484985, _1484983)))], (37565 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484979), _1484983), _1484981))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484979, _1484977), _1484985), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1484979, tc_HOL_Obool)), _1484981), hAPP(hAPP(c_Set_Oinsert(_1484979), _1484983), c_Orderings_Obot__class_Obot(tc_fun(_1484979, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1484979, _1484977), _1484985), _1484981))]]], (37571 ^ _780461) ^ [_1485447, _1485449, _1485451, _1485453, _1485455] : [class_Rings_Oring(_1485447), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485449), _1485451)), hBOOL(hAPP(hAPP(c_member(_1485449), _1485453), _1485451)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485449, _1485447), _1485455), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485449, tc_HOL_Obool)), _1485451), hAPP(hAPP(c_Set_Oinsert(_1485449), _1485453), c_Orderings_Obot__class_Obot(tc_fun(_1485449, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1485447), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485449, _1485447), _1485455), _1485451)), hAPP(_1485455, _1485453)))], (37585 ^ _780461) ^ [_1485772, _1485774, _1485776] : [class_Fields_Ofield(_1485772), -(_1485774 = c_Groups_Oone__class_Oone(_1485772)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1485772), hAPP(c_Power_Opower__class_Opower(_1485772), _1485774)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1485776)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1485772), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1485772), hAPP(hAPP(c_Power_Opower__class_Opower(_1485772), _1485774), _1485776)), c_Groups_Oone__class_Oone(_1485772))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1485772), _1485774), c_Groups_Oone__class_Oone(_1485772))))], (37595 ^ _780461) ^ [_1485974, _1485976] : [class_Rings_Ocomm__semiring__1(_1485974), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1485974), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1485974), c_Groups_Oone__class_Oone(_1485974)), c_Groups_Oone__class_Oone(_1485974))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1485974), c_Nat_Osemiring__1__class_Oof__nat(_1485974)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1485976))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1485974), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1485974), _1485976)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1485974), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1485974), _1485976)), c_Groups_Oone__class_Oone(_1485974))))], (37601 ^ _780461) ^ [_1486175, _1486177, _1486179, _1486181] : [class_Groups_Oab__group__add(_1486175), 37604 ^ _780461 : [(37605 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1486177), _1486179)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1486175), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1486175, _1486175), hAPP(hAPP(c_COMBB(_1486175, tc_fun(_1486175, _1486175), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1486175)), _1486181)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1486175, tc_Nat_Onat), _1486181), 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, _1486177, _1486179)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1486175), hAPP(_1486181, _1486177)), hAPP(_1486181, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1486179), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (37611 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1486177), _1486179))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1486175), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1486175, _1486175), hAPP(hAPP(c_COMBB(_1486175, tc_fun(_1486175, _1486175), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1486175)), _1486181)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1486175, tc_Nat_Onat), _1486181), 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, _1486177, _1486179)) = c_Groups_Ozero__class_Ozero(_1486175))]]], (37617 ^ _780461) ^ [_1486613, _1486615, _1486617, _1486619, _1486621, _1486623] : [hBOOL(hAPP(hAPP(c_member(_1486613), _1486615), _1486617)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1486613, tc_Option_Ooption(_1486619)), c_Map_Orestrict__map(_1486613, _1486619, _1486621, _1486617)), _1486615), _1486623) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1486613, tc_Option_Ooption(_1486619)), c_Map_Orestrict__map(_1486613, _1486619, _1486621, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486613, tc_HOL_Obool)), _1486617), hAPP(hAPP(c_Set_Oinsert(_1486613), _1486615), c_Orderings_Obot__class_Obot(tc_fun(_1486613, tc_HOL_Obool)))))), _1486615), _1486623))], (37623 ^ _780461) ^ [_1486857, _1486859, _1486861, _1486863, _1486865, _1486867] : [hBOOL(hAPP(hAPP(c_member(_1486857), _1486859), _1486861)), -(c_Map_Orestrict__map(_1486857, _1486863, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1486857, tc_Option_Ooption(_1486863)), _1486865), _1486859), _1486867), _1486861) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1486857, tc_Option_Ooption(_1486863)), c_Map_Orestrict__map(_1486857, _1486863, _1486865, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486857, tc_HOL_Obool)), _1486861), hAPP(hAPP(c_Set_Oinsert(_1486857), _1486859), c_Orderings_Obot__class_Obot(tc_fun(_1486857, tc_HOL_Obool)))))), _1486859), _1486867))], (37629 ^ _780461) ^ [_1487074, _1487076, _1487078, _1487080, _1487082, _1487084] : [-(hBOOL(hAPP(hAPP(c_member(_1487074), _1487076), _1487078))), -(c_Map_Orestrict__map(_1487074, _1487080, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1487074, tc_Option_Ooption(_1487080)), _1487082), _1487076), _1487084), _1487078) = c_Map_Orestrict__map(_1487074, _1487080, _1487082, _1487078))], (37635 ^ _780461) ^ [_1487151, _1487153, _1487155, _1487157] : [-(c_Map_Orestrict__map(_1487151, _1487153, _1487155, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487151, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1487151), _1487157), c_Orderings_Obot__class_Obot(tc_fun(_1487151, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1487151, tc_Option_Ooption(_1487153)), _1487155), _1487157), c_Option_Ooption_ONone(_1487153)))], (37637 ^ _780461) ^ [_1487222, _1487224, _1487226, _1487228, _1487230] : [-(c_Map_Orestrict__map(_1487222, _1487224, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1487222, tc_Option_Ooption(_1487224)), _1487226), _1487228), hAPP(c_Option_Ooption_OSome(_1487224), _1487230)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487222, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1487222), _1487228), c_Orderings_Obot__class_Obot(tc_fun(_1487222, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1487222, _1487224, _1487226, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487222, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1487222), _1487228), c_Orderings_Obot__class_Obot(tc_fun(_1487222, tc_HOL_Obool))))))], (37639 ^ _780461) ^ [_1487324, _1487326, _1487328, _1487330] : [class_Rings_Ocomm__semiring__1(_1487324), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1487324), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1487324), c_Groups_Oone__class_Oone(_1487324)), c_Groups_Oone__class_Oone(_1487324))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1487324), hAPP(hAPP(c_COMBB(_1487324, _1487324, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1487324), _1487326)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1487324, _1487324), hAPP(hAPP(c_COMBB(_1487324, tc_fun(_1487324, _1487324), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1487324)), c_Nat_Osemiring__1__class_Oof__nat(_1487324))), _1487328))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1487330))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1487324), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1487324), _1487330)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1487324), _1487326), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1487324), _1487326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1487324), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1487324), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1487330), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1487328)))))], (37645 ^ _780461) ^ [_1487647, _1487649, _1487651, _1487653, _1487655] : [class_Groups_Oordered__comm__monoid__add(_1487647), hBOOL(hAPP(c_Finite__Set_Ofinite(_1487649), _1487651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487649, tc_HOL_Obool)), _1487653), _1487651)), 37659 ^ _780461 : [(37660 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487649), 37658 ^ [_1487647, _1487649, _1487651, _1487653, _1487655]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1487649, tc_HOL_Obool)), _1487651), _1487653))))], (37662 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487647), c_Groups_Ozero__class_Ozero(_1487647)), hAPP(_1487655, 37658 ^ [_1487647, _1487649, _1487651, _1487653, _1487655])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487647), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487649, _1487647), _1487655), _1487653)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1487649, _1487647), _1487655), _1487651))))], (37666 ^ _780461) ^ [_1488133, _1488135, _1488137, _1488139, _1488141] : [class_Groups_Oordered__ab__semigroup__add(_1488133), class_Rings_Osemiring__1(_1488133), 37676 ^ _780461 : [(37677 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488135), 37675 ^ [_1488133, _1488135, _1488137, _1488139, _1488141]), _1488137)))], (37679 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1488133), hAPP(_1488139, 37675 ^ [_1488133, _1488135, _1488137, _1488139, _1488141])), _1488141))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1488133), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488135, _1488133), _1488139), _1488137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1488133), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1488133), hAPP(c_Finite__Set_Ocard(_1488135), _1488137))), _1488141))))], (37683 ^ _780461) ^ [_1488523, _1488525, _1488527, _1488529, _1488531] : [class_Groups_Ocomm__monoid__add(_1488523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488525), _1488527)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488525), _1488529)), 37697 ^ _780461 : [(37698 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488525), 37696 ^ [_1488523, _1488525, _1488527, _1488529, _1488531]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488525, tc_HOL_Obool)), _1488527), _1488529))))], (37700 ^ _780461) ^ [] : [hAPP(_1488531, 37696 ^ [_1488523, _1488525, _1488527, _1488529, _1488531]) = c_Groups_Ozero__class_Ozero(_1488523)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488525, _1488523), _1488531), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488525, tc_HOL_Obool)), _1488527), _1488529)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1488523), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488525, _1488523), _1488531), _1488527)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488525, _1488523), _1488531), _1488529)))], (37704 ^ _780461) ^ [_1489018, _1489020, _1489022] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1489018), _1489020)), 37707 ^ _780461 : [(37718 ^ _780461) ^ [] : [37720 ^ _780461 : [(37721 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489018), 37719 ^ [_1489018, _1489020, _1489022]), _1489020)))], (37723 ^ _780461) ^ [] : [hAPP(_1489022, 37719 ^ [_1489018, _1489020, _1489022]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489018, tc_Nat_Onat), _1489022), _1489020) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37708 ^ _780461) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489018, tc_Nat_Onat), _1489022), _1489020) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 37711 ^ _780461 : [(37712 ^ _780461) ^ [_1489180] : [hBOOL(hAPP(hAPP(c_member(_1489018), _1489180), _1489020)), -(hAPP(_1489022, _1489180) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (37727 ^ _780461) ^ [_1489438, _1489440] : [-(hAPP(c_Finite__Set_Ocard(_1489438), _1489440) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489438, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1489438), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1489440))], (37729 ^ _780461) ^ [_1489483, _1489485, _1489487] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489483, tc_Nat_Onat), _1489485), _1489487)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489483, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1489483), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1489485)), _1489487))], (37731 ^ _780461) ^ [_1489541, _1489543, _1489545] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1489541), _1489543)), 37734 ^ _780461 : [(37735 ^ _780461) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489541, tc_Nat_Onat), _1489545), _1489543) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37739 ^ _780461 : [(37740 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489541), 37738 ^ [_1489541, _1489543, _1489545]), _1489543)))], (37742 ^ _780461) ^ [] : [-(hAPP(_1489545, 37738 ^ [_1489541, _1489543, _1489545]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37744 ^ _780461) ^ [_1489861] : [hBOOL(hAPP(hAPP(c_member(_1489541), _1489861), _1489543)), -(37738 ^ [_1489541, _1489543, _1489545] = _1489861), -(hAPP(_1489545, _1489861) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (37754 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489541, tc_Nat_Onat), _1489545), _1489543) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 37755 ^ _780461 : [(37756 ^ _780461) ^ [_1490022] : [hBOOL(hAPP(hAPP(c_member(_1489541), _1490022), _1489543)), hAPP(_1489545, _1490022) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37764 ^ _780461 : [(37765 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1489541), 37763 ^ [_1489541, _1489543, _1489545, _1490022]), _1489543)))], (37767 ^ _780461) ^ [] : [_1490022 = 37763 ^ [_1489541, _1489543, _1489545, _1490022]], (37769 ^ _780461) ^ [] : [hAPP(_1489545, 37763 ^ [_1489541, _1489543, _1489545, _1490022]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (37773 ^ _780461) ^ [_1490375, _1490377, _1490379] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490375), _1490377)), 37776 ^ _780461 : [(37777 ^ _780461) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490375, tc_Nat_Onat), _1490379), _1490377) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 37781 ^ _780461 : [(37782 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490375), 37780 ^ [_1490375, _1490377, _1490379]), _1490377)))], (37784 ^ _780461) ^ [] : [-(hAPP(_1490379, 37780 ^ [_1490375, _1490377, _1490379]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (37786 ^ _780461) ^ [_1490695] : [hBOOL(hAPP(hAPP(c_member(_1490375), _1490695), _1490377)), -(37780 ^ [_1490375, _1490377, _1490379] = _1490695), -(hAPP(_1490379, _1490695) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (37796 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1490375, tc_Nat_Onat), _1490379), _1490377) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 37797 ^ _780461 : [(37798 ^ _780461) ^ [_1490856] : [hBOOL(hAPP(hAPP(c_member(_1490375), _1490856), _1490377)), hAPP(_1490379, _1490856) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 37806 ^ _780461 : [(37807 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490375), 37805 ^ [_1490375, _1490377, _1490379, _1490856]), _1490377)))], (37809 ^ _780461) ^ [] : [_1490856 = 37805 ^ [_1490375, _1490377, _1490379, _1490856]], (37811 ^ _780461) ^ [] : [hAPP(_1490379, 37805 ^ [_1490375, _1490377, _1490379, _1490856]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (37815 ^ _780461) ^ [_1491209, _1491211] : [hAPP(_1491209, 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), _1491209), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1491211)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1491209), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1491211)))], (37821 ^ _780461) ^ [_1491332, _1491334, _1491336] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491332, tc_Nat_Onat), _1491334), _1491336) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491332, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1491332), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1491334)), _1491336)))], (37823 ^ _780461) ^ [_1491390, _1491392, _1491394, _1491396] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1491390), _1491392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491390, tc_HOL_Obool)), _1491392), _1491394)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491390, tc_Nat_Onat), _1491396), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1491390, tc_HOL_Obool)), _1491394), _1491392)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491390, tc_Nat_Onat), _1491396), _1491394)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491390, tc_Nat_Onat), _1491396), _1491392)))], (37833 ^ _780461) ^ [_1491643, _1491645, _1491647] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1491643), _1491645), _1491647) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1491643), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1491643, tc_Int_Oint), _1491645), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1491647))), class_Groups_Ocomm__monoid__add(_1491643), class_Groups_Ocomm__monoid__mult(_1491643)], (37843 ^ _780461) ^ [_1491849, _1491851, _1491853, _1491855] : [hBOOL(hAPP(hAPP(c_member(_1491849), _1491851), _1491853)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491849, tc_Nat_Onat), _1491855), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1491849, tc_HOL_Obool)), _1491853), hAPP(hAPP(c_Set_Oinsert(_1491849), _1491851), c_Orderings_Obot__class_Obot(tc_fun(_1491849, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1491849, tc_Nat_Onat), _1491855), _1491853)), hAPP(_1491855, _1491851)))], (37849 ^ _780461) ^ [_1492040, _1492042, _1492044, _1492046] : [-(hBOOL(hAPP(hAPP(c_member(_1492040), _1492042), _1492044))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492040, tc_Nat_Onat), _1492046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492040, tc_HOL_Obool)), _1492044), hAPP(hAPP(c_Set_Oinsert(_1492040), _1492042), c_Orderings_Obot__class_Obot(tc_fun(_1492040, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492040, tc_Nat_Onat), _1492046), _1492044))], (37855 ^ _780461) ^ [_1492131, _1492133, _1492135, _1492137] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492131), _1492133)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492131), _1492135)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492131, tc_Nat_Onat), _1492137), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1492131, tc_HOL_Obool)), _1492133), _1492135)) = 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(_1492131, tc_Nat_Onat), _1492137), _1492133)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492131, tc_Nat_Onat), _1492137), _1492135))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492131, tc_Nat_Onat), _1492137), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1492131, tc_HOL_Obool)), _1492133), _1492135))))], (37865 ^ _780461) ^ [_1492424, _1492426, _1492428] : [class_Groups_Ocomm__monoid__add(_1492424), class_Groups_Ocomm__monoid__mult(_1492424), c_Nat__Transfer_Onat__set(_1492426), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1492424), _1492428), _1492426) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1492424), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1492424, tc_Nat_Onat), _1492428), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1492426)))], (37879 ^ _780461) ^ [_1492669, _1492671, _1492673] : [-(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), _1492669)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1492671))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1492673))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492673), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1492669), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1492669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1492673), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1492671)))))], (37881 ^ _780461) ^ [_1492750, _1492752, _1492754] : [37883 ^ _780461 : [(37884 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492750), 37882 ^ [_1492750, _1492752, _1492754]), _1492752)))], (37886 ^ _780461) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1492754, 37882 ^ [_1492750, _1492752, _1492754]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492750, tc_Int_Oint), _1492754), _1492752) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492750, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1492750), c_Int_Onat), _1492754)), _1492752)))], (37890 ^ _780461) ^ [_1492980, _1492982, _1492984, _1492986, _1492988] : [class_Groups_Ocomm__monoid__add(_1492980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492982), _1492984)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492982), _1492986)), 37904 ^ _780461 : [(37905 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492982), 37903 ^ [_1492980, _1492982, _1492984, _1492986, _1492988]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1492982, tc_HOL_Obool)), _1492984), _1492986))))], (37907 ^ _780461) ^ [] : [hAPP(_1492988, 37903 ^ [_1492980, _1492982, _1492984, _1492986, _1492988]) = c_Groups_Ozero__class_Ozero(_1492980)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492982, _1492980), _1492988), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1492982, tc_HOL_Obool)), _1492984), _1492986)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1492980), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492982, _1492980), _1492988), _1492984)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492982, _1492980), _1492988), _1492986)))], (37911 ^ _780461) ^ [_1493475, _1493477, _1493479, _1493481, _1493483] : [class_Groups_Ocomm__monoid__add(_1493475), class_Groups_Oordered__ab__semigroup__add(_1493475), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493477), _1493479)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493477, tc_HOL_Obool)), _1493481), _1493479)), 37929 ^ _780461 : [(37930 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493477), 37928 ^ [_1493475, _1493477, _1493479, _1493481, _1493483]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493477, tc_HOL_Obool)), _1493479), _1493481))))], (37932 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493475), c_Groups_Ozero__class_Ozero(_1493475)), hAPP(_1493483, 37928 ^ [_1493475, _1493477, _1493479, _1493481, _1493483])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493475), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493477, _1493475), _1493483), _1493481)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493477, _1493475), _1493483), _1493479))))], (37936 ^ _780461) ^ [_1494019, _1494021, _1494023, _1494025, _1494027] : [class_Groups_Oordered__ab__group__add(_1494019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494021), _1494023)), 37946 ^ _780461 : [(37947 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494021), 37945 ^ [_1494019, _1494021, _1494023, _1494025, _1494027]), _1494023)))], (37949 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494019), c_Groups_Ozero__class_Ozero(_1494019)), hAPP(_1494025, 37945 ^ [_1494019, _1494021, _1494023, _1494025, _1494027])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1494021, _1494019), _1494025), _1494023) = c_Groups_Ozero__class_Ozero(_1494019), hBOOL(hAPP(hAPP(c_member(_1494021), _1494027), _1494023)), -(hAPP(_1494025, _1494027) = c_Groups_Ozero__class_Ozero(_1494019))], (37961 ^ _780461) ^ [_1494517, _1494519, _1494521, _1494523, _1494525, _1494527] : [class_Groups_Oordered__ab__group__add(_1494517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1494519), _1494521)), 37971 ^ _780461 : [(37972 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494519), 37970 ^ [_1494517, _1494519, _1494521, _1494523, _1494525, _1494527]), _1494521)))], (37974 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494517), c_Groups_Ozero__class_Ozero(_1494517)), hAPP(_1494523, 37970 ^ [_1494517, _1494519, _1494521, _1494523, _1494525, _1494527])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1494519, _1494517), _1494523), _1494521) = _1494525, hBOOL(hAPP(hAPP(c_member(_1494519), _1494527), _1494521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494517), hAPP(_1494523, _1494527)), _1494525)))], (37986 ^ _780461) ^ [_1495037, _1495039, _1495041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1495037, 37987 ^ [_1495037, _1495039, _1495041])), hAPP(_1495039, 37987 ^ [_1495037, _1495039, _1495041]))), -(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), _1495039), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1495041))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1495037), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1495041))) = 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)), _1495039)), _1495037)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1495041)))], (37993 ^ _780461) ^ [_1495270, _1495272, _1495274, _1495276, _1495278] : [class_Groups_Ocomm__monoid__add(_1495270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495272), _1495274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495272, tc_HOL_Obool)), _1495276), _1495274)), 38007 ^ _780461 : [(38008 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1495272), 38006 ^ [_1495270, _1495272, _1495274, _1495276, _1495278]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1495272, tc_HOL_Obool)), _1495274), _1495276))))], (38010 ^ _780461) ^ [] : [hAPP(_1495278, 38006 ^ [_1495270, _1495272, _1495274, _1495276, _1495278]) = c_Groups_Ozero__class_Ozero(_1495270)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495272, _1495270), _1495278), _1495276) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495272, _1495270), _1495278), _1495274))], (38014 ^ _780461) ^ [_1495721, _1495723, _1495725, _1495727, _1495729] : [class_Groups_Ocomm__monoid__add(_1495721), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495723), _1495725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495723, tc_HOL_Obool)), _1495727), _1495725)), 38028 ^ _780461 : [(38029 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1495723), 38027 ^ [_1495721, _1495723, _1495725, _1495727, _1495729]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1495723, tc_HOL_Obool)), _1495725), _1495727))))], (38031 ^ _780461) ^ [] : [hAPP(_1495729, 38027 ^ [_1495721, _1495723, _1495725, _1495727, _1495729]) = c_Groups_Ozero__class_Ozero(_1495721)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495723, _1495721), _1495729), _1495725) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495723, _1495721), _1495729), _1495727))], (38035 ^ _780461) ^ [_1496172, _1496174, _1496176, _1496178, _1496180] : [c_Finite__Set_Ofolding__one__idem(_1496172, _1496174, _1496176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496172), _1496178)), -(_1496178 = c_Orderings_Obot__class_Obot(tc_fun(_1496172, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496172), _1496180)), -(_1496180 = c_Orderings_Obot__class_Obot(tc_fun(_1496172, tc_HOL_Obool))), -(hAPP(_1496176, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496172, tc_HOL_Obool)), _1496178), _1496180)) = hAPP(hAPP(_1496174, hAPP(_1496176, _1496178)), hAPP(_1496176, _1496180)))], (38057 ^ _780461) ^ [_1496537, _1496539, _1496541, _1496543] : [c_Finite__Set_Ofolding__one__idem(_1496537, _1496539, _1496541), -(hAPP(hAPP(_1496539, _1496543), _1496543) = _1496543)], (38063 ^ _780461) ^ [_1496632, _1496634, _1496636, _1496638, _1496640] : [c_Finite__Set_Ofolding__one__idem(_1496632, _1496634, _1496636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496632), _1496638)), hBOOL(hAPP(hAPP(c_member(_1496632), _1496640), _1496638)), -(hAPP(hAPP(_1496634, _1496640), hAPP(_1496636, _1496638)) = hAPP(_1496636, _1496638))], (38077 ^ _780461) ^ [_1496879, _1496881, _1496883, _1496885, _1496887] : [c_Finite__Set_Ofolding__one__idem(_1496879, _1496881, _1496883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496879), _1496885)), -(_1496885 = c_Orderings_Obot__class_Obot(tc_fun(_1496879, tc_HOL_Obool))), -(hAPP(_1496883, hAPP(hAPP(c_Set_Oinsert(_1496879), _1496887), _1496885)) = hAPP(hAPP(_1496881, _1496887), hAPP(_1496883, _1496885)))], (38091 ^ _780461) ^ [_1497095, _1497097, _1497099, _1497101, _1497103] : [c_Finite__Set_Ofolding__one__idem(_1497095, _1497097, _1497099), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497095), _1497101)), -(_1497103 = c_Orderings_Obot__class_Obot(tc_fun(_1497095, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1497095, tc_HOL_Obool)), _1497103), _1497101)), -(hAPP(hAPP(_1497097, hAPP(_1497099, _1497103)), hAPP(_1497099, _1497101)) = hAPP(_1497099, _1497101))], (38109 ^ _780461) ^ [_1497425, _1497427, _1497429, _1497431] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497425), _1497427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1497425, tc_HOL_Obool)), _1497427), _1497429)), hBOOL(hAPP(_1497431, c_Orderings_Obot__class_Obot(tc_fun(_1497425, tc_HOL_Obool)))), 38124 ^ _780461 : [(38125 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497425), 38123 ^ [_1497425, _1497427, _1497429, _1497431])))], (38127 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497425), 38122 ^ [_1497425, _1497427, _1497429, _1497431]), _1497429)))], (38129 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1497425), 38122 ^ [_1497425, _1497427, _1497429, _1497431]), 38123 ^ [_1497425, _1497427, _1497429, _1497431]))], (38131 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1497431, 38123 ^ [_1497425, _1497427, _1497429, _1497431])))], (38133 ^ _780461) ^ [] : [hBOOL(hAPP(_1497431, hAPP(hAPP(c_Set_Oinsert(_1497425), 38122 ^ [_1497425, _1497427, _1497429, _1497431]), 38123 ^ [_1497425, _1497427, _1497429, _1497431])))]], -(hBOOL(hAPP(_1497431, _1497427)))], (38137 ^ _780461) ^ [_1498090, _1498092, _1498094, _1498096, _1498098] : [class_Groups_Ocomm__monoid__add(_1498090), class_Groups_Oordered__cancel__ab__semigroup__add(_1498090), hBOOL(hAPP(c_Finite__Set_Ofinite(_1498092), _1498094)), -(_1498094 = c_Orderings_Obot__class_Obot(tc_fun(_1498092, tc_HOL_Obool))), 38155 ^ _780461 : [(38156 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498092), 38154 ^ [_1498090, _1498092, _1498094, _1498096, _1498098]), _1498094)))], (38158 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498090), hAPP(_1498096, 38154 ^ [_1498090, _1498092, _1498094, _1498096, _1498098])), hAPP(_1498098, 38154 ^ [_1498090, _1498092, _1498094, _1498096, _1498098])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498090), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1498092, _1498090), _1498096), _1498094)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1498092, _1498090), _1498098), _1498094))))], (38162 ^ _780461) ^ [_1498621, _1498623] : [class_Orderings_Oorder(_1498621), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1498621, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1498621), _1498623)), hAPP(c_SetInterval_Oord__class_OatLeast(_1498621), _1498623)) = hAPP(hAPP(c_Set_Oinsert(_1498621), _1498623), c_Orderings_Obot__class_Obot(tc_fun(_1498621, tc_HOL_Obool))))], (38168 ^ _780461) ^ [_1498764, _1498766, _1498768] : [class_Orderings_Olinorder(_1498764), 38171 ^ _780461 : [(38172 ^ _780461) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1498764), _1498766) = hAPP(c_SetInterval_Oord__class_OatLeast(_1498764), _1498768), -(_1498766 = _1498768)], (38178 ^ _780461) ^ [] : [_1498766 = _1498768, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1498764), _1498766) = hAPP(c_SetInterval_Oord__class_OatLeast(_1498764), _1498768))]]], (38184 ^ _780461) ^ [_1499005, _1499007, _1499009] : [class_Orderings_Oord(_1499005), 38187 ^ _780461 : [(38188 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1499005), _1499007), hAPP(c_SetInterval_Oord__class_OatLeast(_1499005), _1499009))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499005), _1499009), _1499007)))], (38194 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499005), _1499009), _1499007)), -(hBOOL(hAPP(hAPP(c_member(_1499005), _1499007), hAPP(c_SetInterval_Oord__class_OatLeast(_1499005), _1499009))))]]], (38200 ^ _780461) ^ [_1499273, _1499275, _1499277] : [class_Orderings_Oorder(_1499273), 38203 ^ _780461 : [(38204 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1499273, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499273), _1499275)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499273), _1499277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499273), _1499277), _1499275)))], (38210 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499273), _1499277), _1499275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1499273, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499273), _1499275)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499273), _1499277))))]]], (38216 ^ _780461) ^ [_1499565, _1499567] : [class_Orderings_Olinorder(_1499565), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1499565, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1499565), _1499567)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1499565), _1499567))], (38222 ^ _780461) ^ [_1499676, _1499678] : [class_Orderings_Olinorder(_1499676), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1499676, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499676), _1499678)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1499676), _1499678))], (38228 ^ _780461) ^ [_1499787, _1499789, _1499791] : [class_Orderings_Olinorder(_1499787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499787), _1499789), _1499791)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1499787, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1499787, _1499789), _1499791)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499787), _1499791)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1499787), _1499789))], (38238 ^ _780461) ^ [_1499986, _1499988, _1499990] : [class_Orderings_Oorder(_1499986), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499986, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1499986, _1499988), _1499990)), hAPP(c_SetInterval_Oord__class_OatLeast(_1499986), _1499990)) = c_Orderings_Obot__class_Obot(tc_fun(_1499986, tc_HOL_Obool)))], (38244 ^ _780461) ^ [_1500117, _1500119, _1500121, _1500123] : [class_Orderings_Olinorder(_1500117), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500117, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1500117, _1500119, _1500121)), hAPP(c_SetInterval_Oord__class_OatLeast(_1500117), _1500123)) = c_SetInterval_Oord__class_OatLeastAtMost(_1500117, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1500117), _1500119), _1500123), _1500121))], (38250 ^ _780461) ^ [_1500260, _1500262, _1500264, _1500266] : [class_Orderings_Olinorder(_1500260), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500260, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1500260), _1500262)), c_SetInterval_Oord__class_OatLeastAtMost(_1500260, _1500264, _1500266)) = c_SetInterval_Oord__class_OatLeastAtMost(_1500260, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1500260), _1500262), _1500264), _1500266))], (38256 ^ _780461) ^ [_1500403, _1500405, _1500407] : [class_Orderings_Oorder(_1500403), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1500403, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1500403, _1500405, _1500407)), hAPP(c_SetInterval_Oord__class_OatLeast(_1500403), _1500407)) = c_Orderings_Obot__class_Obot(tc_fun(_1500403, tc_HOL_Obool)))], (38262 ^ _780461) ^ [_1500530, _1500532] : [class_Groups_Oordered__ab__group__add(_1500530), -(hAPP(c_Set_Oimage(_1500530, _1500530, c_Groups_Ouminus__class_Ouminus(_1500530)), hAPP(c_SetInterval_Oord__class_OatLeast(_1500530), _1500532)) = hAPP(c_SetInterval_Oord__class_OatMost(_1500530), hAPP(c_Groups_Ouminus__class_Ouminus(_1500530), _1500532)))], (38268 ^ _780461) ^ [_1500653, _1500655] : [class_Groups_Oordered__ab__group__add(_1500653), -(hAPP(c_Set_Oimage(_1500653, _1500653, c_Groups_Ouminus__class_Ouminus(_1500653)), hAPP(c_SetInterval_Oord__class_OatMost(_1500653), _1500655)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1500653), hAPP(c_Groups_Ouminus__class_Ouminus(_1500653), _1500655)))], (38274 ^ _780461) ^ [_1500776] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1500776)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1500776)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1500776), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (38276 ^ _780461) ^ [_1500820, _1500822, _1500824] : [class_Orderings_Olinorder(_1500820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500820), _1500822), _1500824)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500820, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1500820, _1500822, _1500824)), hAPP(c_SetInterval_Oord__class_OatLeast(_1500820), _1500824)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1500820), _1500822))], (38286 ^ _780461) ^ [_1501015, _1501017, _1501019] : [class_Orderings_Olinorder(_1501015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501015), _1501017), _1501019)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501015, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1501015, _1501017, _1501019)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501015), _1501019)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1501015), _1501017))], (38296 ^ _780461) ^ [_1501210, _1501212] : [class_Orderings_Olinorder(_1501210), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501210, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1501210), _1501212), c_Orderings_Obot__class_Obot(tc_fun(_1501210, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501210), _1501212)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1501210), _1501212))], (38302 ^ _780461) ^ [_1501353] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1501353)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1501353))], (38304 ^ _780461) ^ [_1501385, _1501387, _1501389] : [class_Orderings_Olinorder(_1501385), 38307 ^ _780461 : [(38308 ^ _780461) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501385), _1501387) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501385), _1501389), -(_1501387 = _1501389)], (38314 ^ _780461) ^ [] : [_1501387 = _1501389, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501385), _1501387) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501385), _1501389))]]], (38320 ^ _780461) ^ [_1501626, _1501628, _1501630] : [class_Orderings_Oord(_1501626), 38323 ^ _780461 : [(38324 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1501626), _1501628), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501626), _1501630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1501626), _1501630), _1501628)))], (38330 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1501626), _1501630), _1501628)), -(hBOOL(hAPP(hAPP(c_member(_1501626), _1501628), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501626), _1501630))))]]], (38336 ^ _780461) ^ [_1501894, _1501896, _1501898] : [class_Orderings_Olinorder(_1501894), 38339 ^ _780461 : [(38340 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501894, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501894), _1501896)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501894), _1501898))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501894), _1501898), _1501896)))], (38346 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501894), _1501898), _1501896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501894, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501894), _1501896)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1501894), _1501898))))]]], (38352 ^ _780461) ^ [_1502186, _1502188] : [class_Orderings_Olinorder(_1502186), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1502186, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1502186), _1502188)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502186), _1502188))], (38358 ^ _780461) ^ [_1502297, _1502299] : [class_Orderings_Olinorder(_1502297), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1502297, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502297), _1502299)) = hAPP(c_SetInterval_Oord__class_OatMost(_1502297), _1502299))], (38364 ^ _780461) ^ [_1502408, _1502410, _1502412] : [class_Orderings_Oorder(_1502408), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502408, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1502408, _1502410, _1502412)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502408), _1502412)) = c_Orderings_Obot__class_Obot(tc_fun(_1502408, tc_HOL_Obool)))], (38370 ^ _780461) ^ [_1502535, _1502537, _1502539] : [class_Orderings_Olinorder(_1502535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1502535), _1502537), _1502539)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1502535, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1502535, _1502537, _1502539)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502535), _1502539)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502535), _1502537))], (38380 ^ _780461) ^ [_1502730, _1502732] : [class_Groups_Oordered__ab__group__add(_1502730), -(hAPP(c_Set_Oimage(_1502730, _1502730, c_Groups_Ouminus__class_Ouminus(_1502730)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502730), _1502732)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1502730), hAPP(c_Groups_Ouminus__class_Ouminus(_1502730), _1502732)))], (38386 ^ _780461) ^ [_1502853, _1502855] : [class_Groups_Oordered__ab__group__add(_1502853), -(hAPP(c_Set_Oimage(_1502853, _1502853, c_Groups_Ouminus__class_Ouminus(_1502853)), hAPP(c_SetInterval_Oord__class_OlessThan(_1502853), _1502855)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502853), hAPP(c_Groups_Ouminus__class_Ouminus(_1502853), _1502855)))], (38392 ^ _780461) ^ [_1502976, _1502978, _1502980] : [class_Orderings_Oorder(_1502976), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502976, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1502976, _1502978, _1502980)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1502976), _1502980)) = c_Orderings_Obot__class_Obot(tc_fun(_1502976, tc_HOL_Obool)))], (38398 ^ _780461) ^ [_1503103] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1503103)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1503103)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1503103)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (38400 ^ _780461) ^ [_1503150, _1503152, _1503154, _1503156, _1503158, _1503160] : [class_Groups_Ocomm__monoid__add(_1503150), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503152), _1503154)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503156), _1503158)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(_1503152, _1503156), _1503150), _1503160), c_Sum__Type_OPlus(_1503152, _1503156, _1503154, _1503158)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1503150), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503152, _1503150), hAPP(c_Fun_Ocomp(tc_sum(_1503152, _1503156), _1503150, _1503152, _1503160), c_Sum__Type_OInl(_1503152, _1503156))), _1503154)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503156, _1503150), hAPP(c_Fun_Ocomp(tc_sum(_1503152, _1503156), _1503150, _1503156, _1503160), c_Sum__Type_OInr(_1503156, _1503152))), _1503158)))], (38414 ^ _780461) ^ [_1503511, _1503513, _1503515, _1503517, _1503519] : [class_Groups_Ocomm__monoid__add(_1503511), class_Groups_Ocomm__monoid__mult(_1503511), _1503513 = _1503515, c_Nat__Transfer_Onat__set(_1503515), 38432 ^ _780461 : [(38433 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 38431 ^ [_1503511, _1503513, _1503515, _1503517, _1503519])))], (38435 ^ _780461) ^ [] : [hAPP(_1503517, 38431 ^ [_1503511, _1503513, _1503515, _1503517, _1503519]) = hAPP(_1503519, 38431 ^ [_1503511, _1503513, _1503515, _1503517, _1503519])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1503511), _1503517), _1503513) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1503511), _1503519), _1503515))], (38439 ^ _780461) ^ [_1503995, _1503997, _1503999, _1504001] : [c_Map_Odom(_1503995, _1503997, _1503999) = hAPP(hAPP(c_Set_Oinsert(_1503995), _1504001), c_Orderings_Obot__class_Obot(tc_fun(_1503995, tc_HOL_Obool))), -(_1503999 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1503995, tc_Option_Ooption(_1503997)), hAPP(c_COMBK(tc_Option_Ooption(_1503997), _1503995), c_Option_Ooption_ONone(_1503997))), _1504001), hAPP(c_Option_Ooption_OSome(_1503997), 38442 ^ [_1503995, _1503997, _1503999, _1504001])))], (38446 ^ _780461) ^ [_1504180, _1504182, _1504184, _1504186] : [38447 ^ _780461 : [(38448 ^ _780461) ^ [_1504269] : [_1504184 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1504180, tc_Option_Ooption(_1504182)), hAPP(c_COMBK(tc_Option_Ooption(_1504182), _1504180), c_Option_Ooption_ONone(_1504182))), _1504186), hAPP(c_Option_Ooption_OSome(_1504182), _1504269))]], -(c_Map_Odom(_1504180, _1504182, _1504184) = hAPP(hAPP(c_Set_Oinsert(_1504180), _1504186), c_Orderings_Obot__class_Obot(tc_fun(_1504180, tc_HOL_Obool))))], (38452 ^ _780461) ^ [_1504368, _1504370, _1504372, _1504374, _1504376, _1504378] : [c_Fun_Oinj__on(_1504368, _1504370, hAPP(c_Fun_Ocomp(_1504372, _1504370, _1504368, _1504374), _1504376), _1504378), -(c_Fun_Oinj__on(_1504372, _1504370, _1504374, hAPP(c_Set_Oimage(_1504368, _1504372, _1504376), _1504378)))], (38458 ^ _780461) ^ [_1504491, _1504493, _1504495, _1504497, _1504499, _1504501] : [c_Fun_Oinj__on(_1504491, _1504493, _1504495, _1504497), c_Fun_Oinj__on(_1504493, _1504499, _1504501, hAPP(c_Set_Oimage(_1504491, _1504493, _1504495), _1504497)), -(c_Fun_Oinj__on(_1504491, _1504499, hAPP(c_Fun_Ocomp(_1504493, _1504499, _1504491, _1504501), _1504495), _1504497))], (38468 ^ _780461) ^ [_1504678, _1504680, _1504682, _1504684, _1504686, _1504688] : [c_Fun_Oinj__on(_1504678, _1504680, _1504682, _1504684), 38471 ^ _780461 : [(38472 ^ _780461) ^ [] : [c_Fun_Oinj__on(_1504680, _1504686, _1504688, hAPP(c_Set_Oimage(_1504678, _1504680, _1504682), _1504684)), -(c_Fun_Oinj__on(_1504678, _1504686, hAPP(c_Fun_Ocomp(_1504680, _1504686, _1504678, _1504688), _1504682), _1504684))], (38478 ^ _780461) ^ [] : [c_Fun_Oinj__on(_1504678, _1504686, hAPP(c_Fun_Ocomp(_1504680, _1504686, _1504678, _1504688), _1504682), _1504684), -(c_Fun_Oinj__on(_1504680, _1504686, _1504688, hAPP(c_Set_Oimage(_1504678, _1504680, _1504682), _1504684)))]]], (38484 ^ _780461) ^ [_1504970, _1504972, _1504974, _1504976, _1504978, _1504980, _1504982, _1504984] : [hAPP(c_Fun_Ocomp(_1504970, _1504972, _1504974, _1504976), _1504978) = hAPP(c_Fun_Ocomp(_1504980, _1504972, _1504974, _1504982), _1504984), 38487 ^ _780461 : [(38488 ^ _780461) ^ [_1505085] : [-(hAPP(_1504976, hAPP(_1504978, _1505085)) = hAPP(_1504982, hAPP(_1504984, _1505085)))]]], (38490 ^ _780461) ^ [_1505124, _1505126, _1505128, _1505130, _1505132, _1505134, _1505136, _1505138, _1505140] : [hAPP(c_Fun_Ocomp(_1505124, _1505126, _1505128, _1505130), _1505132) = hAPP(c_Fun_Ocomp(_1505134, _1505126, _1505128, _1505136), _1505138), -(hAPP(_1505130, hAPP(_1505132, _1505140)) = hAPP(_1505136, hAPP(_1505138, _1505140)))], (38496 ^ _780461) ^ [_1505271, _1505273, _1505275, _1505277, _1505279, _1505281] : [-(hAPP(hAPP(c_Fun_Ocomp(_1505271, _1505273, _1505275, _1505277), _1505279), _1505281) = hAPP(_1505277, hAPP(_1505279, _1505281)))], (38498 ^ _780461) ^ [_1505321, _1505323, _1505325, _1505327, _1505329, _1505331, _1505333] : [-(hAPP(c_Fun_Ocomp(_1505321, _1505323, _1505325, _1505327), hAPP(c_Fun_Ocomp(_1505329, _1505321, _1505325, _1505331), _1505333)) = hAPP(c_Fun_Ocomp(_1505329, _1505323, _1505325, hAPP(c_Fun_Ocomp(_1505321, _1505323, _1505329, _1505327), _1505331)), _1505333))], (38500 ^ _780461) ^ [_1505388, _1505390, _1505392, _1505394, _1505396, _1505398] : [-(hAPP(hAPP(c_Fun_Ocomp(_1505388, _1505390, _1505392, _1505394), _1505396), _1505398) = hAPP(_1505394, hAPP(_1505396, _1505398)))], (38502 ^ _780461) ^ [_1505438, _1505440, _1505442, _1505444, _1505446, _1505448, _1505450, _1505452, _1505454, _1505456, _1505458] : [hAPP(_1505438, hAPP(_1505440, _1505442)) = hAPP(_1505444, hAPP(_1505446, _1505448)), -(hAPP(hAPP(c_Fun_Ocomp(_1505450, _1505452, _1505454, _1505438), _1505440), _1505442) = hAPP(hAPP(c_Fun_Ocomp(_1505456, _1505452, _1505458, _1505444), _1505446), _1505448))], (38508 ^ _780461) ^ [_1505601, _1505603, _1505605, _1505607, _1505609, _1505611, _1505613] : [-(hAPP(c_Product__Type_Oapsnd(_1505601, _1505603, _1505605, _1505607), hAPP(c_Product__Type_Oapsnd(_1505609, _1505601, _1505605, _1505611), _1505613)) = hAPP(c_Product__Type_Oapsnd(_1505609, _1505603, _1505605, hAPP(c_Fun_Ocomp(_1505601, _1505603, _1505609, _1505607), _1505611)), _1505613))], (38510 ^ _780461) ^ [_1505668, _1505670, _1505672, _1505674, _1505676, _1505678, _1505680] : [-(hAPP(c_Product__Type_Oapfst(_1505668, _1505670, _1505672, _1505674), hAPP(c_Product__Type_Oapfst(_1505676, _1505668, _1505672, _1505678), _1505680)) = hAPP(c_Product__Type_Oapfst(_1505676, _1505670, _1505672, hAPP(c_Fun_Ocomp(_1505668, _1505670, _1505676, _1505674), _1505678)), _1505680))], (38512 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (38514 ^ _780461) ^ [_1505753, _1505755, _1505757, _1505759, _1505761, _1505763] : [c_Fun_Oinj__on(_1505753, _1505755, hAPP(c_Fun_Ocomp(_1505757, _1505755, _1505753, _1505759), _1505761), _1505763), -(c_Fun_Oinj__on(_1505753, _1505757, _1505761, _1505763))], (38520 ^ _780461) ^ [_1505862, _1505864, _1505866, _1505868, _1505870, _1505872, _1505874] : [-(hAPP(c_Fun_Ocomp(_1505862, _1505864, _1505866, _1505868), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1505866, _1505862), _1505870), _1505872), _1505874)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1505866, _1505864), hAPP(c_Fun_Ocomp(_1505862, _1505864, _1505866, _1505868), _1505870)), _1505872), hAPP(_1505868, _1505874)))], (38522 ^ _780461) ^ [_1505940, _1505942, _1505944, _1505946, _1505948, _1505950] : [-(hAPP(c_Set_Oimage(_1505940, _1505942, hAPP(c_Fun_Ocomp(_1505944, _1505942, _1505940, _1505946), _1505948)), _1505950) = hAPP(c_Set_Oimage(_1505944, _1505942, _1505946), hAPP(c_Set_Oimage(_1505940, _1505944, _1505948), _1505950)))], (38524 ^ _780461) ^ [_1506023, _1506025, _1506027, _1506029] : [hBOOL(hAPP(hAPP(c_member(_1506023), _1506025), c_Map_Odom(_1506023, _1506027, _1506029))), hAPP(_1506029, _1506025) = c_Option_Ooption_ONone(_1506027)], (38530 ^ _780461) ^ [_1506131, _1506133, _1506135, _1506137] : [-(hAPP(_1506137, _1506133) = c_Option_Ooption_ONone(_1506135)), -(hBOOL(hAPP(hAPP(c_member(_1506131), _1506133), c_Map_Odom(_1506131, _1506135, _1506137))))], (38536 ^ _780461) ^ [_1506189, _1506191, _1506193, _1506195, _1506197] : [hAPP(_1506189, _1506191) = hAPP(c_Option_Ooption_OSome(_1506193), _1506195), -(hBOOL(hAPP(hAPP(c_member(_1506197), _1506191), c_Map_Odom(_1506197, _1506193, _1506189))))], (38542 ^ _780461) ^ [_1506310, _1506312, _1506314, _1506316, _1506318] : [hAPP(_1506310, _1506312) = hAPP(c_Option_Ooption_OSome(_1506314), _1506316), -(hAPP(hAPP(c_Set_Oinsert(_1506318), _1506312), c_Map_Odom(_1506318, _1506314, _1506310)) = c_Map_Odom(_1506318, _1506314, _1506310))], (38548 ^ _780461) ^ [_1506441, _1506443, _1506445, _1506447] : [-(c_Map_Odom(_1506441, _1506443, c_Map_Orestrict__map(_1506441, _1506443, _1506445, _1506447)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506441, tc_HOL_Obool)), c_Map_Odom(_1506441, _1506443, _1506445)), _1506447))], (38550 ^ _780461) ^ [_1506512, _1506514, _1506516] : [c_Map_Odom(_1506512, _1506514, _1506516) = c_Orderings_Obot__class_Obot(tc_fun(_1506512, tc_HOL_Obool)), -(_1506516 = hAPP(c_COMBK(tc_Option_Ooption(_1506514), _1506512), c_Option_Ooption_ONone(_1506514)))], (38556 ^ _780461) ^ [_1506625, _1506627, _1506629] : [_1506629 = hAPP(c_COMBK(tc_Option_Ooption(_1506627), _1506625), c_Option_Ooption_ONone(_1506627)), -(c_Map_Odom(_1506625, _1506627, _1506629) = c_Orderings_Obot__class_Obot(tc_fun(_1506625, tc_HOL_Obool)))], (38562 ^ _780461) ^ [_1506744, _1506746] : [-(c_Map_Odom(_1506744, _1506746, hAPP(c_COMBK(tc_Option_Ooption(_1506746), _1506744), c_Option_Ooption_ONone(_1506746))) = c_Orderings_Obot__class_Obot(tc_fun(_1506744, tc_HOL_Obool)))], (38564 ^ _780461) ^ [_1506788, _1506790, _1506792, _1506794, _1506796, _1506798] : [class_Groups_Ocomm__monoid__add(_1506788), c_Fun_Oinj__on(_1506790, _1506792, _1506794, _1506796), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1506792, _1506788), _1506798), hAPP(c_Set_Oimage(_1506790, _1506792, _1506794), _1506796)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1506790, _1506788), hAPP(c_Fun_Ocomp(_1506792, _1506788, _1506790, _1506798), _1506794)), _1506796))], (38574 ^ _780461) ^ [_1507001, _1507003, _1507005, _1507007, _1507009, _1507011, _1507013, _1507015] : [class_Groups_Ocomm__monoid__mult(_1507001), c_Fun_Oinj__on(_1507003, _1507005, _1507007, _1507009), _1507011 = hAPP(c_Set_Oimage(_1507003, _1507005, _1507007), _1507009), _1507013 = hAPP(c_Fun_Ocomp(_1507005, _1507001, _1507003, _1507015), _1507007), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507005, _1507001), _1507015), _1507011) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507003, _1507001), _1507013), _1507009))], (38592 ^ _780461) ^ [_1507350, _1507352, _1507354, _1507356, _1507358, _1507360] : [class_Groups_Ocomm__monoid__mult(_1507350), c_Fun_Oinj__on(_1507352, _1507354, _1507356, _1507358), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507354, _1507350), _1507360), hAPP(c_Set_Oimage(_1507352, _1507354, _1507356), _1507358)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507352, _1507350), hAPP(c_Fun_Ocomp(_1507354, _1507350, _1507352, _1507360), _1507356)), _1507358))], (38602 ^ _780461) ^ [_1507563, _1507565, _1507567, _1507569, _1507571] : [hAPP(_1507563, _1507565) = c_Option_Ooption_ONone(_1507567), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1507569, tc_HOL_Obool)), c_Map_Odom(_1507569, _1507567, _1507563)), hAPP(hAPP(c_Set_Oinsert(_1507569), _1507565), _1507571)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1507569, tc_HOL_Obool)), c_Map_Odom(_1507569, _1507567, _1507563)), _1507571))], (38608 ^ _780461) ^ [_1507732, _1507734, _1507736, _1507738, _1507740] : [class_Groups_Ocomm__monoid__add(_1507732), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507734), _1507736)), c_Fun_Oinj__on(_1507734, _1507734, _1507738, _1507736), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1507734, _1507732), _1507740), hAPP(c_Set_Oimage(_1507734, _1507734, _1507738), _1507736)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1507734, _1507732), hAPP(c_Fun_Ocomp(_1507734, _1507732, _1507734, _1507740), _1507738)), _1507736))], (38622 ^ _780461) ^ [_1508007, _1508009, _1508011, _1508013, _1508015] : [class_Groups_Ocomm__monoid__mult(_1508007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508009), _1508011)), c_Fun_Oinj__on(_1508009, _1508009, _1508013, _1508011), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1508009, _1508007), _1508015), hAPP(c_Set_Oimage(_1508009, _1508009, _1508013), _1508011)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1508009, _1508007), hAPP(c_Fun_Ocomp(_1508009, _1508007, _1508009, _1508015), _1508013)), _1508011))], (38636 ^ _780461) ^ [_1508282, _1508284, _1508286, _1508288, _1508290, _1508292, _1508294] : [c_Fun_Oinj__on(_1508282, _1508284, _1508286, hAPP(c_Set_Oimage(_1508288, _1508282, _1508290), _1508292)), c_Fun_Oinj__on(_1508288, _1508282, _1508290, _1508292), hBOOL(hAPP(hAPP(c_member(_1508284), _1508294), hAPP(c_Set_Oimage(_1508282, _1508284, _1508286), hAPP(c_Set_Oimage(_1508288, _1508282, _1508290), _1508292)))), -(hAPP(c_Fun_Othe__inv__into(_1508288, _1508284, _1508292, hAPP(c_Fun_Ocomp(_1508282, _1508284, _1508288, _1508286), _1508290)), _1508294) = hAPP(hAPP(c_Fun_Ocomp(_1508282, _1508288, _1508284, c_Fun_Othe__inv__into(_1508288, _1508282, _1508292, _1508290)), c_Fun_Othe__inv__into(_1508282, _1508284, hAPP(c_Set_Oimage(_1508288, _1508282, _1508290), _1508292), _1508286)), _1508294))], (38650 ^ _780461) ^ [_1508645, _1508647, _1508649, _1508651, _1508653, _1508655, _1508657] : [class_Groups_Oab__semigroup__mult(_1508645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508647), _1508649)), c_Fun_Oinj__on(_1508647, _1508651, _1508653, _1508649), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1508645, _1508651, c_Groups_Otimes__class_Otimes(_1508645)), _1508655), _1508657), hAPP(c_Set_Oimage(_1508647, _1508651, _1508653), _1508649)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1508645, _1508647, c_Groups_Otimes__class_Otimes(_1508645)), hAPP(c_Fun_Ocomp(_1508651, _1508645, _1508647, _1508655), _1508653)), _1508657), _1508649))], (38664 ^ _780461) ^ [_1508974, _1508976, _1508978, _1508980, _1508982] : [_1508974 = c_Option_Ooption_ONone(_1508976), -(c_Map_Odom(_1508978, _1508976, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1508978, tc_Option_Ooption(_1508976)), _1508980), _1508982), _1508974)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1508978, tc_HOL_Obool)), c_Map_Odom(_1508978, _1508976, _1508980)), hAPP(hAPP(c_Set_Oinsert(_1508978), _1508982), c_Orderings_Obot__class_Obot(tc_fun(_1508978, tc_HOL_Obool)))))], (38670 ^ _780461) ^ [_1509147, _1509149, _1509151, _1509153, _1509155] : [-(_1509147 = c_Option_Ooption_ONone(_1509149)), -(c_Map_Odom(_1509151, _1509149, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1509151, tc_Option_Ooption(_1509149)), _1509153), _1509155), _1509147)) = hAPP(hAPP(c_Set_Oinsert(_1509151), _1509155), c_Map_Odom(_1509151, _1509149, _1509153)))], (38676 ^ _780461) ^ [_1509223, _1509225, _1509227, _1509229, _1509231, _1509233] : [c_Finite__Set_Ofolding(_1509223, _1509225, _1509227, _1509229), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509223), _1509231)), hBOOL(hAPP(hAPP(c_member(_1509223), _1509233), _1509231)), -(hAPP(_1509229, _1509231) = hAPP(c_Fun_Ocomp(_1509225, _1509225, _1509225, hAPP(_1509229, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1509223, tc_HOL_Obool)), _1509231), hAPP(hAPP(c_Set_Oinsert(_1509223), _1509233), c_Orderings_Obot__class_Obot(tc_fun(_1509223, tc_HOL_Obool)))))), hAPP(_1509227, _1509233)))], (38690 ^ _780461) ^ [_1509536, _1509538, _1509540, _1509542, _1509544, _1509546, _1509548, _1509550] : [c_Finite__Set_Ofolding__image(_1509536, _1509538, _1509540, _1509542, _1509544), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509538), _1509546)), c_Fun_Oinj__on(_1509538, _1509538, _1509548, _1509546), -(hAPP(hAPP(_1509544, _1509550), hAPP(c_Set_Oimage(_1509538, _1509538, _1509548), _1509546)) = hAPP(hAPP(_1509544, hAPP(c_Fun_Ocomp(_1509538, _1509536, _1509538, _1509550), _1509548)), _1509546))], (38704 ^ _780461) ^ [_1509825, _1509827, _1509829, _1509831, _1509833, _1509835] : [c_Finite__Set_Ofolding(_1509825, _1509827, _1509829, _1509831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509825), _1509833)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509825), _1509835)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509825, tc_HOL_Obool)), _1509833), _1509835) = c_Orderings_Obot__class_Obot(tc_fun(_1509825, tc_HOL_Obool)), -(hAPP(_1509831, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509825, tc_HOL_Obool)), _1509833), _1509835)) = hAPP(c_Fun_Ocomp(_1509827, _1509827, _1509827, hAPP(_1509831, _1509833)), hAPP(_1509831, _1509835)))], (38722 ^ _780461) ^ [_1510198, _1510200, _1510202, _1510204, _1510206, _1510208] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510198, tc_fun(_1510200, tc_HOL_Obool)), _1510202), hAPP(c_Fun_Ocomp(_1510204, tc_fun(_1510200, tc_HOL_Obool), _1510198, _1510206), _1510208)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510204, tc_fun(_1510200, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510198, _1510204, _1510208), _1510202)), _1510206))], (38724 ^ _780461) ^ [_1510273, _1510275, _1510277, _1510279, _1510281, _1510283, _1510285, _1510287] : [c_Finite__Set_Ofolding(_1510273, _1510275, _1510277, _1510279), -(hAPP(c_Fun_Ocomp(_1510275, _1510275, _1510281, hAPP(_1510277, _1510283)), hAPP(c_Fun_Ocomp(_1510275, _1510275, _1510281, hAPP(_1510277, _1510285)), _1510287)) = hAPP(c_Fun_Ocomp(_1510275, _1510275, _1510281, hAPP(_1510277, _1510285)), hAPP(c_Fun_Ocomp(_1510275, _1510275, _1510281, hAPP(_1510277, _1510283)), _1510287)))], (38730 ^ _780461) ^ [_1510454, _1510456, _1510458, _1510460, _1510462, _1510464] : [c_Finite__Set_Ofolding(_1510454, _1510456, _1510458, _1510460), -(hAPP(c_Fun_Ocomp(_1510456, _1510456, _1510456, hAPP(_1510458, _1510462)), hAPP(_1510458, _1510464)) = hAPP(c_Fun_Ocomp(_1510456, _1510456, _1510456, hAPP(_1510458, _1510464)), hAPP(_1510458, _1510462)))], (38736 ^ _780461) ^ [_1510599, _1510601, _1510603, _1510605, _1510607, _1510609, _1510611, _1510613, _1510615, _1510617, _1510619] : [c_Finite__Set_Ofolding(_1510599, _1510601, _1510603, _1510605), -(hAPP(c_Fun_Ocomp(_1510607, _1510609, _1510611, _1510613), hAPP(c_Fun_Ocomp(_1510615, _1510607, _1510611, _1510617), _1510619)) = hAPP(c_Fun_Ocomp(_1510615, _1510609, _1510611, hAPP(c_Fun_Ocomp(_1510607, _1510609, _1510615, _1510613), _1510617)), _1510619))], (38742 ^ _780461) ^ [_1510762, _1510764, _1510766, _1510768, _1510770, _1510772, _1510774, _1510776] : [c_Finite__Set_Ofolding__image(_1510762, _1510764, _1510766, _1510768, _1510770), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510764), _1510772)), -(hAPP(hAPP(_1510770, hAPP(hAPP(c_COMBS(_1510764, _1510762, _1510762), hAPP(hAPP(c_COMBB(_1510762, tc_fun(_1510762, _1510762), _1510764), _1510766), _1510774)), _1510776)), _1510772) = hAPP(hAPP(_1510766, hAPP(hAPP(_1510770, _1510774), _1510772)), hAPP(hAPP(_1510770, _1510776), _1510772)))], (38752 ^ _780461) ^ [_1511023, _1511025, _1511027, _1511029, _1511031, _1511033, _1511035] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1511023, _1511025, _1511027), hAPP(c_Fun_Ocomp(_1511029, tc_fun(_1511025, _1511027), _1511023, _1511031), _1511033)), _1511035) = hAPP(hAPP(_1511031, hAPP(_1511033, hAPP(c_Product__Type_Ofst(_1511023, _1511025), _1511035))), hAPP(c_Product__Type_Osnd(_1511023, _1511025), _1511035)))], (38754 ^ _780461) ^ [_1511100, _1511102, _1511104, _1511106, _1511108, _1511110] : [c_Finite__Set_Ofolding(_1511100, _1511102, _1511104, _1511106), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511100), _1511108)), -(hAPP(c_Fun_Ocomp(_1511102, _1511102, _1511102, hAPP(_1511104, _1511110)), hAPP(_1511106, _1511108)) = hAPP(c_Fun_Ocomp(_1511102, _1511102, _1511102, hAPP(_1511106, _1511108)), hAPP(_1511104, _1511110)))], (38764 ^ _780461) ^ [_1511313, _1511315, _1511317, _1511319, _1511321, _1511323, _1511325, _1511327] : [c_Finite__Set_Ofolding(_1511313, _1511315, _1511317, _1511319), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511313), _1511321)), -(hAPP(c_Fun_Ocomp(_1511315, _1511315, _1511323, hAPP(_1511317, _1511325)), hAPP(c_Fun_Ocomp(_1511315, _1511315, _1511323, hAPP(_1511319, _1511321)), _1511327)) = hAPP(c_Fun_Ocomp(_1511315, _1511315, _1511323, hAPP(_1511319, _1511321)), hAPP(c_Fun_Ocomp(_1511315, _1511315, _1511323, hAPP(_1511317, _1511325)), _1511327)))], (38774 ^ _780461) ^ [_1511566, _1511568, _1511570, _1511572, _1511574, _1511576] : [c_Finite__Set_Ofolding(_1511566, _1511568, _1511570, _1511572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511566), _1511574)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511566), _1511576)), -(hAPP(c_Fun_Ocomp(_1511568, _1511568, _1511568, hAPP(_1511572, _1511576)), hAPP(_1511572, _1511574)) = hAPP(c_Fun_Ocomp(_1511568, _1511568, _1511568, hAPP(_1511572, _1511574)), hAPP(_1511572, _1511576)))], (38788 ^ _780461) ^ [_1511847, _1511849, _1511851, _1511853, _1511855, _1511857, _1511859, _1511861] : [c_Finite__Set_Ofolding(_1511847, _1511849, _1511851, _1511853), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511847), _1511855)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511847), _1511857)), -(hAPP(c_Fun_Ocomp(_1511849, _1511849, _1511859, hAPP(_1511853, _1511857)), hAPP(c_Fun_Ocomp(_1511849, _1511849, _1511859, hAPP(_1511853, _1511855)), _1511861)) = hAPP(c_Fun_Ocomp(_1511849, _1511849, _1511859, hAPP(_1511853, _1511855)), hAPP(c_Fun_Ocomp(_1511849, _1511849, _1511859, hAPP(_1511853, _1511857)), _1511861)))], (38802 ^ _780461) ^ [] : [-(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))], (38804 ^ _780461) ^ [] : [-(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))], (38806 ^ _780461) ^ [_1512208, _1512210, _1512212, _1512214, _1512216, _1512218, _1512220] : [c_Finite__Set_Ofolding__image(_1512208, _1512210, _1512212, _1512214, _1512216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512210), _1512218)), -(hAPP(hAPP(_1512216, _1512220), _1512218) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1512208, _1512210, _1512212), _1512220), _1512214), _1512218))], (38816 ^ _780461) ^ [_1512409, _1512411, _1512413, _1512415, _1512417, _1512419] : [c_Finite__Set_Ofolding(_1512409, _1512411, _1512413, _1512415), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512409), _1512417)), -(hBOOL(hAPP(hAPP(c_member(_1512409), _1512419), _1512417))), -(hAPP(_1512415, hAPP(hAPP(c_Set_Oinsert(_1512409), _1512419), _1512417)) = hAPP(c_Fun_Ocomp(_1512411, _1512411, _1512411, hAPP(_1512415, _1512417)), hAPP(_1512413, _1512419)))], (38830 ^ _780461) ^ [_1512645, _1512647, _1512649, _1512651, _1512653, _1512655] : [c_Finite__Set_Ofolding(_1512645, _1512647, _1512649, _1512651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512645), _1512653)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512645), _1512655)), -(hAPP(c_Fun_Ocomp(_1512647, _1512647, _1512647, hAPP(_1512651, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512645, tc_HOL_Obool)), _1512653), _1512655))), hAPP(_1512651, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1512645, tc_HOL_Obool)), _1512653), _1512655))) = hAPP(c_Fun_Ocomp(_1512647, _1512647, _1512647, hAPP(_1512651, _1512653)), hAPP(_1512651, _1512655)))], (38844 ^ _780461) ^ [_1512970, _1512972, _1512974, _1512976, _1512978, _1512980] : [c_Finite__Set_Ofolding(_1512970, _1512972, _1512974, _1512976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512970), _1512978)), -(hAPP(_1512976, hAPP(hAPP(c_Set_Oinsert(_1512970), _1512980), _1512978)) = hAPP(c_Fun_Ocomp(_1512972, _1512972, _1512972, hAPP(_1512976, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1512970, tc_HOL_Obool)), _1512978), hAPP(hAPP(c_Set_Oinsert(_1512970), _1512980), c_Orderings_Obot__class_Obot(tc_fun(_1512970, tc_HOL_Obool)))))), hAPP(_1512974, _1512980)))], (38854 ^ _780461) ^ [_1513225, _1513227, _1513229, _1513231, _1513233] : [c_Hoare__Mirabelle_Ohoare__valids(_1513225, _1513227, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1513225)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1513225), c_Hoare__Mirabelle_Opeek__and(_1513225, _1513229, _1513231)), _1513233), _1513229)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1513225), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1513225, _1513227, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1513225)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1513225), _1513229), c_Com_Ocom_OWhile(_1513231, _1513233)), c_Hoare__Mirabelle_Opeek__and(_1513225, _1513229, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1513231)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1513225), tc_HOL_Obool)))))], (38860 ^ _780461) ^ [_1513452] : [-(c_Nitpick_Onum(_1513452) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1513452, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1513452)))], (38862 ^ _780461) ^ [_1513487] : [-(c_Nitpick_Odenom(_1513487) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1513487, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1513487)))], (38864 ^ _780461) ^ [_1513546, _1513548, _1513550, _1513552, _1513554] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1513546, _1513548, _1513550), _1513552), _1513554)), 38867 ^ _780461 : [(38868 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1513548, _1513552), _1513554)))], (38870 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1513550, _1513554)))]]], (38872 ^ _780461) ^ [_1513683, _1513685, _1513687, _1513689, _1513691] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1513683, _1513685, _1513687), _1513689), _1513691))), hBOOL(hAPP(hAPP(_1513685, _1513689), _1513691)), hBOOL(hAPP(_1513687, _1513691))], (38882 ^ _780461) ^ [_1513858, _1513860, _1513862, _1513864, _1513866] : [c_Hoare__Mirabelle_Ohoare__derivs(_1513858, _1513860, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1513858)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1513858), c_Hoare__Mirabelle_Opeek__and(_1513858, _1513862, _1513864)), _1513866), _1513862)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1513858), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1513858, _1513860, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1513858)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1513858), _1513862), c_Com_Ocom_OWhile(_1513864, _1513866)), c_Hoare__Mirabelle_Opeek__and(_1513858, _1513862, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1513864)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1513858), tc_HOL_Obool)))))], (38888 ^ _780461) ^ [_1514085, _1514087, _1514089, _1514091, _1514093, _1514095, _1514097] : [c_Hoare__Mirabelle_Ohoare__derivs(_1514085, _1514087, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1514085)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1514085), c_Hoare__Mirabelle_Opeek__and(_1514085, _1514089, _1514091)), _1514093), _1514095)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1514085), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1514085, _1514087, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1514085)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1514085), c_Hoare__Mirabelle_Opeek__and(_1514085, _1514089, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1514091))), _1514097), _1514095)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1514085), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1514085, _1514087, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1514085)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1514085), _1514089), c_Com_Ocom_OCond(_1514091, _1514093, _1514097)), _1514095)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1514085), tc_HOL_Obool)))))], (38898 ^ _780461) ^ [_1514438, _1514440, _1514442, _1514444, _1514446, _1514448] : [class_Groups_Ocomm__monoid__add(_1514438), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514440), _1514442)), 38908 ^ _780461 : [(38909 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514440), 38907 ^ [_1514438, _1514440, _1514442, _1514444, _1514446, _1514448]), _1514442)))], (38912 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514440), 38910 ^ [_1514438, _1514440, _1514442, _1514444, _1514446, _1514448]), _1514442)))], (38914 ^ _780461) ^ [] : [38907 ^ [_1514438, _1514440, _1514442, _1514444, _1514446, _1514448] = 38910 ^ [_1514438, _1514440, _1514442, _1514444, _1514446, _1514448]], (38916 ^ _780461) ^ [] : [-(hAPP(_1514444, 38907 ^ [_1514438, _1514440, _1514442, _1514444, _1514446, _1514448]) = hAPP(_1514444, 38910 ^ [_1514438, _1514440, _1514442, _1514444, _1514446, _1514448]))], (38918 ^ _780461) ^ [] : [hAPP(_1514446, hAPP(_1514444, 38907 ^ [_1514438, _1514440, _1514442, _1514444, _1514446, _1514448])) = c_Groups_Ozero__class_Ozero(_1514438)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514448, _1514438), _1514446), hAPP(c_Set_Oimage(_1514440, _1514448, _1514444), _1514442)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514440, _1514438), hAPP(c_Fun_Ocomp(_1514448, _1514438, _1514440, _1514446), _1514444)), _1514442))], (38922 ^ _780461) ^ [_1515175, _1515177, _1515179, _1515181] : [-(c_Random__Sequence_Omap(_1515175, _1515177, _1515179, _1515181) = c_Random__Sequence_Obind(_1515175, _1515177, _1515181, hAPP(c_Fun_Ocomp(_1515177, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1515177)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1515175, c_Random__Sequence_Osingle(_1515177)), _1515179)))], (38924 ^ _780461) ^ [_1515246, _1515248, _1515250, _1515252, _1515254, _1515256] : [c_Finite__Set_Ofolding__idem(_1515246, _1515248, _1515250, _1515252), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515246), _1515254)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515246), _1515256)), -(hAPP(_1515252, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1515246, tc_HOL_Obool)), _1515254), _1515256)) = hAPP(c_Fun_Ocomp(_1515248, _1515248, _1515248, hAPP(_1515252, _1515254)), hAPP(_1515252, _1515256)))], (38938 ^ _780461) ^ [_1515527, _1515529, _1515531, _1515533, _1515535] : [c_Finite__Set_Ofolding__idem(_1515527, _1515529, _1515531, _1515533), -(hAPP(c_Fun_Ocomp(_1515529, _1515529, _1515529, hAPP(_1515531, _1515535)), hAPP(_1515531, _1515535)) = hAPP(_1515531, _1515535))], (38944 ^ _780461) ^ [_1515648, _1515650, _1515652, _1515654, _1515656, _1515658, _1515660] : [c_Finite__Set_Ofolding__idem(_1515648, _1515650, _1515652, _1515654), -(hAPP(c_Fun_Ocomp(_1515650, _1515650, _1515656, hAPP(_1515652, _1515658)), hAPP(c_Fun_Ocomp(_1515650, _1515650, _1515656, hAPP(_1515652, _1515658)), _1515660)) = hAPP(c_Fun_Ocomp(_1515650, _1515650, _1515656, hAPP(_1515652, _1515658)), _1515660))], (38950 ^ _780461) ^ [_1515805, _1515807, _1515809, _1515811, _1515813, _1515815] : [c_Finite__Set_Ofolding__idem(_1515805, _1515807, _1515809, _1515811), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515805), _1515813)), hBOOL(hAPP(hAPP(c_member(_1515805), _1515815), _1515813)), -(hAPP(c_Fun_Ocomp(_1515807, _1515807, _1515807, hAPP(_1515811, _1515813)), hAPP(_1515809, _1515815)) = hAPP(_1515811, _1515813))], (38964 ^ _780461) ^ [_1516070, _1516072, _1516074, _1516076, _1516078, _1516080] : [c_Finite__Set_Ofolding__idem(_1516070, _1516072, _1516074, _1516076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516070), _1516078)), -(hAPP(_1516076, hAPP(hAPP(c_Set_Oinsert(_1516070), _1516080), _1516078)) = hAPP(c_Fun_Ocomp(_1516072, _1516072, _1516072, hAPP(_1516076, _1516078)), hAPP(_1516074, _1516080)))], (38974 ^ _780461) ^ [_1516277, _1516279, _1516281, _1516283, _1516285, _1516287] : [c_Finite__Set_Ofolding__idem(_1516277, _1516279, _1516281, _1516283), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516277), _1516285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1516277, tc_HOL_Obool)), _1516287), _1516285)), -(hAPP(c_Fun_Ocomp(_1516279, _1516279, _1516279, hAPP(_1516283, _1516285)), hAPP(_1516283, _1516287)) = hAPP(_1516283, _1516285))], (38988 ^ _780461) ^ [_1516548, _1516550, _1516552, _1516554, _1516556, _1516558, _1516560, _1516562] : [class_Groups_Ocomm__monoid__mult(_1516548), c_Fun_Oinj__on(_1516550, _1516552, _1516554, _1516556), _1516558 = hAPP(c_Set_Oimage(_1516550, _1516552, _1516554), _1516556), 39002 ^ _780461 : [(39003 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516550), 39001 ^ [_1516548, _1516550, _1516552, _1516554, _1516556, _1516558, _1516560, _1516562]), _1516556)))], (39005 ^ _780461) ^ [] : [hAPP(_1516560, 39001 ^ [_1516548, _1516550, _1516552, _1516554, _1516556, _1516558, _1516560, _1516562]) = hAPP(hAPP(c_Fun_Ocomp(_1516552, _1516548, _1516550, _1516562), _1516554), 39001 ^ [_1516548, _1516550, _1516552, _1516554, _1516556, _1516558, _1516560, _1516562])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1516552, _1516548), _1516562), _1516558) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1516550, _1516548), _1516560), _1516556))], (39009 ^ _780461) ^ [_1517056, _1517058, _1517060, _1517062, _1517064] : [class_Groups_Oab__semigroup__mult(_1517056), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1517056, _1517056, c_Groups_Otimes__class_Otimes(_1517056), _1517058, _1517060), _1517062)), hBOOL(hAPP(hAPP(c_member(_1517056), _1517064), _1517060)), -(hBOOL(hAPP(hAPP(c_member(_1517056), _1517058), _1517060))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1517056, _1517056, c_Groups_Otimes__class_Otimes(_1517056), _1517064, hAPP(hAPP(c_Set_Oinsert(_1517056), _1517058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1517056, tc_HOL_Obool)), _1517060), hAPP(hAPP(c_Set_Oinsert(_1517056), _1517064), c_Orderings_Obot__class_Obot(tc_fun(_1517056, tc_HOL_Obool)))))), _1517062)))], (39027 ^ _780461) ^ [_1517400, _1517402, _1517404, _1517406, _1517408] : [hBOOL(hAPP(hAPP(c_member(_1517400), _1517402), c_Map_Oran(_1517404, _1517400, c_Map_Orestrict__map(_1517404, _1517400, _1517406, _1517408)))), 39031 ^ _780461 : [(39032 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1517404), 39030 ^ [_1517400, _1517402, _1517404, _1517406, _1517408]), _1517408)))], (39034 ^ _780461) ^ [] : [-(hAPP(_1517406, 39030 ^ [_1517400, _1517402, _1517404, _1517406, _1517408]) = hAPP(c_Option_Ooption_OSome(_1517400), _1517402))]]], (39036 ^ _780461) ^ [_1517602, _1517604, _1517606, _1517608, _1517610, _1517612] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1517602, _1517604, _1517606, _1517608, _1517610), _1517612)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1517602), _1517610)))], (39042 ^ _780461) ^ [_1517711, _1517713, _1517715, _1517717] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1517711, _1517713, _1517715, _1517717, c_Orderings_Obot__class_Obot(tc_fun(_1517711, tc_HOL_Obool))), _1517717)))], (39044 ^ _780461) ^ [_1517753, _1517755, _1517757, _1517759] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1517753, _1517755, _1517757, _1517759, c_Orderings_Obot__class_Obot(tc_fun(_1517753, tc_HOL_Obool))), _1517759)))], (39046 ^ _780461) ^ [_1517795, _1517797, _1517799, _1517801, _1517803] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1517795, _1517797, _1517799, _1517801, c_Orderings_Obot__class_Obot(tc_fun(_1517795, tc_HOL_Obool))), _1517803)), -(_1517803 = _1517801)], (39052 ^ _780461) ^ [_1517903, _1517905, _1517907, _1517909, _1517911, _1517913, _1517915] : [-(hBOOL(hAPP(hAPP(c_member(_1517903), _1517905), _1517907))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1517903, _1517909, _1517911, _1517913, _1517907), _1517915)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1517903, _1517909, _1517911, _1517913, hAPP(hAPP(c_Set_Oinsert(_1517903), _1517905), _1517907)), hAPP(hAPP(_1517911, _1517905), _1517915))))], (39062 ^ _780461) ^ [_1518117, _1518119, _1518121, _1518123, _1518125] : [class_Groups_Oab__semigroup__mult(_1518117), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1518117, _1518117, c_Groups_Otimes__class_Otimes(_1518117), _1518119, _1518121), _1518123)), -(hBOOL(hAPP(hAPP(c_member(_1518117), _1518119), _1518121))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1518117, _1518117, c_Groups_Otimes__class_Otimes(_1518117), _1518125, hAPP(hAPP(c_Set_Oinsert(_1518117), _1518119), _1518121)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1518117), _1518125), _1518123))))], (39076 ^ _780461) ^ [_1518357, _1518359, _1518361, _1518363, _1518365, _1518367, _1518369] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1518357, _1518359, _1518361, _1518363, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1518357, tc_HOL_Obool)), _1518365), hAPP(hAPP(c_Set_Oinsert(_1518357), _1518367), c_Orderings_Obot__class_Obot(tc_fun(_1518357, tc_HOL_Obool))))), _1518369)), hBOOL(hAPP(hAPP(c_member(_1518357), _1518367), _1518365)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1518357, _1518359, _1518361, _1518363, _1518365), hAPP(hAPP(_1518361, _1518367), _1518369))))], (39086 ^ _780461) ^ [_1518612, _1518614, _1518616, _1518618, _1518620] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1518612, _1518612, _1518614, _1518616, _1518618), _1518620)), -(hBOOL(hAPP(hAPP(c_member(_1518612), _1518616), _1518618))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1518612, _1518614, hAPP(hAPP(c_Set_Oinsert(_1518612), _1518616), _1518618)), _1518620)))], (39096 ^ _780461) ^ [_1518768, _1518770, _1518772] : [class_Lattices_Oboolean__algebra(_1518768), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1518768), _1518770), _1518772) = c_Orderings_Obot__class_Obot(_1518768), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1518768), _1518770), _1518772) = c_Orderings_Otop__class_Otop(_1518768), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1518768), _1518770) = _1518772)], (39110 ^ _780461) ^ [_1519003, _1519005, _1519007, _1519009, _1519011] : [class_Groups_Ocomm__monoid__add(_1519003), class_Groups_Ocomm__monoid__mult(_1519003), _1519005 = _1519007, c_Nat__Transfer_Onat__set(_1519007), 39128 ^ _780461 : [(39129 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 39127 ^ [_1519003, _1519005, _1519007, _1519009, _1519011])))], (39131 ^ _780461) ^ [] : [hAPP(_1519009, 39127 ^ [_1519003, _1519005, _1519007, _1519009, _1519011]) = hAPP(_1519011, 39127 ^ [_1519003, _1519005, _1519007, _1519009, _1519011])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1519003), _1519009), _1519005) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1519003), _1519011), _1519007))], (39135 ^ _780461) ^ [_1519466, _1519468] : [-(hBOOL(hAPP(hAPP(c_member(_1519466), _1519468), c_Orderings_Otop__class_Otop(tc_fun(_1519466, tc_HOL_Obool)))))], (39137 ^ _780461) ^ [_1519503] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1519503), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1519503)), c_Option_Ooption_ONone(_1519503)), hAPP(c_Set_Oimage(_1519503, tc_Option_Ooption(_1519503), c_Option_Ooption_OSome(_1519503)), c_Orderings_Otop__class_Otop(tc_fun(_1519503, tc_HOL_Obool)))))], (39139 ^ _780461) ^ [_1519561, _1519563, _1519565, _1519567, _1519569] : [-(hAPP(c_Set_Oimage(_1519561, _1519563, hAPP(hAPP(c_COMBB(_1519565, _1519563, _1519561), _1519567), _1519569)), c_Orderings_Otop__class_Otop(tc_fun(_1519561, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1519565, _1519563, _1519567), hAPP(c_Set_Oimage(_1519561, _1519565, _1519569), c_Orderings_Otop__class_Otop(tc_fun(_1519561, tc_HOL_Obool)))))], (39141 ^ _780461) ^ [] : [-(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)))], (39143 ^ _780461) ^ [] : [-(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))))], (39145 ^ _780461) ^ [_1519669, _1519671, _1519673, _1519675, _1519677] : [c_Fun_Oinj__on(_1519669, _1519671, _1519673, c_Orderings_Otop__class_Otop(tc_fun(_1519669, tc_HOL_Obool))), 39148 ^ _780461 : [(39149 ^ _780461) ^ [] : [hAPP(_1519673, _1519675) = hAPP(_1519673, _1519677), -(_1519675 = _1519677)], (39155 ^ _780461) ^ [] : [_1519675 = _1519677, -(hAPP(_1519673, _1519675) = hAPP(_1519673, _1519677))]]], (39161 ^ _780461) ^ [_1519926, _1519928, _1519930, _1519932, _1519934] : [c_Fun_Oinj__on(_1519926, _1519928, _1519930, c_Orderings_Otop__class_Otop(tc_fun(_1519926, tc_HOL_Obool))), hAPP(_1519930, _1519932) = hAPP(_1519930, _1519934), -(_1519932 = _1519934)], (39171 ^ _780461) ^ [_1520093, _1520095] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520093, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1520093, tc_HOL_Obool))), _1520095) = _1520095)], (39173 ^ _780461) ^ [_1520134, _1520136] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1520134, tc_HOL_Obool)), _1520136), c_Orderings_Otop__class_Otop(tc_fun(_1520134, tc_HOL_Obool))) = _1520136)], (39175 ^ _780461) ^ [_1520175, _1520177] : [class_Lattices_Obounded__lattice__top(_1520175), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1520175), c_Orderings_Otop__class_Otop(_1520175)), _1520177) = _1520177)], (39181 ^ _780461) ^ [_1520270, _1520272] : [class_Lattices_Obounded__lattice__top(_1520270), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1520270), _1520272), c_Orderings_Otop__class_Otop(_1520270)) = _1520272)], (39187 ^ _780461) ^ [_1520365, _1520367, _1520369] : [class_Lattices_Obounded__lattice__top(_1520365), 39190 ^ _780461 : [(39191 ^ _780461) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1520365), _1520367), _1520369) = c_Orderings_Otop__class_Otop(_1520365), 39194 ^ _780461 : [(39195 ^ _780461) ^ [] : [-(_1520367 = c_Orderings_Otop__class_Otop(_1520365))], (39197 ^ _780461) ^ [] : [-(_1520369 = c_Orderings_Otop__class_Otop(_1520365))]]], (39199 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1520365), _1520367), _1520369) = c_Orderings_Otop__class_Otop(_1520365)), _1520367 = c_Orderings_Otop__class_Otop(_1520365), _1520369 = c_Orderings_Otop__class_Otop(_1520365)]]], (39209 ^ _780461) ^ [_1520692, _1520694] : [class_Lattices_Obounded__lattice__top(_1520692), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1520692), c_Orderings_Otop__class_Otop(_1520692)), _1520694) = c_Orderings_Otop__class_Otop(_1520692))], (39215 ^ _780461) ^ [_1520791, _1520793] : [class_Lattices_Obounded__lattice__top(_1520791), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1520791), _1520793), c_Orderings_Otop__class_Otop(_1520791)) = c_Orderings_Otop__class_Otop(_1520791))], (39221 ^ _780461) ^ [_1520890, _1520892] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520890, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1520890, tc_HOL_Obool))), _1520892) = c_Orderings_Otop__class_Otop(tc_fun(_1520890, tc_HOL_Obool)))], (39223 ^ _780461) ^ [_1520936, _1520938] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520936, tc_HOL_Obool)), _1520938), c_Orderings_Otop__class_Otop(tc_fun(_1520936, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1520936, tc_HOL_Obool)))], (39225 ^ _780461) ^ [_1520991] : [c_Orderings_Otop__class_Otop(tc_fun(_1520991, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1520991, tc_HOL_Obool))], (39227 ^ _780461) ^ [_1521024, _1521026, _1521028] : [class_Orderings_Otop(_1521024), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1521026, _1521024)), _1521028) = c_Orderings_Otop__class_Otop(_1521024))], (39233 ^ _780461) ^ [_1521121, _1521123] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521121, tc_HOL_Obool)), _1521123), c_Orderings_Otop__class_Otop(tc_fun(_1521121, tc_HOL_Obool)))))], (39235 ^ _780461) ^ [] : [-(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))], (39237 ^ _780461) ^ [_1521179, _1521181] : [class_Orderings_Otop(_1521179), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1521179), _1521181), c_Orderings_Otop__class_Otop(_1521179))))], (39243 ^ _780461) ^ [_1521272, _1521274] : [-(c_Sum__Type_OPlus(_1521272, _1521274, c_Orderings_Otop__class_Otop(tc_fun(_1521272, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1521274, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1521272, _1521274), tc_HOL_Obool)))], (39245 ^ _780461) ^ [] : [-(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))], (39247 ^ _780461) ^ [_1521338] : [-(hAPP(c_Set_OPow(_1521338), c_Orderings_Otop__class_Otop(tc_fun(_1521338, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1521338, tc_HOL_Obool), tc_HOL_Obool)))], (39249 ^ _780461) ^ [] : [-(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)))], (39251 ^ _780461) ^ [_1521397, _1521399] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521397), c_Orderings_Otop__class_Otop(tc_fun(_1521397, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521399), c_Orderings_Otop__class_Otop(tc_fun(_1521399, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521397, _1521399)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1521397, _1521399), tc_HOL_Obool)))))], (39261 ^ _780461) ^ [_1521592, _1521594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1521592, _1521594)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1521592, _1521594), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521594), c_Orderings_Otop__class_Otop(tc_fun(_1521594, tc_HOL_Obool)))))], (39267 ^ _780461) ^ [_1521732, _1521734] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1521732, _1521734)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1521732, _1521734), tc_HOL_Obool)))), 39270 ^ _780461 : [(39271 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521732), c_Orderings_Otop__class_Otop(tc_fun(_1521732, tc_HOL_Obool)))))], (39273 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521734), c_Orderings_Otop__class_Otop(tc_fun(_1521734, tc_HOL_Obool)))))]]], (39275 ^ _780461) ^ [_1521897, _1521899] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1521897, _1521899)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1521897, _1521899), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521897), c_Orderings_Otop__class_Otop(tc_fun(_1521897, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521899), c_Orderings_Otop__class_Otop(tc_fun(_1521899, tc_HOL_Obool))))], (39285 ^ _780461) ^ [_1522106] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1522106)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1522106), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1522106), c_Orderings_Otop__class_Otop(tc_fun(_1522106, tc_HOL_Obool)))))], (39291 ^ _780461) ^ [_1522221] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1522221), c_Orderings_Otop__class_Otop(tc_fun(_1522221, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1522221)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1522221), tc_HOL_Obool)))))], (39297 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (39299 ^ _780461) ^ [_1522366] : [class_Finite__Set_Ofinite(_1522366), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1522366), c_Orderings_Otop__class_Otop(tc_fun(_1522366, tc_HOL_Obool)))))], (39305 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (39307 ^ _780461) ^ [_1522496, _1522498, _1522500] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1522496, _1522498, c_Orderings_Obot__class_Obot(tc_fun(_1522496, tc_HOL_Obool))), _1522500))], (39309 ^ _780461) ^ [_1522534, _1522536, _1522538, _1522540] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1522534, _1522536, _1522538), _1522540)), _1522538 = c_Orderings_Obot__class_Obot(tc_fun(_1522534, tc_HOL_Obool))], (39315 ^ _780461) ^ [_1522638, _1522640, _1522642, _1522644] : [-(hBOOL(hAPP(hAPP(c_member(_1522638), hAPP(_1522640, _1522642)), hAPP(c_Set_Oimage(_1522644, _1522638, _1522640), c_Orderings_Otop__class_Otop(tc_fun(_1522644, tc_HOL_Obool))))))], (39317 ^ _780461) ^ [_1522689, _1522691, _1522693, _1522695, _1522697] : [_1522689 = hAPP(_1522691, _1522693), -(hBOOL(hAPP(hAPP(c_member(_1522695), _1522689), hAPP(c_Set_Oimage(_1522697, _1522695, _1522691), c_Orderings_Otop__class_Otop(tc_fun(_1522697, tc_HOL_Obool))))))], (39323 ^ _780461) ^ [] : [-(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)))], (39325 ^ _780461) ^ [_1522834, _1522836] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1522834, tc_HOL_Obool)), _1522836), c_Orderings_Otop__class_Otop(tc_fun(_1522834, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1522834, tc_HOL_Obool)))], (39327 ^ _780461) ^ [_1522880, _1522882, _1522884, _1522886, _1522888] : [hAPP(c_Set_Oimage(_1522880, _1522882, _1522884), c_Orderings_Otop__class_Otop(tc_fun(_1522880, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522882, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1522882, _1522886, _1522888), c_Orderings_Otop__class_Otop(tc_fun(_1522882, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522886, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1522880, _1522886, hAPP(c_Fun_Ocomp(_1522882, _1522886, _1522880, _1522888), _1522884)), c_Orderings_Otop__class_Otop(tc_fun(_1522880, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1522886, tc_HOL_Obool)))], (39337 ^ _780461) ^ [_1523139, _1523141] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523139), c_Orderings_Otop__class_Otop(tc_fun(_1523139, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1523139), _1523141) = hAPP(c_Finite__Set_Ocard(_1523139), c_Orderings_Otop__class_Otop(tc_fun(_1523139, tc_HOL_Obool))), -(_1523141 = c_Orderings_Otop__class_Otop(tc_fun(_1523139, tc_HOL_Obool)))], (39347 ^ _780461) ^ [_1523326, _1523328, _1523330, _1523332, _1523334] : [c_Fun_Oinj__on(_1523326, _1523328, _1523330, c_Orderings_Otop__class_Otop(tc_fun(_1523326, tc_HOL_Obool))), 39350 ^ _780461 : [(39351 ^ _780461) ^ [] : [hAPP(c_Set_Oimage(_1523326, _1523328, _1523330), _1523332) = hAPP(c_Set_Oimage(_1523326, _1523328, _1523330), _1523334), -(_1523332 = _1523334)], (39357 ^ _780461) ^ [] : [_1523332 = _1523334, -(hAPP(c_Set_Oimage(_1523326, _1523328, _1523330), _1523332) = hAPP(c_Set_Oimage(_1523326, _1523328, _1523330), _1523334))]]], (39363 ^ _780461) ^ [_1523607, _1523609, _1523611, _1523613, _1523615] : [c_Fun_Oinj__on(_1523607, _1523609, _1523611, c_Orderings_Otop__class_Otop(tc_fun(_1523607, tc_HOL_Obool))), c_Fun_Oinj__on(_1523613, _1523607, _1523615, c_Orderings_Otop__class_Otop(tc_fun(_1523613, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1523613, _1523609, hAPP(c_Fun_Ocomp(_1523607, _1523609, _1523613, _1523611), _1523615), c_Orderings_Otop__class_Otop(tc_fun(_1523613, tc_HOL_Obool))))], (39373 ^ _780461) ^ [_1523806] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1523806, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1523806, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1523806, tc_HOL_Obool)))], (39375 ^ _780461) ^ [_1523847] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1523847, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1523847, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1523847, tc_HOL_Obool)))], (39377 ^ _780461) ^ [_1523888, _1523890] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523888), _1523890)), 39380 ^ _780461 : [(39381 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523888), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1523888, tc_HOL_Obool)), _1523890))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523888), c_Orderings_Otop__class_Otop(tc_fun(_1523888, tc_HOL_Obool)))))], (39387 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523888), c_Orderings_Otop__class_Otop(tc_fun(_1523888, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523888), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1523888, tc_HOL_Obool)), _1523890))))]]], (39393 ^ _780461) ^ [_1524166, _1524168] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524166, tc_HOL_Obool)), _1524168), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1524166, tc_HOL_Obool)), _1524168)) = c_Orderings_Otop__class_Otop(tc_fun(_1524166, tc_HOL_Obool)))], (39395 ^ _780461) ^ [_1524215, _1524217] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524215, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1524215, tc_HOL_Obool)), _1524217)), _1524217) = c_Orderings_Otop__class_Otop(tc_fun(_1524215, tc_HOL_Obool)))], (39397 ^ _780461) ^ [_1524264, _1524266] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1524264, tc_HOL_Obool)), _1524266) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1524264, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1524264, tc_HOL_Obool))), _1524266))], (39399 ^ _780461) ^ [_1524313, _1524315] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1524313), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1524315), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 39406 ^ _780461 : [(39407 ^ _780461) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1524313) = hAPP(c_Code__Numeral_Oof__nat, _1524315), -(_1524313 = _1524315)], (39413 ^ _780461) ^ [] : [_1524313 = _1524315, -(hAPP(c_Code__Numeral_Oof__nat, _1524313) = hAPP(c_Code__Numeral_Oof__nat, _1524315))]]], (39419 ^ _780461) ^ [_1524631, _1524633, _1524635, _1524637] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524631, tc_fun(_1524633, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1524631, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1524633, tc_HOL_Obool), tc_fun(_1524633, tc_HOL_Obool), _1524631), hAPP(c_COMBC(_1524633, tc_fun(_1524633, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524633))), _1524635)), _1524637)), -(hBOOL(hAPP(hAPP(c_member(_1524633), _1524637), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524631, tc_fun(_1524633, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1524631, tc_HOL_Obool))), _1524635))))], (39425 ^ _780461) ^ [_1524850, _1524852, _1524854, _1524856] : [hBOOL(hAPP(hAPP(c_member(_1524852), _1524856), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524850, tc_fun(_1524852, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1524850, tc_HOL_Obool))), _1524854))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524850, tc_fun(_1524852, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1524850, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1524852, tc_HOL_Obool), tc_fun(_1524852, tc_HOL_Obool), _1524850), hAPP(c_COMBC(_1524852, tc_fun(_1524852, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524852))), _1524854)), _1524856)))], (39431 ^ _780461) ^ [_1525075, _1525077, _1525079, _1525081, _1525083] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525075), hAPP(c_Set_Oimage(_1525077, _1525075, _1525079), c_Orderings_Otop__class_Otop(tc_fun(_1525077, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1525081), hAPP(c_Set_Oimage(_1525077, _1525081, hAPP(hAPP(c_COMBB(_1525075, _1525081, _1525077), _1525083), _1525079)), c_Orderings_Otop__class_Otop(tc_fun(_1525077, tc_HOL_Obool))))))], (39437 ^ _780461) ^ [_1525242] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1525242)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (39439 ^ _780461) ^ [_1525273, _1525275, _1525277, _1525279] : [c_Fun_Oinj__on(_1525273, _1525275, _1525277, c_Orderings_Otop__class_Otop(tc_fun(_1525273, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1525273, _1525275, c_Orderings_Otop__class_Otop(tc_fun(_1525273, tc_HOL_Obool)), _1525277), hAPP(_1525277, _1525279)) = _1525279)], (39445 ^ _780461) ^ [_1525400, _1525402] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1525400, _1525402)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1525400, _1525402), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1525402), c_Orderings_Otop__class_Otop(tc_fun(_1525402, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1525400), c_Orderings_Otop__class_Otop(tc_fun(_1525400, tc_HOL_Obool)))))], (39455 ^ _780461) ^ [_1525560] : [class_Nat_Osemiring__char__0(_1525560), -(c_Fun_Oinj__on(tc_Nat_Onat, _1525560, c_Nat_Osemiring__1__class_Oof__nat(_1525560), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (39461 ^ _780461) ^ [_1525641, _1525643, _1525645] : [-(c_Map_Odom(_1525641, _1525643, hAPP(hAPP(c_COMBB(_1525643, tc_Option_Ooption(_1525643), _1525641), c_Option_Ooption_OSome(_1525643)), _1525645)) = c_Orderings_Otop__class_Otop(tc_fun(_1525641, tc_HOL_Obool)))], (39463 ^ _780461) ^ [] : [-(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)))], (39465 ^ _780461) ^ [_1525709, _1525711, _1525713, _1525715] : [c_Fun_Oinj__on(_1525709, _1525711, _1525713, c_Orderings_Otop__class_Otop(tc_fun(_1525709, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1525709, tc_fun(_1525715, _1525711), hAPP(hAPP(c_COMBB(_1525711, tc_fun(_1525715, _1525711), _1525709), c_COMBK(_1525711, _1525715)), _1525713), c_Orderings_Otop__class_Otop(tc_fun(_1525709, tc_HOL_Obool))))], (39471 ^ _780461) ^ [_1525856] : [class_Lattices_Oboolean__algebra(_1525856), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1525856), c_Orderings_Otop__class_Otop(_1525856)) = c_Orderings_Obot__class_Obot(_1525856))], (39477 ^ _780461) ^ [_1525947] : [class_Lattices_Oboolean__algebra(_1525947), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1525947), c_Orderings_Obot__class_Obot(_1525947)) = c_Orderings_Otop__class_Otop(_1525947))], (39483 ^ _780461) ^ [_1526038, _1526040] : [class_Lattices_Oboolean__algebra(_1526038), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1526038), _1526040), hAPP(c_Groups_Ouminus__class_Ouminus(_1526038), _1526040)) = c_Orderings_Otop__class_Otop(_1526038))], (39489 ^ _780461) ^ [_1526143, _1526145] : [class_Lattices_Oboolean__algebra(_1526143), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1526143), hAPP(c_Groups_Ouminus__class_Ouminus(_1526143), _1526145)), _1526145) = c_Orderings_Otop__class_Otop(_1526143))], (39495 ^ _780461) ^ [_1526248, _1526250, _1526252, _1526254, _1526256] : [c_Fun_Oinj__on(_1526248, _1526250, _1526252, c_Orderings_Otop__class_Otop(tc_fun(_1526248, tc_HOL_Obool))), 39498 ^ _780461 : [(39499 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1526250), hAPP(_1526252, _1526254)), hAPP(c_Set_Oimage(_1526248, _1526250, _1526252), _1526256))), -(hBOOL(hAPP(hAPP(c_member(_1526248), _1526254), _1526256)))], (39505 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1526248), _1526254), _1526256)), -(hBOOL(hAPP(hAPP(c_member(_1526250), hAPP(_1526252, _1526254)), hAPP(c_Set_Oimage(_1526248, _1526250, _1526252), _1526256))))]]], (39511 ^ _780461) ^ [_1526559, _1526561, _1526563, _1526565] : [c_Fun_Oinj__on(_1526559, _1526561, _1526563, c_Orderings_Otop__class_Otop(tc_fun(_1526559, tc_HOL_Obool))), 39514 ^ _780461 : [(39515 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1526561), _1526565), hAPP(c_Set_Oimage(_1526559, _1526561, _1526563), c_Orderings_Otop__class_Otop(tc_fun(_1526559, tc_HOL_Obool))))), 39519 ^ _780461 : [(39520 ^ _780461) ^ [] : [-(_1526565 = hAPP(_1526563, 39518 ^ [_1526559, _1526561, _1526563, _1526565]))], (39522 ^ _780461) ^ [_1526824] : [_1526565 = hAPP(_1526563, _1526824), -(_1526824 = 39518 ^ [_1526559, _1526561, _1526563, _1526565])]]], (39528 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526561), _1526565), hAPP(c_Set_Oimage(_1526559, _1526561, _1526563), c_Orderings_Otop__class_Otop(tc_fun(_1526559, tc_HOL_Obool)))))), 39529 ^ _780461 : [(39530 ^ _780461) ^ [_1526962] : [_1526565 = hAPP(_1526563, _1526962), 39534 ^ _780461 : [(39535 ^ _780461) ^ [] : [-(_1526565 = hAPP(_1526563, 39533 ^ [_1526559, _1526561, _1526563, _1526565, _1526962]))], (39537 ^ _780461) ^ [] : [39533 ^ [_1526559, _1526561, _1526563, _1526565, _1526962] = _1526962]]]]]]], (39541 ^ _780461) ^ [_1527190, _1527192] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527190), c_Orderings_Otop__class_Otop(tc_fun(_1527190, tc_HOL_Obool)))), c_Fun_Oinj__on(_1527190, _1527190, _1527192, c_Orderings_Otop__class_Otop(tc_fun(_1527190, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1527190, _1527190, _1527192), c_Orderings_Otop__class_Otop(tc_fun(_1527190, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1527190, tc_HOL_Obool)))], (39551 ^ _780461) ^ [_1527385, _1527387] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1527385), c_Orderings_Otop__class_Otop(tc_fun(_1527385, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1527385, _1527385, _1527387), c_Orderings_Otop__class_Otop(tc_fun(_1527385, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1527385, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1527385, _1527385, _1527387, c_Orderings_Otop__class_Otop(tc_fun(_1527385, tc_HOL_Obool))))], (39561 ^ _780461) ^ [_1527580, _1527582, _1527584, _1527586, _1527588] : [c_Fun_Oinj__on(_1527580, _1527582, _1527584, c_Orderings_Otop__class_Otop(tc_fun(_1527580, tc_HOL_Obool))), 39564 ^ _780461 : [(39565 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1527582, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1527580, _1527582, _1527584), _1527586)), hAPP(c_Set_Oimage(_1527580, _1527582, _1527584), _1527588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1527580, tc_HOL_Obool)), _1527586), _1527588)))], (39571 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1527580, tc_HOL_Obool)), _1527586), _1527588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1527582, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1527580, _1527582, _1527584), _1527586)), hAPP(c_Set_Oimage(_1527580, _1527582, _1527584), _1527588))))]]], (39577 ^ _780461) ^ [_1527921, _1527923, _1527925, _1527927, _1527929] : [c_Fun_Oinj__on(_1527921, _1527923, _1527925, c_Orderings_Otop__class_Otop(tc_fun(_1527921, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1527921, _1527923, _1527925), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1527921, tc_HOL_Obool)), _1527927), _1527929)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1527923, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1527921, _1527923, _1527925), _1527927)), hAPP(c_Set_Oimage(_1527921, _1527923, _1527925), _1527929)))], (39583 ^ _780461) ^ [_1528104, _1528106, _1528108, _1528110, _1528112] : [c_Fun_Oinj__on(_1528104, _1528106, _1528108, c_Orderings_Otop__class_Otop(tc_fun(_1528104, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1528104, _1528106, _1528108), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1528104, tc_HOL_Obool)), _1528110), _1528112)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1528106, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1528104, _1528106, _1528108), _1528110)), hAPP(c_Set_Oimage(_1528104, _1528106, _1528108), _1528112)))], (39589 ^ _780461) ^ [_1528287, _1528289, _1528291, _1528293] : [hAPP(c_Set_Oimage(_1528287, _1528289, _1528291), c_Orderings_Otop__class_Otop(tc_fun(_1528287, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1528289, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1528289, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1528289, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1528287, _1528289, _1528291), _1528293))), hAPP(c_Set_Oimage(_1528287, _1528289, _1528291), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1528287, tc_HOL_Obool)), _1528293)))))], (39595 ^ _780461) ^ [_1528482] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1528482), 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, _1528482)) = _1528482)], (39601 ^ _780461) ^ [_1528600, _1528602, _1528604, _1528606] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1528600, _1528602, hAPP(hAPP(c_Set_Oinsert(_1528600), _1528604), c_Orderings_Obot__class_Obot(tc_fun(_1528600, tc_HOL_Obool)))), _1528606)), -(_1528604 = _1528606)], (39607 ^ _780461) ^ [_1528715, _1528717, _1528719, _1528721] : [_1528719 = _1528721, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1528715, _1528717, hAPP(hAPP(c_Set_Oinsert(_1528715), _1528719), c_Orderings_Obot__class_Obot(tc_fun(_1528715, tc_HOL_Obool)))), _1528721)))], (39613 ^ _780461) ^ [_1528836, _1528838, _1528840, _1528842, _1528844] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1528836)), hAPP(c_Set_Oimage(_1528838, tc_Option_Ooption(_1528836), _1528840), c_Orderings_Otop__class_Otop(tc_fun(_1528838, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1528836)), hAPP(c_Set_Oimage(_1528838, tc_Option_Ooption(_1528836), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1528838, tc_Option_Ooption(_1528836)), _1528840), _1528842), hAPP(c_Option_Ooption_OSome(_1528836), _1528844))), c_Orderings_Otop__class_Otop(tc_fun(_1528838, tc_HOL_Obool))))))], (39619 ^ _780461) ^ [_1529037, _1529039] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1529037, 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(_1529037, tc_HOL_Obool)), tc_fun(_1529037, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1529037, tc_HOL_Obool)), tc_fun(_1529037, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1529037, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1529039)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1529037, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1529039))], (39621 ^ _780461) ^ [_1529133] : [-(c_Fun_Oinj__on(_1529133, tc_fun(_1529133, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1529133, tc_fun(_1529133, tc_HOL_Obool), tc_fun(_1529133, tc_HOL_Obool)), c_Set_Oinsert(_1529133)), c_Orderings_Obot__class_Obot(tc_fun(_1529133, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1529133, tc_HOL_Obool))))], (39623 ^ _780461) ^ [_1529189] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529189), c_Orderings_Otop__class_Otop(tc_fun(_1529189, 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(_1529189), c_Orderings_Otop__class_Otop(tc_fun(_1529189, tc_HOL_Obool))))))], (39629 ^ _780461) ^ [] : [-(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))))], (39631 ^ _780461) ^ [_1529324, _1529326, _1529328, _1529330] : [c_Fun_Oinj__on(_1529324, _1529326, _1529328, c_Orderings_Otop__class_Otop(tc_fun(_1529324, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1529326, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1529324, _1529326, _1529328), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1529324, tc_HOL_Obool)), _1529330))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1529326, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1529324, _1529326, _1529328), _1529330)))))], (39637 ^ _780461) ^ [] : [-(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))))], (39639 ^ _780461) ^ [_1529544, _1529546, _1529548, _1529550, _1529552, _1529554] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529544, tc_fun(_1529546, tc_fun(_1529548, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1529544, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1529546, _1529548), tc_HOL_Obool), tc_fun(_1529546, tc_fun(_1529548, tc_HOL_Obool)), _1529544), hAPP(c_COMBC(_1529546, tc_fun(tc_prod(_1529546, _1529548), tc_HOL_Obool), tc_fun(_1529548, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529548, tc_fun(tc_fun(tc_prod(_1529546, _1529548), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529546, _1529548), tc_HOL_Obool), tc_fun(_1529548, tc_HOL_Obool)), _1529546), c_COMBC(_1529548, tc_fun(tc_prod(_1529546, _1529548), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529548, tc_prod(_1529546, _1529548)), tc_fun(_1529548, tc_fun(tc_fun(tc_prod(_1529546, _1529548), tc_HOL_Obool), tc_HOL_Obool)), _1529546), hAPP(c_COMBB(tc_prod(_1529546, _1529548), tc_fun(tc_fun(tc_prod(_1529546, _1529548), tc_HOL_Obool), tc_HOL_Obool), _1529548), c_member(tc_prod(_1529546, _1529548)))), c_Product__Type_OPair(_1529546, _1529548))))), _1529550)), _1529552), _1529554)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529546, _1529548)), hAPP(hAPP(c_Product__Type_OPair(_1529546, _1529548), _1529552), _1529554)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1529544, tc_fun(tc_prod(_1529546, _1529548), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1529544, tc_HOL_Obool))), _1529550))))], (39645 ^ _780461) ^ [_1530027, _1530029, _1530031, _1530033, _1530035, _1530037] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530029, _1530031)), hAPP(hAPP(c_Product__Type_OPair(_1530029, _1530031), _1530035), _1530037)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530027, tc_fun(tc_prod(_1530029, _1530031), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1530027, tc_HOL_Obool))), _1530033))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530027, tc_fun(_1530029, tc_fun(_1530031, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1530027, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530029, _1530031), tc_HOL_Obool), tc_fun(_1530029, tc_fun(_1530031, tc_HOL_Obool)), _1530027), hAPP(c_COMBC(_1530029, tc_fun(tc_prod(_1530029, _1530031), tc_HOL_Obool), tc_fun(_1530031, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530031, tc_fun(tc_fun(tc_prod(_1530029, _1530031), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1530029, _1530031), tc_HOL_Obool), tc_fun(_1530031, tc_HOL_Obool)), _1530029), c_COMBC(_1530031, tc_fun(tc_prod(_1530029, _1530031), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530031, tc_prod(_1530029, _1530031)), tc_fun(_1530031, tc_fun(tc_fun(tc_prod(_1530029, _1530031), tc_HOL_Obool), tc_HOL_Obool)), _1530029), hAPP(c_COMBB(tc_prod(_1530029, _1530031), tc_fun(tc_fun(tc_prod(_1530029, _1530031), tc_HOL_Obool), tc_HOL_Obool), _1530031), c_member(tc_prod(_1530029, _1530031)))), c_Product__Type_OPair(_1530029, _1530031))))), _1530033)), _1530035), _1530037)))], (39651 ^ _780461) ^ [_1530516, _1530518, _1530520, _1530522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530516, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1530516, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 39652 ^ [_1530516, _1530518, _1530520, _1530522])), _1530518)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1530516, 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), 39652 ^ [_1530516, _1530518, _1530520, _1530522]), _1530520))), _1530522))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530516, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1530516, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1530518)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1530516, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1530522))))], (39658 ^ _780461) ^ [_1530846, _1530848, _1530850, _1530852] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1530846, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 39659 ^ [_1530846, _1530848, _1530850, _1530852])), _1530848) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1530846, 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), 39659 ^ [_1530846, _1530848, _1530850, _1530852]), _1530850))), _1530852), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1530846, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1530848) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1530846, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1530852))], (39665 ^ _780461) ^ [_1531126, _1531128, _1531130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531126, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1531126, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 39666 ^ [_1531126, _1531128, _1531130])), _1531128)), _1531130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531126, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1531126, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1531128)), _1531130)))], (39672 ^ _780461) ^ [_1531352, _1531354] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1531352, tc_HOL_Obool)), _1531354)))], (39674 ^ _780461) ^ [] : [-(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))], (39676 ^ _780461) ^ [_1531402, _1531404] : [-(hBOOL(hAPP(hAPP(c_member(_1531402), _1531404), c_Orderings_Otop__class_Otop(tc_fun(_1531402, tc_HOL_Obool)))))], (39678 ^ _780461) ^ [_1531454, _1531456] : [c_Equiv__Relations_Oequiv(_1531454, c_Orderings_Otop__class_Otop(tc_fun(_1531454, tc_HOL_Obool)), _1531456), -(c_Equiv__Relations_Oequivp(_1531454, hAPP(hAPP(c_COMBC(_1531454, tc_fun(tc_prod(_1531454, _1531454), tc_HOL_Obool), tc_fun(_1531454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531454, tc_fun(tc_fun(tc_prod(_1531454, _1531454), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531454, _1531454), tc_HOL_Obool), tc_fun(_1531454, tc_HOL_Obool)), _1531454), c_COMBC(_1531454, tc_fun(tc_prod(_1531454, _1531454), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531454, tc_prod(_1531454, _1531454)), tc_fun(_1531454, tc_fun(tc_fun(tc_prod(_1531454, _1531454), tc_HOL_Obool), tc_HOL_Obool)), _1531454), hAPP(c_COMBB(tc_prod(_1531454, _1531454), tc_fun(tc_fun(tc_prod(_1531454, _1531454), tc_HOL_Obool), tc_HOL_Obool), _1531454), c_member(tc_prod(_1531454, _1531454)))), c_Product__Type_OPair(_1531454, _1531454)))), _1531456)))], (39684 ^ _780461) ^ [_1531775, _1531777] : [c_Equiv__Relations_Oequivp(_1531775, hAPP(hAPP(c_COMBC(_1531775, tc_fun(tc_prod(_1531775, _1531775), tc_HOL_Obool), tc_fun(_1531775, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531775, tc_fun(tc_fun(tc_prod(_1531775, _1531775), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531775, _1531775), tc_HOL_Obool), tc_fun(_1531775, tc_HOL_Obool)), _1531775), c_COMBC(_1531775, tc_fun(tc_prod(_1531775, _1531775), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531775, tc_prod(_1531775, _1531775)), tc_fun(_1531775, tc_fun(tc_fun(tc_prod(_1531775, _1531775), tc_HOL_Obool), tc_HOL_Obool)), _1531775), hAPP(c_COMBB(tc_prod(_1531775, _1531775), tc_fun(tc_fun(tc_prod(_1531775, _1531775), tc_HOL_Obool), tc_HOL_Obool), _1531775), c_member(tc_prod(_1531775, _1531775)))), c_Product__Type_OPair(_1531775, _1531775)))), _1531777)), -(c_Equiv__Relations_Oequiv(_1531775, c_Orderings_Otop__class_Otop(tc_fun(_1531775, tc_HOL_Obool)), _1531777))], (39690 ^ _780461) ^ [_1532102] : [-(c_Equiv__Relations_Oequivp(_1532102, c_fequal))], (39708 ^ _780461) ^ [_1532438, _1532440] : [-(c_Equiv__Relations_Oequivp(_1532438, _1532440)), 39713 ^ _780461 : [(39714 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1532440, 39709 ^ [_1532438, _1532440]), 39710 ^ [_1532438, _1532440])))], (39716 ^ _780461) ^ [] : [hAPP(_1532440, 39709 ^ [_1532438, _1532440]) = hAPP(_1532440, 39710 ^ [_1532438, _1532440])]], 39717 ^ _780461 : [(39718 ^ _780461) ^ [] : [-(hAPP(_1532440, 39709 ^ [_1532438, _1532440]) = hAPP(_1532440, 39710 ^ [_1532438, _1532440]))], (39720 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1532440, 39709 ^ [_1532438, _1532440]), 39710 ^ [_1532438, _1532440]))]]], (39692 ^ _780461) ^ [_1532140, _1532142] : [c_Equiv__Relations_Oequivp(_1532140, _1532142), 39695 ^ _780461 : [(39696 ^ _780461) ^ [_1532234, _1532236] : [hBOOL(hAPP(hAPP(_1532142, _1532236), _1532234)), -(hAPP(_1532142, _1532236) = hAPP(_1532142, _1532234))], (39702 ^ _780461) ^ [_1532333, _1532335] : [hAPP(_1532142, _1532335) = hAPP(_1532142, _1532333), -(hBOOL(hAPP(hAPP(_1532142, _1532335), _1532333)))]]], (39724 ^ _780461) ^ [_1532767, _1532769, _1532771] : [c_Equiv__Relations_Oequivp(_1532767, _1532769), -(hBOOL(hAPP(hAPP(_1532769, _1532771), _1532771)))], (39730 ^ _780461) ^ [_1532856, _1532858, _1532860, _1532862] : [c_Equiv__Relations_Oequivp(_1532856, _1532858), hBOOL(hAPP(hAPP(_1532858, _1532860), _1532862)), -(hBOOL(hAPP(hAPP(_1532858, _1532862), _1532860)))], (39740 ^ _780461) ^ [_1533013, _1533015, _1533017, _1533019, _1533021] : [c_Equiv__Relations_Oequivp(_1533013, _1533015), hBOOL(hAPP(hAPP(_1533015, _1533017), _1533019)), hBOOL(hAPP(hAPP(_1533015, _1533019), _1533021)), -(hBOOL(hAPP(hAPP(_1533015, _1533017), _1533021)))], (39754 ^ _780461) ^ [_1533242] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1533242)), c_Int_OInteg)))], (39756 ^ _780461) ^ [_1533273, _1533275, _1533277, _1533279, _1533281, _1533283, _1533285] : [hAPP(c_Fun_Ocomp(_1533273, _1533275, _1533277, _1533279), _1533281) = _1533283, -(hAPP(_1533279, hAPP(_1533281, _1533285)) = hAPP(_1533283, _1533285))], (39762 ^ _780461) ^ [_1533394, _1533396, _1533398, _1533400, _1533402, _1533404] : [-(hAPP(hAPP(c_Fun_Ocomp(_1533394, _1533396, _1533398, hAPP(c_COMBK(_1533396, _1533394), _1533400)), _1533402), _1533404) = _1533400)], (39764 ^ _780461) ^ [] : [-(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))], (39766 ^ _780461) ^ [_1533462, _1533464, _1533466, _1533468] : [c_Fun_Oinj__on(_1533462, _1533464, _1533466, c_Orderings_Otop__class_Otop(tc_fun(_1533462, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533462, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1533462, _1533464, _1533466), hAPP(hAPP(c_Set_Oinsert(_1533464), _1533468), c_Orderings_Obot__class_Obot(tc_fun(_1533464, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1533462), c_HOL_OThe(_1533462, hAPP(hAPP(c_COMBC(_1533462, _1533464, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1533464, tc_fun(_1533464, tc_HOL_Obool), _1533462), c_fequal), _1533466)), _1533468))), c_Orderings_Obot__class_Obot(tc_fun(_1533462, tc_HOL_Obool))))))], (39772 ^ _780461) ^ [] : [-(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))))], (39774 ^ _780461) ^ [_1533713, _1533715, _1533717, _1533719, _1533721, _1533723] : [hAPP(_1533713, _1533715) = _1533717, hBOOL(hAPP(hAPP(c_member(_1533719), _1533717), _1533721)), -(hBOOL(hAPP(hAPP(c_member(_1533723), _1533715), hAPP(c_Set_Ovimage(_1533723, _1533719, _1533713), _1533721))))], (39784 ^ _780461) ^ [_1533906, _1533908, _1533910, _1533912, _1533914, _1533916] : [-(hAPP(c_Set_Ovimage(_1533906, _1533908, hAPP(c_Fun_Ocomp(_1533910, _1533908, _1533906, _1533912), _1533914)), _1533916) = hAPP(c_Set_Ovimage(_1533906, _1533910, _1533914), hAPP(c_Set_Ovimage(_1533910, _1533908, _1533912), _1533916)))], (39786 ^ _780461) ^ [_1533968, _1533970, _1533972, _1533974, _1533976] : [-(hAPP(c_Set_Ovimage(_1533968, _1533970, _1533972), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1533970, tc_HOL_Obool)), _1533974), _1533976)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1533968, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1533968, _1533970, _1533972), _1533974)), hAPP(c_Set_Ovimage(_1533968, _1533970, _1533972), _1533976)))], (39788 ^ _780461) ^ [_1534042, _1534044] : [-(hAPP(c_Set_Ovimage(_1534042, _1534042, c_COMBI(_1534042)), _1534044) = _1534044)], (39790 ^ _780461) ^ [_1534076, _1534078, _1534080, _1534082, _1534084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1534076, tc_HOL_Obool)), _1534078), _1534080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1534082, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1534082, _1534076, _1534084), _1534078)), hAPP(c_Set_Ovimage(_1534082, _1534076, _1534084), _1534080))))], (39796 ^ _780461) ^ [_1534251, _1534253, _1534255, _1534257, _1534259] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1534251, _1534253, _1534255), _1534257), _1534259)), -(hBOOL(hAPP(_1534257, hAPP(_1534255, _1534259))))], (39802 ^ _780461) ^ [_1534358, _1534360, _1534362, _1534364, _1534366] : [hBOOL(hAPP(_1534364, hAPP(_1534362, _1534366))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1534358, _1534360, _1534362), _1534364), _1534366)))], (39808 ^ _780461) ^ [_1534471, _1534473, _1534475, _1534477] : [-(hAPP(c_Set_Ovimage(_1534471, _1534473, _1534475), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1534473, tc_HOL_Obool)), _1534477)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1534471, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1534471, _1534473, _1534475), _1534477)))], (39810 ^ _780461) ^ [_1534530, _1534532, _1534534] : [-(hAPP(c_Set_Ovimage(_1534530, _1534532, _1534534), c_Orderings_Obot__class_Obot(tc_fun(_1534532, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1534530, tc_HOL_Obool)))], (39812 ^ _780461) ^ [_1534574, _1534576, _1534578, _1534580, _1534582] : [hBOOL(hAPP(hAPP(c_member(_1534574), hAPP(_1534576, _1534578)), _1534580)), -(hBOOL(hAPP(hAPP(c_member(_1534582), _1534578), hAPP(c_Set_Ovimage(_1534582, _1534574, _1534576), _1534580))))], (39818 ^ _780461) ^ [_1534705, _1534707, _1534709, _1534711, _1534713] : [hBOOL(hAPP(hAPP(c_member(_1534705), _1534707), hAPP(c_Set_Ovimage(_1534705, _1534709, _1534711), _1534713))), -(hBOOL(hAPP(hAPP(c_member(_1534709), hAPP(_1534711, _1534707)), _1534713)))], (39824 ^ _780461) ^ [_1534860, _1534862, _1534864, _1534866, _1534868] : [hBOOL(hAPP(hAPP(c_member(_1534860), _1534862), hAPP(c_Set_Ovimage(_1534860, _1534864, _1534866), _1534868))), -(hBOOL(hAPP(hAPP(c_member(_1534864), hAPP(_1534866, _1534862)), _1534868)))], (39830 ^ _780461) ^ [_1534987, _1534989, _1534991, _1534993, _1534995] : [hBOOL(hAPP(hAPP(c_member(_1534991), hAPP(_1534993, _1534989)), _1534995)), -(hBOOL(hAPP(hAPP(c_member(_1534987), _1534989), hAPP(c_Set_Ovimage(_1534987, _1534991, _1534993), _1534995))))], (39836 ^ _780461) ^ [_1535120, _1535122, _1535124, _1535126, _1535128] : [-(hAPP(c_Set_Ovimage(_1535120, _1535122, _1535124), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535122, tc_HOL_Obool)), _1535126), _1535128)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535120, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1535120, _1535122, _1535124), _1535126)), hAPP(c_Set_Ovimage(_1535120, _1535122, _1535124), _1535128)))], (39838 ^ _780461) ^ [_1535194, _1535196, _1535198, _1535200, _1535202] : [-(hAPP(c_Set_Ovimage(_1535194, _1535196, _1535198), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535196, tc_HOL_Obool)), _1535200), _1535202)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535194, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1535194, _1535196, _1535198), _1535200)), hAPP(c_Set_Ovimage(_1535194, _1535196, _1535198), _1535202)))], (39840 ^ _780461) ^ [_1535268, _1535270, _1535272, _1535274] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1535268, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1535270, _1535268, _1535272), hAPP(c_Set_Ovimage(_1535270, _1535268, _1535272), _1535274))), _1535274)))], (39842 ^ _780461) ^ [_1535321, _1535323, _1535325, _1535327, _1535329, _1535331] : [-(hAPP(c_Set_Ovimage(_1535321, _1535323, _1535325), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535327, tc_fun(_1535323, tc_HOL_Obool)), _1535329), _1535331)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535327, tc_fun(_1535321, tc_HOL_Obool)), _1535329), hAPP(hAPP(c_COMBB(tc_fun(_1535323, tc_HOL_Obool), tc_fun(_1535321, tc_HOL_Obool), _1535327), c_Set_Ovimage(_1535321, _1535323, _1535325)), _1535331)))], (39844 ^ _780461) ^ [_1535405, _1535407, _1535409] : [-(hAPP(c_Set_Ovimage(_1535405, _1535407, _1535409), c_Orderings_Otop__class_Otop(tc_fun(_1535407, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1535405, tc_HOL_Obool)))], (39846 ^ _780461) ^ [_1535449, _1535451, _1535453, _1535455] : [hAPP(c_Set_Oimage(_1535449, _1535451, _1535453), c_Orderings_Otop__class_Otop(tc_fun(_1535449, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1535451, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1535449, _1535451, _1535453), hAPP(c_Set_Ovimage(_1535449, _1535451, _1535453), _1535455)) = _1535455)], (39852 ^ _780461) ^ [_1535616, _1535618, _1535620, _1535622, _1535624] : [hBOOL(hAPP(hAPP(c_member(_1535616), _1535618), hAPP(c_Set_Ovimage(_1535616, _1535620, _1535622), hAPP(hAPP(c_Set_Oinsert(_1535620), _1535624), c_Orderings_Obot__class_Obot(tc_fun(_1535620, tc_HOL_Obool)))))), -(hAPP(_1535622, _1535618) = _1535624)], (39858 ^ _780461) ^ [_1535755, _1535757, _1535759, _1535761, _1535763] : [hAPP(_1535761, _1535757) = _1535763, -(hBOOL(hAPP(hAPP(c_member(_1535755), _1535757), hAPP(c_Set_Ovimage(_1535755, _1535759, _1535761), hAPP(hAPP(c_Set_Oinsert(_1535759), _1535763), c_Orderings_Obot__class_Obot(tc_fun(_1535759, tc_HOL_Obool)))))))], (39864 ^ _780461) ^ [_1535900, _1535902, _1535904, _1535906, _1535908] : [-(hAPP(c_Set_Ovimage(_1535900, _1535902, _1535904), hAPP(hAPP(c_Set_Oinsert(_1535902), _1535906), _1535908)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1535900, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1535900, _1535902, _1535904), hAPP(hAPP(c_Set_Oinsert(_1535902), _1535906), c_Orderings_Obot__class_Obot(tc_fun(_1535902, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1535900, _1535902, _1535904), _1535908)))], (39866 ^ _780461) ^ [_1535984, _1535986, _1535988, _1535990] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535984), hAPP(c_Set_Ovimage(_1535984, _1535986, _1535988), _1535990))), hAPP(c_Set_Oimage(_1535984, _1535986, _1535988), c_Orderings_Otop__class_Otop(tc_fun(_1535984, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1535986, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1535986), _1535990)))], (39876 ^ _780461) ^ [_1536185, _1536187, _1536189, _1536191, _1536193] : [hAPP(c_Set_Oimage(_1536185, _1536187, _1536189), c_Orderings_Otop__class_Otop(tc_fun(_1536185, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1536187, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1536185, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1536185, _1536187, _1536189), _1536191)), _1536193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1536187, tc_HOL_Obool)), _1536191), hAPP(c_Set_Oimage(_1536185, _1536187, _1536189), _1536193))))], (39886 ^ _780461) ^ [_1536428, _1536430, _1536432, _1536434] : [-(hAPP(c_Set_Oimage(_1536428, _1536430, _1536432), hAPP(c_Set_Ovimage(_1536428, _1536430, _1536432), _1536434)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1536430, tc_HOL_Obool)), _1536434), hAPP(c_Set_Oimage(_1536428, _1536430, _1536432), c_Orderings_Otop__class_Otop(tc_fun(_1536428, tc_HOL_Obool)))))], (39888 ^ _780461) ^ [_1536494, _1536496, _1536498, _1536500] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1536494), _1536496)), c_Fun_Oinj__on(_1536498, _1536494, _1536500, c_Orderings_Otop__class_Otop(tc_fun(_1536498, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536498), hAPP(c_Set_Ovimage(_1536498, _1536494, _1536500), _1536496))))], (39898 ^ _780461) ^ [_1536675, _1536677, _1536679, _1536681] : [c_Fun_Oinj__on(_1536675, _1536677, _1536679, c_Orderings_Otop__class_Otop(tc_fun(_1536675, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1536675, _1536677, _1536679), hAPP(c_Set_Oimage(_1536675, _1536677, _1536679), _1536681)) = _1536681)], (39904 ^ _780461) ^ [_1536813, _1536815, _1536817, _1536819] : [hBOOL(hAPP(hAPP(c_member(_1536813), _1536815), _1536817)), -(hAPP(c_Set_Ovimage(_1536819, _1536813, hAPP(c_COMBK(_1536813, _1536819), _1536815)), _1536817) = c_Orderings_Otop__class_Otop(tc_fun(_1536819, tc_HOL_Obool)))], (39910 ^ _780461) ^ [_1536938, _1536940, _1536942, _1536944] : [-(hBOOL(hAPP(hAPP(c_member(_1536938), _1536940), _1536942))), -(hAPP(c_Set_Ovimage(_1536944, _1536938, hAPP(c_COMBK(_1536938, _1536944), _1536940)), _1536942) = c_Orderings_Obot__class_Obot(tc_fun(_1536944, tc_HOL_Obool)))], (39916 ^ _780461) ^ [_1537005, _1537007, _1537009, _1537011] : [-(hAPP(c_Set_Ovimage(_1537005, _1537007, _1537009), _1537011) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537007, tc_fun(_1537005, tc_HOL_Obool)), _1537011), hAPP(hAPP(c_COMBB(tc_fun(_1537007, tc_HOL_Obool), tc_fun(_1537005, tc_HOL_Obool), _1537007), c_Set_Ovimage(_1537005, _1537007, _1537009)), hAPP(hAPP(c_COMBC(_1537007, tc_fun(_1537007, tc_HOL_Obool), tc_fun(_1537007, tc_HOL_Obool)), c_Set_Oinsert(_1537007)), c_Orderings_Obot__class_Obot(tc_fun(_1537007, tc_HOL_Obool))))))], (39918 ^ _780461) ^ [_1537096, _1537098, _1537100, _1537102, _1537104] : [c_Fun_Oinj__on(_1537096, _1537098, _1537100, c_Orderings_Otop__class_Otop(tc_fun(_1537096, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537098, tc_HOL_Obool)), _1537102), hAPP(c_Set_Oimage(_1537096, _1537098, _1537100), _1537104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537096, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1537096, _1537098, _1537100), _1537102)), _1537104)))], (39928 ^ _780461) ^ [_1537340, _1537342, _1537344, _1537346, _1537348, _1537350] : [hBOOL(hAPP(hAPP(c_member(_1537340), _1537342), _1537344)), 39931 ^ _780461 : [(39932 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1537340), _1537346), _1537344)), -(hAPP(c_Set_Ovimage(_1537348, _1537340, hAPP(hAPP(c_COMBC(_1537348, _1537340, _1537340), hAPP(hAPP(c_COMBC(_1537348, _1537340, tc_fun(_1537340, _1537340)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1537340, tc_fun(_1537340, _1537340)), _1537348), c_If(_1537340)), hAPP(hAPP(c_COMBC(_1537348, tc_fun(_1537348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537348)), _1537350))), _1537342)), _1537346)), _1537344) = c_Orderings_Otop__class_Otop(tc_fun(_1537348, tc_HOL_Obool)))], (39938 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537340), _1537346), _1537344))), -(hAPP(c_Set_Ovimage(_1537348, _1537340, hAPP(hAPP(c_COMBC(_1537348, _1537340, _1537340), hAPP(hAPP(c_COMBC(_1537348, _1537340, tc_fun(_1537340, _1537340)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1537340, tc_fun(_1537340, _1537340)), _1537348), c_If(_1537340)), hAPP(hAPP(c_COMBC(_1537348, tc_fun(_1537348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537348)), _1537350))), _1537342)), _1537346)), _1537344) = _1537350)]]], (39944 ^ _780461) ^ [_1537831, _1537833, _1537835, _1537837, _1537839, _1537841] : [-(hBOOL(hAPP(hAPP(c_member(_1537831), _1537833), _1537835))), 39947 ^ _780461 : [(39948 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1537831), _1537837), _1537835)), -(hAPP(c_Set_Ovimage(_1537839, _1537831, hAPP(hAPP(c_COMBC(_1537839, _1537831, _1537831), hAPP(hAPP(c_COMBC(_1537839, _1537831, tc_fun(_1537831, _1537831)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1537831, tc_fun(_1537831, _1537831)), _1537839), c_If(_1537831)), hAPP(hAPP(c_COMBC(_1537839, tc_fun(_1537839, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537839)), _1537841))), _1537833)), _1537837)), _1537835) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1537839, tc_HOL_Obool)), _1537841))], (39954 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537831), _1537837), _1537835))), -(hAPP(c_Set_Ovimage(_1537839, _1537831, hAPP(hAPP(c_COMBC(_1537839, _1537831, _1537831), hAPP(hAPP(c_COMBC(_1537839, _1537831, tc_fun(_1537831, _1537831)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1537831, tc_fun(_1537831, _1537831)), _1537839), c_If(_1537831)), hAPP(hAPP(c_COMBC(_1537839, tc_fun(_1537839, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537839)), _1537841))), _1537833)), _1537837)), _1537835) = c_Orderings_Obot__class_Obot(tc_fun(_1537839, tc_HOL_Obool)))]]], (39960 ^ _780461) ^ [_1538336, _1538338, _1538340, _1538342, _1538344] : [c_Typedef_Otype__definition(_1538336, _1538338, _1538340, _1538342, _1538344), -(hAPP(c_Set_Oimage(_1538336, _1538338, _1538340), c_Orderings_Otop__class_Otop(tc_fun(_1538336, tc_HOL_Obool))) = _1538344)], (39966 ^ _780461) ^ [_1538449, _1538451, _1538453, _1538455, _1538457] : [c_Typedef_Otype__definition(_1538449, _1538451, _1538453, _1538455, _1538457), -(hAPP(c_Set_Oimage(_1538451, _1538449, _1538455), _1538457) = c_Orderings_Otop__class_Otop(tc_fun(_1538449, tc_HOL_Obool)))], (39972 ^ _780461) ^ [_1538562, _1538564, _1538566, _1538568, _1538570, _1538572] : [c_Typedef_Otype__definition(_1538562, _1538564, _1538566, _1538568, _1538570), -(hBOOL(hAPP(hAPP(c_member(_1538564), hAPP(_1538566, _1538572)), _1538570)))], (39978 ^ _780461) ^ [_1538673, _1538675, _1538677, _1538679, _1538681, _1538683, _1538685] : [c_Typedef_Otype__definition(_1538673, _1538675, _1538677, _1538679, _1538681), 39981 ^ _780461 : [(39982 ^ _780461) ^ [] : [hAPP(_1538677, _1538683) = hAPP(_1538677, _1538685), -(_1538683 = _1538685)], (39988 ^ _780461) ^ [] : [_1538683 = _1538685, -(hAPP(_1538677, _1538683) = hAPP(_1538677, _1538685))]]], (39994 ^ _780461) ^ [_1538934, _1538936, _1538938, _1538940, _1538942, _1538944] : [c_Typedef_Otype__definition(_1538934, _1538936, _1538938, _1538940, _1538942), -(hAPP(_1538940, hAPP(_1538938, _1538944)) = _1538944)], (40000 ^ _780461) ^ [_1539037, _1539039, _1539041, _1539043, _1539045, _1539047, _1539049] : [c_Typedef_Otype__definition(_1539037, _1539039, _1539041, _1539043, _1539045), hBOOL(hAPP(hAPP(c_member(_1539039), _1539047), _1539045)), hBOOL(hAPP(hAPP(c_member(_1539039), _1539049), _1539045)), 40011 ^ _780461 : [(40012 ^ _780461) ^ [] : [hAPP(_1539043, _1539047) = hAPP(_1539043, _1539049), -(_1539047 = _1539049)], (40018 ^ _780461) ^ [] : [_1539047 = _1539049, -(hAPP(_1539043, _1539047) = hAPP(_1539043, _1539049))]]], (40024 ^ _780461) ^ [_1539450, _1539452, _1539454, _1539456, _1539458, _1539460] : [c_Typedef_Otype__definition(_1539450, _1539452, _1539454, _1539456, _1539458), hBOOL(hAPP(hAPP(c_member(_1539452), _1539460), _1539458)), -(hAPP(_1539454, hAPP(_1539456, _1539460)) = _1539460)], (40034 ^ _780461) ^ [_1539648, _1539650, _1539652, _1539654] : [c_Wellfounded_Omax__extp(_1539648, _1539650, _1539652, _1539654), 40037 ^ _780461 : [(40038 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1539648), _1539652)))], (40040 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1539648), _1539654)))], (40042 ^ _780461) ^ [] : [_1539654 = c_Orderings_Obot__class_Obot(tc_fun(_1539648, tc_HOL_Obool))], (40044 ^ _780461) ^ [_1539864] : [hBOOL(hAPP(hAPP(c_member(_1539648), _1539864), _1539652)), 40048 ^ _780461 : [(40049 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539648), 40047 ^ [_1539648, _1539650, _1539652, _1539654, _1539864]), _1539654)))], (40051 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1539650, _1539864), 40047 ^ [_1539648, _1539650, _1539652, _1539654, _1539864])))]]]]], (40053 ^ _780461) ^ [_1540048, _1540050, _1540052, _1540054] : [-(c_Wellfounded_Omax__extp(_1540048, _1540050, _1540052, _1540054)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540048), _1540052)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540048), _1540054)), -(_1540054 = c_Orderings_Obot__class_Obot(tc_fun(_1540048, tc_HOL_Obool))), 40067 ^ _780461 : [(40068 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540048), 40066 ^ [_1540048, _1540050, _1540052, _1540054]), _1540052)))], (40070 ^ _780461) ^ [_1540393] : [hBOOL(hAPP(hAPP(c_member(_1540048), _1540393), _1540054)), hBOOL(hAPP(hAPP(_1540050, 40066 ^ [_1540048, _1540050, _1540052, _1540054]), _1540393))]]], (40078 ^ _780461) ^ [_1540561, _1540563, _1540565, _1540567] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1540561), _1540563)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1540561), _1540565)), -(_1540565 = c_Orderings_Obot__class_Obot(tc_fun(_1540561, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1540561, tc_HOL_Obool), tc_fun(_1540561, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1540561, tc_HOL_Obool), tc_fun(_1540561, tc_HOL_Obool)), _1540563), _1540565)), c_Wellfounded_Omax__ext(_1540561, _1540567)))), 40092 ^ _780461 : [(40093 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540561), 40091 ^ [_1540561, _1540563, _1540565, _1540567]), _1540563)))], (40095 ^ _780461) ^ [_1540966] : [hBOOL(hAPP(hAPP(c_member(_1540561), _1540966), _1540565)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1540561, _1540561)), hAPP(hAPP(c_Product__Type_OPair(_1540561, _1540561), 40091 ^ [_1540561, _1540563, _1540565, _1540567]), _1540966)), _1540567))]]], (40103 ^ _780461) ^ [_1541216, _1541218, _1541220, _1541222, _1541224] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1541216, _1541218, hAPP(hAPP(c_Set_Oinsert(_1541216), _1541220), _1541222)), _1541224)), 40108 ^ _780461 : [(40109 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1541216), _1541220), _1541222) = hAPP(hAPP(c_Set_Oinsert(_1541216), 40106 ^ [_1541216, _1541218, _1541220, _1541222, _1541224]), 40107 ^ [_1541216, _1541218, _1541220, _1541222, _1541224]))], (40111 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1541216, _1541216, _1541218, 40106 ^ [_1541216, _1541218, _1541220, _1541222, _1541224], 40107 ^ [_1541216, _1541218, _1541220, _1541222, _1541224]), _1541224)))], (40113 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1541216), 40106 ^ [_1541216, _1541218, _1541220, _1541222, _1541224]), 40107 ^ [_1541216, _1541218, _1541220, _1541222, _1541224]))]]], (40115 ^ _780461) ^ [_1541607, _1541609, _1541611, _1541613, _1541615] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1541607, _1541609, hAPP(hAPP(c_Set_Oinsert(_1541607), _1541611), _1541613)), _1541615))), 40116 ^ _780461 : [(40117 ^ _780461) ^ [_1541711, _1541713] : [hAPP(hAPP(c_Set_Oinsert(_1541607), _1541611), _1541613) = hAPP(hAPP(c_Set_Oinsert(_1541607), _1541713), _1541711), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1541607, _1541607, _1541609, _1541713, _1541711), _1541615)), -(hBOOL(hAPP(hAPP(c_member(_1541607), _1541713), _1541711)))]]], (40129 ^ _780461) ^ [_1541968, _1541970, _1541972, _1541974, _1541976] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1541968, _1541970, hAPP(hAPP(c_Set_Oinsert(_1541968), _1541972), _1541974)), _1541976)), 40134 ^ _780461 : [(40135 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1541968), _1541972), _1541974) = hAPP(hAPP(c_Set_Oinsert(_1541968), 40132 ^ [_1541968, _1541970, _1541972, _1541974, _1541976]), 40133 ^ [_1541968, _1541970, _1541972, _1541974, _1541976]))], (40137 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1541968, _1541968, _1541970, 40132 ^ [_1541968, _1541970, _1541972, _1541974, _1541976], 40133 ^ [_1541968, _1541970, _1541972, _1541974, _1541976]), _1541976)))], (40139 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1541968), 40132 ^ [_1541968, _1541970, _1541972, _1541974, _1541976]), 40133 ^ [_1541968, _1541970, _1541972, _1541974, _1541976]))]]], (40141 ^ _780461) ^ [_1542361, _1542363, _1542365, _1542367, _1542369, _1542371] : [-(hAPP(c_Set_Oimage(_1542361, tc_prod(_1542363, _1542365), hAPP(hAPP(c_COMBS(_1542361, _1542365, tc_prod(_1542363, _1542365)), hAPP(hAPP(c_COMBB(_1542363, tc_fun(_1542365, tc_prod(_1542363, _1542365)), _1542361), c_Product__Type_OPair(_1542363, _1542365)), _1542367)), _1542369)), _1542371) = hAPP(hAPP(c_Product__Type_OSigma(_1542363, _1542365), hAPP(c_Set_Oimage(_1542361, _1542363, _1542367), _1542371)), hAPP(hAPP(c_COMBB(tc_fun(_1542361, tc_HOL_Obool), tc_fun(_1542365, tc_HOL_Obool), _1542363), c_Set_Oimage(_1542361, _1542365, _1542369)), hAPP(hAPP(c_COMBC(_1542363, tc_fun(_1542361, tc_HOL_Obool), tc_fun(_1542361, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542361, tc_HOL_Obool), tc_fun(tc_fun(_1542361, tc_HOL_Obool), tc_fun(_1542361, tc_HOL_Obool)), _1542363), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1542361, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1542363, tc_HOL_Obool), tc_fun(_1542361, tc_HOL_Obool), _1542363), c_Set_Ovimage(_1542361, _1542363, _1542367)), hAPP(hAPP(c_COMBC(_1542363, tc_fun(_1542363, tc_HOL_Obool), tc_fun(_1542363, tc_HOL_Obool)), c_Set_Oinsert(_1542363)), c_Orderings_Obot__class_Obot(tc_fun(_1542363, tc_HOL_Obool)))))), _1542371))))], (40143 ^ _780461) ^ [_1542558, _1542560, _1542562] : [class_Groups_Oab__semigroup__mult(_1542558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542558), _1542560)), -(_1542560 = c_Orderings_Obot__class_Obot(tc_fun(_1542558, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542558), _1542562)), -(_1542562 = c_Orderings_Obot__class_Obot(tc_fun(_1542558, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1542558, tc_HOL_Obool)), _1542560), _1542562) = c_Orderings_Obot__class_Obot(tc_fun(_1542558, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1542558, c_Groups_Otimes__class_Otimes(_1542558)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1542558, tc_HOL_Obool)), _1542560), _1542562)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1542558), hAPP(c_Finite__Set_Ofold1(_1542558, c_Groups_Otimes__class_Otimes(_1542558)), _1542560)), hAPP(c_Finite__Set_Ofold1(_1542558, c_Groups_Otimes__class_Otimes(_1542558)), _1542562)))], (40169 ^ _780461) ^ [_1543065, _1543067, _1543069, _1543071, _1543073, _1543075] : [hBOOL(hAPP(hAPP(c_member(_1543065), _1543067), _1543069)), hBOOL(hAPP(hAPP(c_member(_1543071), _1543073), hAPP(_1543075, _1543067))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543065, _1543071)), hAPP(hAPP(c_Product__Type_OPair(_1543065, _1543071), _1543067), _1543073)), hAPP(hAPP(c_Product__Type_OSigma(_1543065, _1543071), _1543069), _1543075))))], (40179 ^ _780461) ^ [_1543300, _1543302, _1543304, _1543306, _1543308, _1543310] : [hBOOL(hAPP(hAPP(c_member(_1543300), _1543302), _1543304)), 40182 ^ _780461 : [(40183 ^ _780461) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1543306, _1543300), _1543308), hAPP(c_COMBK(tc_fun(_1543300, tc_HOL_Obool), _1543306), _1543304)) = hAPP(hAPP(c_Product__Type_OSigma(_1543306, _1543300), _1543310), hAPP(c_COMBK(tc_fun(_1543300, tc_HOL_Obool), _1543306), _1543304)), -(_1543308 = _1543310)], (40189 ^ _780461) ^ [] : [_1543308 = _1543310, -(hAPP(hAPP(c_Product__Type_OSigma(_1543306, _1543300), _1543308), hAPP(c_COMBK(tc_fun(_1543300, tc_HOL_Obool), _1543306), _1543304)) = hAPP(hAPP(c_Product__Type_OSigma(_1543306, _1543300), _1543310), hAPP(c_COMBK(tc_fun(_1543300, tc_HOL_Obool), _1543306), _1543304)))]]], (40195 ^ _780461) ^ [_1543653, _1543655, _1543657] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1543653, _1543655), c_Orderings_Obot__class_Obot(tc_fun(_1543653, tc_HOL_Obool))), _1543657) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543653, _1543655), tc_HOL_Obool)))], (40197 ^ _780461) ^ [_1543702, _1543704, _1543706, _1543708, _1543710] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1543702, _1543704), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1543702, tc_HOL_Obool)), _1543706), _1543708)), _1543710) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1543702, _1543704), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1543702, _1543704), _1543706), _1543710)), hAPP(hAPP(c_Product__Type_OSigma(_1543702, _1543704), _1543708), _1543710)))], (40199 ^ _780461) ^ [_1543785, _1543787, _1543789, _1543791, _1543793] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1543785, _1543787), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1543785, tc_HOL_Obool)), _1543789), _1543791)), hAPP(c_COMBK(tc_fun(_1543787, tc_HOL_Obool), _1543785), _1543793)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1543785, _1543787), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1543785, _1543787), _1543789), hAPP(c_COMBK(tc_fun(_1543787, tc_HOL_Obool), _1543785), _1543793))), hAPP(hAPP(c_Product__Type_OSigma(_1543785, _1543787), _1543791), hAPP(c_COMBK(tc_fun(_1543787, tc_HOL_Obool), _1543785), _1543793))))], (40201 ^ _780461) ^ [_1543895, _1543897, _1543899, _1543901, _1543903] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1543895, _1543897), _1543899), hAPP(hAPP(c_COMBS(_1543895, tc_fun(_1543897, tc_HOL_Obool), tc_fun(_1543897, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1543897, tc_HOL_Obool), tc_fun(tc_fun(_1543897, tc_HOL_Obool), tc_fun(_1543897, tc_HOL_Obool)), _1543895), c_Groups_Ominus__class_Ominus(tc_fun(_1543897, tc_HOL_Obool))), _1543901)), _1543903)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1543895, _1543897), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1543895, _1543897), _1543899), _1543901)), hAPP(hAPP(c_Product__Type_OSigma(_1543895, _1543897), _1543899), _1543903)))], (40203 ^ _780461) ^ [_1544010, _1544012, _1544014, _1544016] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1544010, _1544012)), hAPP(hAPP(c_Product__Type_OSigma(_1544010, _1544012), _1544014), hAPP(c_COMBK(tc_fun(_1544012, tc_HOL_Obool), _1544010), _1544016))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1544010), _1544014)), hAPP(c_Finite__Set_Ocard(_1544012), _1544016)))], (40205 ^ _780461) ^ [_1544081, _1544083, _1544085, _1544087, _1544089, _1544091] : [class_Groups_Ocomm__monoid__add(_1544081), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544083, _1544081), hAPP(hAPP(c_COMBC(_1544083, tc_fun(_1544085, tc_HOL_Obool), _1544081), hAPP(hAPP(c_COMBB(tc_fun(_1544085, _1544081), tc_fun(tc_fun(_1544085, tc_HOL_Obool), _1544081), _1544083), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544085, _1544081)), _1544087)), _1544089)), _1544091) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1544083, _1544085), _1544081), hAPP(c_Product__Type_Oprod_Oprod__case(_1544083, _1544085, _1544081), _1544087)), hAPP(hAPP(c_Product__Type_OSigma(_1544083, _1544085), _1544091), hAPP(c_COMBK(tc_fun(_1544085, tc_HOL_Obool), _1544083), _1544089))))], (40211 ^ _780461) ^ [_1544326, _1544328, _1544330] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1544326, _1544328), _1544330), hAPP(c_COMBK(tc_fun(_1544328, tc_HOL_Obool), _1544326), c_Orderings_Obot__class_Obot(tc_fun(_1544328, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544326, _1544328), tc_HOL_Obool)))], (40223 ^ _780461) ^ [_1544567, _1544569, _1544571, _1544573] : [40224 ^ _780461 : [(40225 ^ _780461) ^ [] : [_1544571 = c_Orderings_Obot__class_Obot(tc_fun(_1544567, tc_HOL_Obool))], (40227 ^ _780461) ^ [] : [_1544573 = c_Orderings_Obot__class_Obot(tc_fun(_1544569, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1544567, _1544569), _1544571), hAPP(c_COMBK(tc_fun(_1544569, tc_HOL_Obool), _1544567), _1544573)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544567, _1544569), tc_HOL_Obool)))], (40213 ^ _780461) ^ [_1544405, _1544407, _1544409, _1544411] : [hAPP(hAPP(c_Product__Type_OSigma(_1544405, _1544407), _1544409), hAPP(c_COMBK(tc_fun(_1544407, tc_HOL_Obool), _1544405), _1544411)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544405, _1544407), tc_HOL_Obool)), -(_1544409 = c_Orderings_Obot__class_Obot(tc_fun(_1544405, tc_HOL_Obool))), -(_1544411 = c_Orderings_Obot__class_Obot(tc_fun(_1544407, tc_HOL_Obool)))], (40231 ^ _780461) ^ [_1544760, _1544762, _1544764] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1544760, _1544762), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1544760, _1544762), c_Orderings_Otop__class_Otop(tc_fun(_1544760, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1544762, tc_HOL_Obool), _1544760), _1544764))) = hAPP(hAPP(c_Product__Type_OSigma(_1544760, _1544762), c_Orderings_Otop__class_Otop(tc_fun(_1544760, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1544762, tc_HOL_Obool), _1544760), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1544762, tc_HOL_Obool)), _1544764))))], (40233 ^ _780461) ^ [_1544852, _1544854, _1544856] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1544852, _1544854), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1544852, _1544854), _1544856), hAPP(c_COMBK(tc_fun(_1544854, tc_HOL_Obool), _1544852), c_Orderings_Otop__class_Otop(tc_fun(_1544854, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1544852, _1544854), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1544852, tc_HOL_Obool)), _1544856)), hAPP(c_COMBK(tc_fun(_1544854, tc_HOL_Obool), _1544852), c_Orderings_Otop__class_Otop(tc_fun(_1544854, tc_HOL_Obool)))))], (40235 ^ _780461) ^ [_1544944, _1544946, _1544948, _1544950, _1544952, _1544954] : [class_Groups_Ocomm__monoid__mult(_1544944), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1544946, _1544944), hAPP(hAPP(c_COMBC(_1544946, tc_fun(_1544948, tc_HOL_Obool), _1544944), hAPP(hAPP(c_COMBB(tc_fun(_1544948, _1544944), tc_fun(tc_fun(_1544948, tc_HOL_Obool), _1544944), _1544946), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1544948, _1544944)), _1544950)), _1544952)), _1544954) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1544946, _1544948), _1544944), hAPP(c_Product__Type_Oprod_Oprod__case(_1544946, _1544948, _1544944), _1544950)), hAPP(hAPP(c_Product__Type_OSigma(_1544946, _1544948), _1544954), hAPP(c_COMBK(tc_fun(_1544948, tc_HOL_Obool), _1544946), _1544952))))], (40241 ^ _780461) ^ [_1545189, _1545191, _1545193, _1545195, _1545197] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1545189, _1545191), _1545193), hAPP(hAPP(c_COMBS(_1545189, tc_fun(_1545191, tc_HOL_Obool), tc_fun(_1545191, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545191, tc_HOL_Obool), tc_fun(tc_fun(_1545191, tc_HOL_Obool), tc_fun(_1545191, tc_HOL_Obool)), _1545189), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1545191, tc_HOL_Obool))), _1545195)), _1545197)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1545189, _1545191), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1545189, _1545191), _1545193), _1545195)), hAPP(hAPP(c_Product__Type_OSigma(_1545189, _1545191), _1545193), _1545197)))], (40243 ^ _780461) ^ [_1545304, _1545306, _1545308, _1545310, _1545312] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1545304, _1545306), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1545304, tc_HOL_Obool)), _1545308), _1545310)), hAPP(c_COMBK(tc_fun(_1545306, tc_HOL_Obool), _1545304), _1545312)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1545304, _1545306), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1545304, _1545306), _1545308), hAPP(c_COMBK(tc_fun(_1545306, tc_HOL_Obool), _1545304), _1545312))), hAPP(hAPP(c_Product__Type_OSigma(_1545304, _1545306), _1545310), hAPP(c_COMBK(tc_fun(_1545306, tc_HOL_Obool), _1545304), _1545312))))], (40245 ^ _780461) ^ [_1545414, _1545416, _1545418, _1545420, _1545422] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1545414, _1545416), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1545414, tc_HOL_Obool)), _1545418), _1545420)), _1545422) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1545414, _1545416), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1545414, _1545416), _1545418), _1545422)), hAPP(hAPP(c_Product__Type_OSigma(_1545414, _1545416), _1545420), _1545422)))], (40247 ^ _780461) ^ [_1545497, _1545499, _1545501, _1545503] : [-(hAPP(c_Set_Oimage(tc_prod(_1545497, _1545499), tc_prod(_1545499, _1545497), hAPP(c_Product__Type_Oprod_Oprod__case(_1545497, _1545499, tc_prod(_1545499, _1545497)), hAPP(c_COMBC(_1545499, _1545497, tc_prod(_1545499, _1545497)), c_Product__Type_OPair(_1545499, _1545497)))), hAPP(hAPP(c_Product__Type_OSigma(_1545497, _1545499), _1545501), hAPP(c_COMBK(tc_fun(_1545499, tc_HOL_Obool), _1545497), _1545503))) = hAPP(hAPP(c_Product__Type_OSigma(_1545499, _1545497), _1545503), hAPP(c_COMBK(tc_fun(_1545497, tc_HOL_Obool), _1545499), _1545501)))], (40249 ^ _780461) ^ [_1545598, _1545600, _1545602, _1545604] : [_1545598 = c_Finite__Set_Ofold1(_1545600, _1545602), -(hAPP(_1545598, hAPP(hAPP(c_Set_Oinsert(_1545600), _1545604), c_Orderings_Obot__class_Obot(tc_fun(_1545600, tc_HOL_Obool)))) = _1545604)], (40255 ^ _780461) ^ [_1545717, _1545719, _1545721] : [-(hAPP(c_Finite__Set_Ofold1(_1545717, _1545719), hAPP(hAPP(c_Set_Oinsert(_1545717), _1545721), c_Orderings_Obot__class_Obot(tc_fun(_1545717, tc_HOL_Obool)))) = _1545721)], (40257 ^ _780461) ^ [_1545763, _1545765, _1545767, _1545769] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1545763), _1545765)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545767), _1545769)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1545763, _1545767)), hAPP(hAPP(c_Product__Type_OSigma(_1545763, _1545767), _1545765), hAPP(c_COMBK(tc_fun(_1545767, tc_HOL_Obool), _1545763), _1545769)))))], (40267 ^ _780461) ^ [_1545966, _1545968, _1545970] : [c_Equiv__Relations_Oequiv(_1545966, _1545968, _1545970), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1545966, _1545966), tc_HOL_Obool)), _1545970), hAPP(hAPP(c_Product__Type_OSigma(_1545966, _1545966), _1545968), hAPP(c_COMBK(tc_fun(_1545966, tc_HOL_Obool), _1545966), _1545968)))))], (40273 ^ _780461) ^ [_1546109, _1546111, _1546113, _1546115, _1546117] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1546109, _1546111), _1546113), hAPP(hAPP(c_COMBS(_1546109, tc_fun(_1546111, tc_HOL_Obool), tc_fun(_1546111, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546111, tc_HOL_Obool), tc_fun(tc_fun(_1546111, tc_HOL_Obool), tc_fun(_1546111, tc_HOL_Obool)), _1546109), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1546111, tc_HOL_Obool))), _1546115)), _1546117)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1546109, _1546111), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1546109, _1546111), _1546113), _1546115)), hAPP(hAPP(c_Product__Type_OSigma(_1546109, _1546111), _1546113), _1546117)))], (40275 ^ _780461) ^ [_1546224, _1546226, _1546228, _1546230, _1546232] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1546224, _1546226), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1546224, tc_HOL_Obool)), _1546228), _1546230)), hAPP(c_COMBK(tc_fun(_1546226, tc_HOL_Obool), _1546224), _1546232)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1546224, _1546226), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1546224, _1546226), _1546228), hAPP(c_COMBK(tc_fun(_1546226, tc_HOL_Obool), _1546224), _1546232))), hAPP(hAPP(c_Product__Type_OSigma(_1546224, _1546226), _1546230), hAPP(c_COMBK(tc_fun(_1546226, tc_HOL_Obool), _1546224), _1546232))))], (40277 ^ _780461) ^ [_1546334, _1546336, _1546338, _1546340, _1546342] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1546334, _1546336), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1546334, tc_HOL_Obool)), _1546338), _1546340)), _1546342) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1546334, _1546336), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1546334, _1546336), _1546338), _1546342)), hAPP(hAPP(c_Product__Type_OSigma(_1546334, _1546336), _1546340), _1546342)))], (40279 ^ _780461) ^ [_1546417, _1546419] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1546417, _1546417), tc_HOL_Obool)), c_Relation_OId__on(_1546417, _1546419)), hAPP(hAPP(c_Product__Type_OSigma(_1546417, _1546417), _1546419), hAPP(c_COMBK(tc_fun(_1546417, tc_HOL_Obool), _1546417), _1546419)))))], (40281 ^ _780461) ^ [_1546476, _1546478] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1546476, _1546478), c_Orderings_Otop__class_Otop(tc_fun(_1546476, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1546478, tc_HOL_Obool), _1546476), c_Orderings_Otop__class_Otop(tc_fun(_1546478, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1546476, _1546478), tc_HOL_Obool)))], (40283 ^ _780461) ^ [_1546537, _1546539, _1546541, _1546543, _1546545, _1546547] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546537, _1546539)), hAPP(hAPP(c_Product__Type_OPair(_1546537, _1546539), _1546541), _1546543)), hAPP(hAPP(c_Product__Type_OSigma(_1546537, _1546539), _1546545), _1546547))), 40286 ^ _780461 : [(40287 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546537), _1546541), _1546545)))], (40289 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546539), _1546543), hAPP(_1546547, _1546541))))]]], (40291 ^ _780461) ^ [_1546742, _1546744, _1546746, _1546748, _1546750, _1546752] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546742, _1546744)), hAPP(hAPP(c_Product__Type_OPair(_1546742, _1546744), _1546746), _1546748)), hAPP(hAPP(c_Product__Type_OSigma(_1546742, _1546744), _1546750), _1546752))), -(hBOOL(hAPP(hAPP(c_member(_1546744), _1546748), hAPP(_1546752, _1546746))))], (40297 ^ _780461) ^ [_1546903, _1546905, _1546907, _1546909, _1546911, _1546913] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546903, _1546905)), hAPP(hAPP(c_Product__Type_OPair(_1546903, _1546905), _1546907), _1546909)), hAPP(hAPP(c_Product__Type_OSigma(_1546903, _1546905), _1546911), _1546913))), -(hBOOL(hAPP(hAPP(c_member(_1546903), _1546907), _1546911)))], (40303 ^ _780461) ^ [_1547085, _1547087, _1547089, _1547091, _1547093, _1547095] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547085, _1547087)), hAPP(hAPP(c_Product__Type_OPair(_1547085, _1547087), _1547089), _1547091)), hAPP(hAPP(c_Product__Type_OSigma(_1547085, _1547087), _1547093), _1547095))), 40306 ^ _780461 : [(40307 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547085), _1547089), _1547093)))], (40309 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547087), _1547091), hAPP(_1547095, _1547089))))]]], (40311 ^ _780461) ^ [_1547282, _1547284, _1547286, _1547288, _1547290, _1547292] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547282, _1547284)), hAPP(hAPP(c_Product__Type_OPair(_1547282, _1547284), _1547286), _1547288)), hAPP(hAPP(c_Product__Type_OSigma(_1547282, _1547284), _1547290), _1547292)))), hBOOL(hAPP(hAPP(c_member(_1547282), _1547286), _1547290)), hBOOL(hAPP(hAPP(c_member(_1547284), _1547288), hAPP(_1547292, _1547286)))], (40321 ^ _780461) ^ [_1547519, _1547521, _1547523, _1547525] : [c_Finite__Set_Ofolding__one(_1547519, _1547521, _1547523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547519), _1547525)), -(hAPP(_1547523, _1547525) = hAPP(c_Finite__Set_Ofold1(_1547519, _1547521), _1547525))], (40331 ^ _780461) ^ [_1547684, _1547686, _1547688, _1547690] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1547684, _1547686)), hAPP(hAPP(c_Product__Type_OSigma(_1547684, _1547686), hAPP(hAPP(c_Set_Oinsert(_1547684), _1547688), c_Orderings_Obot__class_Obot(tc_fun(_1547684, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1547686, tc_HOL_Obool), _1547684), _1547690))) = hAPP(c_Finite__Set_Ocard(_1547686), _1547690))], (40333 ^ _780461) ^ [_1547757, _1547759, _1547761, _1547763, _1547765, _1547767] : [hBOOL(hAPP(hAPP(c_member(_1547757), _1547759), _1547761)), 40336 ^ _780461 : [(40337 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547763, _1547757), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1547763, _1547757), _1547765), hAPP(c_COMBK(tc_fun(_1547757, tc_HOL_Obool), _1547763), _1547761))), hAPP(hAPP(c_Product__Type_OSigma(_1547763, _1547757), _1547767), hAPP(c_COMBK(tc_fun(_1547757, tc_HOL_Obool), _1547763), _1547761)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1547763, tc_HOL_Obool)), _1547765), _1547767)))], (40343 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1547763, tc_HOL_Obool)), _1547765), _1547767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547763, _1547757), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1547763, _1547757), _1547765), hAPP(c_COMBK(tc_fun(_1547757, tc_HOL_Obool), _1547763), _1547761))), hAPP(hAPP(c_Product__Type_OSigma(_1547763, _1547757), _1547767), hAPP(c_COMBK(tc_fun(_1547757, tc_HOL_Obool), _1547763), _1547761)))))]]], (40349 ^ _780461) ^ [_1548179, _1548181, _1548183, _1548185, _1548187, _1548189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1548179, _1548181), tc_HOL_Obool)), _1548183), hAPP(hAPP(c_Product__Type_OSigma(_1548179, _1548181), _1548185), hAPP(c_COMBK(tc_fun(_1548181, tc_HOL_Obool), _1548179), _1548187)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1548181, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1548179, _1548181, _1548183), _1548189)), _1548187)))], (40355 ^ _780461) ^ [_1548360, _1548362, _1548364, _1548366] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548360, _1548362)), hAPP(hAPP(c_Product__Type_OSigma(_1548360, _1548362), _1548364), hAPP(c_COMBK(tc_fun(_1548362, tc_HOL_Obool), _1548360), _1548366)))), -(_1548364 = c_Orderings_Obot__class_Obot(tc_fun(_1548360, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1548362), _1548366)))], (40365 ^ _780461) ^ [_1548524, _1548526, _1548528, _1548530] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548524, _1548526)), hAPP(hAPP(c_Product__Type_OSigma(_1548524, _1548526), _1548528), hAPP(c_COMBK(tc_fun(_1548526, tc_HOL_Obool), _1548524), _1548530)))), -(_1548530 = c_Orderings_Obot__class_Obot(tc_fun(_1548526, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1548524), _1548528)))], (40375 ^ _780461) ^ [_1548703, _1548705, _1548707, _1548709] : [_1548703 = c_Orderings_Obot__class_Obot(tc_fun(_1548705, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1548707, _1548705), _1548707, c_Product__Type_Ofst(_1548707, _1548705)), hAPP(hAPP(c_Product__Type_OSigma(_1548707, _1548705), _1548709), hAPP(c_COMBK(tc_fun(_1548705, tc_HOL_Obool), _1548707), _1548703))) = c_Orderings_Obot__class_Obot(tc_fun(_1548707, tc_HOL_Obool)))], (40381 ^ _780461) ^ [_1548860, _1548862, _1548864, _1548866] : [-(_1548860 = c_Orderings_Obot__class_Obot(tc_fun(_1548862, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1548864, _1548862), _1548864, c_Product__Type_Ofst(_1548864, _1548862)), hAPP(hAPP(c_Product__Type_OSigma(_1548864, _1548862), _1548866), hAPP(c_COMBK(tc_fun(_1548862, tc_HOL_Obool), _1548864), _1548860))) = _1548866)], (40387 ^ _780461) ^ [_1548953, _1548955, _1548957, _1548959] : [_1548953 = c_Orderings_Obot__class_Obot(tc_fun(_1548955, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1548955, _1548957), _1548957, c_Product__Type_Osnd(_1548955, _1548957)), hAPP(hAPP(c_Product__Type_OSigma(_1548955, _1548957), _1548953), hAPP(c_COMBK(tc_fun(_1548957, tc_HOL_Obool), _1548955), _1548959))) = c_Orderings_Obot__class_Obot(tc_fun(_1548957, tc_HOL_Obool)))], (40393 ^ _780461) ^ [_1549110, _1549112, _1549114, _1549116] : [-(_1549110 = c_Orderings_Obot__class_Obot(tc_fun(_1549112, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1549112, _1549114), _1549114, c_Product__Type_Osnd(_1549112, _1549114)), hAPP(hAPP(c_Product__Type_OSigma(_1549112, _1549114), _1549110), hAPP(c_COMBK(tc_fun(_1549114, tc_HOL_Obool), _1549112), _1549116))) = _1549116)], (40399 ^ _780461) ^ [_1549188, _1549190, _1549192] : [-(hAPP(c_Finite__Set_Ofold1(_1549188, _1549190), _1549192) = c_HOL_OThe(_1549188, c_Finite__Set_Ofold1Set(_1549188, _1549190, _1549192)))], (40401 ^ _780461) ^ [_1549228, _1549230] : [class_Lattices_Olattice(_1549228), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549228), _1549230)), -(c_Big__Operators_Olattice__class_OSup__fin(_1549228, _1549230) = hAPP(c_Finite__Set_Ofold1(_1549228, c_Lattices_Osemilattice__sup__class_Osup(_1549228)), _1549230))], (40411 ^ _780461) ^ [_1549385, _1549387] : [class_Lattices_Olattice(_1549385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549385), _1549387)), -(c_Big__Operators_Olattice__class_OInf__fin(_1549385, _1549387) = hAPP(c_Finite__Set_Ofold1(_1549385, c_Lattices_Osemilattice__inf__class_Oinf(_1549385)), _1549387))], (40421 ^ _780461) ^ [_1549542, _1549544] : [class_Orderings_Olinorder(_1549542), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549542), _1549544)), -(c_Big__Operators_Olinorder__class_OMin(_1549542, _1549544) = hAPP(c_Finite__Set_Ofold1(_1549542, c_Orderings_Oord__class_Omin(_1549542)), _1549544))], (40431 ^ _780461) ^ [_1549699, _1549701] : [class_Orderings_Olinorder(_1549699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549699), _1549701)), -(c_Big__Operators_Olinorder__class_OMax(_1549699, _1549701) = hAPP(c_Finite__Set_Ofold1(_1549699, c_Orderings_Oord__class_Omax(_1549699)), _1549701))], (40441 ^ _780461) ^ [_1549856, _1549858] : [class_Orderings_Olinorder(_1549856), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549856), _1549858)), -(c_Big__Operators_Olattice_OInf__fin(_1549856, c_Orderings_Oord__class_Omin(_1549856), _1549858) = hAPP(c_Finite__Set_Ofold1(_1549856, c_Orderings_Oord__class_Omin(_1549856)), _1549858))], (40451 ^ _780461) ^ [_1550019, _1550021] : [class_Orderings_Olinorder(_1550019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550019), _1550021)), -(c_Big__Operators_Olattice_OSup__fin(_1550019, c_Orderings_Oord__class_Omax(_1550019), _1550021) = hAPP(c_Finite__Set_Ofold1(_1550019, c_Orderings_Oord__class_Omax(_1550019)), _1550021))], (40461 ^ _780461) ^ [_1550200, _1550202, _1550204] : [c_Relation_Orefl__on(_1550200, _1550202, _1550204), 40464 ^ _780461 : [(40465 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1550200, _1550200), tc_HOL_Obool)), _1550204), hAPP(hAPP(c_Product__Type_OSigma(_1550200, _1550200), _1550202), hAPP(c_COMBK(tc_fun(_1550200, tc_HOL_Obool), _1550200), _1550202)))))], (40467 ^ _780461) ^ [_1550382] : [hBOOL(hAPP(hAPP(c_member(_1550200), _1550382), _1550202)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1550200, _1550200)), hAPP(hAPP(c_Product__Type_OPair(_1550200, _1550200), _1550382), _1550382)), _1550204)))]]], (40473 ^ _780461) ^ [_1550517, _1550519, _1550521] : [-(c_Relation_Orefl__on(_1550517, _1550519, _1550521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1550517, _1550517), tc_HOL_Obool)), _1550521), hAPP(hAPP(c_Product__Type_OSigma(_1550517, _1550517), _1550519), hAPP(c_COMBK(tc_fun(_1550517, tc_HOL_Obool), _1550517), _1550519)))), 40479 ^ _780461 : [(40480 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550517), 40478 ^ [_1550517, _1550519, _1550521]), _1550519)))], (40482 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1550517, _1550517)), hAPP(hAPP(c_Product__Type_OPair(_1550517, _1550517), 40478 ^ [_1550517, _1550519, _1550521]), 40478 ^ [_1550517, _1550519, _1550521])), _1550521))]]], (40486 ^ _780461) ^ [_1550866, _1550868, _1550870, _1550872, _1550874, _1550876] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1550866, _1550868), hAPP(hAPP(c_Set_Oinsert(_1550866), _1550870), _1550872)), hAPP(c_COMBK(tc_fun(_1550868, tc_HOL_Obool), _1550866), hAPP(hAPP(c_Set_Oinsert(_1550868), _1550874), _1550876))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1550866, _1550868)), hAPP(hAPP(c_Product__Type_OPair(_1550866, _1550868), _1550870), _1550874)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1550866, _1550868), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1550866, _1550868), _1550872), hAPP(c_COMBK(tc_fun(_1550868, tc_HOL_Obool), _1550866), hAPP(hAPP(c_Set_Oinsert(_1550868), _1550874), _1550876)))), hAPP(hAPP(c_Product__Type_OSigma(_1550866, _1550868), hAPP(hAPP(c_Set_Oinsert(_1550866), _1550870), _1550872)), hAPP(c_COMBK(tc_fun(_1550868, tc_HOL_Obool), _1550866), _1550876)))))], (40488 ^ _780461) ^ [_1551019, _1551021, _1551023, _1551025] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1551019), _1551021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1551019, _1551019), tc_HOL_Obool)), _1551023), hAPP(hAPP(c_Product__Type_OSigma(_1551019, _1551019), _1551021), hAPP(c_COMBK(tc_fun(_1551019, tc_HOL_Obool), _1551019), _1551021)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1551019, tc_HOL_Obool)), _1551025), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1551019), _1551021), _1551023))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1551019), _1551025)))], (40502 ^ _780461) ^ [_1551326, _1551328, _1551330, _1551332, _1551334, _1551336, _1551338, _1551340] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1551326, _1551328), tc_fun(tc_prod(_1551330, _1551332), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551326, _1551328), _1551334), hAPP(c_COMBK(tc_fun(_1551328, tc_HOL_Obool), _1551326), _1551336))), hAPP(c_Product__Type_Oprod_Oprod__case(_1551326, _1551328, tc_fun(tc_prod(_1551330, _1551332), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1551326, tc_fun(_1551328, tc_fun(_1551330, tc_fun(_1551332, tc_HOL_Obool))), tc_fun(_1551328, tc_fun(tc_prod(_1551330, _1551332), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1551330, tc_fun(_1551332, tc_HOL_Obool)), tc_fun(tc_prod(_1551330, _1551332), tc_HOL_Obool)), tc_fun(tc_fun(_1551328, tc_fun(_1551330, tc_fun(_1551332, tc_HOL_Obool))), tc_fun(_1551328, tc_fun(tc_prod(_1551330, _1551332), tc_HOL_Obool))), _1551326), c_COMBB(tc_fun(_1551330, tc_fun(_1551332, tc_HOL_Obool)), tc_fun(tc_prod(_1551330, _1551332), tc_HOL_Obool), _1551328)), hAPP(hAPP(c_COMBB(tc_fun(_1551330, tc_HOL_Obool), tc_fun(tc_fun(_1551330, tc_fun(_1551332, tc_HOL_Obool)), tc_fun(tc_prod(_1551330, _1551332), tc_HOL_Obool)), _1551326), c_Product__Type_OSigma(_1551330, _1551332)), _1551338))), hAPP(hAPP(c_COMBB(tc_fun(_1551332, tc_HOL_Obool), tc_fun(_1551330, tc_fun(_1551332, tc_HOL_Obool)), _1551328), c_COMBK(tc_fun(_1551332, tc_HOL_Obool), _1551330)), _1551340)))) = hAPP(hAPP(c_Product__Type_OSigma(_1551330, _1551332), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1551326, tc_fun(_1551330, tc_HOL_Obool)), _1551334), _1551338)), hAPP(c_COMBK(tc_fun(_1551332, tc_HOL_Obool), _1551330), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1551328, tc_fun(_1551332, tc_HOL_Obool)), _1551336), _1551340))))], (40504 ^ _780461) ^ [_1551600, _1551602, _1551604, _1551606] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1551600, _1551602), _1551604), _1551606) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1551600, tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool)), _1551604), hAPP(hAPP(c_COMBS(_1551600, tc_fun(_1551602, tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool)), tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551602, tc_HOL_Obool), tc_fun(tc_fun(_1551602, tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool)), tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool)), _1551600), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1551602, tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool))), _1551606)), hAPP(hAPP(c_COMBC(_1551600, tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool), tc_fun(_1551602, tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1551602, tc_fun(tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool), tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool), tc_fun(_1551602, tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool))), _1551600), c_COMBC(_1551602, tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool), tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1551602, tc_prod(_1551600, _1551602)), tc_fun(_1551602, tc_fun(tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool), tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool))), _1551600), hAPP(c_COMBB(tc_prod(_1551600, _1551602), tc_fun(tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool), tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool)), _1551602), c_Set_Oinsert(tc_prod(_1551600, _1551602)))), c_Product__Type_OPair(_1551600, _1551602)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551600, _1551602), tc_HOL_Obool))))))], (40506 ^ _780461) ^ [_1551880, _1551882, _1551884] : [class_Lattices_Osemilattice__inf(_1551880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551880), _1551882)), hBOOL(hAPP(hAPP(c_member(_1551880), _1551884), _1551882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551880), hAPP(c_Finite__Set_Ofold1(_1551880, c_Lattices_Osemilattice__inf__class_Oinf(_1551880)), _1551882)), _1551884)))], (40520 ^ _780461) ^ [_1552117, _1552119, _1552121] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552117), _1552119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552117, _1552117), tc_HOL_Obool)), _1552121), hAPP(hAPP(c_Product__Type_OSigma(_1552117, _1552117), _1552119), hAPP(c_COMBK(tc_fun(_1552117, tc_HOL_Obool), _1552117), _1552119)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1552117, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1552117), _1552119), _1552121))))], (40530 ^ _780461) ^ [_1552350, _1552352, _1552354] : [class_Lattices_Osemilattice__inf(_1552350), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552350), _1552352)), -(_1552352 = c_Orderings_Obot__class_Obot(tc_fun(_1552350, tc_HOL_Obool))), 40541 ^ _780461 : [(40552 ^ _780461) ^ [] : [40554 ^ _780461 : [(40555 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1552350), 40553 ^ [_1552350, _1552352, _1552354]), _1552352)))], (40557 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552350), _1552354), 40553 ^ [_1552350, _1552352, _1552354]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552350), _1552354), hAPP(c_Finite__Set_Ofold1(_1552350, c_Lattices_Osemilattice__inf__class_Oinf(_1552350)), _1552352))))], (40542 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552350), _1552354), hAPP(c_Finite__Set_Ofold1(_1552350, c_Lattices_Osemilattice__inf__class_Oinf(_1552350)), _1552352))), 40545 ^ _780461 : [(40546 ^ _780461) ^ [_1552643] : [hBOOL(hAPP(hAPP(c_member(_1552350), _1552643), _1552352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552350), _1552354), _1552643)))]]]]], (40561 ^ _780461) ^ [_1552928, _1552930, _1552932] : [class_Orderings_Olinorder(_1552928), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552928), _1552930)), hBOOL(hAPP(hAPP(c_member(_1552928), _1552932), _1552930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552928), hAPP(c_Finite__Set_Ofold1(_1552928, c_Orderings_Oord__class_Omin(_1552928)), _1552930)), _1552932)))], (40575 ^ _780461) ^ [_1553165, _1553167, _1553169] : [class_Lattices_Oab__semigroup__idem__mult(_1553165), -(_1553167 = c_Orderings_Obot__class_Obot(tc_fun(_1553165, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553165), _1553167)), -(hAPP(c_Finite__Set_Ofold1(_1553165, c_Groups_Otimes__class_Otimes(_1553165)), hAPP(hAPP(c_Set_Oinsert(_1553165), _1553169), _1553167)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1553165), _1553169), hAPP(c_Finite__Set_Ofold1(_1553165, c_Groups_Otimes__class_Otimes(_1553165)), _1553167)))], (40589 ^ _780461) ^ [_1553435, _1553437, _1553439] : [class_Orderings_Olinorder(_1553435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553435), _1553437)), -(_1553437 = c_Orderings_Obot__class_Obot(tc_fun(_1553435, tc_HOL_Obool))), 40600 ^ _780461 : [(40601 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553435), hAPP(c_Finite__Set_Ofold1(_1553435, c_Orderings_Oord__class_Omin(_1553435)), _1553437)), _1553439)), 40605 ^ _780461 : [(40606 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553435), 40604 ^ [_1553435, _1553437, _1553439]), _1553437)))], (40608 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553435), 40604 ^ [_1553435, _1553437, _1553439]), _1553439)))]]], (40610 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553435), hAPP(c_Finite__Set_Ofold1(_1553435, c_Orderings_Oord__class_Omin(_1553435)), _1553437)), _1553439))), 40611 ^ _780461 : [(40612 ^ _780461) ^ [_1553824] : [hBOOL(hAPP(hAPP(c_member(_1553435), _1553824), _1553437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553435), _1553824), _1553439))]]]]], (40620 ^ _780461) ^ [_1553985, _1553987, _1553989] : [class_Orderings_Olinorder(_1553985), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553985), _1553987)), -(_1553987 = c_Orderings_Obot__class_Obot(tc_fun(_1553985, tc_HOL_Obool))), 40631 ^ _780461 : [(40642 ^ _780461) ^ [] : [40644 ^ _780461 : [(40645 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553985), 40643 ^ [_1553985, _1553987, _1553989]), _1553987)))], (40647 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553985), _1553989), 40643 ^ [_1553985, _1553987, _1553989]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553985), _1553989), hAPP(c_Finite__Set_Ofold1(_1553985, c_Orderings_Oord__class_Omin(_1553985)), _1553987))))], (40632 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553985), _1553989), hAPP(c_Finite__Set_Ofold1(_1553985, c_Orderings_Oord__class_Omin(_1553985)), _1553987))), 40635 ^ _780461 : [(40636 ^ _780461) ^ [_1554278] : [hBOOL(hAPP(hAPP(c_member(_1553985), _1554278), _1553987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553985), _1553989), _1554278)))]]]]], (40651 ^ _780461) ^ [_1554563, _1554565, _1554567] : [class_Lattices_Oab__semigroup__idem__mult(_1554563), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554563), _1554565)), -(_1554565 = c_Orderings_Obot__class_Obot(tc_fun(_1554563, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554563), _1554567)), -(_1554567 = c_Orderings_Obot__class_Obot(tc_fun(_1554563, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1554563, c_Groups_Otimes__class_Otimes(_1554563)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1554563, tc_HOL_Obool)), _1554565), _1554567)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1554563), hAPP(c_Finite__Set_Ofold1(_1554563, c_Groups_Otimes__class_Otimes(_1554563)), _1554565)), hAPP(c_Finite__Set_Ofold1(_1554563, c_Groups_Otimes__class_Otimes(_1554563)), _1554567)))], (40673 ^ _780461) ^ [_1554942, _1554944, _1554946] : [class_Orderings_Olinorder(_1554942), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554942), _1554944)), -(_1554944 = c_Orderings_Obot__class_Obot(tc_fun(_1554942, tc_HOL_Obool))), 40684 ^ _780461 : [(40685 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554942), hAPP(c_Finite__Set_Ofold1(_1554942, c_Orderings_Oord__class_Omin(_1554942)), _1554944)), _1554946)), 40689 ^ _780461 : [(40690 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554942), 40688 ^ [_1554942, _1554944, _1554946]), _1554944)))], (40692 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554942), 40688 ^ [_1554942, _1554944, _1554946]), _1554946)))]]], (40694 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554942), hAPP(c_Finite__Set_Ofold1(_1554942, c_Orderings_Oord__class_Omin(_1554942)), _1554944)), _1554946))), 40695 ^ _780461 : [(40696 ^ _780461) ^ [_1555331] : [hBOOL(hAPP(hAPP(c_member(_1554942), _1555331), _1554944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1554942), _1555331), _1554946))]]]]], (40704 ^ _780461) ^ [_1555492, _1555494, _1555496] : [class_Orderings_Olinorder(_1555492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555492), _1555494)), -(_1555494 = c_Orderings_Obot__class_Obot(tc_fun(_1555492, tc_HOL_Obool))), 40715 ^ _780461 : [(40726 ^ _780461) ^ [] : [40728 ^ _780461 : [(40729 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555492), 40727 ^ [_1555492, _1555494, _1555496]), _1555494)))], (40731 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555492), _1555496), 40727 ^ [_1555492, _1555494, _1555496]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555492), _1555496), hAPP(c_Finite__Set_Ofold1(_1555492, c_Orderings_Oord__class_Omin(_1555492)), _1555494))))], (40716 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555492), _1555496), hAPP(c_Finite__Set_Ofold1(_1555492, c_Orderings_Oord__class_Omin(_1555492)), _1555494))), 40719 ^ _780461 : [(40720 ^ _780461) ^ [_1555785] : [hBOOL(hAPP(hAPP(c_member(_1555492), _1555785), _1555494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555492), _1555496), _1555785)))]]]]], (40735 ^ _780461) ^ [_1556070, _1556072, _1556074, _1556076, _1556078, _1556080] : [-(hAPP(c_Set_Ovimage(_1556070, tc_prod(_1556072, _1556074), _1556076), hAPP(hAPP(c_Product__Type_OSigma(_1556072, _1556074), _1556078), hAPP(c_COMBK(tc_fun(_1556074, tc_HOL_Obool), _1556072), _1556080))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1556070, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1556070, _1556072, hAPP(c_Fun_Ocomp(tc_prod(_1556072, _1556074), _1556072, _1556070, c_Product__Type_Ofst(_1556072, _1556074)), _1556076)), _1556078)), hAPP(c_Set_Ovimage(_1556070, _1556074, hAPP(c_Fun_Ocomp(tc_prod(_1556072, _1556074), _1556074, _1556070, c_Product__Type_Osnd(_1556072, _1556074)), _1556076)), _1556080)))], (40737 ^ _780461) ^ [_1556184, _1556186, _1556188] : [class_Groups_Oab__semigroup__mult(_1556184), -(_1556186 = c_Orderings_Obot__class_Obot(tc_fun(_1556184, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556184), _1556186)), -(hBOOL(hAPP(hAPP(c_member(_1556184), _1556188), _1556186))), -(hAPP(c_Finite__Set_Ofold1(_1556184, c_Groups_Otimes__class_Otimes(_1556184)), hAPP(hAPP(c_Set_Oinsert(_1556184), _1556188), _1556186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1556184), _1556188), hAPP(c_Finite__Set_Ofold1(_1556184, c_Groups_Otimes__class_Otimes(_1556184)), _1556186)))], (40755 ^ _780461) ^ [_1556483, _1556485, _1556487] : [class_Orderings_Olinorder(_1556483), -(_1556485 = c_Orderings_Obot__class_Obot(tc_fun(_1556483, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1556483, tc_HOL_Obool)), _1556485), _1556487)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556483), _1556487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1556483), hAPP(c_Finite__Set_Ofold1(_1556483, c_Orderings_Oord__class_Omin(_1556483)), _1556487)), hAPP(c_Finite__Set_Ofold1(_1556483, c_Orderings_Oord__class_Omin(_1556483)), _1556485))))], (40773 ^ _780461) ^ [_1556809, _1556811, _1556813, _1556815] : [c_Big__Operators_Osemilattice__big(_1556809, _1556811, _1556813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556809), _1556815)), -(hAPP(_1556813, _1556815) = hAPP(c_Finite__Set_Ofold1(_1556809, _1556811), _1556815))], (40784 ^ _780461) ^ [_1556972, _1556974, _1556976, _1556978] : [-(c_Fun_Oinj__on(_1556972, tc_prod(_1556974, _1556972), 40782 ^ [_1556972, _1556974, _1556976, _1556978], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1556974, tc_fun(_1556972, tc_HOL_Obool)), _1556976), _1556978)))], (40786 ^ _780461) ^ [_1557026, _1557028, _1557030, _1557032] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557028, _1557026), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1557026, tc_prod(_1557028, _1557026), 40782 ^ [_1557026, _1557028, _1557030, _1557032]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557028, tc_fun(_1557026, tc_HOL_Obool)), _1557030), _1557032))), hAPP(hAPP(c_Product__Type_OSigma(_1557028, _1557026), _1557030), _1557032))))], (40788 ^ _780461) ^ [_1557112, _1557114, _1557116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557112, _1557112), tc_HOL_Obool)), _1557114), hAPP(hAPP(c_Product__Type_OSigma(_1557112, _1557112), _1557116), hAPP(c_COMBK(tc_fun(_1557112, tc_HOL_Obool), _1557112), _1557116)))), 40794 ^ _780461 : [(40795 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557112), 40793 ^ [_1557112, _1557114, _1557116]), _1557116)))], (40797 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1557112, _1557112)), hAPP(hAPP(c_Product__Type_OPair(_1557112, _1557112), 40793 ^ [_1557112, _1557114, _1557116]), 40793 ^ [_1557112, _1557114, _1557116])), _1557114))]], -(c_Relation_Orefl__on(_1557112, _1557116, _1557114))], (40801 ^ _780461) ^ [_1557459, _1557461, _1557463, _1557465, _1557467, _1557469] : [class_Groups_Ocomm__monoid__mult(_1557459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557461), _1557463)), 40811 ^ _780461 : [(40812 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557461), 40810 ^ [_1557459, _1557461, _1557463, _1557465, _1557467, _1557469]), _1557463)))], (40814 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1557465), hAPP(_1557467, 40810 ^ [_1557459, _1557461, _1557463, _1557465, _1557467, _1557469])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1557461, _1557459), hAPP(hAPP(c_COMBS(_1557461, tc_fun(_1557465, tc_HOL_Obool), _1557459), hAPP(hAPP(c_COMBB(tc_fun(_1557465, _1557459), tc_fun(tc_fun(_1557465, tc_HOL_Obool), _1557459), _1557461), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1557465, _1557459)), _1557469)), _1557467)), _1557463) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1557461, _1557465), _1557459), hAPP(c_Product__Type_Oprod_Oprod__case(_1557461, _1557465, _1557459), _1557469)), hAPP(hAPP(c_Product__Type_OSigma(_1557461, _1557465), _1557463), _1557467)))], (40818 ^ _780461) ^ [_1557936, _1557938, _1557940, _1557942, _1557944, _1557946] : [class_Groups_Ocomm__monoid__add(_1557936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557938), _1557940)), 40828 ^ _780461 : [(40829 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557938), 40827 ^ [_1557936, _1557938, _1557940, _1557942, _1557944, _1557946]), _1557940)))], (40831 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1557942), hAPP(_1557944, 40827 ^ [_1557936, _1557938, _1557940, _1557942, _1557944, _1557946])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557938, _1557936), hAPP(hAPP(c_COMBS(_1557938, tc_fun(_1557942, tc_HOL_Obool), _1557936), hAPP(hAPP(c_COMBB(tc_fun(_1557942, _1557936), tc_fun(tc_fun(_1557942, tc_HOL_Obool), _1557936), _1557938), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557942, _1557936)), _1557946)), _1557944)), _1557940) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1557938, _1557942), _1557936), hAPP(c_Product__Type_Oprod_Oprod__case(_1557938, _1557942, _1557936), _1557946)), hAPP(hAPP(c_Product__Type_OSigma(_1557938, _1557942), _1557940), _1557944)))], (40835 ^ _780461) ^ [_1558413, _1558415, _1558417, _1558419, _1558421, _1558423] : [class_Groups_Ocomm__monoid__mult(_1558413), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558415), _1558417)), 40845 ^ _780461 : [(40846 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558415), 40844 ^ [_1558413, _1558415, _1558417, _1558419, _1558421, _1558423]), _1558417)))], (40848 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1558419), hAPP(_1558421, 40844 ^ [_1558413, _1558415, _1558417, _1558419, _1558421, _1558423])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1558413, _1558415, c_Groups_Otimes__class_Otimes(_1558413)), hAPP(hAPP(c_COMBS(_1558415, tc_fun(_1558419, tc_HOL_Obool), _1558413), hAPP(hAPP(c_COMBC(_1558415, _1558413, tc_fun(tc_fun(_1558419, tc_HOL_Obool), _1558413)), hAPP(hAPP(c_COMBB(tc_fun(_1558419, _1558413), tc_fun(_1558413, tc_fun(tc_fun(_1558419, tc_HOL_Obool), _1558413)), _1558415), c_Finite__Set_Ofold__image(_1558413, _1558419, c_Groups_Otimes__class_Otimes(_1558413))), _1558423)), c_Groups_Oone__class_Oone(_1558413))), _1558421)), c_Groups_Oone__class_Oone(_1558413)), _1558417) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1558413, tc_prod(_1558415, _1558419), c_Groups_Otimes__class_Otimes(_1558413)), hAPP(c_Product__Type_Oprod_Oprod__case(_1558415, _1558419, _1558413), _1558423)), c_Groups_Oone__class_Oone(_1558413)), hAPP(hAPP(c_Product__Type_OSigma(_1558415, _1558419), _1558417), _1558421)))], (40852 ^ _780461) ^ [_1558970, _1558972, _1558974, _1558976] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1558970), _1558972)), 40858 ^ _780461 : [(40859 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558970), 40857 ^ [_1558970, _1558972, _1558974, _1558976]), _1558972)))], (40861 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1558974), hAPP(_1558976, 40857 ^ [_1558970, _1558972, _1558974, _1558976])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1558970, _1558974)), hAPP(hAPP(c_Product__Type_OSigma(_1558970, _1558974), _1558972), _1558976)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558970, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1558974, tc_HOL_Obool), tc_Nat_Onat, _1558970), c_Finite__Set_Ocard(_1558974)), _1558976)), _1558972))], (40865 ^ _780461) ^ [_1559307, _1559309] : [class_Groups_Oab__semigroup__mult(_1559307), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559307), _1559309)), -(_1559309 = c_Orderings_Obot__class_Obot(tc_fun(_1559307, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1559307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1559307), 40878 ^ [_1559307, _1559309]), 40879 ^ [_1559307, _1559309])), hAPP(hAPP(c_Set_Oinsert(_1559307), 40878 ^ [_1559307, _1559309]), hAPP(hAPP(c_Set_Oinsert(_1559307), 40879 ^ [_1559307, _1559309]), c_Orderings_Obot__class_Obot(tc_fun(_1559307, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1559307), hAPP(c_Finite__Set_Ofold1(_1559307, c_Groups_Otimes__class_Otimes(_1559307)), _1559309)), _1559309)))], (40885 ^ _780461) ^ [_1559761, _1559763, _1559765, _1559767] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559761), _1559763)), 40891 ^ _780461 : [(40892 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559761), 40890 ^ [_1559761, _1559763, _1559765, _1559767]), _1559763)))], (40894 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559765), hAPP(_1559767, 40890 ^ [_1559761, _1559763, _1559765, _1559767])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1559761, _1559765)), hAPP(hAPP(c_Product__Type_OSigma(_1559761, _1559765), _1559763), _1559767))))], (40898 ^ _780461) ^ [_1560048, _1560050, _1560052] : [class_Lattices_Oab__semigroup__idem__mult(_1560048), hAPP(_1560050, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1560048), 40903 ^ [_1560048, _1560050, _1560052]), 40904 ^ [_1560048, _1560050, _1560052])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1560048), hAPP(_1560050, 40903 ^ [_1560048, _1560050, _1560052])), hAPP(_1560050, 40904 ^ [_1560048, _1560050, _1560052])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560048), _1560052)), -(_1560052 = c_Orderings_Obot__class_Obot(tc_fun(_1560048, tc_HOL_Obool))), -(hAPP(_1560050, hAPP(c_Finite__Set_Ofold1(_1560048, c_Groups_Otimes__class_Otimes(_1560048)), _1560052)) = hAPP(c_Finite__Set_Ofold1(_1560048, c_Groups_Otimes__class_Otimes(_1560048)), hAPP(c_Set_Oimage(_1560048, _1560048, _1560050), _1560052)))], (40918 ^ _780461) ^ [_1560471, _1560473, _1560475, _1560477, _1560479] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560471, _1560473)), _1560475), hAPP(hAPP(c_Product__Type_OSigma(_1560471, _1560473), _1560477), _1560479))), 40922 ^ _780461 : [(40923 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560471), 40921 ^ [_1560471, _1560473, _1560475, _1560477, _1560479]), _1560477)))], (40926 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560473), 40924 ^ [_1560471, _1560473, _1560475, _1560477, _1560479]), hAPP(_1560479, 40921 ^ [_1560471, _1560473, _1560475, _1560477, _1560479]))))], (40928 ^ _780461) ^ [] : [-(_1560475 = hAPP(hAPP(c_Product__Type_OPair(_1560471, _1560473), 40921 ^ [_1560471, _1560473, _1560475, _1560477, _1560479]), 40924 ^ [_1560471, _1560473, _1560475, _1560477, _1560479]))]]], (40930 ^ _780461) ^ [_1560773, _1560775, _1560777, _1560779, _1560781, _1560783] : [hAPP(c_Set_Oimage(_1560773, _1560775, _1560777), c_Orderings_Otop__class_Otop(tc_fun(_1560773, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1560775, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1560779, _1560781, _1560783), c_Orderings_Otop__class_Otop(tc_fun(_1560779, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1560781, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1560773, _1560779), tc_prod(_1560775, _1560781), c_Product__Type_Omap__pair(_1560773, _1560775, _1560779, _1560781, _1560777, _1560783)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1560773, _1560779), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1560775, _1560781), tc_HOL_Obool)))], (40940 ^ _780461) ^ [_1561058, _1561060, _1561062, _1561064, _1561066, _1561068, _1561070, _1561072] : [c_Fun_Oinj__on(_1561058, _1561060, _1561062, _1561064), c_Fun_Oinj__on(_1561066, _1561068, _1561070, _1561072), -(c_Fun_Oinj__on(tc_prod(_1561058, _1561066), tc_prod(_1561060, _1561068), c_Product__Type_Omap__pair(_1561058, _1561060, _1561066, _1561068, _1561062, _1561070), hAPP(hAPP(c_Product__Type_OSigma(_1561058, _1561066), _1561064), hAPP(c_COMBK(tc_fun(_1561066, tc_HOL_Obool), _1561058), _1561072))))], (40950 ^ _780461) ^ [_1561285, _1561287, _1561289, _1561291, _1561293, _1561295, _1561297, _1561299, _1561301] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561285, _1561287)), hAPP(hAPP(c_Product__Type_OPair(_1561285, _1561287), _1561289), _1561291)), _1561293)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561295, _1561297)), hAPP(hAPP(c_Product__Type_OPair(_1561295, _1561297), hAPP(_1561299, _1561289)), hAPP(_1561301, _1561291))), hAPP(c_Set_Oimage(tc_prod(_1561285, _1561287), tc_prod(_1561295, _1561297), c_Product__Type_Omap__pair(_1561285, _1561295, _1561287, _1561297, _1561299, _1561301)), _1561293))))], (40956 ^ _780461) ^ [_1561504, _1561506, _1561508, _1561510, _1561512, _1561514] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1561504, _1561506), _1561504, tc_prod(_1561508, _1561510), c_Product__Type_Ofst(_1561504, _1561506)), c_Product__Type_Omap__pair(_1561508, _1561504, _1561510, _1561506, _1561512, _1561514)) = hAPP(c_Fun_Ocomp(_1561508, _1561504, tc_prod(_1561508, _1561510), _1561512), c_Product__Type_Ofst(_1561508, _1561510)))], (40958 ^ _780461) ^ [_1561575, _1561577, _1561579, _1561581, _1561583, _1561585] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1561575, _1561577), _1561577, tc_prod(_1561579, _1561581), c_Product__Type_Osnd(_1561575, _1561577)), c_Product__Type_Omap__pair(_1561579, _1561575, _1561581, _1561577, _1561583, _1561585)) = hAPP(c_Fun_Ocomp(_1561581, _1561577, tc_prod(_1561579, _1561581), _1561585), c_Product__Type_Osnd(_1561579, _1561581)))], (40960 ^ _780461) ^ [_1561646, _1561648, _1561650, _1561652, _1561654, _1561656, _1561658, _1561660, _1561662, _1561664, _1561666] : [-(hAPP(c_Product__Type_Omap__pair(_1561646, _1561648, _1561650, _1561652, _1561654, _1561656), hAPP(c_Product__Type_Omap__pair(_1561658, _1561646, _1561660, _1561650, _1561662, _1561664), _1561666)) = hAPP(c_Product__Type_Omap__pair(_1561658, _1561648, _1561660, _1561652, hAPP(c_Fun_Ocomp(_1561646, _1561648, _1561658, _1561654), _1561662), hAPP(c_Fun_Ocomp(_1561650, _1561652, _1561660, _1561656), _1561664)), _1561666))], (40962 ^ _780461) ^ [_1561735, _1561737, _1561739, _1561741, _1561743, _1561745, _1561747, _1561749, _1561751, _1561753] : [-(c_Product__Type_Omap__pair(_1561735, _1561737, _1561739, _1561741, hAPP(c_Fun_Ocomp(_1561743, _1561737, _1561735, _1561745), _1561747), hAPP(c_Fun_Ocomp(_1561749, _1561741, _1561739, _1561751), _1561753)) = hAPP(c_Fun_Ocomp(tc_prod(_1561743, _1561749), tc_prod(_1561737, _1561741), tc_prod(_1561735, _1561739), c_Product__Type_Omap__pair(_1561743, _1561737, _1561749, _1561741, _1561745, _1561751)), c_Product__Type_Omap__pair(_1561735, _1561743, _1561739, _1561749, _1561747, _1561753)))], (40964 ^ _780461) ^ [_1561830, _1561832, _1561834, _1561836, _1561838, _1561840, _1561842, _1561844, _1561846, _1561848] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1561830, _1561832), tc_prod(_1561834, _1561836), tc_prod(_1561838, _1561840), c_Product__Type_Omap__pair(_1561830, _1561834, _1561832, _1561836, _1561842, _1561844)), c_Product__Type_Omap__pair(_1561838, _1561830, _1561840, _1561832, _1561846, _1561848)) = c_Product__Type_Omap__pair(_1561838, _1561834, _1561840, _1561836, hAPP(c_Fun_Ocomp(_1561830, _1561834, _1561838, _1561842), _1561846), hAPP(c_Fun_Ocomp(_1561832, _1561836, _1561840, _1561844), _1561848)))], (40966 ^ _780461) ^ [_1561925, _1561927, _1561929] : [-(hAPP(c_Product__Type_Omap__pair(_1561925, _1561925, _1561927, _1561927, c_COMBI(_1561925), c_COMBI(_1561927)), _1561929) = _1561929)], (40968 ^ _780461) ^ [_1561966, _1561968, _1561970, _1561972, _1561974, _1561976, _1561978, _1561980] : [-(hAPP(c_Product__Type_Omap__pair(_1561966, _1561968, _1561970, _1561972, _1561974, _1561976), hAPP(hAPP(c_Product__Type_OPair(_1561966, _1561970), _1561978), _1561980)) = hAPP(hAPP(c_Product__Type_OPair(_1561968, _1561972), hAPP(_1561974, _1561978)), hAPP(_1561976, _1561980)))], (40970 ^ _780461) ^ [_1562037, _1562039, _1562041, _1562043, _1562045, _1562047, _1562049] : [-(hAPP(c_Product__Type_Osnd(_1562037, _1562039), hAPP(c_Product__Type_Omap__pair(_1562041, _1562037, _1562043, _1562039, _1562045, _1562047), _1562049)) = hAPP(_1562047, hAPP(c_Product__Type_Osnd(_1562041, _1562043), _1562049)))], (40972 ^ _780461) ^ [_1562097, _1562099, _1562101, _1562103, _1562105, _1562107, _1562109] : [-(hAPP(c_Product__Type_Ofst(_1562097, _1562099), hAPP(c_Product__Type_Omap__pair(_1562101, _1562097, _1562103, _1562099, _1562105, _1562107), _1562109)) = hAPP(_1562105, hAPP(c_Product__Type_Ofst(_1562101, _1562103), _1562109)))], (40974 ^ _780461) ^ [_1562157, _1562159, _1562161, _1562163, _1562165, _1562167] : [-(c_Product__Type_Omap__pair(_1562157, _1562159, _1562161, _1562163, _1562165, _1562167) = hAPP(c_Product__Type_Oprod_Oprod__case(_1562157, _1562161, tc_prod(_1562159, _1562163)), hAPP(hAPP(c_COMBC(_1562157, tc_fun(_1562161, _1562163), tc_fun(_1562161, tc_prod(_1562159, _1562163))), hAPP(hAPP(c_COMBB(tc_fun(_1562163, tc_prod(_1562159, _1562163)), tc_fun(tc_fun(_1562161, _1562163), tc_fun(_1562161, tc_prod(_1562159, _1562163))), _1562157), c_COMBB(_1562163, tc_prod(_1562159, _1562163), _1562161)), hAPP(hAPP(c_COMBB(_1562159, tc_fun(_1562163, tc_prod(_1562159, _1562163)), _1562157), c_Product__Type_OPair(_1562159, _1562163)), _1562165))), _1562167)))], (40976 ^ _780461) ^ [_1562280, _1562282, _1562284, _1562286, _1562288, _1562290, _1562292, _1562294, _1562296, _1562298] : [hAPP(c_Set_Oimage(_1562280, _1562282, _1562284), _1562286) = _1562288, hAPP(c_Set_Oimage(_1562290, _1562292, _1562294), _1562296) = _1562298, -(hAPP(c_Set_Oimage(tc_prod(_1562280, _1562290), tc_prod(_1562282, _1562292), c_Product__Type_Omap__pair(_1562280, _1562282, _1562290, _1562292, _1562284, _1562294)), hAPP(hAPP(c_Product__Type_OSigma(_1562280, _1562290), _1562286), hAPP(c_COMBK(tc_fun(_1562290, tc_HOL_Obool), _1562280), _1562296))) = hAPP(hAPP(c_Product__Type_OSigma(_1562282, _1562292), _1562288), hAPP(c_COMBK(tc_fun(_1562292, tc_HOL_Obool), _1562282), _1562298)))], (40986 ^ _780461) ^ [_1562581, _1562583, _1562585, _1562587, _1562589, _1562591, _1562593, _1562595] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562581, _1562583)), _1562585), hAPP(c_Set_Oimage(tc_prod(_1562587, _1562589), tc_prod(_1562581, _1562583), c_Product__Type_Omap__pair(_1562587, _1562581, _1562589, _1562583, _1562591, _1562593)), _1562595))), 40991 ^ _780461 : [(40992 ^ _780461) ^ [] : [-(_1562585 = hAPP(hAPP(c_Product__Type_OPair(_1562581, _1562583), hAPP(_1562591, 40989 ^ [_1562581, _1562583, _1562585, _1562587, _1562589, _1562591, _1562593, _1562595])), hAPP(_1562593, 40990 ^ [_1562581, _1562583, _1562585, _1562587, _1562589, _1562591, _1562593, _1562595])))], (40994 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562587, _1562589)), hAPP(hAPP(c_Product__Type_OPair(_1562587, _1562589), 40989 ^ [_1562581, _1562583, _1562585, _1562587, _1562589, _1562591, _1562593, _1562595]), 40990 ^ [_1562581, _1562583, _1562585, _1562587, _1562589, _1562591, _1562593, _1562595])), _1562595)))]]], (40996 ^ _780461) ^ [_1562914, _1562916, _1562918] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562914), _1562916)), 41002 ^ _780461 : [(41003 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562914), 41001 ^ [_1562914, _1562916, _1562918]), _1562916)))], (41005 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1562918, 41001 ^ [_1562914, _1562916, _1562918])))]], -(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(_1562914, tc_Nat_Onat), _1562918), _1562916))))], (41009 ^ _780461) ^ [_1563175, _1563177, _1563179, _1563181, _1563183] : [c_Finite__Set_Ofolding__one__idem(_1563175, _1563177, _1563179), hAPP(_1563181, hAPP(hAPP(_1563177, 41014 ^ [_1563175, _1563177, _1563179, _1563181, _1563183]), 41015 ^ [_1563175, _1563177, _1563179, _1563181, _1563183])) = hAPP(hAPP(_1563177, hAPP(_1563181, 41014 ^ [_1563175, _1563177, _1563179, _1563181, _1563183])), hAPP(_1563181, 41015 ^ [_1563175, _1563177, _1563179, _1563181, _1563183])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563175), _1563183)), -(_1563183 = c_Orderings_Obot__class_Obot(tc_fun(_1563175, tc_HOL_Obool))), -(hAPP(_1563181, hAPP(_1563179, _1563183)) = hAPP(_1563179, hAPP(c_Set_Oimage(_1563175, _1563175, _1563181), _1563183)))], (41029 ^ _780461) ^ [_1563610, _1563612] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1563610), c_Int_OInteg)), hBOOL(hAPP(_1563612, hAPP(c_Int_ORep__Integ, 41034 ^ [_1563610, _1563612]))), -(hBOOL(hAPP(_1563612, _1563610)))], (41040 ^ _780461) ^ [_1563792] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1563792), c_Int_OInteg)), -(_1563792 = hAPP(c_Int_ORep__Integ, 41043 ^ [_1563792]))], (41047 ^ _780461) ^ [_1563897, _1563899, _1563901, _1563903, _1563905, _1563907, _1563909, _1563911] : [c_Finite__Set_Ofolding__image__simple(_1563897, _1563899, _1563901, _1563903, _1563905, _1563907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563899), _1563909)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563899), _1563911)), 41061 ^ _780461 : [(41062 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1563899), 41060 ^ [_1563897, _1563899, _1563901, _1563903, _1563905, _1563907, _1563909, _1563911]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1563899, tc_HOL_Obool)), _1563909), _1563911))))], (41064 ^ _780461) ^ [] : [hAPP(_1563905, 41060 ^ [_1563897, _1563899, _1563901, _1563903, _1563905, _1563907, _1563909, _1563911]) = _1563903]], -(hAPP(_1563907, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1563899, tc_HOL_Obool)), _1563909), _1563911)) = hAPP(hAPP(_1563901, hAPP(_1563907, _1563909)), hAPP(_1563907, _1563911)))], (41068 ^ _780461) ^ [_1564398] : [-(c_Finite__Set_Ofun__left__comm__idem(_1564398, tc_fun(_1564398, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1564398, tc_HOL_Obool), tc_fun(tc_fun(_1564398, tc_HOL_Obool), tc_fun(_1564398, tc_HOL_Obool)), _1564398), hAPP(c_COMBC(tc_fun(_1564398, tc_HOL_Obool), tc_fun(_1564398, tc_HOL_Obool), tc_fun(_1564398, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1564398, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1564398, tc_fun(_1564398, tc_HOL_Obool), tc_fun(_1564398, tc_HOL_Obool)), c_Set_Oinsert(_1564398)), c_Orderings_Obot__class_Obot(tc_fun(_1564398, tc_HOL_Obool))))))], (41070 ^ _780461) ^ [_1564487, _1564489] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1564487))), -(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)), _1564487))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1564489)))) = 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)), _1564487))), 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, _1564489))))))], (41076 ^ _780461) ^ [_1564570, _1564572, _1564574] : [hBOOL(hAPP(_1564570, _1564572)), -(hBOOL(hAPP(hAPP(c_member(_1564574), _1564572), hAPP(c_Set_OCollect(_1564574), _1564570))))], (41082 ^ _780461) ^ [_1564677, _1564679, _1564681] : [41083 ^ _780461 : [(41084 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1564677), hAPP(c_Set_OCollect(_1564677), _1564679)))], (41086 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1564677), hAPP(c_Set_OCollect(_1564677), _1564681)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1564677), hAPP(c_Set_OCollect(_1564677), hAPP(hAPP(c_COMBS(_1564677, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1564677), c_fconj), _1564679)), _1564681)))))], (41090 ^ _780461) ^ [_1564888] : [-(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)), _1564888)))))], (41092 ^ _780461) ^ [_1564919] : [-(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)), _1564919)))))], (41094 ^ _780461) ^ [_1564950, _1564952, _1564954, _1564956] : [c_Finite__Set_Ofun__left__comm__idem(_1564950, _1564952, _1564954), -(hAPP(c_Fun_Ocomp(_1564952, _1564952, _1564952, hAPP(_1564954, _1564956)), hAPP(_1564954, _1564956)) = hAPP(_1564954, _1564956))], (41100 ^ _780461) ^ [_1565079, _1565081, _1565083] : [hBOOL(hAPP(_1565079, _1565081)), -(hAPP(c_Set_OCollect(_1565083), hAPP(hAPP(c_COMBS(_1565083, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565083), c_fconj), hAPP(hAPP(c_COMBC(_1565083, _1565083, tc_HOL_Obool), c_fequal), _1565081))), _1565079)) = hAPP(hAPP(c_Set_Oinsert(_1565083), _1565081), c_Orderings_Obot__class_Obot(tc_fun(_1565083, tc_HOL_Obool))))], (41106 ^ _780461) ^ [_1565252, _1565254, _1565256] : [-(hBOOL(hAPP(_1565252, _1565254))), -(hAPP(c_Set_OCollect(_1565256), hAPP(hAPP(c_COMBS(_1565256, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565256), c_fconj), hAPP(hAPP(c_COMBC(_1565256, _1565256, tc_HOL_Obool), c_fequal), _1565254))), _1565252)) = c_Orderings_Obot__class_Obot(tc_fun(_1565256, tc_HOL_Obool)))], (41112 ^ _780461) ^ [_1565346, _1565348, _1565350] : [hBOOL(hAPP(_1565346, _1565348)), -(hAPP(c_Set_OCollect(_1565350), hAPP(hAPP(c_COMBS(_1565350, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565350), c_fconj), hAPP(c_fequal, _1565348))), _1565346)) = hAPP(hAPP(c_Set_Oinsert(_1565350), _1565348), c_Orderings_Obot__class_Obot(tc_fun(_1565350, tc_HOL_Obool))))], (41118 ^ _780461) ^ [_1565505, _1565507, _1565509] : [-(hBOOL(hAPP(_1565505, _1565507))), -(hAPP(c_Set_OCollect(_1565509), hAPP(hAPP(c_COMBS(_1565509, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565509), c_fconj), hAPP(c_fequal, _1565507))), _1565505)) = c_Orderings_Obot__class_Obot(tc_fun(_1565509, tc_HOL_Obool)))], (41124 ^ _780461) ^ [_1565580, _1565582] : [-(hAPP(c_Set_OCollect(_1565580), hAPP(hAPP(c_COMBC(_1565580, _1565580, tc_HOL_Obool), c_fequal), _1565582)) = hAPP(hAPP(c_Set_Oinsert(_1565580), _1565582), c_Orderings_Obot__class_Obot(tc_fun(_1565580, tc_HOL_Obool))))], (41126 ^ _780461) ^ [_1565633, _1565635] : [-(hAPP(c_Set_OCollect(_1565633), hAPP(c_fequal, _1565635)) = hAPP(hAPP(c_Set_Oinsert(_1565633), _1565635), c_Orderings_Obot__class_Obot(tc_fun(_1565633, tc_HOL_Obool))))], (41128 ^ _780461) ^ [_1565679, _1565681, _1565683, _1565685] : [-(hAPP(c_Set_OCollect(tc_prod(_1565679, _1565681)), hAPP(c_Product__Type_Oprod_Oprod__case(_1565679, _1565681, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1565679, tc_fun(_1565681, tc_HOL_Obool), tc_fun(_1565681, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1565681, tc_HOL_Obool), tc_fun(_1565681, tc_HOL_Obool)), _1565679), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1565681)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565679), c_fconj), _1565683))), _1565685))) = hAPP(hAPP(c_Product__Type_OSigma(_1565679, _1565681), hAPP(c_Set_OCollect(_1565679), _1565683)), hAPP(c_COMBK(tc_fun(_1565681, tc_HOL_Obool), _1565679), hAPP(c_Set_OCollect(_1565681), _1565685))))], (41130 ^ _780461) ^ [_1565800, _1565802, _1565804, _1565806] : [-(hAPP(c_Set_OCollect(tc_prod(_1565800, _1565802)), hAPP(c_Product__Type_Oprod_Oprod__case(_1565800, _1565802, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1565800, tc_fun(_1565802, tc_HOL_Obool), tc_fun(_1565802, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1565802, tc_HOL_Obool), tc_fun(_1565802, tc_HOL_Obool)), _1565800), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1565802)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565800), c_fconj), _1565804))), _1565806))) = hAPP(hAPP(c_Product__Type_OSigma(_1565800, _1565802), hAPP(c_Set_OCollect(_1565800), _1565804)), hAPP(hAPP(c_COMBB(tc_fun(_1565802, tc_HOL_Obool), tc_fun(_1565802, tc_HOL_Obool), _1565800), c_Set_OCollect(_1565802)), _1565806)))], (41132 ^ _780461) ^ [_1565925, _1565927] : [-(hAPP(c_Set_OCollect(_1565925), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1565925), c_fNot), _1565927)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1565925, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1565925), _1565927)))], (41134 ^ _780461) ^ [_1565978, _1565980, _1565982, _1565984] : [-(hAPP(c_Set_Ovimage(_1565978, _1565980, _1565982), hAPP(c_Set_OCollect(_1565980), _1565984)) = hAPP(c_Set_OCollect(_1565978), hAPP(hAPP(c_COMBB(_1565980, tc_HOL_Obool, _1565978), _1565984), _1565982)))], (41136 ^ _780461) ^ [_1566034, _1566036, _1566038] : [-(hAPP(hAPP(c_Set_Oinsert(_1566034), _1566036), _1566038) = hAPP(c_Set_OCollect(_1566034), hAPP(hAPP(c_COMBS(_1566034, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566034), c_fdisj), hAPP(hAPP(c_COMBC(_1566034, _1566034, tc_HOL_Obool), c_fequal), _1566036))), hAPP(hAPP(c_COMBC(_1566034, tc_fun(_1566034, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566034)), _1566038))))], (41138 ^ _780461) ^ [_1566119, _1566121, _1566123] : [-(hAPP(hAPP(c_Set_Oinsert(_1566119), _1566121), _1566123) = hAPP(c_Set_OCollect(_1566119), hAPP(hAPP(c_COMBS(_1566119, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566119), c_fdisj), hAPP(hAPP(c_COMBC(_1566119, _1566119, tc_HOL_Obool), c_fequal), _1566121))), hAPP(hAPP(c_COMBC(_1566119, tc_fun(_1566119, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566119)), _1566123))))], (41140 ^ _780461) ^ [_1566204, _1566206] : [-(hAPP(c_Set_OCollect(_1566204), hAPP(hAPP(c_COMBC(_1566204, tc_fun(_1566204, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566204)), _1566206)) = _1566206)], (41142 ^ _780461) ^ [_1566267, _1566269, _1566271] : [hBOOL(hAPP(hAPP(c_member(_1566267), _1566269), hAPP(c_Set_OCollect(_1566267), _1566271))), -(hBOOL(hAPP(_1566271, _1566269)))], (41148 ^ _780461) ^ [_1566370, _1566372, _1566374] : [hBOOL(hAPP(_1566374, _1566372)), -(hBOOL(hAPP(hAPP(c_member(_1566370), _1566372), hAPP(c_Set_OCollect(_1566370), _1566374))))], (41154 ^ _780461) ^ [_1566479, _1566481, _1566483] : [hBOOL(hAPP(hAPP(c_member(_1566479), _1566481), hAPP(c_Set_OCollect(_1566479), _1566483))), -(hBOOL(hAPP(_1566483, _1566481)))], (41160 ^ _780461) ^ [_1566586, _1566588, _1566590] : [hBOOL(hAPP(hAPP(c_member(_1566586), _1566588), hAPP(c_Set_OCollect(_1566586), _1566590))), -(hBOOL(hAPP(_1566590, _1566588)))], (41166 ^ _780461) ^ [_1566693] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1566693, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1566693), hAPP(c_COMBK(tc_HOL_Obool, _1566693), c_fTrue)))], (41168 ^ _780461) ^ [_1566750, _1566752, _1566754] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1566750), hAPP(c_Set_OCollect(_1566750), hAPP(hAPP(c_COMBS(_1566750, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566750), c_fdisj), _1566752)), _1566754)))), 41171 ^ _780461 : [(41172 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566750), hAPP(c_Set_OCollect(_1566750), _1566752))))], (41174 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566750), hAPP(c_Set_OCollect(_1566750), _1566754))))]]], (41176 ^ _780461) ^ [_1566945, _1566947, _1566949] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566945), hAPP(c_Set_OCollect(_1566945), hAPP(hAPP(c_COMBS(_1566945, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566945), c_fdisj), _1566947)), _1566949))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566945), hAPP(c_Set_OCollect(_1566945), _1566947))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1566945), hAPP(c_Set_OCollect(_1566945), _1566949)))], (41186 ^ _780461) ^ [_1567174, _1567176, _1567178] : [-(hAPP(hAPP(c_Set_Oinsert(_1567174), _1567176), hAPP(c_Set_OCollect(_1567174), _1567178)) = hAPP(c_Set_OCollect(_1567174), hAPP(hAPP(c_COMBS(_1567174, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1567174), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1567174), c_fNot), hAPP(hAPP(c_COMBC(_1567174, _1567174, tc_HOL_Obool), c_fequal), _1567176)))), _1567178)))], (41188 ^ _780461) ^ [_1567259] : [-(c_Finite__Set_Ofun__left__comm__idem(_1567259, tc_fun(_1567259, tc_HOL_Obool), c_Set_Oinsert(_1567259)))], (41190 ^ _780461) ^ [_1567288] : [class_Orderings_Olinorder(_1567288), -(c_Finite__Set_Ofun__left__comm__idem(_1567288, _1567288, c_Orderings_Oord__class_Omax(_1567288)))], (41196 ^ _780461) ^ [_1567367] : [class_Lattices_Oab__semigroup__idem__mult(_1567367), -(c_Finite__Set_Ofun__left__comm__idem(_1567367, _1567367, c_Groups_Otimes__class_Otimes(_1567367)))], (41202 ^ _780461) ^ [_1567446, _1567448, _1567450] : [-(hAPP(c_Set_OCollect(_1567446), hAPP(hAPP(c_COMBS(_1567446, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1567446), c_fconj), _1567448)), _1567450)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567446, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1567446), _1567448)), hAPP(c_Set_OCollect(_1567446), _1567450)))], (41204 ^ _780461) ^ [_1567519, _1567521, _1567523] : [-(hAPP(c_Set_OCollect(_1567519), hAPP(hAPP(c_COMBS(_1567519, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1567519), c_fdisj), _1567521)), _1567523)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567519, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1567519), _1567521)), hAPP(c_Set_OCollect(_1567519), _1567523)))], (41206 ^ _780461) ^ [_1567592] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1567592, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1567592), hAPP(c_COMBK(tc_HOL_Obool, _1567592), c_fFalse)))], (41208 ^ _780461) ^ [_1567646, _1567648] : [hAPP(c_Set_OCollect(_1567646), _1567648) = c_Orderings_Obot__class_Obot(tc_fun(_1567646, tc_HOL_Obool)), 41211 ^ _780461 : [(41212 ^ _780461) ^ [_1567731] : [hBOOL(hAPP(_1567648, _1567731))]]], (41214 ^ _780461) ^ [_1567754, _1567756] : [-(hBOOL(hAPP(_1567756, 41215 ^ [_1567754, _1567756]))), -(hAPP(c_Set_OCollect(_1567754), _1567756) = c_Orderings_Obot__class_Obot(tc_fun(_1567754, tc_HOL_Obool)))], (41221 ^ _780461) ^ [_1567826, _1567828] : [c_Orderings_Obot__class_Obot(tc_fun(_1567826, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1567826), _1567828), 41224 ^ _780461 : [(41225 ^ _780461) ^ [_1567911] : [hBOOL(hAPP(_1567828, _1567911))]]], (41227 ^ _780461) ^ [_1567934, _1567936] : [-(hBOOL(hAPP(_1567936, 41228 ^ [_1567934, _1567936]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1567934, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1567934), _1567936))], (41234 ^ _780461) ^ [_1567991, _1567993, _1567995, _1567997, _1567999] : [c_Finite__Set_Ofun__left__comm__idem(_1567991, _1567993, _1567995), -(c_Finite__Set_Ofun__left__comm__idem(_1567997, _1567993, hAPP(hAPP(c_COMBB(_1567991, tc_fun(_1567993, _1567993), _1567997), _1567995), _1567999)))], (41240 ^ _780461) ^ [_1568104, _1568106, _1568108, _1568110, _1568112] : [c_Finite__Set_Ofun__left__comm__idem(_1568104, _1568106, _1568108), -(hAPP(hAPP(_1568108, _1568110), hAPP(hAPP(_1568108, _1568110), _1568112)) = hAPP(hAPP(_1568108, _1568110), _1568112))], (41246 ^ _780461) ^ [_1568225, _1568227] : [-(hAPP(c_Set_OCollect(_1568225), _1568227) = _1568227)], (41248 ^ _780461) ^ [_1568255] : [class_Lattices_Osemilattice__inf(_1568255), -(c_Finite__Set_Ofun__left__comm__idem(_1568255, _1568255, c_Lattices_Osemilattice__inf__class_Oinf(_1568255)))], (41254 ^ _780461) ^ [_1568334] : [class_Lattices_Osemilattice__sup(_1568334), -(c_Finite__Set_Ofun__left__comm__idem(_1568334, _1568334, c_Lattices_Osemilattice__sup__class_Osup(_1568334)))], (41260 ^ _780461) ^ [_1568413] : [class_Orderings_Olinorder(_1568413), -(c_Finite__Set_Ofun__left__comm__idem(_1568413, _1568413, c_Orderings_Oord__class_Omin(_1568413)))], (41266 ^ _780461) ^ [_1568513, _1568515, _1568517, _1568519] : [hBOOL(hAPP(hAPP(c_member(_1568513), _1568515), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568513, tc_HOL_Obool)), _1568517), hAPP(c_Set_OCollect(_1568513), _1568519)))), 41269 ^ _780461 : [(41270 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568513), _1568515), _1568517)))], (41272 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1568519, _1568515)))]]], (41274 ^ _780461) ^ [_1568680, _1568682, _1568684, _1568686] : [-(hBOOL(hAPP(hAPP(c_member(_1568680), _1568682), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568680, tc_HOL_Obool)), _1568684), hAPP(c_Set_OCollect(_1568680), _1568686))))), hBOOL(hAPP(hAPP(c_member(_1568680), _1568682), _1568684)), hBOOL(hAPP(_1568686, _1568682))], (41284 ^ _780461) ^ [_1568883, _1568885, _1568887] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568883, tc_HOL_Obool)), _1568885), _1568887) = hAPP(c_Set_OCollect(_1568883), hAPP(hAPP(c_COMBS(_1568883, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1568883), c_fconj), hAPP(hAPP(c_COMBC(_1568883, tc_fun(_1568883, tc_HOL_Obool), tc_HOL_Obool), c_member(_1568883)), _1568885))), hAPP(hAPP(c_COMBC(_1568883, tc_fun(_1568883, tc_HOL_Obool), tc_HOL_Obool), c_member(_1568883)), _1568887))))], (41286 ^ _780461) ^ [_1568976, _1568978, _1568980] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1568976, tc_HOL_Obool)), _1568978), _1568980) = hAPP(c_Set_OCollect(_1568976), hAPP(hAPP(c_COMBS(_1568976, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1568976), c_fdisj), hAPP(hAPP(c_COMBC(_1568976, tc_fun(_1568976, tc_HOL_Obool), tc_HOL_Obool), c_member(_1568976)), _1568978))), hAPP(hAPP(c_COMBC(_1568976, tc_fun(_1568976, tc_HOL_Obool), tc_HOL_Obool), c_member(_1568976)), _1568980))))], (41288 ^ _780461) ^ [_1569069, _1569071, _1569073] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569069, tc_HOL_Obool)), _1569071), _1569073) = hAPP(c_Set_OCollect(_1569069), hAPP(hAPP(c_COMBS(_1569069, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569069), c_fconj), hAPP(hAPP(c_COMBC(_1569069, tc_fun(_1569069, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569069)), _1569071))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1569069), c_fNot), hAPP(hAPP(c_COMBC(_1569069, tc_fun(_1569069, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569069)), _1569073)))))], (41290 ^ _780461) ^ [_1569172, _1569174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1569172), hAPP(c_Set_OCollect(_1569172), _1569174))), 41293 ^ _780461 : [(41294 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1569172), hAPP(c_Set_OCollect(_1569172), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1569172), c_fNot), _1569174)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1569172), c_Orderings_Otop__class_Otop(tc_fun(_1569172, tc_HOL_Obool)))))], (41300 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1569172), c_Orderings_Otop__class_Otop(tc_fun(_1569172, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1569172), hAPP(c_Set_OCollect(_1569172), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1569172), c_fNot), _1569174)))))]]], (41306 ^ _780461) ^ [_1569481, _1569483, _1569485] : [-(hAPP(hAPP(c_Set_Oinsert(_1569481), _1569483), _1569485) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1569481, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1569481), hAPP(hAPP(c_COMBC(_1569481, _1569481, tc_HOL_Obool), c_fequal), _1569483))), _1569485))], (41308 ^ _780461) ^ [_1569542, _1569544] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1569542, tc_HOL_Obool)), _1569544) = hAPP(c_Set_OCollect(_1569542), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1569542), c_fNot), hAPP(hAPP(c_COMBC(_1569542, tc_fun(_1569542, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569542)), _1569544))))], (41310 ^ _780461) ^ [_1569605, _1569607, _1569609, _1569611] : [-(hAPP(c_Set_Ovimage(_1569605, _1569607, _1569609), _1569611) = hAPP(c_Set_OCollect(_1569605), hAPP(hAPP(c_COMBC(_1569605, tc_fun(_1569607, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1569607, tc_fun(tc_fun(_1569607, tc_HOL_Obool), tc_HOL_Obool), _1569605), c_member(_1569607)), _1569609)), _1569611)))], (41312 ^ _780461) ^ [_1569677, _1569679, _1569681] : [-(hAPP(c_Set_OCollect(_1569677), hAPP(hAPP(c_COMBS(_1569677, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569677), c_fimplies), _1569679)), _1569681)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1569677, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1569677, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1569677), _1569679))), hAPP(c_Set_OCollect(_1569677), _1569681)))], (41314 ^ _780461) ^ [_1569758, _1569760, _1569762] : [-(c_Map_Odom(_1569758, _1569760, _1569762) = hAPP(c_Set_OCollect(_1569758), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1569758), c_fNot), hAPP(hAPP(c_COMBC(_1569758, tc_Option_Ooption(_1569760), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1569760), tc_fun(tc_Option_Ooption(_1569760), tc_HOL_Obool), _1569758), c_fequal), _1569762)), c_Option_Ooption_ONone(_1569760)))))], (41316 ^ _780461) ^ [_1569835, _1569837] : [-(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), _1569835)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1569837))))))], (41318 ^ _780461) ^ [_1569877, _1569879, _1569881, _1569883, _1569885, _1569887, _1569889] : [class_Groups_Ocomm__monoid__add(_1569877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1569879), _1569881)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1569883), _1569885)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1569879, _1569877), hAPP(hAPP(c_COMBS(_1569879, tc_fun(_1569883, tc_HOL_Obool), _1569877), hAPP(hAPP(c_COMBB(tc_fun(_1569883, _1569877), tc_fun(tc_fun(_1569883, tc_HOL_Obool), _1569877), _1569879), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1569883, _1569877)), _1569887)), hAPP(hAPP(c_COMBB(tc_fun(_1569883, tc_HOL_Obool), tc_fun(_1569883, tc_HOL_Obool), _1569879), c_Set_OCollect(_1569883)), hAPP(hAPP(c_COMBB(tc_fun(_1569883, tc_HOL_Obool), tc_fun(_1569883, tc_HOL_Obool), _1569879), hAPP(c_COMBS(_1569883, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569883), c_fconj), hAPP(hAPP(c_COMBC(_1569883, tc_fun(_1569883, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569883)), _1569885)))), _1569889)))), _1569881) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1569883, _1569877), hAPP(hAPP(c_COMBS(_1569883, tc_fun(_1569879, tc_HOL_Obool), _1569877), hAPP(hAPP(c_COMBB(tc_fun(_1569879, _1569877), tc_fun(tc_fun(_1569879, tc_HOL_Obool), _1569877), _1569883), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1569879, _1569877)), hAPP(c_COMBC(_1569879, _1569883, _1569877), _1569887))), hAPP(hAPP(c_COMBB(tc_fun(_1569879, tc_HOL_Obool), tc_fun(_1569879, tc_HOL_Obool), _1569883), c_Set_OCollect(_1569879)), hAPP(hAPP(c_COMBB(tc_fun(_1569879, tc_HOL_Obool), tc_fun(_1569879, tc_HOL_Obool), _1569883), hAPP(c_COMBS(_1569879, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569879), c_fconj), hAPP(hAPP(c_COMBC(_1569879, tc_fun(_1569879, tc_HOL_Obool), tc_HOL_Obool), c_member(_1569879)), _1569881)))), hAPP(c_COMBC(_1569879, _1569883, tc_HOL_Obool), _1569889))))), _1569885))], (41332 ^ _780461) ^ [_1570570, _1570572, _1570574, _1570576, _1570578, _1570580] : [-(hAPP(c_Set_Oimage(_1570570, _1570572, hAPP(hAPP(c_COMBS(_1570570, _1570572, _1570572), hAPP(hAPP(c_COMBS(_1570570, _1570572, tc_fun(_1570572, _1570572)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1570572, tc_fun(_1570572, _1570572)), _1570570), c_If(_1570572)), _1570574)), _1570576)), _1570578)), _1570580) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1570572, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1570570, _1570572, _1570576), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1570570, tc_HOL_Obool)), _1570580), hAPP(c_Set_OCollect(_1570570), _1570574)))), hAPP(c_Set_Oimage(_1570570, _1570572, _1570578), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1570570, tc_HOL_Obool)), _1570580), hAPP(c_Set_OCollect(_1570570), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1570570), c_fNot), _1570574))))))], (41334 ^ _780461) ^ [_1570718, _1570720, _1570722, _1570724, _1570726] : [-(c_Map_Odom(_1570718, _1570720, hAPP(hAPP(c_COMBS(_1570718, tc_Option_Ooption(_1570720), tc_Option_Ooption(_1570720)), hAPP(hAPP(c_COMBS(_1570718, tc_Option_Ooption(_1570720), tc_fun(tc_Option_Ooption(_1570720), tc_Option_Ooption(_1570720))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1570720), tc_fun(tc_Option_Ooption(_1570720), tc_Option_Ooption(_1570720))), _1570718), c_If(tc_Option_Ooption(_1570720))), _1570722)), _1570724)), _1570726)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1570718, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1570718, tc_HOL_Obool)), c_Map_Odom(_1570718, _1570720, _1570724)), hAPP(c_Set_OCollect(_1570718), _1570722))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1570718, tc_HOL_Obool)), c_Map_Odom(_1570718, _1570720, _1570726)), hAPP(c_Set_OCollect(_1570718), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1570718), c_fNot), _1570722)))))], (41336 ^ _780461) ^ [_1570873, _1570875, _1570877, _1570879] : [_1570873 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1570875, _1570877), 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)), _1570879))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1570875), _1570873)))], (41342 ^ _780461) ^ [_1570988, _1570990, _1570992, _1570994, _1570996] : [class_Groups_Ocomm__monoid__add(_1570988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570990), _1570992)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1570990, _1570988), _1570994), hAPP(c_Set_OCollect(_1570990), hAPP(hAPP(c_COMBS(_1570990, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570990), c_fconj), hAPP(hAPP(c_COMBC(_1570990, tc_fun(_1570990, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570990)), _1570992))), hAPP(hAPP(c_COMBC(_1570990, tc_fun(_1570990, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570990)), _1570996)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1570990, _1570988), hAPP(hAPP(c_COMBC(_1570990, _1570988, _1570988), hAPP(hAPP(c_COMBS(_1570990, _1570988, tc_fun(_1570988, _1570988)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1570988, tc_fun(_1570988, _1570988)), _1570990), c_If(_1570988)), hAPP(hAPP(c_COMBC(_1570990, tc_fun(_1570990, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570990)), _1570996))), _1570994)), c_Groups_Ozero__class_Ozero(_1570988))), _1570992))], (41352 ^ _780461) ^ [_1571397, _1571399, _1571401, _1571403, _1571405, _1571407] : [class_Groups_Ocomm__monoid__add(_1571397), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571399), _1571401)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1571399, _1571397), _1571403), _1571401) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1571405, _1571397), hAPP(hAPP(c_COMBB(tc_fun(_1571399, tc_HOL_Obool), _1571397, _1571405), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1571399, _1571397), _1571403)), hAPP(hAPP(c_COMBB(tc_fun(_1571399, tc_HOL_Obool), tc_fun(_1571399, tc_HOL_Obool), _1571405), c_Set_OCollect(_1571399)), hAPP(hAPP(c_COMBB(tc_fun(_1571399, tc_HOL_Obool), tc_fun(_1571399, tc_HOL_Obool), _1571405), hAPP(c_COMBS(_1571399, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571399), c_fconj), hAPP(hAPP(c_COMBC(_1571399, tc_fun(_1571399, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571399)), _1571401)))), hAPP(c_COMBC(_1571399, _1571405, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1571405, tc_fun(_1571405, tc_HOL_Obool), _1571399), c_fequal), _1571407)))))), hAPP(c_Set_Oimage(_1571399, _1571405, _1571407), _1571401)))], (41362 ^ _780461) ^ [_1571808, _1571810, _1571812, _1571814] : [-(hAPP(c_Relation_OImage(_1571808, _1571810, _1571812), hAPP(hAPP(c_Set_Oinsert(_1571808), _1571814), c_Orderings_Obot__class_Obot(tc_fun(_1571808, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1571810), hAPP(hAPP(c_COMBC(_1571810, tc_fun(tc_prod(_1571808, _1571810), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1571808, _1571810), tc_fun(tc_fun(tc_prod(_1571808, _1571810), tc_HOL_Obool), tc_HOL_Obool), _1571810), c_member(tc_prod(_1571808, _1571810))), hAPP(c_Product__Type_OPair(_1571808, _1571810), _1571814))), _1571812)))], (41364 ^ _780461) ^ [_1571911, _1571913, _1571915, _1571917, _1571919, _1571921] : [class_Groups_Ocomm__monoid__add(_1571911), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571913), _1571915)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1571913, _1571911), hAPP(hAPP(c_COMBS(_1571913, _1571911, _1571911), hAPP(hAPP(c_COMBS(_1571913, _1571911, tc_fun(_1571911, _1571911)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1571911, tc_fun(_1571911, _1571911)), _1571913), c_If(_1571911)), _1571917)), _1571919)), _1571921)), _1571915) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1571911), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1571913, _1571911), _1571919), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1571913, tc_HOL_Obool)), _1571915), hAPP(c_Set_OCollect(_1571913), _1571917)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1571913, _1571911), _1571921), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1571913, tc_HOL_Obool)), _1571915), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1571913, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1571913), _1571917))))))], (41374 ^ _780461) ^ [_1572294, _1572296] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1572294)), -(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)), _1572294))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1572296))))) = 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)), _1572294))), 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, _1572296))))))], (41380 ^ _780461) ^ [_1572471, _1572473] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1572471)), 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)), _1572471))), 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, _1572473))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (41386 ^ _780461) ^ [_1572601, _1572603, _1572605, _1572607, _1572609] : [-(c_Map_Odom(_1572601, _1572603, c_Fun_Ooverride__on(_1572601, tc_Option_Ooption(_1572603), _1572605, _1572607, _1572609)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1572601, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1572601, tc_HOL_Obool)), c_Map_Odom(_1572601, _1572603, _1572605)), hAPP(c_Set_OCollect(_1572601), hAPP(hAPP(c_COMBC(_1572601, tc_fun(_1572601, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572601)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1572601, tc_HOL_Obool)), _1572609), c_Map_Odom(_1572601, _1572603, _1572607)))))), hAPP(c_Set_OCollect(_1572601), hAPP(hAPP(c_COMBC(_1572601, tc_fun(_1572601, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572601)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1572601, tc_HOL_Obool)), _1572609), c_Map_Odom(_1572601, _1572603, _1572607))))))], (41388 ^ _780461) ^ [_1572740, _1572742, _1572744, _1572746, _1572748, _1572750] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1572740), _1572742)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572744), _1572746)), 41398 ^ _780461 : [(41399 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1572744), 41397 ^ [_1572740, _1572742, _1572744, _1572746, _1572748, _1572750]), _1572746)))], (41401 ^ _780461) ^ [] : [hAPP(c_Finite__Set_Ocard(_1572740), hAPP(c_Set_OCollect(_1572740), hAPP(hAPP(c_COMBS(_1572740, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572740), c_fconj), hAPP(hAPP(c_COMBC(_1572740, tc_fun(_1572740, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572740)), _1572742))), hAPP(hAPP(c_COMBC(_1572740, _1572744, tc_HOL_Obool), _1572748), 41397 ^ [_1572740, _1572742, _1572744, _1572746, _1572748, _1572750])))) = _1572750]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1572740, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1572744, tc_HOL_Obool), tc_Nat_Onat, _1572740), c_Finite__Set_Ocard(_1572744)), hAPP(hAPP(c_COMBB(tc_fun(_1572744, tc_HOL_Obool), tc_fun(_1572744, tc_HOL_Obool), _1572740), c_Set_OCollect(_1572744)), hAPP(hAPP(c_COMBB(tc_fun(_1572744, tc_HOL_Obool), tc_fun(_1572744, tc_HOL_Obool), _1572740), hAPP(c_COMBS(_1572744, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572744), c_fconj), hAPP(hAPP(c_COMBC(_1572744, tc_fun(_1572744, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572744)), _1572746)))), _1572748)))), _1572742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1572750), hAPP(c_Finite__Set_Ocard(_1572744), _1572746)))], (41405 ^ _780461) ^ [_1573430, _1573432] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1573430), _1573432)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1573430, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1573430, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1573430, tc_HOL_Obool), tc_fun(_1573430, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1573430, tc_HOL_Obool))), _1573432)))))], (41411 ^ _780461) ^ [_1573587, _1573589] : [-(hAPP(c_Set_OPow(_1573587), _1573589) = hAPP(c_Set_OCollect(tc_fun(_1573587, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1573587, tc_HOL_Obool), tc_fun(_1573587, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1573587, tc_HOL_Obool))), _1573589)))], (41413 ^ _780461) ^ [_1573642, _1573644, _1573646, _1573648, _1573650, _1573652] : [-(hBOOL(hAPP(hAPP(c_member(_1573642), _1573644), _1573646))), -(hAPP(c_Fun_Ooverride__on(_1573642, _1573648, _1573650, _1573652, _1573646), _1573644) = hAPP(_1573650, _1573644))], (41419 ^ _780461) ^ [_1573705, _1573707, _1573709, _1573711, _1573713, _1573715] : [hBOOL(hAPP(hAPP(c_member(_1573705), _1573707), _1573709)), -(hAPP(c_Fun_Ooverride__on(_1573705, _1573711, _1573713, _1573715, _1573709), _1573707) = hAPP(_1573715, _1573707))], (41425 ^ _780461) ^ [_1573828, _1573830, _1573832, _1573834] : [-(c_Fun_Ooverride__on(_1573828, _1573830, _1573832, _1573834, c_Orderings_Obot__class_Obot(tc_fun(_1573828, tc_HOL_Obool))) = _1573832)], (41427 ^ _780461) ^ [_1573868, _1573870] : [-(c_Fun_Oinj__on(tc_fun(_1573868, _1573870), tc_fun(tc_prod(_1573868, _1573870), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1573868, _1573870), tc_HOL_Obool), tc_fun(tc_prod(_1573868, _1573870), tc_HOL_Obool), tc_fun(_1573868, _1573870)), c_Set_OCollect(tc_prod(_1573868, _1573870))), hAPP(hAPP(c_COMBB(tc_fun(_1573868, tc_fun(_1573870, tc_HOL_Obool)), tc_fun(tc_prod(_1573868, _1573870), tc_HOL_Obool), tc_fun(_1573868, _1573870)), c_Product__Type_Oprod_Oprod__case(_1573868, _1573870, tc_HOL_Obool)), hAPP(c_COMBB(_1573870, tc_fun(_1573870, tc_HOL_Obool), _1573868), hAPP(c_COMBC(_1573870, _1573870, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1573868, _1573870), tc_HOL_Obool))))], (41429 ^ _780461) ^ [_1573988] : [-(c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1573988))))], (41431 ^ _780461) ^ [_1574037, _1574039, _1574041, _1574043, _1574045, _1574047] : [hBOOL(hAPP(hAPP(c_member(_1574037), _1574039), _1574041)), -(hAPP(c_Fun_Ooverride__on(_1574037, _1574043, _1574045, _1574047, _1574041), _1574039) = hAPP(_1574047, _1574039))], (41437 ^ _780461) ^ [_1574154, _1574156, _1574158, _1574160, _1574162, _1574164] : [-(hBOOL(hAPP(hAPP(c_member(_1574154), _1574156), _1574158))), -(hAPP(c_Fun_Ooverride__on(_1574154, _1574160, _1574162, _1574164, _1574158), _1574156) = hAPP(_1574162, _1574156))], (41443 ^ _780461) ^ [_1574219] : [-(c_Wellfounded_Ofinite__psubset(_1574219) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1574219, tc_HOL_Obool), tc_fun(_1574219, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1574219, tc_HOL_Obool), tc_fun(_1574219, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1574219, tc_HOL_Obool), tc_fun(tc_fun(_1574219, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1574219, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1574219, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1574219, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1574219, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1574219, tc_HOL_Obool)), c_COMBS(tc_fun(_1574219, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1574219, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1574219, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1574219, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1574219, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1574219, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1574219)))))], (41445 ^ _780461) ^ [_1574379, _1574381, _1574383, _1574385] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1574379, _1574381), _1574383), _1574385) = hAPP(c_Set_OCollect(tc_prod(_1574381, _1574381)), hAPP(c_Product__Type_Oprod_Oprod__case(_1574381, _1574381, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1574381, tc_fun(tc_prod(_1574379, _1574379), tc_HOL_Obool), tc_fun(_1574381, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574381, tc_fun(tc_fun(tc_prod(_1574379, _1574379), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1574379, _1574379), tc_HOL_Obool), tc_fun(_1574381, tc_HOL_Obool)), _1574381), c_COMBC(_1574381, tc_fun(tc_prod(_1574379, _1574379), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1574381, tc_prod(_1574379, _1574379)), tc_fun(_1574381, tc_fun(tc_fun(tc_prod(_1574379, _1574379), tc_HOL_Obool), tc_HOL_Obool)), _1574381), hAPP(c_COMBB(tc_prod(_1574379, _1574379), tc_fun(tc_fun(tc_prod(_1574379, _1574379), tc_HOL_Obool), tc_HOL_Obool), _1574381), c_member(tc_prod(_1574379, _1574379)))), hAPP(hAPP(c_COMBC(_1574381, tc_fun(_1574381, _1574379), tc_fun(_1574381, tc_prod(_1574379, _1574379))), hAPP(hAPP(c_COMBB(tc_fun(_1574379, tc_prod(_1574379, _1574379)), tc_fun(tc_fun(_1574381, _1574379), tc_fun(_1574381, tc_prod(_1574379, _1574379))), _1574381), c_COMBB(_1574379, tc_prod(_1574379, _1574379), _1574381)), hAPP(hAPP(c_COMBB(_1574379, tc_fun(_1574379, tc_prod(_1574379, _1574379)), _1574381), c_Product__Type_OPair(_1574379, _1574379)), _1574385))), _1574385)))), _1574383))))], (41447 ^ _780461) ^ [_1574620] : [-(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)))), _1574620)) = 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), _1574620), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (41449 ^ _780461) ^ [_1574661] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1574661) = 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), _1574661), c_Int_Onat)))))], (41451 ^ _780461) ^ [_1574702, _1574704, _1574706, _1574708] : [-(c_Nitpick_Oprod(_1574702, _1574704, _1574706, _1574708) = hAPP(c_Set_OCollect(tc_prod(_1574702, _1574704)), hAPP(c_Product__Type_Oprod_Oprod__case(_1574702, _1574704, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1574702, tc_fun(_1574704, tc_HOL_Obool), tc_fun(_1574704, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1574704, tc_HOL_Obool), tc_fun(_1574704, tc_HOL_Obool)), _1574702), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1574704)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574702), c_fconj), hAPP(hAPP(c_COMBC(_1574702, tc_fun(_1574702, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574702)), _1574706)))), hAPP(hAPP(c_COMBC(_1574704, tc_fun(_1574704, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574704)), _1574708)))))], (41453 ^ _780461) ^ [_1574830] : [-(c_Int_Oint__ge__less__than2(_1574830) = 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), _1574830)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (41455 ^ _780461) ^ [_1574876] : [-(c_Int_Oint__ge__less__than(_1574876) = 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), _1574876)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (41457 ^ _780461) ^ [_1574937, _1574939] : [c_Predicate_Oreflp(_1574937, _1574939), -(c_Relation_Orefl__on(_1574937, c_Orderings_Otop__class_Otop(tc_fun(_1574937, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1574937, _1574937)), hAPP(c_Product__Type_Oprod_Oprod__case(_1574937, _1574937, tc_HOL_Obool), _1574939))))], (41463 ^ _780461) ^ [_1575052, _1575054] : [c_Relation_Orefl__on(_1575052, c_Orderings_Otop__class_Otop(tc_fun(_1575052, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1575052, _1575052)), hAPP(c_Product__Type_Oprod_Oprod__case(_1575052, _1575052, tc_HOL_Obool), _1575054))), -(c_Predicate_Oreflp(_1575052, _1575054))], (41469 ^ _780461) ^ [_1575173, _1575175, _1575177] : [c_Predicate_Oreflp(_1575173, _1575175), -(hBOOL(hAPP(hAPP(_1575175, _1575177), _1575177)))], (41475 ^ _780461) ^ [_1575262, _1575264, _1575266] : [class_Orderings_Olinorder(_1575262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575262), _1575264)), -(_1575264 = c_Orderings_Obot__class_Obot(tc_fun(_1575262, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1575262), _1575266)), -(_1575266 = c_Orderings_Obot__class_Obot(tc_fun(_1575262, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1575262), c_Big__Operators_Olattice_OSup__fin(_1575262, c_Orderings_Oord__class_Omax(_1575262), _1575264)), c_Big__Operators_Olattice_OSup__fin(_1575262, c_Orderings_Oord__class_Omax(_1575262), _1575266)) = c_Big__Operators_Olattice_OSup__fin(_1575262, c_Orderings_Oord__class_Omax(_1575262), hAPP(c_Set_OCollect(_1575262), hAPP(hAPP(c_COMBB(tc_fun(_1575262, tc_HOL_Obool), tc_HOL_Obool, _1575262), c_HOL_OEx(_1575262)), hAPP(hAPP(c_COMBB(tc_fun(_1575262, tc_fun(_1575262, tc_HOL_Obool)), tc_fun(_1575262, tc_HOL_Obool), _1575262), hAPP(c_COMBB(tc_fun(_1575262, tc_HOL_Obool), tc_HOL_Obool, _1575262), c_HOL_OEx(_1575262))), hAPP(hAPP(c_COMBC(_1575262, tc_fun(_1575262, tc_fun(_1575262, tc_HOL_Obool)), tc_fun(_1575262, tc_fun(_1575262, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1575262, tc_fun(tc_fun(_1575262, tc_HOL_Obool), tc_fun(_1575262, tc_HOL_Obool))), tc_fun(tc_fun(_1575262, tc_fun(_1575262, tc_HOL_Obool)), tc_fun(_1575262, tc_fun(_1575262, tc_HOL_Obool))), _1575262), c_COMBS(_1575262, tc_fun(_1575262, tc_HOL_Obool), tc_fun(_1575262, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1575262, tc_fun(_1575262, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1575262, tc_fun(tc_fun(_1575262, tc_HOL_Obool), tc_fun(_1575262, tc_HOL_Obool))), _1575262), hAPP(c_COMBB(tc_fun(_1575262, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1575262, tc_HOL_Obool), tc_fun(_1575262, tc_HOL_Obool)), _1575262), c_COMBS(_1575262, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1575262, tc_fun(_1575262, tc_HOL_Obool)), tc_fun(_1575262, tc_fun(_1575262, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1575262), hAPP(c_COMBB(tc_fun(_1575262, tc_HOL_Obool), tc_fun(_1575262, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1575262), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1575262), c_fconj))), hAPP(hAPP(c_COMBC(_1575262, tc_fun(_1575262, tc_fun(_1575262, _1575262)), tc_fun(_1575262, tc_fun(_1575262, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575262, _1575262), tc_fun(_1575262, tc_HOL_Obool)), tc_fun(tc_fun(_1575262, tc_fun(_1575262, _1575262)), tc_fun(_1575262, tc_fun(_1575262, tc_HOL_Obool))), _1575262), c_COMBB(tc_fun(_1575262, _1575262), tc_fun(_1575262, tc_HOL_Obool), _1575262)), hAPP(hAPP(c_COMBB(tc_fun(_1575262, tc_HOL_Obool), tc_fun(tc_fun(_1575262, _1575262), tc_fun(_1575262, tc_HOL_Obool)), _1575262), c_COMBB(_1575262, tc_HOL_Obool, _1575262)), c_fequal))), c_Orderings_Oord__class_Omin(_1575262)))))), hAPP(hAPP(c_COMBC(_1575262, tc_fun(_1575262, tc_HOL_Obool), tc_fun(_1575262, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1575262, tc_HOL_Obool), tc_fun(_1575262, tc_HOL_Obool)), _1575262), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1575262)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1575262), c_fconj), hAPP(hAPP(c_COMBC(_1575262, tc_fun(_1575262, tc_HOL_Obool), tc_HOL_Obool), c_member(_1575262)), _1575264)))), hAPP(hAPP(c_COMBC(_1575262, tc_fun(_1575262, tc_HOL_Obool), tc_HOL_Obool), c_member(_1575262)), _1575266))))))))], (41497 ^ _780461) ^ [_1576379, _1576381, _1576383] : [class_Orderings_Olinorder(_1576379), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576379), _1576381)), -(_1576381 = c_Orderings_Obot__class_Obot(tc_fun(_1576379, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1576379), _1576383)), -(_1576383 = c_Orderings_Obot__class_Obot(tc_fun(_1576379, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1576379), c_Big__Operators_Olattice_OInf__fin(_1576379, c_Orderings_Oord__class_Omin(_1576379), _1576381)), c_Big__Operators_Olattice_OInf__fin(_1576379, c_Orderings_Oord__class_Omin(_1576379), _1576383)) = c_Big__Operators_Olattice_OInf__fin(_1576379, c_Orderings_Oord__class_Omin(_1576379), hAPP(c_Set_OCollect(_1576379), hAPP(hAPP(c_COMBB(tc_fun(_1576379, tc_HOL_Obool), tc_HOL_Obool, _1576379), c_HOL_OEx(_1576379)), hAPP(hAPP(c_COMBB(tc_fun(_1576379, tc_fun(_1576379, tc_HOL_Obool)), tc_fun(_1576379, tc_HOL_Obool), _1576379), hAPP(c_COMBB(tc_fun(_1576379, tc_HOL_Obool), tc_HOL_Obool, _1576379), c_HOL_OEx(_1576379))), hAPP(hAPP(c_COMBC(_1576379, tc_fun(_1576379, tc_fun(_1576379, tc_HOL_Obool)), tc_fun(_1576379, tc_fun(_1576379, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1576379, tc_fun(tc_fun(_1576379, tc_HOL_Obool), tc_fun(_1576379, tc_HOL_Obool))), tc_fun(tc_fun(_1576379, tc_fun(_1576379, tc_HOL_Obool)), tc_fun(_1576379, tc_fun(_1576379, tc_HOL_Obool))), _1576379), c_COMBS(_1576379, tc_fun(_1576379, tc_HOL_Obool), tc_fun(_1576379, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1576379, tc_fun(_1576379, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1576379, tc_fun(tc_fun(_1576379, tc_HOL_Obool), tc_fun(_1576379, tc_HOL_Obool))), _1576379), hAPP(c_COMBB(tc_fun(_1576379, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1576379, tc_HOL_Obool), tc_fun(_1576379, tc_HOL_Obool)), _1576379), c_COMBS(_1576379, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1576379, tc_fun(_1576379, tc_HOL_Obool)), tc_fun(_1576379, tc_fun(_1576379, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1576379), hAPP(c_COMBB(tc_fun(_1576379, tc_HOL_Obool), tc_fun(_1576379, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1576379), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576379), c_fconj))), hAPP(hAPP(c_COMBC(_1576379, tc_fun(_1576379, tc_fun(_1576379, _1576379)), tc_fun(_1576379, tc_fun(_1576379, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1576379, _1576379), tc_fun(_1576379, tc_HOL_Obool)), tc_fun(tc_fun(_1576379, tc_fun(_1576379, _1576379)), tc_fun(_1576379, tc_fun(_1576379, tc_HOL_Obool))), _1576379), c_COMBB(tc_fun(_1576379, _1576379), tc_fun(_1576379, tc_HOL_Obool), _1576379)), hAPP(hAPP(c_COMBB(tc_fun(_1576379, tc_HOL_Obool), tc_fun(tc_fun(_1576379, _1576379), tc_fun(_1576379, tc_HOL_Obool)), _1576379), c_COMBB(_1576379, tc_HOL_Obool, _1576379)), c_fequal))), c_Orderings_Oord__class_Omax(_1576379)))))), hAPP(hAPP(c_COMBC(_1576379, tc_fun(_1576379, tc_HOL_Obool), tc_fun(_1576379, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1576379, tc_HOL_Obool), tc_fun(_1576379, tc_HOL_Obool)), _1576379), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1576379)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1576379), c_fconj), hAPP(hAPP(c_COMBC(_1576379, tc_fun(_1576379, tc_HOL_Obool), tc_HOL_Obool), c_member(_1576379)), _1576381)))), hAPP(hAPP(c_COMBC(_1576379, tc_fun(_1576379, tc_HOL_Obool), tc_HOL_Obool), c_member(_1576379)), _1576383))))))))], (41519 ^ _780461) ^ [_1577496, _1577498, _1577500, _1577502] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1577496), hAPP(c_Set_OCollect(_1577496), _1577498))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577500), hAPP(c_Set_OCollect(_1577500), hAPP(hAPP(c_COMBB(tc_fun(_1577496, tc_HOL_Obool), tc_HOL_Obool, _1577500), c_HOL_OEx(_1577496)), hAPP(hAPP(c_COMBC(_1577500, tc_fun(_1577496, tc_HOL_Obool), tc_fun(_1577496, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577496, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1577496, tc_HOL_Obool), tc_fun(_1577496, tc_HOL_Obool)), _1577500), c_COMBS(_1577496, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577496, tc_HOL_Obool), tc_fun(_1577496, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1577500), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577496), c_fconj)), hAPP(hAPP(c_COMBC(_1577500, tc_fun(_1577496, _1577500), tc_fun(_1577496, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577500, tc_HOL_Obool), tc_fun(tc_fun(_1577496, _1577500), tc_fun(_1577496, tc_HOL_Obool)), _1577500), c_COMBB(_1577500, tc_HOL_Obool, _1577496)), c_fequal)), _1577502)))), _1577498))))))], (41525 ^ _780461) ^ [_1577857, _1577859, _1577861, _1577863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1577857), hAPP(c_Set_OCollect(_1577857), _1577859))), 41528 ^ _780461 : [(41539 ^ _780461) ^ [] : [41541 ^ _780461 : [(41542 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1577859, 41540 ^ [_1577857, _1577859, _1577861, _1577863])))], (41544 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1577861), hAPP(c_Set_OCollect(_1577861), hAPP(hAPP(c_COMBC(_1577861, _1577857, tc_HOL_Obool), _1577863), 41540 ^ [_1577857, _1577859, _1577861, _1577863]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577861), hAPP(c_Set_OCollect(_1577861), hAPP(hAPP(c_COMBB(tc_fun(_1577857, tc_HOL_Obool), tc_HOL_Obool, _1577861), c_HOL_OEx(_1577857)), hAPP(hAPP(c_COMBB(tc_fun(_1577857, tc_HOL_Obool), tc_fun(_1577857, tc_HOL_Obool), _1577861), hAPP(c_COMBS(_1577857, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577857), c_fconj), _1577859))), _1577863))))))], (41529 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1577861), hAPP(c_Set_OCollect(_1577861), hAPP(hAPP(c_COMBB(tc_fun(_1577857, tc_HOL_Obool), tc_HOL_Obool, _1577861), c_HOL_OEx(_1577857)), hAPP(hAPP(c_COMBB(tc_fun(_1577857, tc_HOL_Obool), tc_fun(_1577857, tc_HOL_Obool), _1577861), hAPP(c_COMBS(_1577857, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577857), c_fconj), _1577859))), _1577863))))), 41532 ^ _780461 : [(41533 ^ _780461) ^ [_1578140] : [hBOOL(hAPP(_1577859, _1578140)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577861), hAPP(c_Set_OCollect(_1577861), hAPP(hAPP(c_COMBC(_1577861, _1577857, tc_HOL_Obool), _1577863), _1578140)))))]]]]], (41548 ^ _780461) ^ [_1578505, _1578507, _1578509] : [-(c_Map_Oran(_1578505, _1578507, _1578509) = hAPP(c_Set_OCollect(_1578507), hAPP(hAPP(c_COMBB(tc_fun(_1578505, tc_HOL_Obool), tc_HOL_Obool, _1578507), c_HOL_OEx(_1578505)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1578507), tc_fun(_1578505, tc_HOL_Obool), _1578507), hAPP(c_COMBC(_1578505, tc_Option_Ooption(_1578507), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1578507), tc_fun(tc_Option_Ooption(_1578507), tc_HOL_Obool), _1578505), c_fequal), _1578509))), c_Option_Ooption_OSome(_1578507)))))], (41550 ^ _780461) ^ [_1578599, _1578601] : [-(hAPP(c_Set_OPow(_1578599), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1578599, tc_HOL_Obool)), _1578601)) = hAPP(c_Set_OCollect(tc_fun(_1578599, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1578599, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1578599, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1578599, tc_HOL_Obool), tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1578599, tc_HOL_Obool)), c_COMBS(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1578599, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1578599, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1578599, tc_HOL_Obool), tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_fun(_1578599, tc_HOL_Obool)), tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_fun(_1578599, tc_HOL_Obool)), tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1578599, tc_HOL_Obool)), c_COMBB(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1578599, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1578599, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1578599, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1578599, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1578599, tc_HOL_Obool)), _1578601)), c_Set_OPow(_1578599))))))], (41552 ^ _780461) ^ [_1578879, _1578881, _1578883] : [class_Groups_Olinordered__ab__semigroup__add(_1578879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578879), _1578881)), -(_1578881 = c_Orderings_Obot__class_Obot(tc_fun(_1578879, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1578879), _1578883), c_Big__Operators_Olinorder__class_OMax(_1578879, _1578881)) = c_Big__Operators_Olinorder__class_OMax(_1578879, hAPP(c_Set_OCollect(_1578879), hAPP(hAPP(c_COMBB(tc_fun(_1578879, tc_HOL_Obool), tc_HOL_Obool, _1578879), c_HOL_OEx(_1578879)), hAPP(hAPP(c_COMBC(_1578879, tc_fun(_1578879, tc_HOL_Obool), tc_fun(_1578879, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578879, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1578879, tc_HOL_Obool), tc_fun(_1578879, tc_HOL_Obool)), _1578879), c_COMBS(_1578879, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578879, tc_HOL_Obool), tc_fun(_1578879, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1578879), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578879), c_fconj)), hAPP(hAPP(c_COMBC(_1578879, tc_fun(_1578879, _1578879), tc_fun(_1578879, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578879, tc_HOL_Obool), tc_fun(tc_fun(_1578879, _1578879), tc_fun(_1578879, tc_HOL_Obool)), _1578879), c_COMBB(_1578879, tc_HOL_Obool, _1578879)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1578879), _1578883))))), hAPP(hAPP(c_COMBC(_1578879, tc_fun(_1578879, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578879)), _1578881))))))], (41566 ^ _780461) ^ [_1579365, _1579367, _1579369] : [class_Groups_Olinordered__ab__semigroup__add(_1579365), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579365), _1579367)), -(_1579367 = c_Orderings_Obot__class_Obot(tc_fun(_1579365, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1579365), _1579369), c_Big__Operators_Olinorder__class_OMin(_1579365, _1579367)) = c_Big__Operators_Olinorder__class_OMin(_1579365, hAPP(c_Set_OCollect(_1579365), hAPP(hAPP(c_COMBB(tc_fun(_1579365, tc_HOL_Obool), tc_HOL_Obool, _1579365), c_HOL_OEx(_1579365)), hAPP(hAPP(c_COMBC(_1579365, tc_fun(_1579365, tc_HOL_Obool), tc_fun(_1579365, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1579365, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1579365, tc_HOL_Obool), tc_fun(_1579365, tc_HOL_Obool)), _1579365), c_COMBS(_1579365, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1579365, tc_HOL_Obool), tc_fun(_1579365, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1579365), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579365), c_fconj)), hAPP(hAPP(c_COMBC(_1579365, tc_fun(_1579365, _1579365), tc_fun(_1579365, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1579365, tc_HOL_Obool), tc_fun(tc_fun(_1579365, _1579365), tc_fun(_1579365, tc_HOL_Obool)), _1579365), c_COMBB(_1579365, tc_HOL_Obool, _1579365)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1579365), _1579369))))), hAPP(hAPP(c_COMBC(_1579365, tc_fun(_1579365, tc_HOL_Obool), tc_HOL_Obool), c_member(_1579365)), _1579367))))))], (41580 ^ _780461) ^ [_1579851, _1579853, _1579855] : [class_Lattices_Odistrib__lattice(_1579851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579851), _1579853)), -(_1579853 = c_Orderings_Obot__class_Obot(tc_fun(_1579851, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1579851), _1579855)), -(_1579855 = c_Orderings_Obot__class_Obot(tc_fun(_1579851, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1579851), c_Big__Operators_Olattice__class_OInf__fin(_1579851, _1579853)), c_Big__Operators_Olattice__class_OInf__fin(_1579851, _1579855)) = c_Big__Operators_Olattice__class_OInf__fin(_1579851, hAPP(c_Set_OCollect(_1579851), hAPP(hAPP(c_COMBB(tc_fun(_1579851, tc_HOL_Obool), tc_HOL_Obool, _1579851), c_HOL_OEx(_1579851)), hAPP(hAPP(c_COMBB(tc_fun(_1579851, tc_fun(_1579851, tc_HOL_Obool)), tc_fun(_1579851, tc_HOL_Obool), _1579851), hAPP(c_COMBB(tc_fun(_1579851, tc_HOL_Obool), tc_HOL_Obool, _1579851), c_HOL_OEx(_1579851))), hAPP(hAPP(c_COMBC(_1579851, tc_fun(_1579851, tc_fun(_1579851, tc_HOL_Obool)), tc_fun(_1579851, tc_fun(_1579851, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1579851, tc_fun(tc_fun(_1579851, tc_HOL_Obool), tc_fun(_1579851, tc_HOL_Obool))), tc_fun(tc_fun(_1579851, tc_fun(_1579851, tc_HOL_Obool)), tc_fun(_1579851, tc_fun(_1579851, tc_HOL_Obool))), _1579851), c_COMBS(_1579851, tc_fun(_1579851, tc_HOL_Obool), tc_fun(_1579851, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1579851, tc_fun(_1579851, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1579851, tc_fun(tc_fun(_1579851, tc_HOL_Obool), tc_fun(_1579851, tc_HOL_Obool))), _1579851), hAPP(c_COMBB(tc_fun(_1579851, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1579851, tc_HOL_Obool), tc_fun(_1579851, tc_HOL_Obool)), _1579851), c_COMBS(_1579851, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1579851, tc_fun(_1579851, tc_HOL_Obool)), tc_fun(_1579851, tc_fun(_1579851, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1579851), hAPP(c_COMBB(tc_fun(_1579851, tc_HOL_Obool), tc_fun(_1579851, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1579851), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579851), c_fconj))), hAPP(hAPP(c_COMBC(_1579851, tc_fun(_1579851, tc_fun(_1579851, _1579851)), tc_fun(_1579851, tc_fun(_1579851, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1579851, _1579851), tc_fun(_1579851, tc_HOL_Obool)), tc_fun(tc_fun(_1579851, tc_fun(_1579851, _1579851)), tc_fun(_1579851, tc_fun(_1579851, tc_HOL_Obool))), _1579851), c_COMBB(tc_fun(_1579851, _1579851), tc_fun(_1579851, tc_HOL_Obool), _1579851)), hAPP(hAPP(c_COMBB(tc_fun(_1579851, tc_HOL_Obool), tc_fun(tc_fun(_1579851, _1579851), tc_fun(_1579851, tc_HOL_Obool)), _1579851), c_COMBB(_1579851, tc_HOL_Obool, _1579851)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1579851)))))), hAPP(hAPP(c_COMBC(_1579851, tc_fun(_1579851, tc_HOL_Obool), tc_fun(_1579851, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1579851, tc_HOL_Obool), tc_fun(_1579851, tc_HOL_Obool)), _1579851), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1579851)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579851), c_fconj), hAPP(hAPP(c_COMBC(_1579851, tc_fun(_1579851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1579851)), _1579853)))), hAPP(hAPP(c_COMBC(_1579851, tc_fun(_1579851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1579851)), _1579855))))))))], (41602 ^ _780461) ^ [_1580950, _1580952, _1580954] : [class_Lattices_Odistrib__lattice(_1580950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1580950), _1580952)), -(_1580952 = c_Orderings_Obot__class_Obot(tc_fun(_1580950, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1580950), _1580954), c_Big__Operators_Olattice__class_OInf__fin(_1580950, _1580952)) = c_Big__Operators_Olattice__class_OInf__fin(_1580950, hAPP(c_Set_OCollect(_1580950), hAPP(hAPP(c_COMBB(tc_fun(_1580950, tc_HOL_Obool), tc_HOL_Obool, _1580950), c_HOL_OEx(_1580950)), hAPP(hAPP(c_COMBC(_1580950, tc_fun(_1580950, tc_HOL_Obool), tc_fun(_1580950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580950, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1580950, tc_HOL_Obool), tc_fun(_1580950, tc_HOL_Obool)), _1580950), c_COMBS(_1580950, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580950, tc_HOL_Obool), tc_fun(_1580950, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1580950), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1580950), c_fconj)), hAPP(hAPP(c_COMBC(_1580950, tc_fun(_1580950, _1580950), tc_fun(_1580950, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580950, tc_HOL_Obool), tc_fun(tc_fun(_1580950, _1580950), tc_fun(_1580950, tc_HOL_Obool)), _1580950), c_COMBB(_1580950, tc_HOL_Obool, _1580950)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1580950), _1580954))))), hAPP(hAPP(c_COMBC(_1580950, tc_fun(_1580950, tc_HOL_Obool), tc_HOL_Obool), c_member(_1580950)), _1580952))))))], (41616 ^ _780461) ^ [_1581436, _1581438, _1581440] : [class_Lattices_Odistrib__lattice(_1581436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581436), _1581438)), -(_1581438 = c_Orderings_Obot__class_Obot(tc_fun(_1581436, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1581436), _1581440), c_Big__Operators_Olattice__class_OSup__fin(_1581436, _1581438)) = c_Big__Operators_Olattice__class_OSup__fin(_1581436, hAPP(c_Set_OCollect(_1581436), hAPP(hAPP(c_COMBB(tc_fun(_1581436, tc_HOL_Obool), tc_HOL_Obool, _1581436), c_HOL_OEx(_1581436)), hAPP(hAPP(c_COMBC(_1581436, tc_fun(_1581436, tc_HOL_Obool), tc_fun(_1581436, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581436, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1581436, tc_HOL_Obool), tc_fun(_1581436, tc_HOL_Obool)), _1581436), c_COMBS(_1581436, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581436, tc_HOL_Obool), tc_fun(_1581436, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1581436), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1581436), c_fconj)), hAPP(hAPP(c_COMBC(_1581436, tc_fun(_1581436, _1581436), tc_fun(_1581436, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581436, tc_HOL_Obool), tc_fun(tc_fun(_1581436, _1581436), tc_fun(_1581436, tc_HOL_Obool)), _1581436), c_COMBB(_1581436, tc_HOL_Obool, _1581436)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1581436), _1581440))))), hAPP(hAPP(c_COMBC(_1581436, tc_fun(_1581436, tc_HOL_Obool), tc_HOL_Obool), c_member(_1581436)), _1581438))))))], (41630 ^ _780461) ^ [_1581922, _1581924, _1581926] : [class_Lattices_Odistrib__lattice(_1581922), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581922), _1581924)), -(_1581924 = c_Orderings_Obot__class_Obot(tc_fun(_1581922, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581922), _1581926)), -(_1581926 = c_Orderings_Obot__class_Obot(tc_fun(_1581922, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1581922), c_Big__Operators_Olattice__class_OSup__fin(_1581922, _1581924)), c_Big__Operators_Olattice__class_OSup__fin(_1581922, _1581926)) = c_Big__Operators_Olattice__class_OSup__fin(_1581922, hAPP(c_Set_OCollect(_1581922), hAPP(hAPP(c_COMBB(tc_fun(_1581922, tc_HOL_Obool), tc_HOL_Obool, _1581922), c_HOL_OEx(_1581922)), hAPP(hAPP(c_COMBB(tc_fun(_1581922, tc_fun(_1581922, tc_HOL_Obool)), tc_fun(_1581922, tc_HOL_Obool), _1581922), hAPP(c_COMBB(tc_fun(_1581922, tc_HOL_Obool), tc_HOL_Obool, _1581922), c_HOL_OEx(_1581922))), hAPP(hAPP(c_COMBC(_1581922, tc_fun(_1581922, tc_fun(_1581922, tc_HOL_Obool)), tc_fun(_1581922, tc_fun(_1581922, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1581922, tc_fun(tc_fun(_1581922, tc_HOL_Obool), tc_fun(_1581922, tc_HOL_Obool))), tc_fun(tc_fun(_1581922, tc_fun(_1581922, tc_HOL_Obool)), tc_fun(_1581922, tc_fun(_1581922, tc_HOL_Obool))), _1581922), c_COMBS(_1581922, tc_fun(_1581922, tc_HOL_Obool), tc_fun(_1581922, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1581922, tc_fun(_1581922, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1581922, tc_fun(tc_fun(_1581922, tc_HOL_Obool), tc_fun(_1581922, tc_HOL_Obool))), _1581922), hAPP(c_COMBB(tc_fun(_1581922, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1581922, tc_HOL_Obool), tc_fun(_1581922, tc_HOL_Obool)), _1581922), c_COMBS(_1581922, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1581922, tc_fun(_1581922, tc_HOL_Obool)), tc_fun(_1581922, tc_fun(_1581922, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1581922), hAPP(c_COMBB(tc_fun(_1581922, tc_HOL_Obool), tc_fun(_1581922, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1581922), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1581922), c_fconj))), hAPP(hAPP(c_COMBC(_1581922, tc_fun(_1581922, tc_fun(_1581922, _1581922)), tc_fun(_1581922, tc_fun(_1581922, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1581922, _1581922), tc_fun(_1581922, tc_HOL_Obool)), tc_fun(tc_fun(_1581922, tc_fun(_1581922, _1581922)), tc_fun(_1581922, tc_fun(_1581922, tc_HOL_Obool))), _1581922), c_COMBB(tc_fun(_1581922, _1581922), tc_fun(_1581922, tc_HOL_Obool), _1581922)), hAPP(hAPP(c_COMBB(tc_fun(_1581922, tc_HOL_Obool), tc_fun(tc_fun(_1581922, _1581922), tc_fun(_1581922, tc_HOL_Obool)), _1581922), c_COMBB(_1581922, tc_HOL_Obool, _1581922)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1581922)))))), hAPP(hAPP(c_COMBC(_1581922, tc_fun(_1581922, tc_HOL_Obool), tc_fun(_1581922, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1581922, tc_HOL_Obool), tc_fun(_1581922, tc_HOL_Obool)), _1581922), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1581922)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1581922), c_fconj), hAPP(hAPP(c_COMBC(_1581922, tc_fun(_1581922, tc_HOL_Obool), tc_HOL_Obool), c_member(_1581922)), _1581924)))), hAPP(hAPP(c_COMBC(_1581922, tc_fun(_1581922, tc_HOL_Obool), tc_HOL_Obool), c_member(_1581922)), _1581926))))))))], (41652 ^ _780461) ^ [_1583021, _1583023, _1583025] : [class_Orderings_Olinorder(_1583021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583021), _1583023)), -(_1583023 = c_Orderings_Obot__class_Obot(tc_fun(_1583021, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1583021), _1583025), c_Big__Operators_Olattice_OInf__fin(_1583021, c_Orderings_Oord__class_Omin(_1583021), _1583023)) = c_Big__Operators_Olattice_OInf__fin(_1583021, c_Orderings_Oord__class_Omin(_1583021), hAPP(c_Set_OCollect(_1583021), hAPP(hAPP(c_COMBB(tc_fun(_1583021, tc_HOL_Obool), tc_HOL_Obool, _1583021), c_HOL_OEx(_1583021)), hAPP(hAPP(c_COMBC(_1583021, tc_fun(_1583021, tc_HOL_Obool), tc_fun(_1583021, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583021, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1583021, tc_HOL_Obool), tc_fun(_1583021, tc_HOL_Obool)), _1583021), c_COMBS(_1583021, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583021, tc_HOL_Obool), tc_fun(_1583021, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1583021), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1583021), c_fconj)), hAPP(hAPP(c_COMBC(_1583021, tc_fun(_1583021, _1583021), tc_fun(_1583021, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583021, tc_HOL_Obool), tc_fun(tc_fun(_1583021, _1583021), tc_fun(_1583021, tc_HOL_Obool)), _1583021), c_COMBB(_1583021, tc_HOL_Obool, _1583021)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1583021), _1583025))))), hAPP(hAPP(c_COMBC(_1583021, tc_fun(_1583021, tc_HOL_Obool), tc_HOL_Obool), c_member(_1583021)), _1583023))))))], (41666 ^ _780461) ^ [_1583519, _1583521, _1583523] : [class_Orderings_Olinorder(_1583519), hBOOL(hAPP(c_Finite__Set_Ofinite(_1583519), _1583521)), -(_1583521 = c_Orderings_Obot__class_Obot(tc_fun(_1583519, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1583519), _1583523), c_Big__Operators_Olattice_OSup__fin(_1583519, c_Orderings_Oord__class_Omax(_1583519), _1583521)) = c_Big__Operators_Olattice_OSup__fin(_1583519, c_Orderings_Oord__class_Omax(_1583519), hAPP(c_Set_OCollect(_1583519), hAPP(hAPP(c_COMBB(tc_fun(_1583519, tc_HOL_Obool), tc_HOL_Obool, _1583519), c_HOL_OEx(_1583519)), hAPP(hAPP(c_COMBC(_1583519, tc_fun(_1583519, tc_HOL_Obool), tc_fun(_1583519, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583519, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1583519, tc_HOL_Obool), tc_fun(_1583519, tc_HOL_Obool)), _1583519), c_COMBS(_1583519, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583519, tc_HOL_Obool), tc_fun(_1583519, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1583519), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1583519), c_fconj)), hAPP(hAPP(c_COMBC(_1583519, tc_fun(_1583519, _1583519), tc_fun(_1583519, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1583519, tc_HOL_Obool), tc_fun(tc_fun(_1583519, _1583519), tc_fun(_1583519, tc_HOL_Obool)), _1583519), c_COMBB(_1583519, tc_HOL_Obool, _1583519)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1583519), _1583523))))), hAPP(hAPP(c_COMBC(_1583519, tc_fun(_1583519, tc_HOL_Obool), tc_HOL_Obool), c_member(_1583519)), _1583521))))))], (41680 ^ _780461) ^ [_1584017, _1584019, _1584021, _1584023, _1584025, _1584027, _1584029] : [class_Rings_Osemiring__0(_1584017), c_Fun_Oinj__on(tc_prod(_1584019, _1584021), _1584017, hAPP(c_Product__Type_Oprod_Oprod__case(_1584019, _1584021, _1584017), hAPP(hAPP(c_COMBC(_1584019, tc_fun(_1584021, _1584017), tc_fun(_1584021, _1584017)), hAPP(hAPP(c_COMBB(tc_fun(_1584017, _1584017), tc_fun(tc_fun(_1584021, _1584017), tc_fun(_1584021, _1584017)), _1584019), c_COMBB(_1584017, _1584017, _1584021)), hAPP(hAPP(c_COMBB(_1584017, tc_fun(_1584017, _1584017), _1584019), c_Groups_Otimes__class_Otimes(_1584017)), _1584023))), _1584025)), hAPP(hAPP(c_Product__Type_OSigma(_1584019, _1584021), _1584027), hAPP(c_COMBK(tc_fun(_1584021, tc_HOL_Obool), _1584019), _1584029))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1584017), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1584019, _1584017), _1584023), _1584027)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1584021, _1584017), _1584025), _1584029)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1584017, _1584017), c_Fun_Oid(_1584017)), hAPP(c_Set_OCollect(_1584017), hAPP(hAPP(c_COMBB(tc_fun(_1584019, tc_HOL_Obool), tc_HOL_Obool, _1584017), c_HOL_OEx(_1584019)), hAPP(hAPP(c_COMBB(tc_fun(_1584019, tc_fun(_1584021, tc_HOL_Obool)), tc_fun(_1584019, tc_HOL_Obool), _1584017), hAPP(c_COMBB(tc_fun(_1584021, tc_HOL_Obool), tc_HOL_Obool, _1584019), c_HOL_OEx(_1584021))), hAPP(hAPP(c_COMBC(_1584017, tc_fun(_1584019, tc_fun(_1584021, tc_HOL_Obool)), tc_fun(_1584019, tc_fun(_1584021, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1584019, tc_fun(tc_fun(_1584021, tc_HOL_Obool), tc_fun(_1584021, tc_HOL_Obool))), tc_fun(tc_fun(_1584019, tc_fun(_1584021, tc_HOL_Obool)), tc_fun(_1584019, tc_fun(_1584021, tc_HOL_Obool))), _1584017), c_COMBS(_1584019, tc_fun(_1584021, tc_HOL_Obool), tc_fun(_1584021, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1584019, tc_fun(_1584021, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1584019, tc_fun(tc_fun(_1584021, tc_HOL_Obool), tc_fun(_1584021, tc_HOL_Obool))), _1584017), hAPP(c_COMBB(tc_fun(_1584021, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1584021, tc_HOL_Obool), tc_fun(_1584021, tc_HOL_Obool)), _1584019), c_COMBS(_1584021, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1584019, tc_fun(_1584021, tc_HOL_Obool)), tc_fun(_1584019, tc_fun(_1584021, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1584017), hAPP(c_COMBB(tc_fun(_1584021, tc_HOL_Obool), tc_fun(_1584021, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1584019), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1584021), c_fconj))), hAPP(hAPP(c_COMBC(_1584017, tc_fun(_1584019, tc_fun(_1584021, _1584017)), tc_fun(_1584019, tc_fun(_1584021, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1584021, _1584017), tc_fun(_1584021, tc_HOL_Obool)), tc_fun(tc_fun(_1584019, tc_fun(_1584021, _1584017)), tc_fun(_1584019, tc_fun(_1584021, tc_HOL_Obool))), _1584017), c_COMBB(tc_fun(_1584021, _1584017), tc_fun(_1584021, tc_HOL_Obool), _1584019)), hAPP(hAPP(c_COMBB(tc_fun(_1584017, tc_HOL_Obool), tc_fun(tc_fun(_1584021, _1584017), tc_fun(_1584021, tc_HOL_Obool)), _1584017), c_COMBB(_1584017, tc_HOL_Obool, _1584021)), c_fequal))), hAPP(hAPP(c_COMBC(_1584019, tc_fun(_1584021, _1584017), tc_fun(_1584021, _1584017)), hAPP(hAPP(c_COMBB(tc_fun(_1584017, _1584017), tc_fun(tc_fun(_1584021, _1584017), tc_fun(_1584021, _1584017)), _1584019), c_COMBB(_1584017, _1584017, _1584021)), hAPP(hAPP(c_COMBB(_1584017, tc_fun(_1584017, _1584017), _1584019), c_Groups_Otimes__class_Otimes(_1584017)), _1584023))), _1584025)))))), hAPP(hAPP(c_COMBC(_1584019, tc_fun(_1584021, tc_HOL_Obool), tc_fun(_1584021, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1584021, tc_HOL_Obool), tc_fun(_1584021, tc_HOL_Obool)), _1584019), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1584021)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1584019), c_fconj), hAPP(hAPP(c_COMBC(_1584019, tc_fun(_1584019, tc_HOL_Obool), tc_HOL_Obool), c_member(_1584019)), _1584027)))), hAPP(hAPP(c_COMBC(_1584021, tc_fun(_1584021, tc_HOL_Obool), tc_HOL_Obool), c_member(_1584021)), _1584029))))))))], (41690 ^ _780461) ^ [_1585294, _1585296, _1585298, _1585300, _1585302, _1585304] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1585294), _1585296)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585298), _1585300)), 41700 ^ _780461 : [(41701 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1585298), 41699 ^ [_1585294, _1585296, _1585298, _1585300, _1585302, _1585304]), _1585300)))], (41703 ^ _780461) ^ [] : [hAPP(c_Finite__Set_Ocard(_1585294), hAPP(c_Set_OCollect(_1585294), hAPP(hAPP(c_COMBS(_1585294, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1585294), c_fconj), hAPP(hAPP(c_COMBC(_1585294, tc_fun(_1585294, tc_HOL_Obool), tc_HOL_Obool), c_member(_1585294)), _1585296))), hAPP(hAPP(c_COMBC(_1585294, _1585298, tc_HOL_Obool), _1585302), 41699 ^ [_1585294, _1585296, _1585298, _1585300, _1585302, _1585304])))) = hAPP(_1585304, 41699 ^ [_1585294, _1585296, _1585298, _1585300, _1585302, _1585304])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1585294, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1585298, tc_HOL_Obool), tc_Nat_Onat, _1585294), c_Finite__Set_Ocard(_1585298)), hAPP(hAPP(c_COMBB(tc_fun(_1585298, tc_HOL_Obool), tc_fun(_1585298, tc_HOL_Obool), _1585294), c_Set_OCollect(_1585298)), hAPP(hAPP(c_COMBB(tc_fun(_1585298, tc_HOL_Obool), tc_fun(_1585298, tc_HOL_Obool), _1585294), hAPP(c_COMBS(_1585298, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1585298), c_fconj), hAPP(hAPP(c_COMBC(_1585298, tc_fun(_1585298, tc_HOL_Obool), tc_HOL_Obool), c_member(_1585298)), _1585300)))), _1585302)))), _1585296) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1585298, tc_Nat_Onat), _1585304), _1585300))], (41707 ^ _780461) ^ [_1586004, _1586006] : [-(c_Fun_Oinj__on(_1586004, _1586004, c_Fun_Oid(_1586004), _1586006))], (41709 ^ _780461) ^ [_1586033, _1586035] : [-(c_Product__Type_Omap__pair(_1586033, _1586033, _1586035, _1586035, c_Fun_Oid(_1586033), c_Fun_Oid(_1586035)) = c_Fun_Oid(tc_prod(_1586033, _1586035)))], (41711 ^ _780461) ^ [_1586074, _1586076] : [-(c_Product__Type_Omap__pair(_1586074, _1586074, _1586076, _1586076, c_COMBI(_1586074), c_COMBI(_1586076)) = c_Fun_Oid(tc_prod(_1586074, _1586076)))], (41713 ^ _780461) ^ [_1586115, _1586117] : [-(hAPP(c_Fun_Oid(_1586115), _1586117) = _1586117)], (41715 ^ _780461) ^ [_1586145, _1586147] : [-(hAPP(c_Fun_Oid(_1586145), _1586147) = _1586147)], (41717 ^ _780461) ^ [_1586175, _1586177] : [-(c_Product__Type_Oapsnd(_1586175, _1586175, _1586177, c_Fun_Oid(_1586175)) = c_Fun_Oid(tc_prod(_1586177, _1586175)))], (41719 ^ _780461) ^ [_1586212, _1586214] : [-(c_Product__Type_Oapfst(_1586212, _1586212, _1586214, c_Fun_Oid(_1586212)) = c_Fun_Oid(tc_prod(_1586212, _1586214)))], (41721 ^ _780461) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (41723 ^ _780461) ^ [_1586267, _1586269] : [-(hAPP(c_Set_Ovimage(_1586267, _1586267, c_Fun_Oid(_1586267)), _1586269) = _1586269)], (41725 ^ _780461) ^ [_1586301, _1586303, _1586305, _1586307, _1586309, _1586311, _1586313] : [hAPP(c_Fun_Ocomp(_1586301, _1586303, _1586305, _1586307), _1586309) = hAPP(c_Fun_Ocomp(_1586303, _1586303, _1586305, c_Fun_Oid(_1586303)), _1586311), -(hAPP(_1586307, hAPP(_1586309, _1586313)) = hAPP(_1586311, _1586313))], (41731 ^ _780461) ^ [_1586442, _1586444, _1586446] : [-(hAPP(c_Fun_Ocomp(_1586442, _1586444, _1586442, _1586446), c_Fun_Oid(_1586442)) = _1586446)], (41733 ^ _780461) ^ [_1586479, _1586481, _1586483] : [-(hAPP(c_Fun_Ocomp(_1586479, _1586479, _1586481, c_Fun_Oid(_1586479)), _1586483) = _1586483)], (41735 ^ _780461) ^ [_1586516, _1586518] : [-(hAPP(c_Set_Oimage(_1586516, _1586516, c_Fun_Oid(_1586516)), _1586518) = _1586518)], (41737 ^ _780461) ^ [_1586550] : [-(hAPP(c_Set_Oimage(_1586550, _1586550, c_Fun_Oid(_1586550)), c_Orderings_Otop__class_Otop(tc_fun(_1586550, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1586550, tc_HOL_Obool)))], (41739 ^ _780461) ^ [_1586592, _1586594, _1586596, _1586598] : [c_Finite__Set_Ofolding(_1586592, _1586594, _1586596, _1586598), -(hAPP(_1586598, c_Orderings_Obot__class_Obot(tc_fun(_1586592, tc_HOL_Obool))) = c_Fun_Oid(_1586594))], (41745 ^ _780461) ^ [_1586697, _1586699, _1586701, _1586703] : [-(c_Product__Type_Oapsnd(_1586697, _1586699, _1586701, _1586703) = c_Product__Type_Omap__pair(_1586701, _1586701, _1586697, _1586699, c_Fun_Oid(_1586701), _1586703))], (41747 ^ _780461) ^ [_1586740, _1586742, _1586744, _1586746] : [-(c_Product__Type_Oapfst(_1586740, _1586742, _1586744, _1586746) = c_Product__Type_Omap__pair(_1586740, _1586742, _1586744, _1586744, _1586746, c_Fun_Oid(_1586744)))], (41749 ^ _780461) ^ [_1586783, _1586785] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1586783, _1586785, tc_prod(_1586783, _1586785)), c_Product__Type_OPair(_1586783, _1586785)) = c_Fun_Oid(tc_prod(_1586783, _1586785)))], (41751 ^ _780461) ^ [_1586826, _1586828, _1586830, _1586832] : [class_Groups_Ocomm__monoid__add(_1586826), c_Fun_Oinj__on(_1586828, _1586826, _1586830, _1586832), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1586828, _1586826), _1586830), _1586832) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1586826, _1586826), c_Fun_Oid(_1586826)), hAPP(c_Set_Oimage(_1586828, _1586826, _1586830), _1586832)))], (41761 ^ _780461) ^ [_1587019, _1587021, _1587023, _1587025] : [class_Groups_Ocomm__monoid__mult(_1587019), c_Fun_Oinj__on(_1587021, _1587019, _1587023, _1587025), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1587021, _1587019), _1587023), _1587025) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1587019, _1587019), c_Fun_Oid(_1587019)), hAPP(c_Set_Oimage(_1587021, _1587019, _1587023), _1587025)))], (41771 ^ _780461) ^ [_1587227, _1587229] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1587227), _1587229)), -(_1587229 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1587227, 41775 ^ [_1587227, _1587229]), 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)), 41774 ^ [_1587227, _1587229]))))], (41779 ^ _780461) ^ [_1587358, _1587360] : [41780 ^ _780461 : [(41781 ^ _780461) ^ [_1587422, _1587424] : [_1587360 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1587358, _1587422), 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)), _1587424)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1587358), _1587360)))], (41785 ^ _780461) ^ [_1587494, _1587496, _1587498, _1587500, _1587502] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1587494, _1587496, _1587498), _1587500), _1587502) = hAPP(c_Set_OCollect(tc_prod(_1587494, _1587498)), hAPP(c_Product__Type_Oprod_Oprod__case(_1587494, _1587498, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1587498, tc_fun(_1587496, tc_HOL_Obool)), tc_fun(_1587498, tc_HOL_Obool), _1587494), hAPP(c_COMBB(tc_fun(_1587496, tc_HOL_Obool), tc_HOL_Obool, _1587498), c_HOL_OEx(_1587496))), hAPP(hAPP(c_COMBC(_1587494, tc_fun(_1587498, tc_fun(_1587496, tc_HOL_Obool)), tc_fun(_1587498, tc_fun(_1587496, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1587496, tc_HOL_Obool), tc_fun(_1587496, tc_HOL_Obool)), tc_fun(tc_fun(_1587498, tc_fun(_1587496, tc_HOL_Obool)), tc_fun(_1587498, tc_fun(_1587496, tc_HOL_Obool))), _1587494), c_COMBB(tc_fun(_1587496, tc_HOL_Obool), tc_fun(_1587496, tc_HOL_Obool), _1587498)), hAPP(hAPP(c_COMBB(tc_fun(_1587496, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1587496, tc_HOL_Obool), tc_fun(_1587496, tc_HOL_Obool)), _1587494), c_COMBS(_1587496, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587496, tc_HOL_Obool), tc_fun(_1587496, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1587494), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1587496), c_fconj)), hAPP(hAPP(c_COMBC(_1587494, tc_fun(tc_prod(_1587494, _1587496), tc_HOL_Obool), tc_fun(_1587496, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587496, tc_fun(tc_fun(tc_prod(_1587494, _1587496), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1587494, _1587496), tc_HOL_Obool), tc_fun(_1587496, tc_HOL_Obool)), _1587494), c_COMBC(_1587496, tc_fun(tc_prod(_1587494, _1587496), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587496, tc_prod(_1587494, _1587496)), tc_fun(_1587496, tc_fun(tc_fun(tc_prod(_1587494, _1587496), tc_HOL_Obool), tc_HOL_Obool)), _1587494), hAPP(c_COMBB(tc_prod(_1587494, _1587496), tc_fun(tc_fun(tc_prod(_1587494, _1587496), tc_HOL_Obool), tc_HOL_Obool), _1587496), c_member(tc_prod(_1587494, _1587496)))), c_Product__Type_OPair(_1587494, _1587496)))), _1587500))))), hAPP(hAPP(c_COMBC(_1587498, tc_fun(tc_prod(_1587496, _1587498), tc_HOL_Obool), tc_fun(_1587496, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587496, tc_fun(tc_fun(tc_prod(_1587496, _1587498), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1587496, _1587498), tc_HOL_Obool), tc_fun(_1587496, tc_HOL_Obool)), _1587498), c_COMBC(_1587496, tc_fun(tc_prod(_1587496, _1587498), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587496, tc_prod(_1587496, _1587498)), tc_fun(_1587496, tc_fun(tc_fun(tc_prod(_1587496, _1587498), tc_HOL_Obool), tc_HOL_Obool)), _1587498), hAPP(c_COMBB(tc_prod(_1587496, _1587498), tc_fun(tc_fun(tc_prod(_1587496, _1587498), tc_HOL_Obool), tc_HOL_Obool), _1587496), c_member(tc_prod(_1587496, _1587498)))), hAPP(c_COMBC(_1587496, _1587498, tc_prod(_1587496, _1587498)), c_Product__Type_OPair(_1587496, _1587498))))), _1587502))))))], (41787 ^ _780461) ^ [_1587942, _1587944, _1587946, _1587948, _1587950, _1587952, _1587954, _1587956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587942, _1587944)), hAPP(hAPP(c_Product__Type_OPair(_1587942, _1587944), _1587946), _1587948)), _1587950)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587944, _1587952)), hAPP(hAPP(c_Product__Type_OPair(_1587944, _1587952), _1587948), _1587954)), _1587956)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587942, _1587952)), hAPP(hAPP(c_Product__Type_OPair(_1587942, _1587952), _1587946), _1587954)), hAPP(hAPP(c_Relation_Orel__comp(_1587942, _1587944, _1587952), _1587950), _1587956))))], (41797 ^ _780461) ^ [_1588229, _1588231, _1588233, _1588235, _1588237, _1588239, _1588241] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588229, _1588231, _1588233), _1588235), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588237, tc_fun(tc_prod(_1588231, _1588233), tc_HOL_Obool)), _1588239), _1588241)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588237, tc_fun(tc_prod(_1588229, _1588233), tc_HOL_Obool)), _1588239), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1588231, _1588233), tc_HOL_Obool), tc_fun(tc_prod(_1588229, _1588233), tc_HOL_Obool), _1588237), hAPP(c_Relation_Orel__comp(_1588229, _1588231, _1588233), _1588235)), _1588241)))], (41799 ^ _780461) ^ [_1588333, _1588335, _1588337, _1588339, _1588341, _1588343, _1588345] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588333, _1588335, _1588337), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588339, tc_fun(tc_prod(_1588333, _1588335), tc_HOL_Obool)), _1588341), _1588343)), _1588345) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1588339, tc_fun(tc_prod(_1588333, _1588337), tc_HOL_Obool)), _1588341), hAPP(hAPP(c_COMBC(_1588339, tc_fun(tc_prod(_1588335, _1588337), tc_HOL_Obool), tc_fun(tc_prod(_1588333, _1588337), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1588333, _1588335), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1588335, _1588337), tc_HOL_Obool), tc_fun(tc_prod(_1588333, _1588337), tc_HOL_Obool)), _1588339), c_Relation_Orel__comp(_1588333, _1588335, _1588337)), _1588343)), _1588345)))], (41801 ^ _780461) ^ [_1588465, _1588467, _1588469, _1588471, _1588473, _1588475] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588465, _1588467, _1588469), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588465, _1588467), tc_HOL_Obool)), _1588471), _1588473)), _1588475) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588465, _1588469), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1588465, _1588467, _1588469), _1588471), _1588475)), hAPP(hAPP(c_Relation_Orel__comp(_1588465, _1588467, _1588469), _1588473), _1588475)))], (41803 ^ _780461) ^ [_1588556, _1588558, _1588560, _1588562, _1588564, _1588566] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588556, _1588558, _1588560), _1588562), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588558, _1588560), tc_HOL_Obool)), _1588564), _1588566)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588556, _1588560), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1588556, _1588558, _1588560), _1588562), _1588564)), hAPP(hAPP(c_Relation_Orel__comp(_1588556, _1588558, _1588560), _1588562), _1588566)))], (41805 ^ _780461) ^ [_1588647, _1588649, _1588651, _1588653] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588647, _1588649, _1588651), _1588653), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1588649, _1588651), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1588647, _1588651), tc_HOL_Obool)))], (41807 ^ _780461) ^ [_1588702, _1588704, _1588706, _1588708] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588702, _1588704, _1588706), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1588702, _1588704), tc_HOL_Obool))), _1588708) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1588702, _1588706), tc_HOL_Obool)))], (41809 ^ _780461) ^ [_1588757, _1588759, _1588761, _1588763, _1588765, _1588767, _1588769] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588757, _1588759, _1588761), hAPP(hAPP(c_Relation_Orel__comp(_1588757, _1588763, _1588759), _1588765), _1588767)), _1588769) = hAPP(hAPP(c_Relation_Orel__comp(_1588757, _1588763, _1588761), _1588765), hAPP(hAPP(c_Relation_Orel__comp(_1588763, _1588759, _1588761), _1588767), _1588769)))], (41811 ^ _780461) ^ [_1588832, _1588834, _1588836, _1588838, _1588840, _1588842, _1588844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588832, _1588834), tc_HOL_Obool)), _1588836), _1588838)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588834, _1588840), tc_HOL_Obool)), _1588842), _1588844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588832, _1588840), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1588832, _1588834, _1588840), _1588836), _1588842)), hAPP(hAPP(c_Relation_Orel__comp(_1588832, _1588834, _1588840), _1588838), _1588844))))], (41821 ^ _780461) ^ [_1589099, _1589101, _1589103, _1589105] : [hAPP(hAPP(c_Relation_Orel__comp(_1589099, _1589099, _1589099), _1589101), _1589103) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1589099, _1589099), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1589099, _1589099, _1589099), _1589105), _1589103) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1589099, _1589099), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1589099, _1589099, _1589099), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1589099, _1589099), tc_HOL_Obool)), _1589101), _1589105)), _1589103) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1589099, _1589099), tc_HOL_Obool)))], (41831 ^ _780461) ^ [_1589372, _1589374, _1589376, _1589378] : [hAPP(hAPP(c_Relation_Orel__comp(_1589372, _1589372, _1589372), _1589374), _1589376) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1589372, _1589372), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1589372, _1589372, _1589372), _1589374), _1589378) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1589372, _1589372), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1589372, _1589372, _1589372), _1589374), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1589372, _1589372), tc_HOL_Obool)), _1589376), _1589378)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1589372, _1589372), tc_HOL_Obool)))], (41841 ^ _780461) ^ [_1589645, _1589647, _1589649, _1589651, _1589653, _1589655, _1589657, _1589659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589645, _1589647), tc_HOL_Obool)), _1589649), hAPP(hAPP(c_Product__Type_OSigma(_1589645, _1589647), _1589651), hAPP(c_COMBK(tc_fun(_1589647, tc_HOL_Obool), _1589645), _1589653)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589647, _1589655), tc_HOL_Obool)), _1589657), hAPP(hAPP(c_Product__Type_OSigma(_1589647, _1589655), _1589653), hAPP(c_COMBK(tc_fun(_1589655, tc_HOL_Obool), _1589647), _1589659)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1589645, _1589655), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1589645, _1589647, _1589655), _1589649), _1589657)), hAPP(hAPP(c_Product__Type_OSigma(_1589645, _1589655), _1589651), hAPP(c_COMBK(tc_fun(_1589655, tc_HOL_Obool), _1589645), _1589659)))))], (41851 ^ _780461) ^ [_1590004, _1590006, _1590008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1590004, _1590004), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1590004, _1590004, _1590004), _1590006), _1590008)), _1590006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1590004, tc_HOL_Obool), tc_fun(_1590004, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1590004, tc_HOL_Obool), tc_fun(_1590004, tc_HOL_Obool), tc_fun(_1590004, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1590004, _1590006)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1590004, tc_HOL_Obool), tc_fun(_1590004, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1590004, _1590008)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1590004, tc_HOL_Obool), tc_fun(_1590004, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1590004, tc_HOL_Obool), tc_fun(_1590004, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1590004, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1590004, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1590004, tc_HOL_Obool), tc_fun(_1590004, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1590004, _1590006))))], (41857 ^ _780461) ^ [_1590375, _1590377, _1590379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1590375, _1590375), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1590375, _1590375, _1590375), _1590377), _1590379)), _1590377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1590375, tc_HOL_Obool), tc_fun(_1590375, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1590375, tc_HOL_Obool), tc_fun(_1590375, tc_HOL_Obool), tc_fun(_1590375, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1590375, _1590377)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1590375, tc_HOL_Obool), tc_fun(_1590375, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1590375, _1590379)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1590375, tc_HOL_Obool), tc_fun(_1590375, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1590375, tc_HOL_Obool), tc_fun(_1590375, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1590375, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1590375, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1590375, tc_HOL_Obool), tc_fun(_1590375, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1590375, _1590377))))], (41863 ^ _780461) ^ [_1590776, _1590778, _1590780, _1590782, _1590784, _1590786, _1590788] : [c_Predicate_Opred__comp(_1590776, _1590778, _1590780, hAPP(hAPP(c_COMBC(_1590776, tc_fun(tc_prod(_1590776, _1590778), tc_HOL_Obool), tc_fun(_1590778, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1590778, tc_fun(tc_fun(tc_prod(_1590776, _1590778), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1590776, _1590778), tc_HOL_Obool), tc_fun(_1590778, tc_HOL_Obool)), _1590776), c_COMBC(_1590778, tc_fun(tc_prod(_1590776, _1590778), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1590778, tc_prod(_1590776, _1590778)), tc_fun(_1590778, tc_fun(tc_fun(tc_prod(_1590776, _1590778), tc_HOL_Obool), tc_HOL_Obool)), _1590776), hAPP(c_COMBB(tc_prod(_1590776, _1590778), tc_fun(tc_fun(tc_prod(_1590776, _1590778), tc_HOL_Obool), tc_HOL_Obool), _1590778), c_member(tc_prod(_1590776, _1590778)))), c_Product__Type_OPair(_1590776, _1590778)))), _1590782), hAPP(hAPP(c_COMBC(_1590778, tc_fun(tc_prod(_1590778, _1590780), tc_HOL_Obool), tc_fun(_1590780, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1590780, tc_fun(tc_fun(tc_prod(_1590778, _1590780), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1590778, _1590780), tc_HOL_Obool), tc_fun(_1590780, tc_HOL_Obool)), _1590778), c_COMBC(_1590780, tc_fun(tc_prod(_1590778, _1590780), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1590780, tc_prod(_1590778, _1590780)), tc_fun(_1590780, tc_fun(tc_fun(tc_prod(_1590778, _1590780), tc_HOL_Obool), tc_HOL_Obool)), _1590778), hAPP(c_COMBB(tc_prod(_1590778, _1590780), tc_fun(tc_fun(tc_prod(_1590778, _1590780), tc_HOL_Obool), tc_HOL_Obool), _1590780), c_member(tc_prod(_1590778, _1590780)))), c_Product__Type_OPair(_1590778, _1590780)))), _1590784), _1590786, _1590788), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590776, _1590780)), hAPP(hAPP(c_Product__Type_OPair(_1590776, _1590780), _1590786), _1590788)), hAPP(hAPP(c_Relation_Orel__comp(_1590776, _1590778, _1590780), _1590782), _1590784))))], (41869 ^ _780461) ^ [_1591399, _1591401, _1591403, _1591405, _1591407, _1591409, _1591411] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591399, _1591403)), hAPP(hAPP(c_Product__Type_OPair(_1591399, _1591403), _1591409), _1591411)), hAPP(hAPP(c_Relation_Orel__comp(_1591399, _1591401, _1591403), _1591405), _1591407))), -(c_Predicate_Opred__comp(_1591399, _1591401, _1591403, hAPP(hAPP(c_COMBC(_1591399, tc_fun(tc_prod(_1591399, _1591401), tc_HOL_Obool), tc_fun(_1591401, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1591401, tc_fun(tc_fun(tc_prod(_1591399, _1591401), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1591399, _1591401), tc_HOL_Obool), tc_fun(_1591401, tc_HOL_Obool)), _1591399), c_COMBC(_1591401, tc_fun(tc_prod(_1591399, _1591401), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1591401, tc_prod(_1591399, _1591401)), tc_fun(_1591401, tc_fun(tc_fun(tc_prod(_1591399, _1591401), tc_HOL_Obool), tc_HOL_Obool)), _1591399), hAPP(c_COMBB(tc_prod(_1591399, _1591401), tc_fun(tc_fun(tc_prod(_1591399, _1591401), tc_HOL_Obool), tc_HOL_Obool), _1591401), c_member(tc_prod(_1591399, _1591401)))), c_Product__Type_OPair(_1591399, _1591401)))), _1591405), hAPP(hAPP(c_COMBC(_1591401, tc_fun(tc_prod(_1591401, _1591403), tc_HOL_Obool), tc_fun(_1591403, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1591403, tc_fun(tc_fun(tc_prod(_1591401, _1591403), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1591401, _1591403), tc_HOL_Obool), tc_fun(_1591403, tc_HOL_Obool)), _1591401), c_COMBC(_1591403, tc_fun(tc_prod(_1591401, _1591403), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1591403, tc_prod(_1591401, _1591403)), tc_fun(_1591403, tc_fun(tc_fun(tc_prod(_1591401, _1591403), tc_HOL_Obool), tc_HOL_Obool)), _1591401), hAPP(c_COMBB(tc_prod(_1591401, _1591403), tc_fun(tc_fun(tc_prod(_1591401, _1591403), tc_HOL_Obool), tc_HOL_Obool), _1591403), c_member(tc_prod(_1591401, _1591403)))), c_Product__Type_OPair(_1591401, _1591403)))), _1591407), _1591409, _1591411))], (41875 ^ _780461) ^ [_1592028, _1592030, _1592032] : [c_Wellfounded_Owf(_1592028, _1592030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1592028, _1592028), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1592028, _1592028, _1592028), _1592030), _1592032)), _1592030)), -(c_FunDef_Oreduction__pair(_1592028, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1592028, _1592028), tc_HOL_Obool), tc_fun(tc_prod(_1592028, _1592028), tc_HOL_Obool)), _1592030), _1592032)))], (41885 ^ _780461) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (41887 ^ _780461) ^ [_1592267, _1592269, _1592271, _1592273, _1592275, _1592277, _1592279, _1592281] : [hBOOL(hAPP(hAPP(_1592267, _1592269), _1592271)), hBOOL(hAPP(hAPP(_1592273, _1592271), _1592275)), -(c_Predicate_Opred__comp(_1592277, _1592279, _1592281, _1592267, _1592273, _1592269, _1592275))], (41897 ^ _780461) ^ [_1592450] : [-(c_Wellfounded_Owf(_1592450, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1592450, _1592450), tc_HOL_Obool))))], (41899 ^ _780461) ^ [_1592481, _1592483, _1592485, _1592487] : [c_Wellfounded_Owf(_1592481, _1592483), -(c_Wellfounded_Owf(_1592485, hAPP(hAPP(c_Relation_Oinv__image(_1592481, _1592485), _1592483), _1592487)))], (41905 ^ _780461) ^ [_1592580, _1592582, _1592584, _1592586] : [c_Wellfounded_Owf(_1592580, _1592582), c_Wellfounded_Owf(_1592584, _1592586), -(c_Wellfounded_Owf(tc_prod(_1592580, _1592584), c_Wellfounded_Olex__prod(_1592580, _1592584, _1592582, _1592586)))], (41915 ^ _780461) ^ [_1592733, _1592735] : [-(c_Wellfounded_Owf(_1592733, hAPP(c_Wellfounded_Omeasure(_1592733), _1592735)))], (41917 ^ _780461) ^ [_1592781, _1592783, _1592785] : [c_Wellfounded_Owf(_1592781, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1592781, _1592781), tc_HOL_Obool)), _1592783), _1592785)), -(c_Wellfounded_Owf(_1592781, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1592781, _1592781), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1592781, _1592781), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1592781, _1592781, _1592781), _1592783), _1592783)), hAPP(hAPP(c_Relation_Orel__comp(_1592781, _1592781, _1592781), _1592785), _1592783))), _1592785)))], (41923 ^ _780461) ^ [_1592980, _1592982, _1592984] : [c_Wellfounded_Owf(_1592980, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1592980, _1592980), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1592980, _1592980), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1592980, _1592980, _1592980), _1592982), _1592982)), hAPP(hAPP(c_Relation_Orel__comp(_1592980, _1592980, _1592980), _1592984), _1592982))), _1592984)), -(c_Wellfounded_Owf(_1592980, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1592980, _1592980), tc_HOL_Obool)), _1592982), _1592984)))], (41929 ^ _780461) ^ [_1593185, _1593187] : [hAPP(hAPP(c_Relation_Orel__comp(_1593185, _1593185, _1593185), _1593187), _1593187) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1593185, _1593185), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1593185, _1593187))], (41935 ^ _780461) ^ [_1593313, _1593315] : [c_Wellfounded_Owf(_1593313, _1593315), -(c_Wellfounded_Owf(_1593313, hAPP(hAPP(c_Relation_Orel__comp(_1593313, _1593313, _1593313), _1593315), _1593315)))], (41941 ^ _780461) ^ [_1593406, _1593408] : [c_Wellfounded_Owf(_1593406, hAPP(hAPP(c_Relation_Orel__comp(_1593406, _1593406, _1593406), _1593408), _1593408)), -(c_Wellfounded_Owf(_1593406, _1593408))], (41947 ^ _780461) ^ [] : [-(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)))))], (41949 ^ _780461) ^ [_1593523] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1593523)))], (41951 ^ _780461) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (41953 ^ _780461) ^ [_1593566, _1593568, _1593570] : [c_Wellfounded_Owf(_1593566, _1593568), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1593566, _1593566), tc_HOL_Obool)), _1593570), _1593568)), -(c_Wellfounded_Owf(_1593566, _1593570))], (41963 ^ _780461) ^ [_1593725, _1593727] : [c_Wellfounded_Owf(_1593725, _1593727), -(c_Wellfounded_Owf(tc_fun(_1593725, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1593725, _1593727)))], (41969 ^ _780461) ^ [_1593844, _1593846, _1593848, _1593850, _1593852, _1593854, _1593856] : [c_Predicate_Opred__comp(_1593844, _1593846, _1593848, _1593850, _1593852, _1593854, _1593856), 41973 ^ _780461 : [(41974 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1593850, _1593854), 41972 ^ [_1593844, _1593846, _1593848, _1593850, _1593852, _1593854, _1593856])))], (41976 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1593852, 41972 ^ [_1593844, _1593846, _1593848, _1593850, _1593852, _1593854, _1593856]), _1593856)))]]], (41978 ^ _780461) ^ [_1594022, _1594024, _1594026, _1594028, _1594030, _1594032, _1594034] : [-(c_Predicate_Opred__comp(_1594022, _1594024, _1594026, _1594028, _1594030, _1594032, _1594034)), 41979 ^ _780461 : [(41980 ^ _780461) ^ [_1594087] : [hBOOL(hAPP(hAPP(_1594028, _1594032), _1594087)), hBOOL(hAPP(hAPP(_1594030, _1594087), _1594034))]]], (41988 ^ _780461) ^ [_1594230, _1594232] : [c_Wellfounded_Owf(_1594230, _1594232), -(c_Wellfounded_Owf(tc_fun(_1594230, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1594230, _1594232)))], (41994 ^ _780461) ^ [_1594319] : [-(c_Wellfounded_Owf(tc_fun(_1594319, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1594319)))], (41996 ^ _780461) ^ [_1594347, _1594349, _1594351] : [c_Wellfounded_Owf(_1594347, _1594349), -(c_Wellfounded_Owf(_1594347, c_Wellfounded_Omlex__prod(_1594347, _1594351, _1594349)))], (42002 ^ _780461) ^ [_1594434, _1594436, _1594438] : [c_Wellfounded_Owf(_1594434, _1594436), -(c_Wellfounded_Owf(_1594434, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594434, _1594434), tc_HOL_Obool)), _1594438), _1594436)))], (42008 ^ _780461) ^ [_1594541, _1594543, _1594545] : [c_Wellfounded_Owf(_1594541, _1594543), -(c_Wellfounded_Owf(_1594541, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594541, _1594541), tc_HOL_Obool)), _1594543), _1594545)))], (42014 ^ _780461) ^ [_1594648, _1594650, _1594652] : [c_Wellfounded_Owf(_1594648, _1594650), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594648, _1594648)), hAPP(hAPP(c_Product__Type_OPair(_1594648, _1594648), _1594652), _1594652)), _1594650))], (42020 ^ _780461) ^ [_1594766, _1594768, _1594770, _1594772] : [c_Wellfounded_Owf(_1594766, _1594768), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594766, _1594766)), hAPP(hAPP(c_Product__Type_OPair(_1594766, _1594766), _1594770), _1594772)), _1594768)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594766, _1594766)), hAPP(hAPP(c_Product__Type_OPair(_1594766, _1594766), _1594772), _1594770)), _1594768))], (42030 ^ _780461) ^ [_1594980, _1594982, _1594984, _1594986] : [c_Wellfounded_Owf(_1594980, _1594982), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594980, _1594980)), hAPP(hAPP(c_Product__Type_OPair(_1594980, _1594980), _1594984), _1594986)), _1594982)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594980, _1594980)), hAPP(hAPP(c_Product__Type_OPair(_1594980, _1594980), _1594986), _1594984)), _1594982))], (42040 ^ _780461) ^ [_1595194, _1595196, _1595198] : [c_Wellfounded_Owf(_1595194, _1595196), hBOOL(hAPP(hAPP(c_member(tc_prod(_1595194, _1595194)), hAPP(hAPP(c_Product__Type_OPair(_1595194, _1595194), _1595198), _1595198)), _1595196))], (42046 ^ _780461) ^ [_1595312, _1595314, _1595316] : [c_Wellfounded_Owf(_1595312, _1595314), -(hBOOL(hAPP(hAPP(c_member(_1595312), _1595316), c_Wellfounded_Oacc(_1595312, _1595314))))], (42052 ^ _780461) ^ [_1595426, _1595428] : [c_Wellfounded_Owf(_1595426, _1595428), 42055 ^ _780461 : [(42056 ^ _780461) ^ [_1595495] : [-(hBOOL(hAPP(hAPP(c_member(_1595426), _1595495), c_Wellfounded_Oacc(_1595426, _1595428))))]]], (42058 ^ _780461) ^ [_1595528, _1595530] : [hBOOL(hAPP(hAPP(c_member(_1595528), 42059 ^ [_1595528, _1595530]), c_Wellfounded_Oacc(_1595528, _1595530))), -(c_Wellfounded_Owf(_1595528, _1595530))], (42065 ^ _780461) ^ [_1595661] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1595661)))], (42067 ^ _780461) ^ [_1595701, _1595703] : [c_Wellfounded_Owf(_1595701, _1595703), 42071 ^ _780461 : [(42072 ^ _780461) ^ [_1595837] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595701, _1595701)), hAPP(hAPP(c_Product__Type_OPair(_1595701, _1595701), hAPP(_1595837, hAPP(c_Nat_OSuc, 42070 ^ [_1595701, _1595703, _1595837]))), hAPP(_1595837, 42070 ^ [_1595701, _1595703, _1595837]))), _1595703))]]], (42074 ^ _780461) ^ [_1595904, _1595906] : [42076 ^ _780461 : [(42077 ^ _780461) ^ [_1595929] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595904, _1595904)), hAPP(hAPP(c_Product__Type_OPair(_1595904, _1595904), hAPP(42075 ^ [_1595904, _1595906], hAPP(c_Nat_OSuc, _1595929))), hAPP(42075 ^ [_1595904, _1595906], _1595929))), _1595906)))]], -(c_Wellfounded_Owf(_1595904, _1595906))], (42081 ^ _780461) ^ [_1596005, _1596007, _1596009] : [c_Wellfounded_Owf(_1596005, _1596007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1596005, tc_HOL_Obool)), _1596009), hAPP(c_Relation_OImage(_1596005, _1596005, _1596007), _1596009))), -(_1596009 = c_Orderings_Obot__class_Obot(tc_fun(_1596005, tc_HOL_Obool)))], (42091 ^ _780461) ^ [_1596182, _1596184, _1596186] : [c_Wellfounded_Owf(_1596182, _1596184), c_Wellfounded_Owf(_1596182, _1596186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1596182, _1596182), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1596182, _1596182, _1596182), _1596184), _1596186)), _1596184)), -(c_Wellfounded_Owf(_1596182, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1596182, _1596182), tc_HOL_Obool)), _1596184), _1596186)))], (42105 ^ _780461) ^ [_1596443] : [class_Orderings_Owellorder(_1596443), -(c_Wellfounded_Owf(_1596443, hAPP(c_Set_OCollect(tc_prod(_1596443, _1596443)), hAPP(c_Product__Type_Oprod_Oprod__case(_1596443, _1596443, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1596443)))))], (42111 ^ _780461) ^ [_1596565, _1596567] : [c_FunDef_Oreduction__pair(_1596565, _1596567), 42114 ^ _780461 : [(42115 ^ _780461) ^ [] : [-(c_Wellfounded_Owf(_1596565, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool), tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool)), _1596567)))], (42117 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1596565, _1596565, _1596565), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool), tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool)), _1596567)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool), tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool)), _1596567))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool), tc_fun(tc_prod(_1596565, _1596565), tc_HOL_Obool)), _1596567))))]]], (42119 ^ _780461) ^ [_1596854, _1596856] : [-(c_FunDef_Oreduction__pair(_1596854, _1596856)), c_Wellfounded_Owf(_1596854, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool), tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool)), _1596856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1596854, _1596854, _1596854), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool), tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool)), _1596856)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool), tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool)), _1596856))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool), tc_fun(tc_prod(_1596854, _1596854), tc_HOL_Obool)), _1596856)))], (42129 ^ _780461) ^ [_1597175, _1597177, _1597179, _1597181] : [c_FunDef_Oreduction__pair(_1597175, _1597177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1597175, _1597175), tc_HOL_Obool)), _1597179), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1597175, _1597175), tc_HOL_Obool), tc_fun(tc_prod(_1597175, _1597175), tc_HOL_Obool)), _1597177))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1597175, _1597175), tc_HOL_Obool)), _1597181), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1597175, _1597175), tc_HOL_Obool), tc_fun(tc_prod(_1597175, _1597175), tc_HOL_Obool)), _1597177))), c_Wellfounded_Owf(_1597175, _1597181), -(c_Wellfounded_Owf(_1597175, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1597175, _1597175), tc_HOL_Obool)), _1597179), _1597181)))], (42147 ^ _780461) ^ [_1597576, _1597578, _1597580, _1597582] : [c_Wellfounded_Owf(_1597576, _1597578), c_Fun_Oinj__on(_1597576, _1597580, _1597582, c_Orderings_Otop__class_Otop(tc_fun(_1597576, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1597580, hAPP(c_Set_Oimage(tc_prod(_1597576, _1597576), tc_prod(_1597580, _1597580), c_Product__Type_Omap__pair(_1597576, _1597580, _1597576, _1597580, _1597582, _1597582)), _1597578)))], (42157 ^ _780461) ^ [_1597767, _1597769] : [c_Wellfounded_Owf(_1597767, _1597769), -(c_Wellfounded_Owf(tc_List_Olist(_1597767), c_List_Olenlex(_1597767, _1597769)))], (42163 ^ _780461) ^ [_1597854, _1597856, _1597858, _1597860] : [42165 ^ _780461 : [(42166 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1597854, 42164 ^ [_1597854, _1597856, _1597858, _1597860])))], (42168 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1597856, hAPP(_1597858, 42164 ^ [_1597854, _1597856, _1597858, _1597860]))), hAPP(_1597856, 42164 ^ [_1597854, _1597856, _1597858, _1597860])))]], -(c_Wellfounded_Owf(_1597860, hAPP(c_Set_OCollect(tc_prod(_1597860, _1597860)), hAPP(c_Product__Type_Oprod_Oprod__case(_1597860, _1597860, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1597860, tc_HOL_Obool), tc_fun(_1597860, tc_HOL_Obool), _1597860), hAPP(c_COMBS(_1597860, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1597860), c_fconj), _1597854))), hAPP(hAPP(c_COMBC(_1597860, tc_fun(_1597860, _1597860), tc_fun(_1597860, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1597860, tc_HOL_Obool), tc_fun(tc_fun(_1597860, _1597860), tc_fun(_1597860, tc_HOL_Obool)), _1597860), c_COMBB(_1597860, tc_HOL_Obool, _1597860)), c_fequal)), _1597858))))))], (42172 ^ _780461) ^ [] : [-(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))))], (42174 ^ _780461) ^ [_1598265, _1598267] : [c_Wellfounded_Owf(_1598265, _1598267), -(c_Wellfounded_Owf(tc_List_Olist(_1598265), c_List_Olex(_1598265, _1598267)))], (42180 ^ _780461) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (42182 ^ _780461) ^ [_1598370, _1598372] : [-(c_List_Olex(_1598370, _1598372) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1598370), tc_List_Olist(_1598370)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1598370, _1598372)))], (42184 ^ _780461) ^ [_1598420, _1598422, _1598424] : [c_Wellfounded_Owf(_1598420, _1598422), -(c_Wellfounded_Owf(tc_List_Olist(_1598420), hAPP(c_List_Olexn(_1598420, _1598422), _1598424)))], (42190 ^ _780461) ^ [_1598515, _1598517] : [-(hAPP(c_List_Olexn(_1598515, _1598517), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1598515), tc_List_Olist(_1598515)), tc_HOL_Obool)))], (42192 ^ _780461) ^ [_1598558, _1598560, _1598562, _1598564] : [42194 ^ _780461 : [(42195 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1598558, 42193 ^ [_1598558, _1598560, _1598562, _1598564])))], (42197 ^ _780461) ^ [] : [c_Wellfounded_Owf(_1598560, hAPP(_1598562, 42193 ^ [_1598558, _1598560, _1598562, _1598564]))]], -(c_Wellfounded_Owf(tc_prod(_1598564, _1598560), c_Recdef_Osame__fst(_1598564, _1598560, _1598558, _1598562)))], (42201 ^ _780461) ^ [_1598743, _1598745, _1598747] : [-(hAPP(c_Relation_ORange(_1598743, _1598745), hAPP(c_Set_OCollect(tc_prod(_1598743, _1598745)), hAPP(c_Product__Type_Oprod_Oprod__case(_1598743, _1598745, tc_HOL_Obool), _1598747))) = hAPP(c_Set_OCollect(_1598745), hAPP(hAPP(c_COMBB(tc_fun(_1598743, tc_HOL_Obool), tc_HOL_Obool, _1598745), c_HOL_OEx(_1598743)), hAPP(c_COMBC(_1598743, _1598745, tc_HOL_Obool), _1598747))))], (42203 ^ _780461) ^ [_1598818, _1598820, _1598822, _1598824, _1598826] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1598818, _1598820)), hAPP(hAPP(c_Product__Type_OPair(_1598818, _1598820), _1598822), _1598824)), _1598826)), -(hBOOL(hAPP(hAPP(c_member(_1598820), _1598824), hAPP(c_Relation_ORange(_1598818, _1598820), _1598826))))], (42209 ^ _780461) ^ [_1598965, _1598967] : [-(hAPP(c_Relation_ORange(_1598965, _1598965), c_Relation_OId__on(_1598965, _1598967)) = _1598967)], (42211 ^ _780461) ^ [_1599017, _1599019, _1599021] : [hAPP(c_Relation_ORange(_1599017, _1599019), _1599021) = c_Orderings_Obot__class_Obot(tc_fun(_1599019, tc_HOL_Obool)), -(_1599021 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1599017, _1599019), tc_HOL_Obool)))], (42217 ^ _780461) ^ [_1599130, _1599132, _1599134] : [_1599134 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1599130, _1599132), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1599130, _1599132), _1599134) = c_Orderings_Obot__class_Obot(tc_fun(_1599132, tc_HOL_Obool)))], (42223 ^ _780461) ^ [_1599249, _1599251] : [-(hAPP(c_Relation_ORange(_1599249, _1599251), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1599249, _1599251), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1599251, tc_HOL_Obool)))], (42225 ^ _780461) ^ [_1599293, _1599295, _1599297, _1599299] : [-(hAPP(c_Relation_ORange(_1599293, _1599295), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1599293, _1599295), tc_HOL_Obool)), _1599297), _1599299)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1599295, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1599293, _1599295), _1599297)), hAPP(c_Relation_ORange(_1599293, _1599295), _1599299)))], (42227 ^ _780461) ^ [_1599365, _1599367, _1599369] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1599365, _1599367)), _1599369)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1599367), hAPP(c_Relation_ORange(_1599365, _1599367), _1599369))))], (42233 ^ _780461) ^ [_1599478, _1599480, _1599482] : [-(hAPP(c_Set_Oimage(tc_prod(_1599478, _1599480), _1599480, c_Product__Type_Osnd(_1599478, _1599480)), _1599482) = hAPP(c_Relation_ORange(_1599478, _1599480), _1599482))], (42235 ^ _780461) ^ [_1599545, _1599547, _1599549, _1599551] : [hBOOL(hAPP(hAPP(c_member(_1599545), _1599547), hAPP(c_Relation_ORange(_1599549, _1599545), _1599551))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599549, _1599545)), hAPP(hAPP(c_Product__Type_OPair(_1599549, _1599545), 42238 ^ [_1599545, _1599547, _1599549, _1599551]), _1599547)), _1599551)))], (42242 ^ _780461) ^ [_1599702, _1599704, _1599706, _1599708] : [42243 ^ _780461 : [(42244 ^ _780461) ^ [_1599777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599706, _1599702)), hAPP(hAPP(c_Product__Type_OPair(_1599706, _1599702), _1599777), _1599704)), _1599708))]], -(hBOOL(hAPP(hAPP(c_member(_1599702), _1599704), hAPP(c_Relation_ORange(_1599706, _1599702), _1599708))))], (42248 ^ _780461) ^ [_1599862, _1599864, _1599866, _1599868, _1599870] : [-(hAPP(c_Relation_ORange(_1599862, _1599864), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1599862, _1599864)), hAPP(hAPP(c_Product__Type_OPair(_1599862, _1599864), _1599866), _1599868)), _1599870)) = hAPP(hAPP(c_Set_Oinsert(_1599864), _1599868), hAPP(c_Relation_ORange(_1599862, _1599864), _1599870)))], (42250 ^ _780461) ^ [_1599933, _1599935, _1599937, _1599939] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1599933, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1599935, _1599933), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1599935, _1599933), tc_HOL_Obool)), _1599937), _1599939))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599933, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1599935, _1599933), _1599937)), hAPP(c_Relation_ORange(_1599935, _1599933), _1599939)))))], (42252 ^ _780461) ^ [_1600015, _1600017, _1600019, _1600021] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1600015, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1600015, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1600017, _1600015), _1600019)), hAPP(c_Relation_ORange(_1600017, _1600015), _1600021))), hAPP(c_Relation_ORange(_1600017, _1600015), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1600017, _1600015), tc_HOL_Obool)), _1600019), _1600021)))))], (42254 ^ _780461) ^ [_1600118, _1600120, _1600122, _1600124] : [hBOOL(hAPP(c_Predicate_ORangeP(_1600118, _1600120, hAPP(hAPP(c_COMBC(_1600118, tc_fun(tc_prod(_1600118, _1600120), tc_HOL_Obool), tc_fun(_1600120, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1600120, tc_fun(tc_fun(tc_prod(_1600118, _1600120), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1600118, _1600120), tc_HOL_Obool), tc_fun(_1600120, tc_HOL_Obool)), _1600118), c_COMBC(_1600120, tc_fun(tc_prod(_1600118, _1600120), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1600120, tc_prod(_1600118, _1600120)), tc_fun(_1600120, tc_fun(tc_fun(tc_prod(_1600118, _1600120), tc_HOL_Obool), tc_HOL_Obool)), _1600118), hAPP(c_COMBB(tc_prod(_1600118, _1600120), tc_fun(tc_fun(tc_prod(_1600118, _1600120), tc_HOL_Obool), tc_HOL_Obool), _1600120), c_member(tc_prod(_1600118, _1600120)))), c_Product__Type_OPair(_1600118, _1600120)))), _1600122)), _1600124)), -(hBOOL(hAPP(hAPP(c_member(_1600120), _1600124), hAPP(c_Relation_ORange(_1600118, _1600120), _1600122))))], (42260 ^ _780461) ^ [_1600469, _1600471, _1600473, _1600475] : [hBOOL(hAPP(hAPP(c_member(_1600471), _1600475), hAPP(c_Relation_ORange(_1600469, _1600471), _1600473))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1600469, _1600471, hAPP(hAPP(c_COMBC(_1600469, tc_fun(tc_prod(_1600469, _1600471), tc_HOL_Obool), tc_fun(_1600471, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1600471, tc_fun(tc_fun(tc_prod(_1600469, _1600471), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1600469, _1600471), tc_HOL_Obool), tc_fun(_1600471, tc_HOL_Obool)), _1600469), c_COMBC(_1600471, tc_fun(tc_prod(_1600469, _1600471), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1600471, tc_prod(_1600469, _1600471)), tc_fun(_1600471, tc_fun(tc_fun(tc_prod(_1600469, _1600471), tc_HOL_Obool), tc_HOL_Obool)), _1600469), hAPP(c_COMBB(tc_prod(_1600469, _1600471), tc_fun(tc_fun(tc_prod(_1600469, _1600471), tc_HOL_Obool), tc_HOL_Obool), _1600471), c_member(tc_prod(_1600469, _1600471)))), c_Product__Type_OPair(_1600469, _1600471)))), _1600473)), _1600475)))], (42266 ^ _780461) ^ [_1600826, _1600828, _1600830, _1600832] : [hBOOL(hAPP(hAPP(c_member(_1600826), _1600828), hAPP(c_Relation_ORange(_1600830, _1600826), _1600832))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600830, _1600826)), hAPP(hAPP(c_Product__Type_OPair(_1600830, _1600826), 42269 ^ [_1600826, _1600828, _1600830, _1600832]), _1600828)), _1600832)))], (42273 ^ _780461) ^ [_1600991, _1600993, _1600995, _1600997, _1600999] : [hBOOL(hAPP(hAPP(_1600991, _1600993), _1600995)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1600997, _1600999, _1600991), _1600995)))], (42279 ^ _780461) ^ [_1601117, _1601119, _1601121, _1601123] : [hBOOL(hAPP(c_Predicate_ORangeP(_1601117, _1601119, _1601121), _1601123)), -(hBOOL(hAPP(hAPP(_1601121, 42282 ^ [_1601117, _1601119, _1601121, _1601123]), _1601123)))], (42286 ^ _780461) ^ [_1601232, _1601234, _1601236, _1601238] : [42287 ^ _780461 : [(42288 ^ _780461) ^ [_1601286] : [hBOOL(hAPP(hAPP(_1601236, _1601286), _1601238))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1601232, _1601234, _1601236), _1601238)))], (42292 ^ _780461) ^ [_1601350, _1601352, _1601354] : [c_Wellfounded_Owf(_1601350, _1601352), c_Wellfounded_Owf(_1601350, _1601354), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1601350, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1601350, _1601350), _1601352)), hAPP(c_Relation_ORange(_1601350, _1601350), _1601354)) = c_Orderings_Obot__class_Obot(tc_fun(_1601350, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1601350, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1601350, _1601350), tc_HOL_Obool)), _1601352), _1601354)))], (42306 ^ _780461) ^ [_1601636, _1601638] : [c_Wellfounded_OwfP(_1601636, _1601638), -(c_Wellfounded_Owf(_1601636, hAPP(c_Set_OCollect(tc_prod(_1601636, _1601636)), hAPP(c_Product__Type_Oprod_Oprod__case(_1601636, _1601636, tc_HOL_Obool), _1601638))))], (42312 ^ _780461) ^ [_1601739, _1601741] : [c_Wellfounded_Owf(_1601739, hAPP(c_Set_OCollect(tc_prod(_1601739, _1601739)), hAPP(c_Product__Type_Oprod_Oprod__case(_1601739, _1601739, tc_HOL_Obool), _1601741))), -(c_Wellfounded_OwfP(_1601739, _1601741))], (42318 ^ _780461) ^ [_1601848] : [-(c_Wellfounded_OwfP(_1601848, hAPP(c_COMBK(tc_fun(_1601848, tc_HOL_Obool), _1601848), hAPP(c_COMBK(tc_HOL_Obool, _1601848), c_fFalse))))], (42320 ^ _780461) ^ [_1601886, _1601888, _1601890, _1601892, _1601894] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601886, _1601888)), hAPP(hAPP(c_Product__Type_OPair(_1601886, _1601888), _1601890), _1601892)), _1601894)), -(hBOOL(hAPP(hAPP(c_member(_1601886), _1601890), hAPP(c_Relation_ODomain(_1601886, _1601888), _1601894))))], (42326 ^ _780461) ^ [_1602033, _1602035] : [-(hAPP(c_Relation_ODomain(_1602033, _1602033), c_Relation_OId__on(_1602033, _1602035)) = _1602035)], (42328 ^ _780461) ^ [_1602082, _1602084] : [c_Wellfounded_OwfP(_1602082, _1602084), 42331 ^ _780461 : [(42332 ^ _780461) ^ [_1602146] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1602082, _1602084), _1602146)))]]], (42334 ^ _780461) ^ [_1602174, _1602176] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1602174, _1602176), 42335 ^ [_1602174, _1602176])), -(c_Wellfounded_OwfP(_1602174, _1602176))], (42341 ^ _780461) ^ [_1602292, _1602294, _1602296] : [c_Wellfounded_OwfP(_1602292, _1602294), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1602292, _1602294), _1602296)))], (42347 ^ _780461) ^ [_1602381, _1602383, _1602385] : [c_Wellfounded_OwfP(_1602381, _1602383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1602381, tc_fun(_1602381, tc_HOL_Obool))), _1602385), _1602383)), -(c_Wellfounded_OwfP(_1602381, _1602385))], (42357 ^ _780461) ^ [_1602558, _1602560, _1602562] : [hAPP(c_Relation_ODomain(_1602558, _1602560), _1602562) = c_Orderings_Obot__class_Obot(tc_fun(_1602558, tc_HOL_Obool)), -(_1602562 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1602558, _1602560), tc_HOL_Obool)))], (42363 ^ _780461) ^ [_1602671, _1602673, _1602675] : [_1602675 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1602671, _1602673), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1602671, _1602673), _1602675) = c_Orderings_Obot__class_Obot(tc_fun(_1602671, tc_HOL_Obool)))], (42369 ^ _780461) ^ [_1602790, _1602792] : [-(hAPP(c_Relation_ODomain(_1602790, _1602792), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1602790, _1602792), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1602790, tc_HOL_Obool)))], (42371 ^ _780461) ^ [_1602834, _1602836, _1602838, _1602840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602834, _1602836), tc_HOL_Obool)), _1602838), _1602840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1602834, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1602834, _1602836), _1602838)), hAPP(c_Relation_ODomain(_1602834, _1602836), _1602840))))], (42377 ^ _780461) ^ [_1602985, _1602987, _1602989, _1602991] : [-(hAPP(c_Relation_ODomain(_1602985, _1602987), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1602985, _1602987), tc_HOL_Obool)), _1602989), _1602991)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1602985, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1602985, _1602987), _1602989)), hAPP(c_Relation_ODomain(_1602985, _1602987), _1602991)))], (42379 ^ _780461) ^ [_1603057, _1603059, _1603061] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1603057, _1603059)), _1603061)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1603057), hAPP(c_Relation_ODomain(_1603057, _1603059), _1603061))))], (42385 ^ _780461) ^ [_1603170, _1603172, _1603174] : [-(hAPP(c_Set_Oimage(tc_prod(_1603170, _1603172), _1603170, c_Product__Type_Ofst(_1603170, _1603172)), _1603174) = hAPP(c_Relation_ODomain(_1603170, _1603172), _1603174))], (42387 ^ _780461) ^ [_1603237, _1603239, _1603241, _1603243] : [hBOOL(hAPP(hAPP(c_member(_1603237), _1603239), hAPP(c_Relation_ODomain(_1603237, _1603241), _1603243))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603237, _1603241)), hAPP(hAPP(c_Product__Type_OPair(_1603237, _1603241), _1603239), 42390 ^ [_1603237, _1603239, _1603241, _1603243])), _1603243)))], (42394 ^ _780461) ^ [_1603394, _1603396, _1603398, _1603400] : [42395 ^ _780461 : [(42396 ^ _780461) ^ [_1603469] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603394, _1603398)), hAPP(hAPP(c_Product__Type_OPair(_1603394, _1603398), _1603396), _1603469)), _1603400))]], -(hBOOL(hAPP(hAPP(c_member(_1603394), _1603396), hAPP(c_Relation_ODomain(_1603394, _1603398), _1603400))))], (42400 ^ _780461) ^ [_1603554, _1603556, _1603558, _1603560, _1603562] : [-(hAPP(c_Relation_ODomain(_1603554, _1603556), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1603554, _1603556)), hAPP(hAPP(c_Product__Type_OPair(_1603554, _1603556), _1603558), _1603560)), _1603562)) = hAPP(hAPP(c_Set_Oinsert(_1603554), _1603558), hAPP(c_Relation_ODomain(_1603554, _1603556), _1603562)))], (42402 ^ _780461) ^ [_1603625, _1603627, _1603629, _1603631] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603625, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1603625, _1603627), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1603625, _1603627), tc_HOL_Obool)), _1603629), _1603631))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1603625, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1603625, _1603627), _1603629)), hAPP(c_Relation_ODomain(_1603625, _1603627), _1603631)))))], (42404 ^ _780461) ^ [_1603707, _1603709, _1603711, _1603713] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603707, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603707, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1603707, _1603709), _1603711)), hAPP(c_Relation_ODomain(_1603707, _1603709), _1603713))), hAPP(c_Relation_ODomain(_1603707, _1603709), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1603707, _1603709), tc_HOL_Obool)), _1603711), _1603713)))))], (42406 ^ _780461) ^ [_1603789, _1603791] : [-(hAPP(c_Relation_OField(_1603789), _1603791) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1603789, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1603789, _1603789), _1603791)), hAPP(c_Relation_ORange(_1603789, _1603789), _1603791)))], (42408 ^ _780461) ^ [_1603842, _1603844] : [c_Wellfounded_Owf(_1603842, _1603844), -(c_Wellfounded_OwfP(_1603842, c_FunDef_Oin__rel(_1603842, _1603842, _1603844)))], (42414 ^ _780461) ^ [_1603942, _1603944] : [c_Wellfounded_OwfP(_1603942, hAPP(hAPP(c_COMBC(_1603942, tc_fun(tc_prod(_1603942, _1603942), tc_HOL_Obool), tc_fun(_1603942, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603942, tc_fun(tc_fun(tc_prod(_1603942, _1603942), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603942, _1603942), tc_HOL_Obool), tc_fun(_1603942, tc_HOL_Obool)), _1603942), c_COMBC(_1603942, tc_fun(tc_prod(_1603942, _1603942), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603942, tc_prod(_1603942, _1603942)), tc_fun(_1603942, tc_fun(tc_fun(tc_prod(_1603942, _1603942), tc_HOL_Obool), tc_HOL_Obool)), _1603942), hAPP(c_COMBB(tc_prod(_1603942, _1603942), tc_fun(tc_fun(tc_prod(_1603942, _1603942), tc_HOL_Obool), tc_HOL_Obool), _1603942), c_member(tc_prod(_1603942, _1603942)))), c_Product__Type_OPair(_1603942, _1603942)))), _1603944)), -(c_Wellfounded_Owf(_1603942, _1603944))], (42420 ^ _780461) ^ [_1604251, _1604253] : [c_Wellfounded_Owf(_1604251, _1604253), -(c_Wellfounded_OwfP(_1604251, hAPP(hAPP(c_COMBC(_1604251, tc_fun(tc_prod(_1604251, _1604251), tc_HOL_Obool), tc_fun(_1604251, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604251, tc_fun(tc_fun(tc_prod(_1604251, _1604251), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1604251, _1604251), tc_HOL_Obool), tc_fun(_1604251, tc_HOL_Obool)), _1604251), c_COMBC(_1604251, tc_fun(tc_prod(_1604251, _1604251), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604251, tc_prod(_1604251, _1604251)), tc_fun(_1604251, tc_fun(tc_fun(tc_prod(_1604251, _1604251), tc_HOL_Obool), tc_HOL_Obool)), _1604251), hAPP(c_COMBB(tc_prod(_1604251, _1604251), tc_fun(tc_fun(tc_prod(_1604251, _1604251), tc_HOL_Obool), tc_HOL_Obool), _1604251), c_member(tc_prod(_1604251, _1604251)))), c_Product__Type_OPair(_1604251, _1604251)))), _1604253)))], (42426 ^ _780461) ^ [_1604566, _1604568, _1604570] : [-(hAPP(c_Relation_ODomain(_1604566, _1604568), hAPP(c_Set_OCollect(tc_prod(_1604566, _1604568)), hAPP(c_Product__Type_Oprod_Oprod__case(_1604566, _1604568, tc_HOL_Obool), _1604570))) = hAPP(c_Set_OCollect(_1604566), hAPP(hAPP(c_COMBB(tc_fun(_1604568, tc_HOL_Obool), tc_HOL_Obool, _1604566), c_HOL_OEx(_1604568)), _1604570)))], (42428 ^ _780461) ^ [_1604655, _1604657, _1604659, _1604661] : [hBOOL(hAPP(c_Predicate_ODomainP(_1604655, _1604657, hAPP(hAPP(c_COMBC(_1604655, tc_fun(tc_prod(_1604655, _1604657), tc_HOL_Obool), tc_fun(_1604657, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604657, tc_fun(tc_fun(tc_prod(_1604655, _1604657), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1604655, _1604657), tc_HOL_Obool), tc_fun(_1604657, tc_HOL_Obool)), _1604655), c_COMBC(_1604657, tc_fun(tc_prod(_1604655, _1604657), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604657, tc_prod(_1604655, _1604657)), tc_fun(_1604657, tc_fun(tc_fun(tc_prod(_1604655, _1604657), tc_HOL_Obool), tc_HOL_Obool)), _1604655), hAPP(c_COMBB(tc_prod(_1604655, _1604657), tc_fun(tc_fun(tc_prod(_1604655, _1604657), tc_HOL_Obool), tc_HOL_Obool), _1604657), c_member(tc_prod(_1604655, _1604657)))), c_Product__Type_OPair(_1604655, _1604657)))), _1604659)), _1604661)), -(hBOOL(hAPP(hAPP(c_member(_1604655), _1604661), hAPP(c_Relation_ODomain(_1604655, _1604657), _1604659))))], (42434 ^ _780461) ^ [_1605006, _1605008, _1605010, _1605012] : [hBOOL(hAPP(hAPP(c_member(_1605006), _1605012), hAPP(c_Relation_ODomain(_1605006, _1605008), _1605010))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1605006, _1605008, hAPP(hAPP(c_COMBC(_1605006, tc_fun(tc_prod(_1605006, _1605008), tc_HOL_Obool), tc_fun(_1605008, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1605008, tc_fun(tc_fun(tc_prod(_1605006, _1605008), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1605006, _1605008), tc_HOL_Obool), tc_fun(_1605008, tc_HOL_Obool)), _1605006), c_COMBC(_1605008, tc_fun(tc_prod(_1605006, _1605008), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1605008, tc_prod(_1605006, _1605008)), tc_fun(_1605008, tc_fun(tc_fun(tc_prod(_1605006, _1605008), tc_HOL_Obool), tc_HOL_Obool)), _1605006), hAPP(c_COMBB(tc_prod(_1605006, _1605008), tc_fun(tc_fun(tc_prod(_1605006, _1605008), tc_HOL_Obool), tc_HOL_Obool), _1605008), c_member(tc_prod(_1605006, _1605008)))), c_Product__Type_OPair(_1605006, _1605008)))), _1605010)), _1605012)))], (42440 ^ _780461) ^ [_1605363, _1605365, _1605367, _1605369] : [hBOOL(hAPP(hAPP(c_member(_1605363), _1605365), hAPP(c_Relation_ODomain(_1605363, _1605367), _1605369))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605363, _1605367)), hAPP(hAPP(c_Product__Type_OPair(_1605363, _1605367), _1605365), 42443 ^ [_1605363, _1605365, _1605367, _1605369])), _1605369)))], (42447 ^ _780461) ^ [_1605528, _1605530, _1605532, _1605534, _1605536] : [hBOOL(hAPP(hAPP(_1605528, _1605530), _1605532)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1605534, _1605536, _1605528), _1605530)))], (42453 ^ _780461) ^ [_1605654, _1605656, _1605658, _1605660] : [hBOOL(hAPP(c_Predicate_ODomainP(_1605654, _1605656, _1605658), _1605660)), -(hBOOL(hAPP(hAPP(_1605658, _1605660), 42456 ^ [_1605654, _1605656, _1605658, _1605660])))], (42460 ^ _780461) ^ [_1605769, _1605771, _1605773, _1605775] : [42461 ^ _780461 : [(42462 ^ _780461) ^ [_1605823] : [hBOOL(hAPP(hAPP(_1605773, _1605775), _1605823))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1605769, _1605771, _1605773), _1605775)))], (42466 ^ _780461) ^ [_1605887, _1605889] : [c_Wellfounded_OwfP(_1605887, _1605889), -(c_Wellfounded_Oacyclic(_1605887, hAPP(c_Set_OCollect(tc_prod(_1605887, _1605887)), hAPP(c_Product__Type_Oprod_Oprod__case(_1605887, _1605887, tc_HOL_Obool), _1605889))))], (42472 ^ _780461) ^ [_1605994, _1605996, _1605998, _1606000] : [-(c_New__Random__Sequence_Opos__map(_1605994, _1605996, _1605998, _1606000) = c_New__Random__Sequence_Opos__bind(_1605994, _1605996, _1606000, hAPP(c_Fun_Ocomp(_1605996, 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(_1605996))))), _1605994, c_New__Random__Sequence_Opos__single(_1605996)), _1605998)))], (42474 ^ _780461) ^ [_1606057, _1606059] : [c_Wellfounded_Owf(_1606057, _1606059), -(c_Wellfounded_Oacyclic(_1606057, _1606059))], (42480 ^ _780461) ^ [_1606134, _1606136, _1606138] : [c_Wellfounded_Oacyclic(_1606134, _1606136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1606134, _1606134), tc_HOL_Obool)), _1606138), _1606136)), -(c_Wellfounded_Oacyclic(_1606134, _1606138))], (42490 ^ _780461) ^ [_1606293, _1606295] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1606293, _1606293)), _1606295)), 42493 ^ _780461 : [(42494 ^ _780461) ^ [] : [c_Wellfounded_Owf(_1606293, _1606295), -(c_Wellfounded_Oacyclic(_1606293, _1606295))], (42500 ^ _780461) ^ [] : [c_Wellfounded_Oacyclic(_1606293, _1606295), -(c_Wellfounded_Owf(_1606293, _1606295))]]], (42506 ^ _780461) ^ [_1606514, _1606516] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1606514, _1606514)), _1606516)), c_Wellfounded_Oacyclic(_1606514, _1606516), -(c_Wellfounded_Owf(_1606514, _1606516))], (42516 ^ _780461) ^ [_1606657, _1606659, _1606661, _1606663, _1606665] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1606657), _1606659), _1606661), _1606663), _1606665) = c_New__DSequence_Opos__single(_1606657, _1606659))], (42518 ^ _780461) ^ [_1606720, _1606722] : [c_Nitpick_Owf_H(_1606720, _1606722), 42521 ^ _780461 : [(42522 ^ _780461) ^ [] : [-(c_Wellfounded_Oacyclic(_1606720, _1606722))], (42524 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1606720, _1606720)), _1606722))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (42530 ^ _780461) ^ [_1606840, _1606842] : [-(c_Nitpick_Owf_H(_1606840, _1606842)), c_Wellfounded_Oacyclic(_1606840, _1606842), 42535 ^ _780461 : [(42536 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1606840, _1606840)), _1606842))], (42538 ^ _780461) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (42542 ^ _780461) ^ [_1607017, _1607019, _1607021] : [-(hAPP(c_New__DSequence_Opos__single(_1607017, _1607019), _1607021) = c_Lazy__Sequence_Osingle(_1607017, _1607019))], (42544 ^ _780461) ^ [_1607053, _1607055, _1607057, _1607059] : [-(c_New__Random__Sequence_Oneg__map(_1607053, _1607055, _1607057, _1607059) = c_New__Random__Sequence_Oneg__bind(_1607053, _1607055, _1607059, hAPP(c_Fun_Ocomp(_1607055, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1607055)))))), _1607053, c_New__Random__Sequence_Oneg__single(_1607055)), _1607057)))], (42546 ^ _780461) ^ [_1607118, _1607120, _1607122, _1607124, _1607126] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1607118), _1607120), _1607122), _1607124), _1607126) = c_New__DSequence_Oneg__single(_1607118, _1607120))], (42548 ^ _780461) ^ [_1607165, _1607167, _1607169, _1607171] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1607165), _1607167))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1607169), hAPP(c_Set_Oimage(_1607165, _1607169, _1607171), _1607167))), 42556 ^ _780461 : [(42557 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1607165), 42555 ^ [_1607165, _1607167, _1607169, _1607171]), _1607167)))], (42559 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1607165), hAPP(c_Set_OCollect(_1607165), hAPP(hAPP(c_COMBS(_1607165, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1607165), c_fconj), hAPP(hAPP(c_COMBC(_1607165, tc_fun(_1607165, tc_HOL_Obool), tc_HOL_Obool), c_member(_1607165)), _1607167))), hAPP(hAPP(c_COMBC(_1607165, _1607169, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1607169, tc_fun(_1607169, tc_HOL_Obool), _1607165), c_fequal), _1607171)), hAPP(_1607171, 42555 ^ [_1607165, _1607167, _1607169, _1607171]))))))]]], (42561 ^ _780461) ^ [_1607630, _1607632, _1607634] : [-(hAPP(c_New__DSequence_Oneg__single(_1607630, _1607632), _1607634) = c_Lazy__Sequence_Ohb__single(_1607630, _1607632))], (42564 ^ _780461) ^ [_1607664] : [-(_1607664 = hAPP(c_Int_OAbs__Integ, 42562 ^ [_1607664]))], (42566 ^ _780461) ^ [_1607692] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42562 ^ [_1607692]), c_Int_OInteg)))], (42568 ^ _780461) ^ [_1607727, _1607729] : [42570 ^ _780461 : [(42571 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 42569 ^ [_1607727, _1607729]), c_Int_OInteg)))], (42573 ^ _780461) ^ [] : [hBOOL(hAPP(_1607727, hAPP(c_Int_OAbs__Integ, 42569 ^ [_1607727, _1607729])))]], -(hBOOL(hAPP(_1607727, _1607729)))], (42577 ^ _780461) ^ [_1607896, _1607898, _1607900, _1607902] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1607896), _1607898)), 42583 ^ _780461 : [(42584 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1607896), 42582 ^ [_1607896, _1607898, _1607900, _1607902]), _1607898)))], (42586 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1607900), hAPP(_1607902, 42582 ^ [_1607896, _1607898, _1607900, _1607902])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1607900), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1607896, tc_fun(_1607900, tc_HOL_Obool)), _1607898), _1607902))))], (42590 ^ _780461) ^ [_1608183, _1608185] : [42592 ^ _780461 : [(42593 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42591 ^ [_1608183, _1608185]), _1608183)))], (42595 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1608185), 42591 ^ [_1608183, _1608185]))]], -(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)), _1608185), _1608183))], (42599 ^ _780461) ^ [_1608358, _1608360, _1608362] : [c_Wellfounded_OwfP(_1608358, hAPP(_1608360, 42600 ^ [_1608358, _1608360, _1608362])), 42607 ^ _780461 : [(42608 ^ _780461) ^ [] : [hAPP(_1608360, 42605 ^ [_1608358, _1608360, _1608362]) = hAPP(_1608360, 42606 ^ [_1608358, _1608360, _1608362])], (42610 ^ _780461) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1608358, tc_HOL_Obool)), c_Predicate_ODomainP(_1608358, _1608358, hAPP(_1608360, 42605 ^ [_1608358, _1608360, _1608362]))), c_Predicate_ORangeP(_1608358, _1608358, hAPP(_1608360, 42606 ^ [_1608358, _1608360, _1608362]))) = c_Orderings_Obot__class_Obot(tc_fun(_1608358, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1608358, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1608362, tc_fun(_1608358, tc_fun(_1608358, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1608362, tc_HOL_Obool))), _1608360)))], (42614 ^ _780461) ^ [_1608798, _1608800] : [class_Orderings_Oorder(_1608798), 42621 ^ _780461 : [(42622 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 42619 ^ [_1608798, _1608800]), 42620 ^ [_1608798, _1608800])))], (42624 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), 42620 ^ [_1608798, _1608800]), 42619 ^ [_1608798, _1608800]))], (42626 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1608798), hAPP(_1608800, 42619 ^ [_1608798, _1608800])), hAPP(_1608800, 42620 ^ [_1608798, _1608800])))]], -(c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1608798, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1608800))], (42630 ^ _780461) ^ [_1609161, _1609163, _1609165] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1609161), c_Map_Odom(_1609161, _1609163, _1609165))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1609161), c_Orderings_Otop__class_Otop(tc_fun(_1609161, tc_HOL_Obool))))), -(hAPP(_1609165, 42637 ^ [_1609161, _1609163, _1609165]) = c_Option_Ooption_ONone(_1609163))], (42641 ^ _780461) ^ [_1609313, _1609315, _1609317, _1609319, _1609321, _1609323] : [hBOOL(hAPP(hAPP(c_member(_1609313), _1609315), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1609317, _1609319, tc_fun(_1609313, tc_HOL_Obool)), _1609321), _1609323))), 42646 ^ _780461 : [(42647 ^ _780461) ^ [] : [-(_1609323 = hAPP(hAPP(c_Product__Type_OPair(_1609317, _1609319), 42644 ^ [_1609313, _1609315, _1609317, _1609319, _1609321, _1609323]), 42645 ^ [_1609313, _1609315, _1609317, _1609319, _1609321, _1609323]))], (42649 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609313), _1609315), hAPP(hAPP(_1609321, 42644 ^ [_1609313, _1609315, _1609317, _1609319, _1609321, _1609323]), 42645 ^ [_1609313, _1609315, _1609317, _1609319, _1609321, _1609323]))))]]], (42651 ^ _780461) ^ [_1609582, _1609584, _1609586, _1609588, _1609590, _1609592] : [42654 ^ _780461 : [(42655 ^ _780461) ^ [] : [-(_1609582 = hAPP(hAPP(c_Product__Type_OPair(_1609584, _1609586), 42652 ^ [_1609582, _1609584, _1609586, _1609588, _1609590, _1609592]), 42653 ^ [_1609582, _1609584, _1609586, _1609588, _1609590, _1609592]))], (42657 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1609588), _1609590), hAPP(hAPP(_1609592, 42652 ^ [_1609582, _1609584, _1609586, _1609588, _1609590, _1609592]), 42653 ^ [_1609582, _1609584, _1609586, _1609588, _1609590, _1609592])))]], -(hBOOL(hAPP(hAPP(c_member(_1609588), _1609590), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1609584, _1609586, tc_fun(_1609588, tc_HOL_Obool)), _1609592), _1609582))))], (42661 ^ _780461) ^ [_1609907, _1609909, _1609911, _1609913] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1609907, tc_Nat_Onat), _1609909), _1609911) = hAPP(c_Nat_OSuc, _1609913), 42665 ^ _780461 : [(42666 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609907), 42664 ^ [_1609907, _1609909, _1609911, _1609913]), _1609911)))], (42668 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1609909, 42664 ^ [_1609907, _1609909, _1609911, _1609913]))))]]], (42670 ^ _780461) ^ [_1610089, _1610091, _1610093] : [-(c_Hilbert__Choice_OEps(tc_prod(_1610089, _1610091), hAPP(c_Product__Type_Oprod_Oprod__case(_1610089, _1610091, tc_HOL_Obool), _1610093)) = c_Hilbert__Choice_OEps(tc_prod(_1610089, _1610091), hAPP(hAPP(c_COMBS(tc_prod(_1610089, _1610091), _1610091, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1610089, tc_fun(_1610091, tc_HOL_Obool), tc_prod(_1610089, _1610091)), _1610093), c_Product__Type_Ofst(_1610089, _1610091))), c_Product__Type_Osnd(_1610089, _1610091))))], (42672 ^ _780461) ^ [_1610170, _1610172, _1610174] : [42673 ^ _780461 : [(42674 ^ _780461) ^ [_1610224] : [hBOOL(hAPP(_1610170, _1610224))]], _1610172 = c_Hilbert__Choice_OEps(_1610174, _1610170), -(hBOOL(hAPP(_1610170, _1610172)))], (42682 ^ _780461) ^ [_1610330, _1610332] : [-(c_Hilbert__Choice_OEps(_1610330, hAPP(c_fequal, _1610332)) = _1610332)], (42684 ^ _780461) ^ [_1610361, _1610363] : [-(c_Hilbert__Choice_OEps(_1610361, hAPP(hAPP(c_COMBC(_1610361, _1610361, tc_HOL_Obool), c_fequal), _1610363)) = _1610363)], (42686 ^ _780461) ^ [_1610414, _1610416] : [hBOOL(hAPP(_1610414, c_Hilbert__Choice_OEps(_1610416, _1610414))), -(hBOOL(hAPP(_1610414, 42689 ^ [_1610414, _1610416])))], (42693 ^ _780461) ^ [_1610513, _1610515] : [42694 ^ _780461 : [(42695 ^ _780461) ^ [_1610559] : [hBOOL(hAPP(_1610513, _1610559))]], -(hBOOL(hAPP(_1610513, c_Hilbert__Choice_OEps(_1610515, _1610513))))], (42699 ^ _780461) ^ [_1610619, _1610621] : [42700 ^ _780461 : [(42701 ^ _780461) ^ [_1610665] : [hBOOL(hAPP(_1610619, _1610665))]], -(hBOOL(hAPP(_1610619, c_Hilbert__Choice_OEps(_1610621, _1610619))))], (42705 ^ _780461) ^ [_1610723, _1610725] : [42706 ^ _780461 : [(42707 ^ _780461) ^ [_1610769] : [hBOOL(hAPP(_1610723, _1610769))]], -(hBOOL(hAPP(_1610723, c_Hilbert__Choice_OEps(_1610725, _1610723))))], (42711 ^ _780461) ^ [_1610827, _1610829, _1610831] : [hBOOL(hAPP(_1610827, _1610829)), -(hBOOL(hAPP(_1610827, c_Hilbert__Choice_OEps(_1610831, _1610827))))], (42717 ^ _780461) ^ [_1610920, _1610922, _1610924] : [-(c_Hilbert__Choice_OEps(tc_prod(_1610920, _1610922), _1610924) = c_Hilbert__Choice_OEps(tc_prod(_1610920, _1610922), hAPP(c_Product__Type_Oprod_Oprod__case(_1610920, _1610922, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1610922, tc_prod(_1610920, _1610922)), tc_fun(_1610922, tc_HOL_Obool), _1610920), hAPP(c_COMBB(tc_prod(_1610920, _1610922), tc_HOL_Obool, _1610922), _1610924)), c_Product__Type_OPair(_1610920, _1610922)))))], (42719 ^ _780461) ^ [_1610998, _1611000, _1611002, _1611004] : [-(c_Hilbert__Choice_OEps(tc_prod(_1610998, _1611000), hAPP(c_Product__Type_Oprod_Oprod__case(_1610998, _1611000, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1610998, tc_fun(_1611000, tc_HOL_Obool), tc_fun(_1611000, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1611000, tc_HOL_Obool), tc_fun(_1611000, tc_HOL_Obool)), _1610998), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1611000)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1610998), c_fconj), hAPP(c_fequal, _1611002)))), hAPP(c_fequal, _1611004)))) = hAPP(hAPP(c_Product__Type_OPair(_1610998, _1611000), _1611002), _1611004))], (42721 ^ _780461) ^ [_1611104, _1611106] : [42723 ^ _780461 : [(42724 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611104, tc_HOL_Obool)), 42722 ^ [_1611104, _1611106]), hAPP(c_Relation_OImage(_1611104, _1611104, _1611106), 42722 ^ [_1611104, _1611106]))))], (42726 ^ _780461) ^ [] : [42722 ^ [_1611104, _1611106] = c_Orderings_Obot__class_Obot(tc_fun(_1611104, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1611104, _1611106))], (42730 ^ _780461) ^ [_1611301, _1611303, _1611305, _1611307, _1611309, _1611311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611301, tc_HOL_Obool)), _1611303), _1611305)), 42736 ^ _780461 : [(42737 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611301), 42735 ^ [_1611301, _1611303, _1611305, _1611307, _1611309, _1611311]), _1611303)))], (42739 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611307, tc_HOL_Obool)), hAPP(_1611309, 42735 ^ [_1611301, _1611303, _1611305, _1611307, _1611309, _1611311])), hAPP(_1611311, 42735 ^ [_1611301, _1611303, _1611305, _1611307, _1611309, _1611311])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1611301, _1611307), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1611301, _1611307), _1611303), _1611309)), hAPP(hAPP(c_Product__Type_OSigma(_1611301, _1611307), _1611305), _1611311))))], (42743 ^ _780461) ^ [_1611692, _1611694, _1611696] : [42745 ^ _780461 : [(42746 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611692, _1611692)), hAPP(hAPP(c_Product__Type_OPair(_1611692, _1611692), 42744 ^ [_1611692, _1611694, _1611696]), _1611694)), _1611696)))], (42748 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1611692), 42744 ^ [_1611692, _1611694, _1611696]), c_Wellfounded_Oacc(_1611692, _1611696)))]], -(hBOOL(hAPP(hAPP(c_member(_1611692), _1611694), c_Wellfounded_Oacc(_1611692, _1611696))))], (42752 ^ _780461) ^ [_1611929, _1611931, _1611933] : [-(hBOOL(hAPP(hAPP(c_member(_1611929), _1611931), c_Wellfounded_Oacc(_1611929, _1611933)))), 42756 ^ _780461 : [(42757 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611929, _1611929)), hAPP(hAPP(c_Product__Type_OPair(_1611929, _1611929), 42755 ^ [_1611929, _1611931, _1611933]), _1611931)), _1611933)))], (42759 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1611929), 42755 ^ [_1611929, _1611931, _1611933]), c_Wellfounded_Oacc(_1611929, _1611933)))]]], (42761 ^ _780461) ^ [_1612156, _1612158, _1612160, _1612162] : [class_Groups_Ocomm__monoid__mult(_1612156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612158), _1612160)), 42771 ^ _780461 : [(42772 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612158), 42770 ^ [_1612156, _1612158, _1612160, _1612162]), _1612160)))], (42774 ^ _780461) ^ [] : [hAPP(_1612162, 42770 ^ [_1612156, _1612158, _1612160, _1612162]) = c_Groups_Oone__class_Oone(_1612156)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1612156, _1612158, c_Groups_Otimes__class_Otimes(_1612156)), _1612162), c_Groups_Oone__class_Oone(_1612156)), _1612160) = c_Groups_Oone__class_Oone(_1612156))], (42778 ^ _780461) ^ [_1612497, _1612499] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1612497), _1612499)), 42784 ^ _780461 : [(42785 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612497), 42783 ^ [_1612497, _1612499]), _1612499)))], (42787 ^ _780461) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1612497), _1612499) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42791 ^ _780461) ^ [_1612718, _1612720, _1612722, _1612724] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1612718, tc_HOL_Obool), tc_fun(_1612718, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1612718, tc_HOL_Obool), tc_fun(_1612718, tc_HOL_Obool)), _1612720), _1612722)), c_Wellfounded_Omax__ext(_1612718, _1612724))), 42794 ^ _780461 : [(42795 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1612718), _1612720)))], (42797 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1612718), _1612722)))], (42799 ^ _780461) ^ [] : [_1612722 = c_Orderings_Obot__class_Obot(tc_fun(_1612718, tc_HOL_Obool))], (42801 ^ _780461) ^ [_1613012] : [hBOOL(hAPP(hAPP(c_member(_1612718), _1613012), _1612720)), 42805 ^ _780461 : [(42806 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612718), 42804 ^ [_1612718, _1612720, _1612722, _1612724, _1613012]), _1612722)))], (42808 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612718, _1612718)), hAPP(hAPP(c_Product__Type_OPair(_1612718, _1612718), _1613012), 42804 ^ [_1612718, _1612720, _1612722, _1612724, _1613012])), _1612724)))]]]]], (42810 ^ _780461) ^ [_1613224, _1613226, _1613228, _1613230] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1613224, tc_HOL_Obool), tc_fun(_1613224, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1613224, tc_HOL_Obool), tc_fun(_1613224, tc_HOL_Obool)), _1613226), _1613228)), c_Wellfounded_Omax__ext(_1613224, _1613230)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613224), _1613226)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613224), _1613228)), -(_1613228 = c_Orderings_Obot__class_Obot(tc_fun(_1613224, tc_HOL_Obool))), 42824 ^ _780461 : [(42825 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613224), 42823 ^ [_1613224, _1613226, _1613228, _1613230]), _1613226)))], (42827 ^ _780461) ^ [_1613629] : [hBOOL(hAPP(hAPP(c_member(_1613224), _1613629), _1613228)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1613224, _1613224)), hAPP(hAPP(c_Product__Type_OPair(_1613224, _1613224), 42823 ^ [_1613224, _1613226, _1613228, _1613230]), _1613629)), _1613230))]]], (42835 ^ _780461) ^ [_1613857, _1613859, _1613861, _1613863, _1613865, _1613867] : [class_Groups_Oab__semigroup__mult(_1613857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613859), _1613861)), 42845 ^ _780461 : [(42846 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613859), 42844 ^ [_1613857, _1613859, _1613861, _1613863, _1613865, _1613867]), _1613861)))], (42848 ^ _780461) ^ [] : [hAPP(_1613863, 42844 ^ [_1613857, _1613859, _1613861, _1613863, _1613865, _1613867]) = hAPP(_1613865, 42844 ^ [_1613857, _1613859, _1613861, _1613863, _1613865, _1613867])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1613857, _1613859, c_Groups_Otimes__class_Otimes(_1613857)), _1613863), _1613867), _1613861) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1613857, _1613859, c_Groups_Otimes__class_Otimes(_1613857)), _1613865), _1613867), _1613861))], (42852 ^ _780461) ^ [_1614262, _1614264, _1614266, _1614268, _1614270, _1614272] : [class_Rings_Ocomm__semiring__1(_1614262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614264), _1614266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1614264, tc_HOL_Obool)), _1614268), _1614266)), 42866 ^ _780461 : [(42867 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614264), 42865 ^ [_1614262, _1614264, _1614266, _1614268, _1614270, _1614272]), _1614268)))], (42869 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1614262), hAPP(_1614270, 42865 ^ [_1614262, _1614264, _1614266, _1614268, _1614270, _1614272])), hAPP(_1614272, 42865 ^ [_1614262, _1614264, _1614266, _1614268, _1614270, _1614272])))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1614262), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1614264, _1614262), _1614270), _1614268)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1614264, _1614262), _1614272), _1614266))))], (42873 ^ _780461) ^ [_1614758, _1614760, _1614762] : [class_Orderings_Olinorder(_1614758), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614758), _1614760)), 42883 ^ _780461 : [(42884 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614758), 42882 ^ [_1614758, _1614760, _1614762]), _1614760)))], (42886 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1614758), 42882 ^ [_1614758, _1614760, _1614762]), _1614762))]], hBOOL(hAPP(hAPP(c_member(_1614758), _1614762), _1614760)), -(c_Big__Operators_Olinorder__class_OMax(_1614758, _1614760) = _1614762)], (42894 ^ _780461) ^ [_1615130, _1615132, _1615134] : [class_Orderings_Olinorder(_1615130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615130), _1615132)), 42904 ^ _780461 : [(42905 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1615130), 42903 ^ [_1615130, _1615132, _1615134]), _1615132)))], (42907 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615130), _1615134), 42903 ^ [_1615130, _1615132, _1615134]))]], hBOOL(hAPP(hAPP(c_member(_1615130), _1615134), _1615132)), -(c_Big__Operators_Olinorder__class_OMin(_1615130, _1615132) = _1615134)], (42915 ^ _780461) ^ [_1615502, _1615504, _1615506] : [c_Wellfounded_Owf(_1615502, _1615504), hBOOL(hAPP(hAPP(c_member(tc_prod(_1615502, _1615502)), hAPP(hAPP(c_Product__Type_OPair(_1615502, _1615502), hAPP(_1615506, hAPP(c_Nat_OSuc, 42918 ^ [_1615502, _1615504, _1615506]))), hAPP(_1615506, 42918 ^ [_1615502, _1615504, _1615506]))), _1615504))], (42922 ^ _780461) ^ [_1615703, _1615705, _1615707, _1615709, _1615711, _1615713, _1615715, _1615717] : [class_Groups_Ocomm__monoid__add(_1615703), c_Fun_Oinj__on(_1615705, _1615707, _1615709, _1615711), _1615713 = hAPP(c_Set_Oimage(_1615705, _1615707, _1615709), _1615711), 42936 ^ _780461 : [(42937 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1615705), 42935 ^ [_1615703, _1615705, _1615707, _1615709, _1615711, _1615713, _1615715, _1615717]), _1615711)))], (42939 ^ _780461) ^ [] : [hAPP(_1615715, 42935 ^ [_1615703, _1615705, _1615707, _1615709, _1615711, _1615713, _1615715, _1615717]) = hAPP(_1615717, hAPP(_1615709, 42935 ^ [_1615703, _1615705, _1615707, _1615709, _1615711, _1615713, _1615715, _1615717]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1615707, _1615703), _1615717), _1615713) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1615705, _1615703), _1615715), _1615711))], (42943 ^ _780461) ^ [_1616195, _1616197, _1616199, _1616201, _1616203, _1616205, _1616207, _1616209] : [class_Groups_Ocomm__monoid__add(_1616195), class_Orderings_Oord(_1616197), _1616199 = _1616201, _1616203 = _1616205, 42961 ^ _780461 : [(42962 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1616197), _1616201), 42960 ^ [_1616195, _1616197, _1616199, _1616201, _1616203, _1616205, _1616207, _1616209])))], (42964 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616197), 42960 ^ [_1616195, _1616197, _1616199, _1616201, _1616203, _1616205, _1616207, _1616209]), _1616205)))], (42966 ^ _780461) ^ [] : [hAPP(_1616207, 42960 ^ [_1616195, _1616197, _1616199, _1616201, _1616203, _1616205, _1616207, _1616209]) = hAPP(_1616209, 42960 ^ [_1616195, _1616197, _1616199, _1616201, _1616203, _1616205, _1616207, _1616209])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1616197, _1616195), _1616207), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1616197, _1616199), _1616203)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1616197, _1616195), _1616209), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1616197, _1616201), _1616205)))], (42970 ^ _780461) ^ [_1616839, _1616841] : [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), _1616839), _1616841)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1616839), _1616841)))], (42976 ^ _780461) ^ [_1616944, _1616946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1616944), _1616946)), -(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), _1616944), _1616946)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (42982 ^ _780461) ^ [_1617055, _1617057, _1617059] : [class_Orderings_Olinorder(_1617055), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617055), _1617057)), -(hBOOL(hAPP(hAPP(c_member(_1617055), _1617059), _1617057))), -(c_Big__Operators_Olattice_OSup__fin(_1617055, c_Orderings_Oord__class_Omax(_1617055), hAPP(hAPP(c_Set_Oinsert(_1617055), _1617059), _1617057)) = hAPP(hAPP(c_Finite__Set_Ofold(_1617055, _1617055, c_Orderings_Oord__class_Omax(_1617055)), _1617059), _1617057))], (42996 ^ _780461) ^ [_1617275, _1617277, _1617279, _1617281] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1617275, _1617277, _1617279), _1617281), c_Orderings_Obot__class_Obot(tc_fun(_1617275, tc_HOL_Obool))) = _1617281)], (42998 ^ _780461) ^ [_1617319, _1617321, _1617323, _1617325, _1617327, _1617329] : [c_Finite__Set_Ofolding(_1617319, _1617321, _1617323, _1617325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617319), _1617327)), -(hAPP(hAPP(_1617325, _1617327), _1617329) = hAPP(hAPP(c_Finite__Set_Ofold(_1617319, _1617321, _1617323), _1617329), _1617327))], (43008 ^ _780461) ^ [_1617508, _1617510, _1617512, _1617514] : [-(hAPP(c_Finite__Set_Ofold__image(_1617508, _1617510, _1617512), _1617514) = c_Finite__Set_Ofold(_1617510, _1617508, hAPP(hAPP(c_COMBB(_1617508, tc_fun(_1617508, _1617508), _1617510), _1617512), _1617514)))], (43010 ^ _780461) ^ [_1617561, _1617563] : [c_Wellfounded_Owf(_1617561, _1617563), -(c_Wellfounded_Owf(_1617561, c_Transitive__Closure_Otrancl(_1617561, _1617563)))], (43016 ^ _780461) ^ [_1617644, _1617646, _1617648, _1617650, _1617652] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1617644, _1617646, _1617648), _1617650), _1617652) = c_HOL_OThe(_1617646, c_Finite__Set_Ofold__graph(_1617644, _1617646, _1617648, _1617650, _1617652)))], (43018 ^ _780461) ^ [_1617694, _1617696, _1617698] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1617694), _1617696)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1617694, tc_HOL_Obool)), _1617696), _1617698) = hAPP(hAPP(c_Finite__Set_Ofold(_1617694, tc_fun(_1617694, tc_HOL_Obool), c_Set_Oinsert(_1617694)), _1617698), _1617696))], (43024 ^ _780461) ^ [_1617833, _1617835, _1617837, _1617839] : [class_Lattices_Osemilattice__sup(_1617833), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617833), _1617835)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617833, _1617833, c_Lattices_Osemilattice__sup__class_Osup(_1617833)), _1617837), hAPP(hAPP(c_Set_Oinsert(_1617833), _1617839), _1617835)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1617833), _1617839), hAPP(hAPP(c_Finite__Set_Ofold(_1617833, _1617833, c_Lattices_Osemilattice__sup__class_Osup(_1617833)), _1617837), _1617835)))], (43034 ^ _780461) ^ [_1618056, _1618058, _1618060, _1618062] : [class_Lattices_Osemilattice__inf(_1618056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618056), _1618058)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1618056, _1618056, c_Lattices_Osemilattice__inf__class_Oinf(_1618056)), _1618060), hAPP(hAPP(c_Set_Oinsert(_1618056), _1618062), _1618058)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1618056), _1618062), hAPP(hAPP(c_Finite__Set_Ofold(_1618056, _1618056, c_Lattices_Osemilattice__inf__class_Oinf(_1618056)), _1618060), _1618058)))], (43044 ^ _780461) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (43046 ^ _780461) ^ [_1618297, _1618299, _1618301, _1618303] : [class_Orderings_Olinorder(_1618297), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618297), _1618299)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1618297, _1618297, c_Orderings_Oord__class_Omin(_1618297)), _1618301), hAPP(hAPP(c_Set_Oinsert(_1618297), _1618303), _1618299)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1618297), _1618303), hAPP(hAPP(c_Finite__Set_Ofold(_1618297, _1618297, c_Orderings_Oord__class_Omin(_1618297)), _1618301), _1618299)))], (43056 ^ _780461) ^ [_1618520, _1618522, _1618524, _1618526] : [class_Orderings_Olinorder(_1618520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618520), _1618522)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1618520, _1618520, c_Orderings_Oord__class_Omax(_1618520)), _1618524), hAPP(hAPP(c_Set_Oinsert(_1618520), _1618526), _1618522)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1618520), _1618526), hAPP(hAPP(c_Finite__Set_Ofold(_1618520, _1618520, c_Orderings_Oord__class_Omax(_1618520)), _1618524), _1618522)))], (43066 ^ _780461) ^ [_1618758, _1618760] : [c_Wellfounded_Oacyclic(_1618758, _1618760), 43069 ^ _780461 : [(43070 ^ _780461) ^ [_1618843] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618758, _1618758)), hAPP(hAPP(c_Product__Type_OPair(_1618758, _1618758), _1618843), _1618843)), c_Transitive__Closure_Otrancl(_1618758, _1618760)))]]], (43072 ^ _780461) ^ [_1618886, _1618888] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618886, _1618886)), hAPP(hAPP(c_Product__Type_OPair(_1618886, _1618886), 43073 ^ [_1618886, _1618888]), 43073 ^ [_1618886, _1618888])), c_Transitive__Closure_Otrancl(_1618886, _1618888)))), -(c_Wellfounded_Oacyclic(_1618886, _1618888))], (43079 ^ _780461) ^ [_1618960, _1618962, _1618964, _1618966, _1618968, _1618970] : [c_Finite__Set_Ofun__left__comm__idem(_1618960, _1618962, _1618964), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618960), _1618966)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1618960, _1618962, _1618964), _1618968), hAPP(hAPP(c_Set_Oinsert(_1618960), _1618970), _1618966)) = hAPP(hAPP(_1618964, _1618970), hAPP(hAPP(c_Finite__Set_Ofold(_1618960, _1618962, _1618964), _1618968), _1618966)))], (43089 ^ _780461) ^ [_1619183, _1619185, _1619187, _1619189, _1619191, _1619193] : [c_Finite__Set_Ofun__left__comm__idem(_1619183, _1619185, _1619187), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619183), _1619189)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1619183, _1619185, _1619187), _1619191), hAPP(hAPP(c_Set_Oinsert(_1619183), _1619193), _1619189)) = hAPP(hAPP(c_Finite__Set_Ofold(_1619183, _1619185, _1619187), hAPP(hAPP(_1619187, _1619193), _1619191)), _1619189))], (43099 ^ _780461) ^ [_1619406, _1619408, _1619410, _1619412, _1619414] : [class_Complete__Lattice_Ocomplete__lattice(_1619406), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619408), _1619410)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1619406), _1619412), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1619408, _1619406), _1619410), _1619414)) = hAPP(hAPP(c_Finite__Set_Ofold(_1619408, _1619406, hAPP(hAPP(c_COMBB(_1619406, tc_fun(_1619406, _1619406), _1619408), c_Lattices_Osemilattice__sup__class_Osup(_1619406)), _1619414)), _1619412), _1619410))], (43109 ^ _780461) ^ [_1619637, _1619639, _1619641, _1619643, _1619645] : [c_Finite__Set_Ofolding__one__idem(_1619637, _1619639, _1619641), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619637), _1619643)), -(hAPP(_1619641, hAPP(hAPP(c_Set_Oinsert(_1619637), _1619645), _1619643)) = hAPP(hAPP(c_Finite__Set_Ofold(_1619637, _1619637, _1619639), _1619645), _1619643))], (43119 ^ _780461) ^ [_1619830, _1619832, _1619834, _1619836] : [class_Lattices_Osemilattice__sup(_1619830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619830), _1619832)), hBOOL(hAPP(hAPP(c_member(_1619830), _1619834), _1619832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1619830), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1619830), _1619834), _1619836)), hAPP(hAPP(c_Finite__Set_Ofold(_1619830, _1619830, c_Lattices_Osemilattice__sup__class_Osup(_1619830)), _1619836), _1619832))))], (43133 ^ _780461) ^ [_1620097, _1620099, _1620101, _1620103] : [class_Lattices_Osemilattice__inf(_1620097), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620097), _1620099)), hBOOL(hAPP(hAPP(c_member(_1620097), _1620101), _1620099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620097), hAPP(hAPP(c_Finite__Set_Ofold(_1620097, _1620097, c_Lattices_Osemilattice__inf__class_Oinf(_1620097)), _1620103), _1620099)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1620097), _1620101), _1620103))))], (43147 ^ _780461) ^ [_1620364, _1620366, _1620368, _1620370] : [class_Orderings_Olinorder(_1620364), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620364), _1620366)), hBOOL(hAPP(hAPP(c_member(_1620364), _1620368), _1620366)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620364), hAPP(hAPP(c_Finite__Set_Ofold(_1620364, _1620364, c_Orderings_Oord__class_Omin(_1620364)), _1620370), _1620366)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1620364), _1620368), _1620370))))], (43161 ^ _780461) ^ [_1620631, _1620633, _1620635, _1620637] : [class_Orderings_Olinorder(_1620631), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620631), _1620633)), hBOOL(hAPP(hAPP(c_member(_1620631), _1620635), _1620633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620631), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1620631), _1620635), _1620637)), hAPP(hAPP(c_Finite__Set_Ofold(_1620631, _1620631, c_Orderings_Oord__class_Omax(_1620631)), _1620637), _1620633))))], (43175 ^ _780461) ^ [_1620898, _1620900, _1620902] : [class_Lattices_Oab__semigroup__idem__mult(_1620898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620898), _1620900)), -(hAPP(c_Finite__Set_Ofold1(_1620898, c_Groups_Otimes__class_Otimes(_1620898)), hAPP(hAPP(c_Set_Oinsert(_1620898), _1620902), _1620900)) = hAPP(hAPP(c_Finite__Set_Ofold(_1620898, _1620898, c_Groups_Otimes__class_Otimes(_1620898)), _1620902), _1620900))], (43185 ^ _780461) ^ [_1621093, _1621095, _1621097] : [class_Lattices_Olattice(_1621093), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621093), _1621095)), -(c_Big__Operators_Olattice__class_OSup__fin(_1621093, hAPP(hAPP(c_Set_Oinsert(_1621093), _1621097), _1621095)) = hAPP(hAPP(c_Finite__Set_Ofold(_1621093, _1621093, c_Lattices_Osemilattice__sup__class_Osup(_1621093)), _1621097), _1621095))], (43195 ^ _780461) ^ [_1621278, _1621280, _1621282] : [class_Lattices_Olattice(_1621278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621278), _1621280)), -(c_Big__Operators_Olattice__class_OInf__fin(_1621278, hAPP(hAPP(c_Set_Oinsert(_1621278), _1621282), _1621280)) = hAPP(hAPP(c_Finite__Set_Ofold(_1621278, _1621278, c_Lattices_Osemilattice__inf__class_Oinf(_1621278)), _1621282), _1621280))], (43205 ^ _780461) ^ [_1621463, _1621465, _1621467] : [class_Orderings_Olinorder(_1621463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621463), _1621465)), -(c_Big__Operators_Olinorder__class_OMin(_1621463, hAPP(hAPP(c_Set_Oinsert(_1621463), _1621467), _1621465)) = hAPP(hAPP(c_Finite__Set_Ofold(_1621463, _1621463, c_Orderings_Oord__class_Omin(_1621463)), _1621467), _1621465))], (43215 ^ _780461) ^ [_1621648, _1621650, _1621652] : [class_Orderings_Olinorder(_1621648), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621648), _1621650)), -(c_Big__Operators_Olinorder__class_OMax(_1621648, hAPP(hAPP(c_Set_Oinsert(_1621648), _1621652), _1621650)) = hAPP(hAPP(c_Finite__Set_Ofold(_1621648, _1621648, c_Orderings_Oord__class_Omax(_1621648)), _1621652), _1621650))], (43225 ^ _780461) ^ [_1621833, _1621835, _1621837] : [class_Orderings_Olinorder(_1621833), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621833), _1621835)), -(c_Big__Operators_Olattice_OInf__fin(_1621833, c_Orderings_Oord__class_Omin(_1621833), hAPP(hAPP(c_Set_Oinsert(_1621833), _1621837), _1621835)) = hAPP(hAPP(c_Finite__Set_Ofold(_1621833, _1621833, c_Orderings_Oord__class_Omin(_1621833)), _1621837), _1621835))], (43235 ^ _780461) ^ [_1622024, _1622026, _1622028] : [class_Orderings_Olinorder(_1622024), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622024), _1622026)), -(c_Big__Operators_Olattice_OSup__fin(_1622024, c_Orderings_Oord__class_Omax(_1622024), hAPP(hAPP(c_Set_Oinsert(_1622024), _1622028), _1622026)) = hAPP(hAPP(c_Finite__Set_Ofold(_1622024, _1622024, c_Orderings_Oord__class_Omax(_1622024)), _1622028), _1622026))], (43245 ^ _780461) ^ [_1622215, _1622217, _1622219] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1622215), _1622217)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1622215, tc_HOL_Obool)), _1622219), _1622217) = hAPP(hAPP(c_Finite__Set_Ofold(_1622215, tc_fun(_1622215, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1622215, tc_HOL_Obool), tc_fun(tc_fun(_1622215, tc_HOL_Obool), tc_fun(_1622215, tc_HOL_Obool)), _1622215), hAPP(c_COMBC(tc_fun(_1622215, tc_HOL_Obool), tc_fun(_1622215, tc_HOL_Obool), tc_fun(_1622215, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1622215, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1622215, tc_fun(_1622215, tc_HOL_Obool), tc_fun(_1622215, tc_HOL_Obool)), c_Set_Oinsert(_1622215)), c_Orderings_Obot__class_Obot(tc_fun(_1622215, tc_HOL_Obool))))), _1622219), _1622217))], (43251 ^ _780461) ^ [_1622482, _1622484, _1622486, _1622488, _1622490] : [c_Finite__Set_Ofolding__one(_1622482, _1622484, _1622486), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622482), _1622488)), -(hBOOL(hAPP(hAPP(c_member(_1622482), _1622490), _1622488))), -(hAPP(_1622486, hAPP(hAPP(c_Set_Oinsert(_1622482), _1622490), _1622488)) = hAPP(hAPP(c_Finite__Set_Ofold(_1622482, _1622482, _1622484), _1622490), _1622488))], (43265 ^ _780461) ^ [_1622704, _1622706, _1622708, _1622710] : [class_Complete__Lattice_Ocomplete__lattice(_1622704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622706), _1622708)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1622706, _1622704), _1622708), _1622710) = hAPP(hAPP(c_Finite__Set_Ofold(_1622706, _1622704, hAPP(hAPP(c_COMBB(_1622704, tc_fun(_1622704, _1622704), _1622706), c_Lattices_Osemilattice__sup__class_Osup(_1622704)), _1622710)), c_Orderings_Obot__class_Obot(_1622704)), _1622708))], (43275 ^ _780461) ^ [_1622919, _1622921, _1622923] : [class_Groups_Oab__semigroup__mult(_1622919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622919), _1622921)), -(hBOOL(hAPP(hAPP(c_member(_1622919), _1622923), _1622921))), -(hAPP(c_Finite__Set_Ofold1(_1622919, c_Groups_Otimes__class_Otimes(_1622919)), hAPP(hAPP(c_Set_Oinsert(_1622919), _1622923), _1622921)) = hAPP(hAPP(c_Finite__Set_Ofold(_1622919, _1622919, c_Groups_Otimes__class_Otimes(_1622919)), _1622923), _1622921))], (43289 ^ _780461) ^ [_1623143, _1623145, _1623147] : [class_Lattices_Olattice(_1623143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623143), _1623145)), -(hBOOL(hAPP(hAPP(c_member(_1623143), _1623147), _1623145))), -(c_Big__Operators_Olattice__class_OSup__fin(_1623143, hAPP(hAPP(c_Set_Oinsert(_1623143), _1623147), _1623145)) = hAPP(hAPP(c_Finite__Set_Ofold(_1623143, _1623143, c_Lattices_Osemilattice__sup__class_Osup(_1623143)), _1623147), _1623145))], (43303 ^ _780461) ^ [_1623357, _1623359, _1623361] : [class_Lattices_Olattice(_1623357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623357), _1623359)), -(hBOOL(hAPP(hAPP(c_member(_1623357), _1623361), _1623359))), -(c_Big__Operators_Olattice__class_OInf__fin(_1623357, hAPP(hAPP(c_Set_Oinsert(_1623357), _1623361), _1623359)) = hAPP(hAPP(c_Finite__Set_Ofold(_1623357, _1623357, c_Lattices_Osemilattice__inf__class_Oinf(_1623357)), _1623361), _1623359))], (43317 ^ _780461) ^ [_1623571, _1623573, _1623575] : [class_Orderings_Olinorder(_1623571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623571), _1623573)), -(hBOOL(hAPP(hAPP(c_member(_1623571), _1623575), _1623573))), -(c_Big__Operators_Olinorder__class_OMin(_1623571, hAPP(hAPP(c_Set_Oinsert(_1623571), _1623575), _1623573)) = hAPP(hAPP(c_Finite__Set_Ofold(_1623571, _1623571, c_Orderings_Oord__class_Omin(_1623571)), _1623575), _1623573))], (43331 ^ _780461) ^ [_1623785, _1623787, _1623789] : [class_Orderings_Olinorder(_1623785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623785), _1623787)), -(hBOOL(hAPP(hAPP(c_member(_1623785), _1623789), _1623787))), -(c_Big__Operators_Olinorder__class_OMax(_1623785, hAPP(hAPP(c_Set_Oinsert(_1623785), _1623789), _1623787)) = hAPP(hAPP(c_Finite__Set_Ofold(_1623785, _1623785, c_Orderings_Oord__class_Omax(_1623785)), _1623789), _1623787))], (43345 ^ _780461) ^ [_1623999, _1624001, _1624003] : [class_Orderings_Olinorder(_1623999), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623999), _1624001)), -(hBOOL(hAPP(hAPP(c_member(_1623999), _1624003), _1624001))), -(c_Big__Operators_Olattice_OInf__fin(_1623999, c_Orderings_Oord__class_Omin(_1623999), hAPP(hAPP(c_Set_Oinsert(_1623999), _1624003), _1624001)) = hAPP(hAPP(c_Finite__Set_Ofold(_1623999, _1623999, c_Orderings_Oord__class_Omin(_1623999)), _1624003), _1624001))], (43359 ^ _780461) ^ [_1624219, _1624221, _1624223, _1624225] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624219, _1624219)), hAPP(hAPP(c_Product__Type_OPair(_1624219, _1624219), _1624221), _1624223)), _1624225)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624219, _1624219)), hAPP(hAPP(c_Product__Type_OPair(_1624219, _1624219), _1624221), _1624223)), c_Transitive__Closure_Otrancl(_1624219, _1624225))))], (43365 ^ _780461) ^ [_1624382, _1624384] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1624382, _1624382), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1624382, _1624384)), hAPP(hAPP(c_Product__Type_OSigma(_1624382, _1624382), hAPP(c_Relation_OField(_1624382), _1624384)), hAPP(c_COMBK(tc_fun(_1624382, tc_HOL_Obool), _1624382), hAPP(c_Relation_OField(_1624382), _1624384))))))], (43367 ^ _780461) ^ [_1624451, _1624453, _1624455] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624451, _1624451)), _1624453), _1624455)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624451, _1624451)), _1624453), c_Transitive__Closure_Otrancl(_1624451, _1624455))))], (43373 ^ _780461) ^ [_1624576] : [-(c_Transitive__Closure_Otrancl(_1624576, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1624576, _1624576), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1624576, _1624576), tc_HOL_Obool)))], (43375 ^ _780461) ^ [_1624618, _1624620] : [-(hAPP(c_Relation_ODomain(_1624618, _1624618), c_Transitive__Closure_Otrancl(_1624618, _1624620)) = hAPP(c_Relation_ODomain(_1624618, _1624618), _1624620))], (43377 ^ _780461) ^ [_1624658, _1624660] : [-(hAPP(c_Relation_ORange(_1624658, _1624658), c_Transitive__Closure_Otrancl(_1624658, _1624660)) = hAPP(c_Relation_ORange(_1624658, _1624658), _1624660))], (43379 ^ _780461) ^ [_1624713, _1624715] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1624713, _1624713)), c_Transitive__Closure_Otrancl(_1624713, _1624715))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1624713, _1624713)), _1624715)))], (43385 ^ _780461) ^ [_1624820, _1624822] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1624820, _1624820)), _1624822)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1624820, _1624820)), c_Transitive__Closure_Otrancl(_1624820, _1624822))))], (43391 ^ _780461) ^ [_1624933, _1624935, _1624937, _1624939, _1624941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624933, _1624933)), hAPP(hAPP(c_Product__Type_OPair(_1624933, _1624933), _1624935), _1624937)), c_Transitive__Closure_Otrancl(_1624933, _1624939))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1624933, _1624933)), hAPP(hAPP(c_Product__Type_OPair(_1624933, _1624933), _1624937), _1624941)), c_Transitive__Closure_Otrancl(_1624933, _1624939))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624933, _1624933)), hAPP(hAPP(c_Product__Type_OPair(_1624933, _1624933), _1624935), _1624941)), c_Transitive__Closure_Otrancl(_1624933, _1624939))))], (43401 ^ _780461) ^ [_1625206, _1625208, _1625210, _1625212, _1625214] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625206, _1625206)), hAPP(hAPP(c_Product__Type_OPair(_1625206, _1625206), _1625208), _1625210)), c_Transitive__Closure_Otrancl(_1625206, _1625212))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1625206, _1625206)), hAPP(hAPP(c_Product__Type_OPair(_1625206, _1625206), _1625210), _1625214)), _1625212)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625206, _1625206)), hAPP(hAPP(c_Product__Type_OPair(_1625206, _1625206), _1625208), _1625214)), c_Transitive__Closure_Otrancl(_1625206, _1625212))))], (43411 ^ _780461) ^ [_1625473, _1625475, _1625477, _1625479, _1625481] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625473, _1625473)), hAPP(hAPP(c_Product__Type_OPair(_1625473, _1625473), _1625475), _1625477)), _1625479)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1625473, _1625473)), hAPP(hAPP(c_Product__Type_OPair(_1625473, _1625473), _1625477), _1625481)), c_Transitive__Closure_Otrancl(_1625473, _1625479))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625473, _1625473)), hAPP(hAPP(c_Product__Type_OPair(_1625473, _1625473), _1625475), _1625481)), c_Transitive__Closure_Otrancl(_1625473, _1625479))))], (43421 ^ _780461) ^ [_1625740, _1625742, _1625744, _1625746, _1625748] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625740, _1625740)), hAPP(hAPP(c_Product__Type_OPair(_1625740, _1625740), _1625742), _1625744)), _1625746)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1625740, _1625740)), hAPP(hAPP(c_Product__Type_OPair(_1625740, _1625740), _1625744), _1625748)), _1625746)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625740, _1625740)), hAPP(hAPP(c_Product__Type_OPair(_1625740, _1625740), _1625742), _1625748)), c_Transitive__Closure_Otrancl(_1625740, _1625746))))], (43431 ^ _780461) ^ [_1626001, _1626003, _1626005, _1626007] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626001, _1626001)), _1626003), c_Transitive__Closure_Otrancl(_1626001, _1626005))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1626001, _1626001), tc_HOL_Obool)), _1626005), _1626007)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626001, _1626001)), _1626003), c_Transitive__Closure_Otrancl(_1626001, _1626007))))], (43441 ^ _780461) ^ [_1626216, _1626218] : [-(c_Transitive__Closure_Otrancl(_1626216, _1626218) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1626216, _1626216), tc_HOL_Obool)), _1626218), hAPP(hAPP(c_Relation_Orel__comp(_1626216, _1626216, _1626216), c_Transitive__Closure_Otrancl(_1626216, _1626218)), _1626218)))], (43443 ^ _780461) ^ [_1626271, _1626273, _1626275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1626271, _1626271), tc_HOL_Obool)), _1626273), hAPP(hAPP(c_Product__Type_OSigma(_1626271, _1626271), _1626275), hAPP(c_COMBK(tc_fun(_1626271, tc_HOL_Obool), _1626271), _1626275)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1626271, _1626271), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1626271, _1626273)), hAPP(hAPP(c_Product__Type_OSigma(_1626271, _1626271), _1626275), hAPP(c_COMBK(tc_fun(_1626271, tc_HOL_Obool), _1626271), _1626275)))))], (43449 ^ _780461) ^ [_1626480, _1626482, _1626484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1626480, _1626480), tc_HOL_Obool)), _1626482), _1626484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1626480, _1626480), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1626480, _1626480, _1626480), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1626480, _1626480), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1626480, _1626482)), _1626484)), _1626482)), _1626484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1626480, _1626480), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1626480, _1626482)), _1626484)))], (43459 ^ _780461) ^ [_1626751, _1626753, _1626755, _1626757, _1626759, _1626761] : [c_Finite__Set_Ofun__left__comm(_1626751, _1626753, _1626755), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626751), _1626757)), hBOOL(hAPP(hAPP(c_member(_1626751), _1626759), _1626757)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1626751, _1626753, _1626755), _1626761), _1626757) = hAPP(hAPP(_1626755, _1626759), hAPP(hAPP(c_Finite__Set_Ofold(_1626751, _1626753, _1626755), _1626761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1626751, tc_HOL_Obool)), _1626757), hAPP(hAPP(c_Set_Oinsert(_1626751), _1626759), c_Orderings_Obot__class_Obot(tc_fun(_1626751, tc_HOL_Obool)))))))], (43473 ^ _780461) ^ [_1627080, _1627082, _1627084, _1627086, _1627088, _1627090] : [c_Finite__Set_Ofun__left__comm(_1627080, _1627082, _1627084), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627080), _1627086)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1627080, _1627082, _1627084), _1627088), hAPP(hAPP(c_Set_Oinsert(_1627080), _1627090), _1627086)) = hAPP(hAPP(_1627084, _1627090), hAPP(hAPP(c_Finite__Set_Ofold(_1627080, _1627082, _1627084), _1627088), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627080, tc_HOL_Obool)), _1627086), hAPP(hAPP(c_Set_Oinsert(_1627080), _1627090), c_Orderings_Obot__class_Obot(tc_fun(_1627080, tc_HOL_Obool)))))))], (43483 ^ _780461) ^ [_1627351, _1627353, _1627355, _1627357, _1627359] : [c_Finite__Set_Ofun__left__comm(_1627351, _1627353, _1627355), -(hAPP(c_Fun_Ocomp(_1627353, _1627353, _1627353, hAPP(_1627355, _1627357)), hAPP(_1627355, _1627359)) = hAPP(c_Fun_Ocomp(_1627353, _1627353, _1627353, hAPP(_1627355, _1627359)), hAPP(_1627355, _1627357)))], (43489 ^ _780461) ^ [_1627492, _1627494, _1627496, _1627498, _1627500, _1627502, _1627504] : [c_Finite__Set_Ofun__left__comm(_1627492, _1627494, _1627496), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1627492, _1627494, _1627496, _1627498, _1627500), _1627502)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1627492, _1627494, _1627496, _1627498, _1627500), _1627504)), -(_1627504 = _1627502)], (43503 ^ _780461) ^ [_1627737, _1627739, _1627741, _1627743, _1627745] : [c_Finite__Set_Ofun__left__comm(_1627737, _1627739, _1627741), -(c_Finite__Set_Ofun__left__comm(_1627743, _1627739, hAPP(hAPP(c_COMBB(_1627737, tc_fun(_1627739, _1627739), _1627743), _1627741), _1627745)))], (43509 ^ _780461) ^ [_1627850, _1627852, _1627854, _1627856, _1627858, _1627860] : [c_Finite__Set_Ofun__left__comm(_1627850, _1627852, _1627854), -(hAPP(hAPP(_1627854, _1627856), hAPP(hAPP(_1627854, _1627858), _1627860)) = hAPP(hAPP(_1627854, _1627858), hAPP(hAPP(_1627854, _1627856), _1627860)))], (43515 ^ _780461) ^ [_1627985] : [class_Groups_Oab__semigroup__mult(_1627985), -(c_Finite__Set_Ofun__left__comm(_1627985, _1627985, c_Groups_Otimes__class_Otimes(_1627985)))], (43521 ^ _780461) ^ [_1628064, _1628066, _1628068, _1628070, _1628072, _1628074] : [c_Finite__Set_Ofun__left__comm(_1628064, _1628066, _1628068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628064), _1628070)), -(hAPP(hAPP(_1628068, _1628072), hAPP(hAPP(c_Finite__Set_Ofold(_1628064, _1628066, _1628068), _1628074), _1628070)) = hAPP(hAPP(c_Finite__Set_Ofold(_1628064, _1628066, _1628068), hAPP(hAPP(_1628068, _1628072), _1628074)), _1628070))], (43531 ^ _780461) ^ [_1628283, _1628285, _1628287, _1628289, _1628291, _1628293] : [c_Finite__Set_Ofun__left__comm(_1628283, _1628285, _1628287), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1628283, _1628285, _1628287, _1628289, _1628291), _1628293)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1628283, _1628285, _1628287), _1628289), _1628291) = _1628293)], (43541 ^ _780461) ^ [_1628466, _1628468, _1628470, _1628472, _1628474] : [c_Finite__Set_Ofun__left__comm(_1628466, _1628468, _1628470), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628466), _1628472)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1628466, _1628468, _1628470, _1628474, _1628472), hAPP(hAPP(c_Finite__Set_Ofold(_1628466, _1628468, _1628470), _1628474), _1628472))))], (43551 ^ _780461) ^ [_1628653, _1628655, _1628657, _1628659, _1628661, _1628663] : [c_Finite__Set_Ofun__left__comm(_1628653, _1628655, _1628657), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628653), _1628659)), -(hBOOL(hAPP(hAPP(c_member(_1628653), _1628661), _1628659))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1628653, _1628655, _1628657), _1628663), hAPP(hAPP(c_Set_Oinsert(_1628653), _1628661), _1628659)) = hAPP(hAPP(c_Finite__Set_Ofold(_1628653, _1628655, _1628657), hAPP(hAPP(_1628657, _1628661), _1628663)), _1628659))], (43565 ^ _780461) ^ [_1628905, _1628907, _1628909, _1628911, _1628913, _1628915] : [c_Finite__Set_Ofun__left__comm(_1628905, _1628907, _1628909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1628905), _1628911)), -(hBOOL(hAPP(hAPP(c_member(_1628905), _1628913), _1628911))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1628905, _1628907, _1628909), _1628915), hAPP(hAPP(c_Set_Oinsert(_1628905), _1628913), _1628911)) = hAPP(hAPP(_1628909, _1628913), hAPP(hAPP(c_Finite__Set_Ofold(_1628905, _1628907, _1628909), _1628915), _1628911)))], (43579 ^ _780461) ^ [_1629157, _1629159, _1629161, _1629163, _1629165, _1629167, _1629169] : [c_Finite__Set_Ofun__left__comm(_1629157, _1629159, _1629161), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1629157, _1629159, _1629161, _1629163, _1629165), _1629167)), hBOOL(hAPP(hAPP(c_member(_1629157), _1629169), _1629165)), 43591 ^ _780461 : [(43592 ^ _780461) ^ [] : [-(_1629167 = hAPP(hAPP(_1629161, _1629169), 43590 ^ [_1629157, _1629159, _1629161, _1629163, _1629165, _1629167, _1629169]))], (43594 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1629157, _1629159, _1629161, _1629163, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1629157, tc_HOL_Obool)), _1629165), hAPP(hAPP(c_Set_Oinsert(_1629157), _1629169), c_Orderings_Obot__class_Obot(tc_fun(_1629157, tc_HOL_Obool))))), 43590 ^ [_1629157, _1629159, _1629161, _1629163, _1629165, _1629167, _1629169])))]]], (43596 ^ _780461) ^ [_1629541, _1629543, _1629545, _1629547] : [-(c_Transitive__Closure_Otrancl(_1629541, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1629541, _1629541)), hAPP(hAPP(c_Product__Type_OPair(_1629541, _1629541), _1629543), _1629545)), _1629547)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1629541, _1629541), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1629541, _1629547)), hAPP(c_Set_OCollect(tc_prod(_1629541, _1629541)), hAPP(c_Product__Type_Oprod_Oprod__case(_1629541, _1629541, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1629541, tc_fun(_1629541, tc_HOL_Obool), tc_fun(_1629541, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1629541, tc_HOL_Obool), tc_fun(_1629541, tc_HOL_Obool)), _1629541), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1629541)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1629541), c_fconj), hAPP(hAPP(c_COMBC(_1629541, tc_fun(tc_prod(_1629541, _1629541), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1629541, _1629541), tc_fun(tc_fun(tc_prod(_1629541, _1629541), tc_HOL_Obool), tc_HOL_Obool), _1629541), c_member(tc_prod(_1629541, _1629541))), hAPP(hAPP(c_COMBC(_1629541, _1629541, tc_prod(_1629541, _1629541)), c_Product__Type_OPair(_1629541, _1629541)), _1629543))), c_Transitive__Closure_Ortrancl(_1629541, _1629547))))), hAPP(hAPP(c_COMBC(_1629541, tc_fun(tc_prod(_1629541, _1629541), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1629541, _1629541), tc_fun(tc_fun(tc_prod(_1629541, _1629541), tc_HOL_Obool), tc_HOL_Obool), _1629541), c_member(tc_prod(_1629541, _1629541))), hAPP(c_Product__Type_OPair(_1629541, _1629541), _1629545))), c_Transitive__Closure_Ortrancl(_1629541, _1629547)))))))], (43598 ^ _780461) ^ [_1629788, _1629790, _1629792] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629788, _1629788)), _1629790), _1629792)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629788, _1629788)), _1629790), c_Transitive__Closure_Ortrancl(_1629788, _1629792))))], (43604 ^ _780461) ^ [_1629913, _1629915, _1629917] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629913, _1629913)), hAPP(hAPP(c_Product__Type_OPair(_1629913, _1629913), _1629915), _1629915)), c_Transitive__Closure_Ortrancl(_1629913, _1629917))))], (43606 ^ _780461) ^ [_1629962, _1629964, _1629966, _1629968] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629962, _1629962)), hAPP(hAPP(c_Product__Type_OPair(_1629962, _1629962), _1629964), _1629966)), c_Transitive__Closure_Otrancl(_1629962, _1629968))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629962, _1629962)), hAPP(hAPP(c_Product__Type_OPair(_1629962, _1629962), _1629964), _1629966)), c_Transitive__Closure_Ortrancl(_1629962, _1629968))))], (43612 ^ _780461) ^ [_1630131, _1630133] : [-(hAPP(c_Relation_ODomain(_1630131, _1630131), c_Transitive__Closure_Ortrancl(_1630131, _1630133)) = c_Orderings_Otop__class_Otop(tc_fun(_1630131, tc_HOL_Obool)))], (43614 ^ _780461) ^ [_1630170, _1630172] : [-(hAPP(c_Relation_ORange(_1630170, _1630170), c_Transitive__Closure_Ortrancl(_1630170, _1630172)) = c_Orderings_Otop__class_Otop(tc_fun(_1630170, tc_HOL_Obool)))], (43616 ^ _780461) ^ [_1630209, _1630211] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1630209, _1630209, _1630209), c_Transitive__Closure_Ortrancl(_1630209, _1630211)), c_Transitive__Closure_Ortrancl(_1630209, _1630211)) = c_Transitive__Closure_Ortrancl(_1630209, _1630211))], (43618 ^ _780461) ^ [_1630253, _1630255] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1630253, _1630253, _1630253), _1630255), c_Transitive__Closure_Ortrancl(_1630253, _1630255)) = hAPP(hAPP(c_Relation_Orel__comp(_1630253, _1630253, _1630253), c_Transitive__Closure_Ortrancl(_1630253, _1630255)), _1630255))], (43620 ^ _780461) ^ [_1630304, _1630306, _1630308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630304, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1630304, _1630304, _1630306), _1630308)), _1630308)), -(hAPP(c_Relation_OImage(_1630304, _1630304, c_Transitive__Closure_Ortrancl(_1630304, _1630306)), _1630308) = _1630308)], (43626 ^ _780461) ^ [_1630437, _1630439, _1630441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1630437, _1630437), tc_HOL_Obool)), _1630439), _1630441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1630437, _1630437), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1630437, _1630439)), c_Transitive__Closure_Ortrancl(_1630437, _1630441))))], (43632 ^ _780461) ^ [_1630580, _1630582, _1630584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1630580, _1630580), tc_HOL_Obool)), _1630582), _1630584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1630580, _1630580), tc_HOL_Obool)), _1630584), c_Transitive__Closure_Ortrancl(_1630580, _1630582))), -(c_Transitive__Closure_Ortrancl(_1630580, _1630584) = c_Transitive__Closure_Ortrancl(_1630580, _1630582))], (43642 ^ _780461) ^ [_1630783, _1630785, _1630787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1630783, _1630783), tc_HOL_Obool)), _1630785), c_Transitive__Closure_Ortrancl(_1630783, _1630787))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1630783, _1630783), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1630783, _1630785)), c_Transitive__Closure_Ortrancl(_1630783, _1630787))))], (43648 ^ _780461) ^ [_1630932, _1630934, _1630936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1630932, _1630932), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1630932, _1630932), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1630932, _1630934)), c_Transitive__Closure_Ortrancl(_1630932, _1630936))), c_Transitive__Closure_Ortrancl(_1630932, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1630932, _1630932), tc_HOL_Obool)), _1630934), _1630936)))))], (43650 ^ _780461) ^ [_1631009, _1631011, _1631013] : [-(c_Transitive__Closure_Ortrancl(_1631009, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1631009, _1631009), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1631009, _1631011)), c_Transitive__Closure_Ortrancl(_1631009, _1631013))) = c_Transitive__Closure_Ortrancl(_1631009, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1631009, _1631009), tc_HOL_Obool)), _1631011), _1631013)))], (43652 ^ _780461) ^ [_1631076, _1631078, _1631080, _1631082] : [43653 ^ _780461 : [(43654 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631076, _1631076)), _1631078), c_Transitive__Closure_Ortrancl(_1631076, _1631080)))], (43656 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631076, _1631076)), _1631078), c_Transitive__Closure_Ortrancl(_1631076, _1631082)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631076, _1631076)), _1631078), c_Transitive__Closure_Ortrancl(_1631076, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1631076, _1631076), tc_HOL_Obool)), _1631080), _1631082)))))], (43660 ^ _780461) ^ [_1631301, _1631303, _1631305, _1631307, _1631309] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631301, _1631301)), hAPP(hAPP(c_Product__Type_OPair(_1631301, _1631301), _1631303), _1631305)), _1631307)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1631301, _1631301)), hAPP(hAPP(c_Product__Type_OPair(_1631301, _1631301), _1631305), _1631309)), c_Transitive__Closure_Ortrancl(_1631301, _1631307))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631301, _1631301)), hAPP(hAPP(c_Product__Type_OPair(_1631301, _1631301), _1631303), _1631309)), c_Transitive__Closure_Ortrancl(_1631301, _1631307))))], (43670 ^ _780461) ^ [_1631568, _1631570, _1631572, _1631574, _1631576] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631568, _1631568)), hAPP(hAPP(c_Product__Type_OPair(_1631568, _1631568), _1631570), _1631572)), c_Transitive__Closure_Ortrancl(_1631568, _1631574))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1631568, _1631568)), hAPP(hAPP(c_Product__Type_OPair(_1631568, _1631568), _1631572), _1631576)), _1631574)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631568, _1631568)), hAPP(hAPP(c_Product__Type_OPair(_1631568, _1631568), _1631570), _1631576)), c_Transitive__Closure_Ortrancl(_1631568, _1631574))))], (43680 ^ _780461) ^ [_1631835, _1631837, _1631839, _1631841, _1631843] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631835, _1631835)), hAPP(hAPP(c_Product__Type_OPair(_1631835, _1631835), _1631837), _1631839)), c_Transitive__Closure_Ortrancl(_1631835, _1631841))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1631835, _1631835)), hAPP(hAPP(c_Product__Type_OPair(_1631835, _1631835), _1631839), _1631843)), c_Transitive__Closure_Ortrancl(_1631835, _1631841))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1631835, _1631835)), hAPP(hAPP(c_Product__Type_OPair(_1631835, _1631835), _1631837), _1631843)), c_Transitive__Closure_Ortrancl(_1631835, _1631841))))], (43690 ^ _780461) ^ [_1632108, _1632110] : [-(c_Relation_Orefl__on(_1632108, c_Orderings_Otop__class_Otop(tc_fun(_1632108, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1632108, _1632110)))], (43692 ^ _780461) ^ [_1632142, _1632144] : [-(c_Transitive__Closure_Ortrancl(_1632142, c_Transitive__Closure_Ortrancl(_1632142, _1632144)) = c_Transitive__Closure_Ortrancl(_1632142, _1632144))], (43694 ^ _780461) ^ [_1632176, _1632178] : [-(c_Transitive__Closure_Otrancl(_1632176, c_Transitive__Closure_Ortrancl(_1632176, _1632178)) = c_Transitive__Closure_Ortrancl(_1632176, _1632178))], (43696 ^ _780461) ^ [_1632210, _1632212] : [-(c_Transitive__Closure_Ortrancl(_1632210, c_Transitive__Closure_Otrancl(_1632210, _1632212)) = c_Transitive__Closure_Ortrancl(_1632210, _1632212))], (43698 ^ _780461) ^ [_1632244, _1632246] : [-(c_Transitive__Closure_Otrancl(_1632244, _1632246) = hAPP(hAPP(c_Relation_Orel__comp(_1632244, _1632244, _1632244), _1632246), c_Transitive__Closure_Ortrancl(_1632244, _1632246)))], (43700 ^ _780461) ^ [_1632285, _1632287] : [-(c_Transitive__Closure_Otrancl(_1632285, _1632287) = hAPP(hAPP(c_Relation_Orel__comp(_1632285, _1632285, _1632285), c_Transitive__Closure_Ortrancl(_1632285, _1632287)), _1632287))], (43702 ^ _780461) ^ [_1632347, _1632349, _1632351, _1632353] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632347, _1632347)), hAPP(hAPP(c_Product__Type_OPair(_1632347, _1632347), _1632349), _1632351)), c_Transitive__Closure_Ortrancl(_1632347, _1632353))), -(_1632349 = _1632351), 43709 ^ _780461 : [(43710 ^ _780461) ^ [] : [_1632349 = _1632351], (43712 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632347, _1632347)), hAPP(hAPP(c_Product__Type_OPair(_1632347, _1632347), _1632349), _1632351)), c_Transitive__Closure_Otrancl(_1632347, _1632353))))]]], (43714 ^ _780461) ^ [_1632605, _1632607, _1632609, _1632611] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632605, _1632605)), hAPP(hAPP(c_Product__Type_OPair(_1632605, _1632605), _1632607), _1632609)), c_Transitive__Closure_Ortrancl(_1632605, _1632611)))), 43715 ^ _780461 : [(43716 ^ _780461) ^ [] : [_1632607 = _1632609], (43718 ^ _780461) ^ [] : [-(_1632607 = _1632609), hBOOL(hAPP(hAPP(c_member(tc_prod(_1632605, _1632605)), hAPP(hAPP(c_Product__Type_OPair(_1632605, _1632605), _1632607), _1632609)), c_Transitive__Closure_Otrancl(_1632605, _1632611)))]]], (43726 ^ _780461) ^ [_1632871, _1632873, _1632875, _1632877, _1632879] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632871, _1632871)), hAPP(hAPP(c_Product__Type_OPair(_1632871, _1632871), _1632873), _1632875)), _1632877)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1632871, _1632871)), hAPP(hAPP(c_Product__Type_OPair(_1632871, _1632871), _1632875), _1632879)), c_Transitive__Closure_Ortrancl(_1632871, _1632877))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632871, _1632871)), hAPP(hAPP(c_Product__Type_OPair(_1632871, _1632871), _1632873), _1632879)), c_Transitive__Closure_Otrancl(_1632871, _1632877))))], (43736 ^ _780461) ^ [_1633138, _1633140, _1633142, _1633144] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633138, _1633138)), hAPP(hAPP(c_Product__Type_OPair(_1633138, _1633138), _1633140), _1633142)), c_Transitive__Closure_Ortrancl(_1633138, _1633144))), -(_1633140 = _1633142), 43743 ^ _780461 : [(43744 ^ _780461) ^ [] : [_1633140 = _1633142], (43746 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633138, _1633138)), hAPP(hAPP(c_Product__Type_OPair(_1633138, _1633138), _1633140), _1633142)), c_Transitive__Closure_Otrancl(_1633138, _1633144))))]]], (43748 ^ _780461) ^ [_1633400, _1633402, _1633404, _1633406, _1633408] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633400, _1633400)), hAPP(hAPP(c_Product__Type_OPair(_1633400, _1633400), _1633402), _1633404)), c_Transitive__Closure_Ortrancl(_1633400, _1633406))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1633400, _1633400)), hAPP(hAPP(c_Product__Type_OPair(_1633400, _1633400), _1633404), _1633408)), _1633406)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633400, _1633400)), hAPP(hAPP(c_Product__Type_OPair(_1633400, _1633400), _1633402), _1633408)), c_Transitive__Closure_Otrancl(_1633400, _1633406))))], (43758 ^ _780461) ^ [_1633667, _1633669, _1633671, _1633673, _1633675] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633667, _1633667)), hAPP(hAPP(c_Product__Type_OPair(_1633667, _1633667), _1633669), _1633671)), c_Transitive__Closure_Otrancl(_1633667, _1633673))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1633667, _1633667)), hAPP(hAPP(c_Product__Type_OPair(_1633667, _1633667), _1633671), _1633675)), c_Transitive__Closure_Ortrancl(_1633667, _1633673))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633667, _1633667)), hAPP(hAPP(c_Product__Type_OPair(_1633667, _1633667), _1633669), _1633675)), c_Transitive__Closure_Otrancl(_1633667, _1633673))))], (43768 ^ _780461) ^ [_1633940, _1633942, _1633944, _1633946, _1633948] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633940, _1633940)), hAPP(hAPP(c_Product__Type_OPair(_1633940, _1633940), _1633942), _1633944)), c_Transitive__Closure_Ortrancl(_1633940, _1633946))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1633940, _1633940)), hAPP(hAPP(c_Product__Type_OPair(_1633940, _1633940), _1633944), _1633948)), c_Transitive__Closure_Otrancl(_1633940, _1633946))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633940, _1633940)), hAPP(hAPP(c_Product__Type_OPair(_1633940, _1633940), _1633942), _1633948)), c_Transitive__Closure_Otrancl(_1633940, _1633946))))], (43778 ^ _780461) ^ [_1634212, _1634214, _1634216, _1634218] : [-(hBOOL(hAPP(hAPP(c_member(_1634212), _1634214), hAPP(c_Relation_ODomain(_1634212, _1634212), _1634216)))), 43781 ^ _780461 : [(43782 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634212, _1634212)), hAPP(hAPP(c_Product__Type_OPair(_1634212, _1634212), _1634214), _1634218)), c_Transitive__Closure_Ortrancl(_1634212, _1634216))), -(_1634214 = _1634218)], (43788 ^ _780461) ^ [] : [_1634214 = _1634218, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634212, _1634212)), hAPP(hAPP(c_Product__Type_OPair(_1634212, _1634212), _1634214), _1634218)), c_Transitive__Closure_Ortrancl(_1634212, _1634216))))]]], (43794 ^ _780461) ^ [_1634508, _1634510, _1634512, _1634514] : [hBOOL(hAPP(hAPP(c_member(_1634508), _1634510), c_Wellfounded_Oacc(_1634508, _1634512))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1634508, _1634508)), hAPP(hAPP(c_Product__Type_OPair(_1634508, _1634508), _1634514), _1634510)), c_Transitive__Closure_Ortrancl(_1634508, _1634512))), -(hBOOL(hAPP(hAPP(c_member(_1634508), _1634514), c_Wellfounded_Oacc(_1634508, _1634512))))], (43804 ^ _780461) ^ [_1634729, _1634731, _1634733, _1634735] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634729, _1634729)), hAPP(hAPP(c_Product__Type_OPair(_1634729, _1634729), _1634731), _1634733)), c_Transitive__Closure_Ortrancl(_1634729, _1634735))), hBOOL(hAPP(hAPP(c_member(_1634729), _1634733), c_Wellfounded_Oacc(_1634729, _1634735))), -(hBOOL(hAPP(hAPP(c_member(_1634729), _1634731), c_Wellfounded_Oacc(_1634729, _1634735))))], (43814 ^ _780461) ^ [_1634971, _1634973, _1634975, _1634977] : [c_Wellfounded_Owf(_1634971, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1634971, _1634971)), hAPP(hAPP(c_Product__Type_OPair(_1634971, _1634971), _1634973), _1634975)), _1634977)), 43817 ^ _780461 : [(43818 ^ _780461) ^ [] : [-(c_Wellfounded_Owf(_1634971, _1634977))], (43820 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634971, _1634971)), hAPP(hAPP(c_Product__Type_OPair(_1634971, _1634971), _1634975), _1634973)), c_Transitive__Closure_Ortrancl(_1634971, _1634977)))]]], (43822 ^ _780461) ^ [_1635166, _1635168, _1635170, _1635172] : [-(c_Wellfounded_Owf(_1635166, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1635166, _1635166)), hAPP(hAPP(c_Product__Type_OPair(_1635166, _1635166), _1635168), _1635170)), _1635172))), c_Wellfounded_Owf(_1635166, _1635172), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635166, _1635166)), hAPP(hAPP(c_Product__Type_OPair(_1635166, _1635166), _1635170), _1635168)), c_Transitive__Closure_Ortrancl(_1635166, _1635172))))], (43832 ^ _780461) ^ [_1635413, _1635415, _1635417, _1635419] : [c_Wellfounded_Oacyclic(_1635413, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1635413, _1635413)), hAPP(hAPP(c_Product__Type_OPair(_1635413, _1635413), _1635415), _1635417)), _1635419)), 43835 ^ _780461 : [(43836 ^ _780461) ^ [] : [-(c_Wellfounded_Oacyclic(_1635413, _1635419))], (43838 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635413, _1635413)), hAPP(hAPP(c_Product__Type_OPair(_1635413, _1635413), _1635417), _1635415)), c_Transitive__Closure_Ortrancl(_1635413, _1635419)))]]], (43840 ^ _780461) ^ [_1635608, _1635610, _1635612, _1635614] : [-(c_Wellfounded_Oacyclic(_1635608, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1635608, _1635608)), hAPP(hAPP(c_Product__Type_OPair(_1635608, _1635608), _1635610), _1635612)), _1635614))), c_Wellfounded_Oacyclic(_1635608, _1635614), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635608, _1635608)), hAPP(hAPP(c_Product__Type_OPair(_1635608, _1635608), _1635612), _1635610)), c_Transitive__Closure_Ortrancl(_1635608, _1635614))))], (43850 ^ _780461) ^ [_1635849, _1635851] : [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), _1635849), _1635851)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1635849), _1635851)))], (43856 ^ _780461) ^ [_1635954, _1635956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1635954), _1635956)), -(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), _1635954), _1635956)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (43862 ^ _780461) ^ [_1636065, _1636067, _1636069, _1636071, _1636073] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1636065, _1636065)), hAPP(hAPP(c_Product__Type_OPair(_1636065, _1636065), _1636067), _1636069)), c_Transitive__Closure_Ortrancl(_1636065, _1636071))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1636065, _1636065), tc_HOL_Obool)), _1636071), hAPP(hAPP(c_Product__Type_OSigma(_1636065, _1636065), _1636073), hAPP(c_COMBK(tc_fun(_1636065, tc_HOL_Obool), _1636065), _1636073)))), -(_1636067 = _1636069), -(hBOOL(hAPP(hAPP(c_member(_1636065), _1636067), _1636073)))], (43876 ^ _780461) ^ [_1636339, _1636341, _1636343] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1636339, _1636339), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1636339, _1636339), _1636341)), c_Transitive__Closure_Ortrancl(_1636339, _1636341)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1636339, _1636339), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1636339, _1636339)), hAPP(hAPP(c_Product__Type_OPair(_1636339, _1636339), _1636343), _1636343)), c_Transitive__Closure_Otrancl(_1636339, _1636341)))], (43882 ^ _780461) ^ [_1636525, _1636527, _1636529, _1636531] : [class_Complete__Lattice_Ocomplete__lattice(_1636525), hBOOL(hAPP(c_Finite__Set_Ofinite(_1636527), _1636529)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636527, _1636525), _1636529), _1636531) = hAPP(hAPP(c_Finite__Set_Ofold(_1636527, _1636525, hAPP(hAPP(c_COMBB(_1636525, tc_fun(_1636525, _1636525), _1636527), c_Lattices_Osemilattice__inf__class_Oinf(_1636525)), _1636531)), c_Orderings_Otop__class_Otop(_1636525)), _1636529))], (43892 ^ _780461) ^ [_1636740, _1636742, _1636744, _1636746, _1636748, _1636750] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636740, tc_fun(_1636742, tc_HOL_Obool)), _1636744), _1636746), _1636748)), -(hBOOL(hAPP(hAPP(_1636746, _1636750), _1636748))), hBOOL(hAPP(hAPP(c_member(_1636740), _1636750), _1636744))], (43902 ^ _780461) ^ [_1636941, _1636943, _1636945, _1636947, _1636949, _1636951] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1636941, tc_fun(_1636943, tc_HOL_Obool)), _1636945), _1636947), _1636949)), hBOOL(hAPP(hAPP(c_member(_1636941), _1636951), _1636945)), -(hBOOL(hAPP(hAPP(_1636947, _1636951), _1636949)))], (43912 ^ _780461) ^ [_1637138, _1637140, _1637142, _1637144, _1637146, _1637148] : [hBOOL(hAPP(hAPP(c_member(_1637138), _1637140), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637142, tc_fun(_1637138, tc_HOL_Obool)), _1637144), _1637146))), -(hBOOL(hAPP(hAPP(c_member(_1637138), _1637140), hAPP(_1637146, _1637148)))), hBOOL(hAPP(hAPP(c_member(_1637142), _1637148), _1637144))], (43922 ^ _780461) ^ [_1637359, _1637361, _1637363, _1637365, _1637367, _1637369] : [hBOOL(hAPP(hAPP(c_member(_1637359), _1637361), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637363, tc_fun(_1637359, tc_HOL_Obool)), _1637365), _1637367))), hBOOL(hAPP(hAPP(c_member(_1637363), _1637369), _1637365)), -(hBOOL(hAPP(hAPP(c_member(_1637359), _1637361), hAPP(_1637367, _1637369))))], (43932 ^ _780461) ^ [_1637576, _1637578, _1637580, _1637582, _1637584, _1637586, _1637588, _1637590] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637576, tc_fun(_1637578, tc_fun(_1637580, tc_HOL_Obool))), _1637582), _1637584), _1637586), _1637588)), -(hBOOL(hAPP(hAPP(hAPP(_1637584, _1637590), _1637586), _1637588))), hBOOL(hAPP(hAPP(c_member(_1637576), _1637590), _1637582))], (43942 ^ _780461) ^ [_1637803, _1637805, _1637807, _1637809, _1637811, _1637813, _1637815, _1637817] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1637803, tc_fun(_1637805, tc_fun(_1637807, tc_HOL_Obool))), _1637809), _1637811), _1637813), _1637815)), hBOOL(hAPP(hAPP(c_member(_1637803), _1637817), _1637809)), -(hBOOL(hAPP(hAPP(hAPP(_1637811, _1637817), _1637813), _1637815)))], (43952 ^ _780461) ^ [_1638026, _1638028, _1638030, _1638032] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1638030), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638026, tc_fun(_1638030, tc_HOL_Obool)), _1638028), _1638032)))), 43953 ^ _780461 : [(43954 ^ _780461) ^ [_1638100] : [hBOOL(hAPP(hAPP(c_member(_1638026), _1638100), _1638028)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1638030), hAPP(_1638032, _1638100)))]]], (43962 ^ _780461) ^ [_1638254, _1638256] : [-(c_Transitive__Closure_Ortrancl(_1638254, hAPP(c_Relation_Oconverse(_1638254, _1638254), _1638256)) = hAPP(c_Relation_Oconverse(_1638254, _1638254), c_Transitive__Closure_Ortrancl(_1638254, _1638256)))], (43964 ^ _780461) ^ [_1638297, _1638299] : [-(c_Transitive__Closure_Otrancl(_1638297, hAPP(c_Relation_Oconverse(_1638297, _1638297), _1638299)) = hAPP(c_Relation_Oconverse(_1638297, _1638297), c_Transitive__Closure_Otrancl(_1638297, _1638299)))], (43966 ^ _780461) ^ [_1638340, _1638342] : [c_Wellfounded_Owf(_1638340, hAPP(c_Relation_Oconverse(_1638340, _1638340), _1638342)), -(c_Wellfounded_Owf(_1638340, hAPP(c_Relation_Oconverse(_1638340, _1638340), c_Transitive__Closure_Otrancl(_1638340, _1638342))))], (43972 ^ _780461) ^ [_1638462, _1638464] : [c_Wellfounded_Oacyclic(_1638462, hAPP(c_Relation_Oconverse(_1638462, _1638462), _1638464)), -(c_Wellfounded_Oacyclic(_1638462, _1638464))], (43978 ^ _780461) ^ [_1638547, _1638549] : [c_Wellfounded_Oacyclic(_1638547, _1638549), -(c_Wellfounded_Oacyclic(_1638547, hAPP(c_Relation_Oconverse(_1638547, _1638547), _1638549)))], (43984 ^ _780461) ^ [_1638656, _1638658, _1638660, _1638662, _1638664] : [_1638656 = c_Orderings_Obot__class_Obot(tc_fun(_1638658, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638660, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638658, tc_fun(_1638660, tc_HOL_Obool)), _1638656), _1638662)), _1638664) = _1638664)], (43990 ^ _780461) ^ [_1638789, _1638791, _1638793, _1638795, _1638797] : [-(_1638789 = c_Orderings_Obot__class_Obot(tc_fun(_1638791, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638793, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638791, tc_fun(_1638793, tc_HOL_Obool)), _1638789), _1638795)), _1638797) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638791, tc_fun(_1638793, tc_HOL_Obool)), _1638789), hAPP(hAPP(c_COMBC(_1638791, tc_fun(_1638793, tc_HOL_Obool), tc_fun(_1638793, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638793, tc_HOL_Obool), tc_fun(tc_fun(_1638793, tc_HOL_Obool), tc_fun(_1638793, tc_HOL_Obool)), _1638791), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638793, tc_HOL_Obool))), _1638795)), _1638797)))], (43996 ^ _780461) ^ [_1638934, _1638936, _1638938, _1638940, _1638942] : [_1638934 = c_Orderings_Obot__class_Obot(tc_fun(_1638936, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638938, tc_HOL_Obool)), _1638940), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1638936, tc_fun(_1638938, tc_HOL_Obool)), _1638934), _1638942)) = _1638940)], (44002 ^ _780461) ^ [_1639067, _1639069, _1639071, _1639073, _1639075] : [-(_1639067 = c_Orderings_Obot__class_Obot(tc_fun(_1639069, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639071, tc_HOL_Obool)), _1639073), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639069, tc_fun(_1639071, tc_HOL_Obool)), _1639067), _1639075)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639069, tc_fun(_1639071, tc_HOL_Obool)), _1639067), hAPP(hAPP(c_COMBB(tc_fun(_1639071, tc_HOL_Obool), tc_fun(_1639071, tc_HOL_Obool), _1639069), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639071, tc_HOL_Obool)), _1639073)), _1639075)))], (44008 ^ _780461) ^ [_1639175, _1639177, _1639179, _1639181] : [class_Complete__Lattice_Ocomplete__lattice(_1639175), -(_1639177 = c_Orderings_Obot__class_Obot(tc_fun(_1639179, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639179, _1639175), _1639177), hAPP(c_COMBK(_1639175, _1639179), _1639181)) = _1639181)], (44018 ^ _780461) ^ [_1639324, _1639326, _1639328, _1639330] : [_1639324 = c_Orderings_Obot__class_Obot(tc_fun(_1639326, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639326, tc_fun(_1639328, tc_HOL_Obool)), _1639324), hAPP(c_COMBK(tc_fun(_1639328, tc_HOL_Obool), _1639326), _1639330)) = c_Orderings_Otop__class_Otop(tc_fun(_1639328, tc_HOL_Obool)))], (44024 ^ _780461) ^ [_1639461, _1639463, _1639465, _1639467] : [-(_1639461 = c_Orderings_Obot__class_Obot(tc_fun(_1639463, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639463, tc_fun(_1639465, tc_HOL_Obool)), _1639461), hAPP(c_COMBK(tc_fun(_1639465, tc_HOL_Obool), _1639463), _1639467)) = _1639467)], (44030 ^ _780461) ^ [_1639529, _1639531, _1639533] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639529, tc_fun(_1639531, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1639529, tc_HOL_Obool))), _1639533) = c_Orderings_Otop__class_Otop(tc_fun(_1639531, tc_HOL_Obool)))], (44032 ^ _780461) ^ [_1639578, _1639580, _1639582, _1639584, _1639586] : [-(hAPP(c_Relation_Oconverse(_1639578, _1639580), hAPP(hAPP(c_Relation_Orel__comp(_1639578, _1639582, _1639580), _1639584), _1639586)) = hAPP(hAPP(c_Relation_Orel__comp(_1639580, _1639582, _1639578), hAPP(c_Relation_Oconverse(_1639582, _1639580), _1639586)), hAPP(c_Relation_Oconverse(_1639578, _1639582), _1639584)))], (44034 ^ _780461) ^ [_1639647, _1639649, _1639651, _1639653, _1639655] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639647, tc_fun(_1639649, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1639647), _1639651), _1639653)), _1639655) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639649, tc_HOL_Obool)), hAPP(_1639655, _1639651)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639647, tc_fun(_1639649, tc_HOL_Obool)), _1639653), _1639655)))], (44036 ^ _780461) ^ [_1639724, _1639726, _1639728, _1639730, _1639732] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639724, tc_fun(_1639726, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1639724, tc_HOL_Obool)), _1639728), _1639730)), _1639732) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1639726, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639724, tc_fun(_1639726, tc_HOL_Obool)), _1639728), _1639732)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639724, tc_fun(_1639726, tc_HOL_Obool)), _1639730), _1639732)))], (44048 ^ _780461) ^ [_1640095, _1640097, _1640099, _1640101, _1640103] : [44050 ^ _780461 : [(44051 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1640099), 44049 ^ [_1640095, _1640097, _1640099, _1640101, _1640103]), _1640101)))], (44053 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1640095, tc_HOL_Obool)), _1640097), hAPP(_1640103, 44049 ^ [_1640095, _1640097, _1640099, _1640101, _1640103])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1640095, tc_HOL_Obool)), _1640097), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640099, tc_fun(_1640095, tc_HOL_Obool)), _1640101), _1640103))))], (44038 ^ _780461) ^ [_1639837, _1639839, _1639841, _1639843, _1639845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1639837, tc_HOL_Obool)), _1639839), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1639841, tc_fun(_1639837, tc_HOL_Obool)), _1639843), _1639845))), 44041 ^ _780461 : [(44042 ^ _780461) ^ [_1639970] : [hBOOL(hAPP(hAPP(c_member(_1639841), _1639970), _1639843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1639837, tc_HOL_Obool)), _1639839), hAPP(_1639845, _1639970))))]]], (44057 ^ _780461) ^ [_1640358, _1640360, _1640362, _1640364, _1640366, _1640368, _1640370] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640358, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640360, tc_fun(_1640358, tc_HOL_Obool)), _1640362), _1640364)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640366, tc_fun(_1640358, tc_HOL_Obool)), _1640368), _1640370)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640360, tc_fun(_1640358, tc_HOL_Obool)), _1640362), hAPP(hAPP(c_COMBB(tc_fun(_1640366, tc_fun(_1640358, tc_HOL_Obool)), tc_fun(_1640358, tc_HOL_Obool), _1640360), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640366, tc_fun(_1640358, tc_HOL_Obool)), _1640368)), hAPP(hAPP(c_COMBC(_1640360, tc_fun(_1640366, tc_fun(_1640358, tc_HOL_Obool)), tc_fun(_1640366, tc_fun(_1640358, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1640358, tc_HOL_Obool), tc_fun(_1640358, tc_HOL_Obool)), tc_fun(tc_fun(_1640366, tc_fun(_1640358, tc_HOL_Obool)), tc_fun(_1640366, tc_fun(_1640358, tc_HOL_Obool))), _1640360), c_COMBB(tc_fun(_1640358, tc_HOL_Obool), tc_fun(_1640358, tc_HOL_Obool), _1640366)), hAPP(hAPP(c_COMBB(tc_fun(_1640358, tc_HOL_Obool), tc_fun(tc_fun(_1640358, tc_HOL_Obool), tc_fun(_1640358, tc_HOL_Obool)), _1640360), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640358, tc_HOL_Obool))), _1640364))), _1640370))))], (44059 ^ _780461) ^ [_1640561, _1640563, _1640565, _1640567, _1640569] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640561, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640563, tc_fun(_1640561, tc_HOL_Obool)), _1640565), _1640567)), _1640569) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640563, tc_fun(_1640561, tc_HOL_Obool)), _1640565), hAPP(hAPP(c_COMBC(_1640563, tc_fun(_1640561, tc_HOL_Obool), tc_fun(_1640561, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1640561, tc_HOL_Obool), tc_fun(tc_fun(_1640561, tc_HOL_Obool), tc_fun(_1640561, tc_HOL_Obool)), _1640563), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640561, tc_HOL_Obool))), _1640567)), _1640569)))], (44061 ^ _780461) ^ [_1640670, _1640672, _1640674, _1640676, _1640678] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640670, tc_HOL_Obool)), _1640672), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640674, tc_fun(_1640670, tc_HOL_Obool)), _1640676), _1640678)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640674, tc_fun(_1640670, tc_HOL_Obool)), _1640676), hAPP(hAPP(c_COMBB(tc_fun(_1640670, tc_HOL_Obool), tc_fun(_1640670, tc_HOL_Obool), _1640674), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640670, tc_HOL_Obool)), _1640672)), _1640678)))], (44063 ^ _780461) ^ [_1640760, _1640762, _1640764, _1640766, _1640768] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640760, tc_HOL_Obool)), _1640762), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640764, tc_fun(_1640760, tc_HOL_Obool)), _1640766), _1640768)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640764, tc_fun(_1640760, tc_HOL_Obool)), _1640766), hAPP(hAPP(c_COMBB(tc_fun(_1640760, tc_HOL_Obool), tc_fun(_1640760, tc_HOL_Obool), _1640764), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640760, tc_HOL_Obool)), _1640762)), _1640768)))], (44065 ^ _780461) ^ [_1640850, _1640852, _1640854, _1640856, _1640858] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640850, tc_fun(_1640852, tc_HOL_Obool)), _1640854), hAPP(hAPP(c_COMBC(_1640850, tc_fun(_1640852, tc_HOL_Obool), tc_fun(_1640852, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1640852, tc_HOL_Obool), tc_fun(tc_fun(_1640852, tc_HOL_Obool), tc_fun(_1640852, tc_HOL_Obool)), _1640850), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640852, tc_HOL_Obool))), _1640856)), _1640858)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640852, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640850, tc_fun(_1640852, tc_HOL_Obool)), _1640854), _1640856)), _1640858))], (44067 ^ _780461) ^ [_1640959, _1640961, _1640963, _1640965, _1640967] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640959, tc_fun(_1640961, tc_HOL_Obool)), _1640963), hAPP(hAPP(c_COMBB(tc_fun(_1640961, tc_HOL_Obool), tc_fun(_1640961, tc_HOL_Obool), _1640959), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640961, tc_HOL_Obool)), _1640965)), _1640967)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640961, tc_HOL_Obool)), _1640965), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1640959, tc_fun(_1640961, tc_HOL_Obool)), _1640963), _1640967)))], (44069 ^ _780461) ^ [_1641049, _1641051, _1641053, _1641055] : [-(hAPP(c_Relation_Oconverse(_1641049, _1641051), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1641049, _1641051), tc_HOL_Obool)), _1641053), _1641055)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1641051, _1641049), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1641049, _1641051), _1641053)), hAPP(c_Relation_Oconverse(_1641049, _1641051), _1641055)))], (44071 ^ _780461) ^ [_1641124, _1641126, _1641128, _1641130, _1641132] : [class_Complete__Lattice_Ocomplete__lattice(_1641124), 44074 ^ _780461 : [(44085 ^ _780461) ^ [] : [44087 ^ _780461 : [(44088 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1641128), 44086 ^ [_1641124, _1641126, _1641128, _1641130, _1641132]), _1641130)))], (44090 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1641124), _1641126), hAPP(_1641132, 44086 ^ [_1641124, _1641126, _1641128, _1641130, _1641132])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1641124), _1641126), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641128, _1641124), _1641130), _1641132))))], (44075 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1641124), _1641126), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641128, _1641124), _1641130), _1641132))), 44078 ^ _780461 : [(44079 ^ _780461) ^ [_1641305] : [hBOOL(hAPP(hAPP(c_member(_1641128), _1641305), _1641130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1641124), _1641126), hAPP(_1641132, _1641305))))]]]]], (44094 ^ _780461) ^ [_1641618, _1641620, _1641622, _1641624, _1641626] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641618, tc_fun(_1641620, tc_HOL_Obool)), _1641622), hAPP(hAPP(c_COMBB(tc_fun(_1641620, tc_HOL_Obool), tc_fun(_1641620, tc_HOL_Obool), _1641618), hAPP(c_Set_Oinsert(_1641620), _1641624)), _1641626)) = hAPP(hAPP(c_Set_Oinsert(_1641620), _1641624), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641618, tc_fun(_1641620, tc_HOL_Obool)), _1641622), _1641626)))], (44096 ^ _780461) ^ [_1641702, _1641704, _1641706, _1641708, _1641710] : [-(hAPP(hAPP(c_Set_Oinsert(_1641702), _1641704), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641706, tc_fun(_1641702, tc_HOL_Obool)), _1641708), _1641710)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641706, tc_fun(_1641702, tc_HOL_Obool)), _1641708), hAPP(hAPP(c_COMBB(tc_fun(_1641702, tc_HOL_Obool), tc_fun(_1641702, tc_HOL_Obool), _1641706), hAPP(c_Set_Oinsert(_1641702), _1641704)), _1641710)))], (44098 ^ _780461) ^ [_1641786, _1641788, _1641790, _1641792, _1641794, _1641796] : [hBOOL(hAPP(hAPP(c_member(_1641786), _1641788), _1641790)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641786, tc_fun(_1641792, tc_HOL_Obool)), _1641790), hAPP(hAPP(c_COMBB(tc_fun(_1641792, tc_HOL_Obool), tc_fun(_1641792, tc_HOL_Obool), _1641786), hAPP(c_Set_Oinsert(_1641792), _1641794)), _1641796)) = hAPP(hAPP(c_Set_Oinsert(_1641792), _1641794), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641786, tc_fun(_1641792, tc_HOL_Obool)), _1641790), _1641796)))], (44104 ^ _780461) ^ [_1641991, _1641993, _1641995, _1641997, _1641999] : [hBOOL(hAPP(hAPP(c_member(_1641991), _1641993), _1641995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1641997, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1641991, tc_fun(_1641997, tc_HOL_Obool)), _1641995), _1641999)), hAPP(_1641999, _1641993))))], (44110 ^ _780461) ^ [_1642138, _1642140, _1642142, _1642144, _1642146, _1642148] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1642138, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1642140, _1642138, _1642142), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642144, tc_fun(_1642140, tc_HOL_Obool)), _1642146), _1642148))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642144, tc_fun(_1642138, tc_HOL_Obool)), _1642146), hAPP(hAPP(c_COMBB(tc_fun(_1642140, tc_HOL_Obool), tc_fun(_1642138, tc_HOL_Obool), _1642144), c_Relation_OImage(_1642140, _1642138, _1642142)), _1642148)))))], (44112 ^ _780461) ^ [_1642232, _1642234, _1642236, _1642238, _1642240, _1642242] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642232, tc_fun(_1642234, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1642236, _1642232, _1642238), _1642240)), _1642242) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642236, tc_fun(_1642234, tc_HOL_Obool)), _1642240), hAPP(hAPP(c_COMBB(_1642232, tc_fun(_1642234, tc_HOL_Obool), _1642236), _1642242), _1642238)))], (44114 ^ _780461) ^ [_1642309, _1642311, _1642313, _1642315, _1642317, _1642319] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642309, tc_fun(_1642311, tc_HOL_Obool)), _1642313), hAPP(hAPP(c_COMBB(_1642315, tc_fun(_1642311, tc_HOL_Obool), _1642309), _1642317), _1642319)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642315, tc_fun(_1642311, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1642309, _1642315, _1642319), _1642313)), _1642317))], (44116 ^ _780461) ^ [_1642386, _1642388, _1642390, _1642392, _1642394, _1642396] : [-(hAPP(c_Set_Ovimage(_1642386, _1642388, _1642390), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642392, tc_fun(_1642388, tc_HOL_Obool)), _1642394), _1642396)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642392, tc_fun(_1642386, tc_HOL_Obool)), _1642394), hAPP(hAPP(c_COMBB(tc_fun(_1642388, tc_HOL_Obool), tc_fun(_1642386, tc_HOL_Obool), _1642392), c_Set_Ovimage(_1642386, _1642388, _1642390)), _1642396)))], (44128 ^ _780461) ^ [_1642737, _1642739, _1642741, _1642743, _1642745] : [44130 ^ _780461 : [(44131 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1642741), 44129 ^ [_1642737, _1642739, _1642741, _1642743, _1642745]), _1642743)))], (44133 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642737), _1642739), hAPP(_1642745, 44129 ^ [_1642737, _1642739, _1642741, _1642743, _1642745])))]], -(hBOOL(hAPP(hAPP(c_member(_1642737), _1642739), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642741, tc_fun(_1642737, tc_HOL_Obool)), _1642743), _1642745))))], (44118 ^ _780461) ^ [_1642494, _1642496, _1642498, _1642500, _1642502] : [hBOOL(hAPP(hAPP(c_member(_1642494), _1642496), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642498, tc_fun(_1642494, tc_HOL_Obool)), _1642500), _1642502))), 44121 ^ _780461 : [(44122 ^ _780461) ^ [_1642618] : [hBOOL(hAPP(hAPP(c_member(_1642498), _1642618), _1642500)), -(hBOOL(hAPP(hAPP(c_member(_1642494), _1642496), hAPP(_1642502, _1642618))))]]], (44137 ^ _780461) ^ [_1642985, _1642987, _1642989, _1642991, _1642993] : [hBOOL(hAPP(hAPP(c_member(_1642985), _1642987), _1642989)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1642991, tc_HOL_Obool)), hAPP(_1642993, _1642987)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642985, tc_fun(_1642991, tc_HOL_Obool)), _1642989), _1642993)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1642985, tc_fun(_1642991, tc_HOL_Obool)), _1642989), _1642993))], (44143 ^ _780461) ^ [_1643158, _1643160, _1643162, _1643164, _1643166] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643158, _1643160)), hAPP(hAPP(c_Product__Type_OPair(_1643158, _1643160), _1643162), _1643164)), hAPP(c_Relation_Oconverse(_1643160, _1643158), _1643166))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643160, _1643158)), hAPP(hAPP(c_Product__Type_OPair(_1643160, _1643158), _1643164), _1643162)), _1643166)))], (44149 ^ _780461) ^ [_1643329, _1643331, _1643333, _1643335, _1643337] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643329, _1643331)), hAPP(hAPP(c_Product__Type_OPair(_1643329, _1643331), _1643333), _1643335)), _1643337)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643331, _1643329)), hAPP(hAPP(c_Product__Type_OPair(_1643331, _1643329), _1643335), _1643333)), hAPP(c_Relation_Oconverse(_1643329, _1643331), _1643337))))], (44155 ^ _780461) ^ [_1643524, _1643526, _1643528, _1643530, _1643532] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643524, _1643526)), hAPP(hAPP(c_Product__Type_OPair(_1643524, _1643526), _1643528), _1643530)), hAPP(c_Relation_Oconverse(_1643526, _1643524), _1643532))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643526, _1643524)), hAPP(hAPP(c_Product__Type_OPair(_1643526, _1643524), _1643530), _1643528)), _1643532)))], (44161 ^ _780461) ^ [_1643691, _1643693, _1643695, _1643697, _1643699] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1643693, _1643691)), hAPP(hAPP(c_Product__Type_OPair(_1643693, _1643691), _1643697), _1643695)), _1643699)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643691, _1643693)), hAPP(hAPP(c_Product__Type_OPair(_1643691, _1643693), _1643695), _1643697)), hAPP(c_Relation_Oconverse(_1643693, _1643691), _1643699))))], (44167 ^ _780461) ^ [_1643885, _1643887, _1643889, _1643891] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643885, tc_fun(_1643887, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1643885, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1643887, tc_HOL_Obool), tc_fun(_1643887, tc_HOL_Obool), _1643885), hAPP(c_COMBC(_1643887, tc_fun(_1643887, tc_HOL_Obool), tc_HOL_Obool), c_member(_1643887))), _1643889)), _1643891)), -(hBOOL(hAPP(hAPP(c_member(_1643887), _1643891), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1643885, tc_fun(_1643887, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1643885, tc_HOL_Obool))), _1643889))))], (44173 ^ _780461) ^ [_1644104, _1644106, _1644108, _1644110] : [hBOOL(hAPP(hAPP(c_member(_1644106), _1644110), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644104, tc_fun(_1644106, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1644104, tc_HOL_Obool))), _1644108))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644104, tc_fun(_1644106, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1644104, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1644106, tc_HOL_Obool), tc_fun(_1644106, tc_HOL_Obool), _1644104), hAPP(c_COMBC(_1644106, tc_fun(_1644106, tc_HOL_Obool), tc_HOL_Obool), c_member(_1644106))), _1644108)), _1644110)))], (44179 ^ _780461) ^ [_1644356, _1644358, _1644360, _1644362, _1644364, _1644366] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644356, tc_fun(_1644358, tc_fun(_1644360, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1644356, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1644358, _1644360), tc_HOL_Obool), tc_fun(_1644358, tc_fun(_1644360, tc_HOL_Obool)), _1644356), hAPP(c_COMBC(_1644358, tc_fun(tc_prod(_1644358, _1644360), tc_HOL_Obool), tc_fun(_1644360, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1644360, tc_fun(tc_fun(tc_prod(_1644358, _1644360), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1644358, _1644360), tc_HOL_Obool), tc_fun(_1644360, tc_HOL_Obool)), _1644358), c_COMBC(_1644360, tc_fun(tc_prod(_1644358, _1644360), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1644360, tc_prod(_1644358, _1644360)), tc_fun(_1644360, tc_fun(tc_fun(tc_prod(_1644358, _1644360), tc_HOL_Obool), tc_HOL_Obool)), _1644358), hAPP(c_COMBB(tc_prod(_1644358, _1644360), tc_fun(tc_fun(tc_prod(_1644358, _1644360), tc_HOL_Obool), tc_HOL_Obool), _1644360), c_member(tc_prod(_1644358, _1644360)))), c_Product__Type_OPair(_1644358, _1644360))))), _1644362)), _1644364), _1644366)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1644358, _1644360)), hAPP(hAPP(c_Product__Type_OPair(_1644358, _1644360), _1644364), _1644366)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644356, tc_fun(tc_prod(_1644358, _1644360), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1644356, tc_HOL_Obool))), _1644362))))], (44185 ^ _780461) ^ [_1644839, _1644841, _1644843, _1644845, _1644847, _1644849] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644841, _1644843)), hAPP(hAPP(c_Product__Type_OPair(_1644841, _1644843), _1644847), _1644849)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644839, tc_fun(tc_prod(_1644841, _1644843), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1644839, tc_HOL_Obool))), _1644845))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1644839, tc_fun(_1644841, tc_fun(_1644843, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1644839, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1644841, _1644843), tc_HOL_Obool), tc_fun(_1644841, tc_fun(_1644843, tc_HOL_Obool)), _1644839), hAPP(c_COMBC(_1644841, tc_fun(tc_prod(_1644841, _1644843), tc_HOL_Obool), tc_fun(_1644843, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1644843, tc_fun(tc_fun(tc_prod(_1644841, _1644843), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1644841, _1644843), tc_HOL_Obool), tc_fun(_1644843, tc_HOL_Obool)), _1644841), c_COMBC(_1644843, tc_fun(tc_prod(_1644841, _1644843), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1644843, tc_prod(_1644841, _1644843)), tc_fun(_1644843, tc_fun(tc_fun(tc_prod(_1644841, _1644843), tc_HOL_Obool), tc_HOL_Obool)), _1644841), hAPP(c_COMBB(tc_prod(_1644841, _1644843), tc_fun(tc_fun(tc_prod(_1644841, _1644843), tc_HOL_Obool), tc_HOL_Obool), _1644843), c_member(tc_prod(_1644841, _1644843)))), c_Product__Type_OPair(_1644841, _1644843))))), _1644845)), _1644847), _1644849)))], (44201 ^ _780461) ^ [_1645578, _1645580, _1645582, _1645584] : [44203 ^ _780461 : [(44204 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1645580), 44202 ^ [_1645578, _1645580, _1645582, _1645584]), _1645582)))], (44206 ^ _780461) ^ [] : [hAPP(_1645584, 44202 ^ [_1645578, _1645580, _1645582, _1645584]) = c_Orderings_Otop__class_Otop(tc_fun(_1645578, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1645578, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645580, tc_fun(_1645578, tc_HOL_Obool)), _1645582), _1645584))], (44191 ^ _780461) ^ [_1645349, _1645351, _1645353, _1645355] : [c_Orderings_Otop__class_Otop(tc_fun(_1645349, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645351, tc_fun(_1645349, tc_HOL_Obool)), _1645353), _1645355), 44194 ^ _780461 : [(44195 ^ _780461) ^ [_1645465] : [hBOOL(hAPP(hAPP(c_member(_1645351), _1645465), _1645353)), -(hAPP(_1645355, _1645465) = c_Orderings_Otop__class_Otop(tc_fun(_1645349, tc_HOL_Obool)))]]], (44220 ^ _780461) ^ [_1646058, _1646060, _1646062, _1646064] : [44222 ^ _780461 : [(44223 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1646058), 44221 ^ [_1646058, _1646060, _1646062, _1646064]), _1646062)))], (44225 ^ _780461) ^ [] : [hAPP(_1646064, 44221 ^ [_1646058, _1646060, _1646062, _1646064]) = c_Orderings_Otop__class_Otop(tc_fun(_1646060, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646058, tc_fun(_1646060, tc_HOL_Obool)), _1646062), _1646064) = c_Orderings_Otop__class_Otop(tc_fun(_1646060, tc_HOL_Obool)))], (44210 ^ _780461) ^ [_1645829, _1645831, _1645833, _1645835] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1645829, tc_fun(_1645831, tc_HOL_Obool)), _1645833), _1645835) = c_Orderings_Otop__class_Otop(tc_fun(_1645831, tc_HOL_Obool)), 44213 ^ _780461 : [(44214 ^ _780461) ^ [_1645945] : [hBOOL(hAPP(hAPP(c_member(_1645829), _1645945), _1645833)), -(hAPP(_1645835, _1645945) = c_Orderings_Otop__class_Otop(tc_fun(_1645831, tc_HOL_Obool)))]]], (44229 ^ _780461) ^ [_1646306, _1646308, _1646310] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1646306, _1646308)), hAPP(c_Relation_Oconverse(_1646308, _1646306), _1646310))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1646308, _1646306)), _1646310)))], (44235 ^ _780461) ^ [_1646421, _1646423, _1646425] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1646423, _1646421)), _1646425)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1646421, _1646423)), hAPP(c_Relation_Oconverse(_1646423, _1646421), _1646425))))], (44241 ^ _780461) ^ [_1646542, _1646544, _1646546, _1646548, _1646550] : [class_Complete__Lattice_Ocomplete__lattice(_1646542), class_Orderings_Olinorder(_1646542), 44248 ^ _780461 : [(44249 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1646542), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646544, _1646542), _1646546), _1646548)), _1646550)), 44253 ^ _780461 : [(44254 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1646544), 44252 ^ [_1646542, _1646544, _1646546, _1646548, _1646550]), _1646546)))], (44256 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1646542), hAPP(_1646548, 44252 ^ [_1646542, _1646544, _1646546, _1646548, _1646550])), _1646550)))]]], (44258 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1646542), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1646544, _1646542), _1646546), _1646548)), _1646550))), 44259 ^ _780461 : [(44260 ^ _780461) ^ [_1646890] : [hBOOL(hAPP(hAPP(c_member(_1646544), _1646890), _1646546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1646542), hAPP(_1646548, _1646890)), _1646550))]]]]], (44268 ^ _780461) ^ [_1647060, _1647062, _1647064, _1647066] : [-(hAPP(c_Relation_Oconverse(_1647060, _1647062), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1647060, _1647062), tc_HOL_Obool)), _1647064), _1647066)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1647062, _1647060), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1647060, _1647062), _1647064)), hAPP(c_Relation_Oconverse(_1647060, _1647062), _1647066)))], (44270 ^ _780461) ^ [_1647135, _1647137, _1647139, _1647141, _1647143] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647135, tc_fun(_1647137, tc_HOL_Obool)), _1647139), hAPP(hAPP(c_COMBS(_1647135, tc_fun(_1647137, tc_HOL_Obool), tc_fun(_1647137, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1647137, tc_HOL_Obool), tc_fun(tc_fun(_1647137, tc_HOL_Obool), tc_fun(_1647137, tc_HOL_Obool)), _1647135), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1647137, tc_HOL_Obool))), _1647141)), _1647143)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1647137, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647135, tc_fun(_1647137, tc_HOL_Obool)), _1647139), _1647141)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647135, tc_fun(_1647137, tc_HOL_Obool)), _1647139), _1647143)))], (44272 ^ _780461) ^ [_1647256, _1647258, _1647260, _1647262, _1647264, _1647266] : [class_Complete__Lattice_Ocomplete__lattice(_1647256), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647258, _1647256), _1647260), hAPP(hAPP(c_COMBB(tc_fun(_1647262, _1647256), _1647256, _1647258), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647262, _1647256), _1647264)), _1647266)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647262, _1647256), _1647264), hAPP(hAPP(c_COMBB(tc_fun(_1647258, _1647256), _1647256, _1647262), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647258, _1647256), _1647260)), hAPP(c_COMBC(_1647258, _1647262, _1647256), _1647266))))], (44278 ^ _780461) ^ [_1647465, _1647467, _1647469, _1647471, _1647473, _1647475] : [class_Complete__Lattice_Ocomplete__lattice(_1647465), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647467, tc_fun(_1647469, _1647465)), _1647471), _1647473), _1647475) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647467, _1647465), _1647471), hAPP(hAPP(c_COMBC(_1647467, _1647469, _1647465), _1647473), _1647475)))], (44284 ^ _780461) ^ [_1647616, _1647618, _1647620, _1647622] : [-(hAPP(c_Relation_Oconverse(_1647616, _1647616), hAPP(hAPP(c_Relation_Oinv__image(_1647618, _1647616), _1647620), _1647622)) = hAPP(hAPP(c_Relation_Oinv__image(_1647618, _1647616), hAPP(c_Relation_Oconverse(_1647618, _1647618), _1647620)), _1647622))], (44286 ^ _780461) ^ [_1647675, _1647677] : [-(hAPP(c_Relation_OField(_1647675), hAPP(c_Relation_Oconverse(_1647675, _1647675), _1647677)) = hAPP(c_Relation_OField(_1647675), _1647677))], (44288 ^ _780461) ^ [_1647716, _1647718, _1647720, _1647722, _1647724] : [-(hAPP(c_Relation_Oconverse(_1647716, _1647718), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647720, tc_fun(tc_prod(_1647716, _1647718), tc_HOL_Obool)), _1647722), _1647724)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647720, tc_fun(tc_prod(_1647718, _1647716), tc_HOL_Obool)), _1647722), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1647716, _1647718), tc_HOL_Obool), tc_fun(tc_prod(_1647718, _1647716), tc_HOL_Obool), _1647720), c_Relation_Oconverse(_1647716, _1647718)), _1647724)))], (44290 ^ _780461) ^ [_1647808, _1647810, _1647812] : [-(hAPP(c_Relation_Oconverse(_1647808, _1647810), hAPP(c_Relation_Oconverse(_1647810, _1647808), _1647812)) = _1647812)], (44292 ^ _780461) ^ [_1647847] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647847, tc_HOL_Obool) = c_Set_OBall(_1647847))], (44294 ^ _780461) ^ [_1647893, _1647895, _1647897] : [c_Relation_Orefl__on(_1647893, _1647895, hAPP(c_Relation_Oconverse(_1647893, _1647893), _1647897)), -(c_Relation_Orefl__on(_1647893, _1647895, _1647897))], (44300 ^ _780461) ^ [_1647984, _1647986, _1647988] : [c_Relation_Orefl__on(_1647984, _1647986, _1647988), -(c_Relation_Orefl__on(_1647984, _1647986, hAPP(c_Relation_Oconverse(_1647984, _1647984), _1647988)))], (44306 ^ _780461) ^ [_1648081, _1648083] : [-(hAPP(c_Relation_Oconverse(_1648081, _1648081), c_Relation_OId__on(_1648081, _1648083)) = c_Relation_OId__on(_1648081, _1648083))], (44308 ^ _780461) ^ [_1648118, _1648120, _1648122, _1648124] : [-(hAPP(c_Set_OPow(_1648118), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648120, tc_fun(_1648118, tc_HOL_Obool)), _1648122), _1648124)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648120, tc_fun(tc_fun(_1648118, tc_HOL_Obool), tc_HOL_Obool)), _1648122), hAPP(hAPP(c_COMBB(tc_fun(_1648118, tc_HOL_Obool), tc_fun(tc_fun(_1648118, tc_HOL_Obool), tc_HOL_Obool), _1648120), c_Set_OPow(_1648118)), _1648124)))], (44310 ^ _780461) ^ [_1648200, _1648202, _1648204, _1648206] : [-(hAPP(c_Set_OCollect(_1648200), hAPP(hAPP(c_COMBB(tc_fun(_1648202, tc_HOL_Obool), tc_HOL_Obool, _1648200), c_HOL_OAll(_1648202)), hAPP(hAPP(c_COMBB(tc_fun(_1648202, tc_HOL_Obool), tc_fun(_1648202, tc_HOL_Obool), _1648200), hAPP(c_COMBS(_1648202, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1648202), c_fimplies), hAPP(hAPP(c_COMBC(_1648202, tc_fun(_1648202, tc_HOL_Obool), tc_HOL_Obool), c_member(_1648202)), _1648204)))), _1648206))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648202, tc_fun(_1648200, tc_HOL_Obool)), _1648204), hAPP(hAPP(c_COMBB(tc_fun(_1648200, tc_HOL_Obool), tc_fun(_1648200, tc_HOL_Obool), _1648202), c_Set_OCollect(_1648200)), hAPP(c_COMBC(_1648200, _1648202, tc_HOL_Obool), _1648206))))], (44312 ^ _780461) ^ [_1648334, _1648336, _1648338, _1648340, _1648342] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648334, tc_HOL_Obool)), _1648336), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648338, tc_fun(_1648334, tc_HOL_Obool)), _1648340), _1648342)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648338, tc_fun(_1648334, tc_HOL_Obool)), _1648340), hAPP(hAPP(c_COMBB(tc_fun(_1648334, tc_HOL_Obool), tc_fun(_1648334, tc_HOL_Obool), _1648338), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648334, tc_HOL_Obool)), _1648336)), _1648342)))], (44314 ^ _780461) ^ [_1648424, _1648426, _1648428, _1648430, _1648432] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648424, tc_fun(_1648426, tc_HOL_Obool)), _1648428), hAPP(hAPP(c_COMBB(tc_fun(_1648426, tc_HOL_Obool), tc_fun(_1648426, tc_HOL_Obool), _1648424), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648426, tc_HOL_Obool)), _1648430)), _1648432)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1648426, tc_HOL_Obool)), _1648430), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648424, tc_fun(_1648426, tc_HOL_Obool)), _1648428), _1648432)))], (44316 ^ _780461) ^ [_1648514, _1648516, _1648518, _1648520, _1648522] : [-(hAPP(c_Relation_Oconverse(_1648514, _1648516), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648518, tc_fun(tc_prod(_1648514, _1648516), tc_HOL_Obool)), _1648520), _1648522)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648518, tc_fun(tc_prod(_1648516, _1648514), tc_HOL_Obool)), _1648520), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1648514, _1648516), tc_HOL_Obool), tc_fun(tc_prod(_1648516, _1648514), tc_HOL_Obool), _1648518), c_Relation_Oconverse(_1648514, _1648516)), _1648522)))], (44318 ^ _780461) ^ [_1648606, _1648608, _1648610, _1648612, _1648614, _1648616] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648606, tc_fun(_1648608, tc_HOL_Obool)), _1648610), hAPP(hAPP(c_COMBC(_1648606, tc_fun(_1648612, tc_fun(_1648608, tc_HOL_Obool)), tc_fun(_1648608, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1648612, tc_HOL_Obool), tc_fun(tc_fun(_1648612, tc_fun(_1648608, tc_HOL_Obool)), tc_fun(_1648608, tc_HOL_Obool)), _1648606), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648612, tc_fun(_1648608, tc_HOL_Obool))), _1648614)), _1648616)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648612, tc_fun(_1648608, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648606, tc_fun(_1648612, tc_HOL_Obool)), _1648610), _1648614)), _1648616))], (44320 ^ _780461) ^ [_1648725, _1648727, _1648729, _1648731, _1648733, _1648735] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648725, tc_fun(_1648727, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648729, tc_fun(_1648725, tc_HOL_Obool)), _1648731), _1648733)), _1648735) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648729, tc_fun(_1648727, tc_HOL_Obool)), _1648731), hAPP(hAPP(c_COMBC(_1648729, tc_fun(_1648725, tc_fun(_1648727, tc_HOL_Obool)), tc_fun(_1648727, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1648725, tc_HOL_Obool), tc_fun(tc_fun(_1648725, tc_fun(_1648727, tc_HOL_Obool)), tc_fun(_1648727, tc_HOL_Obool)), _1648729), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648725, tc_fun(_1648727, tc_HOL_Obool))), _1648733)), _1648735)))], (44322 ^ _780461) ^ [_1648844, _1648846, _1648848, _1648850] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1648844, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648846, tc_fun(_1648844, tc_HOL_Obool)), _1648848), _1648850)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648846, tc_fun(_1648844, tc_HOL_Obool)), _1648848), hAPP(hAPP(c_COMBB(tc_fun(_1648844, tc_HOL_Obool), tc_fun(_1648844, tc_HOL_Obool), _1648846), c_Groups_Ouminus__class_Ouminus(tc_fun(_1648844, tc_HOL_Obool))), _1648850)))], (44324 ^ _780461) ^ [_1648926, _1648928, _1648930, _1648932] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1648926, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1648928, tc_fun(_1648926, tc_HOL_Obool)), _1648930), _1648932)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1648928, tc_fun(_1648926, tc_HOL_Obool)), _1648930), hAPP(hAPP(c_COMBB(tc_fun(_1648926, tc_HOL_Obool), tc_fun(_1648926, tc_HOL_Obool), _1648928), c_Groups_Ouminus__class_Ouminus(tc_fun(_1648926, tc_HOL_Obool))), _1648932)))], (44326 ^ _780461) ^ [_1649008, _1649010, _1649012] : [c_Equiv__Relations_Oequiv(_1649008, _1649010, _1649012), -(hAPP(hAPP(c_Relation_Orel__comp(_1649008, _1649008, _1649008), hAPP(c_Relation_Oconverse(_1649008, _1649008), _1649012)), _1649012) = _1649012)], (44332 ^ _780461) ^ [_1649121, _1649123, _1649125] : [-(hAPP(c_Relation_ORange(_1649121, _1649123), hAPP(c_Relation_Oconverse(_1649123, _1649121), _1649125)) = hAPP(c_Relation_ODomain(_1649123, _1649121), _1649125))], (44334 ^ _780461) ^ [_1649166, _1649168, _1649170] : [-(hAPP(c_Relation_ODomain(_1649166, _1649168), hAPP(c_Relation_Oconverse(_1649168, _1649166), _1649170)) = hAPP(c_Relation_ORange(_1649168, _1649166), _1649170))], (44336 ^ _780461) ^ [_1649211, _1649213, _1649215] : [-(hAPP(c_Relation_ORange(_1649211, _1649213), _1649215) = hAPP(c_Relation_ODomain(_1649213, _1649211), hAPP(c_Relation_Oconverse(_1649211, _1649213), _1649215)))], (44338 ^ _780461) ^ [_1649256, _1649258, _1649260, _1649262, _1649264] : [class_Complete__Lattice_Ocomplete__lattice(_1649256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1649258, tc_HOL_Obool)), _1649260), _1649262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1649256), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649258, _1649256), _1649262), _1649264)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649258, _1649256), _1649260), _1649264))))], (44348 ^ _780461) ^ [_1649465, _1649467, _1649469, _1649471] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649465, tc_fun(_1649467, tc_HOL_Obool)), _1649469), _1649471) = hAPP(c_Set_OCollect(_1649467), hAPP(hAPP(c_COMBB(tc_fun(_1649465, tc_HOL_Obool), tc_HOL_Obool, _1649467), c_HOL_OAll(_1649465)), hAPP(hAPP(c_COMBB(tc_fun(_1649465, tc_HOL_Obool), tc_fun(_1649465, tc_HOL_Obool), _1649467), hAPP(c_COMBS(_1649465, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1649465), c_fimplies), hAPP(hAPP(c_COMBC(_1649465, tc_fun(_1649465, tc_HOL_Obool), tc_HOL_Obool), c_member(_1649465)), _1649469)))), hAPP(hAPP(c_COMBC(_1649467, tc_fun(_1649465, tc_fun(_1649467, tc_HOL_Obool)), tc_fun(_1649465, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1649467, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1649465, tc_fun(_1649467, tc_HOL_Obool)), tc_fun(_1649465, tc_HOL_Obool)), _1649467), c_COMBB(tc_fun(_1649467, tc_HOL_Obool), tc_HOL_Obool, _1649465)), c_member(_1649467))), _1649471)))))], (44350 ^ _780461) ^ [_1649648, _1649650, _1649652, _1649654, _1649656] : [_1649648 = c_Orderings_Obot__class_Obot(tc_fun(_1649650, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649650, tc_fun(_1649652, tc_HOL_Obool)), _1649648), hAPP(hAPP(c_COMBB(tc_fun(_1649652, tc_HOL_Obool), tc_fun(_1649652, tc_HOL_Obool), _1649650), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1649652, tc_HOL_Obool)), _1649654)), _1649656)) = c_Orderings_Otop__class_Otop(tc_fun(_1649652, tc_HOL_Obool)))], (44356 ^ _780461) ^ [_1649817, _1649819, _1649821, _1649823, _1649825] : [-(_1649817 = c_Orderings_Obot__class_Obot(tc_fun(_1649819, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649819, tc_fun(_1649821, tc_HOL_Obool)), _1649817), hAPP(hAPP(c_COMBB(tc_fun(_1649821, tc_HOL_Obool), tc_fun(_1649821, tc_HOL_Obool), _1649819), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1649821, tc_HOL_Obool)), _1649823)), _1649825)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1649821, tc_HOL_Obool)), _1649823), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649819, tc_fun(_1649821, tc_HOL_Obool)), _1649817), _1649825)))], (44362 ^ _780461) ^ [_1649943, _1649945, _1649947, _1649949, _1649951] : [_1649943 = c_Orderings_Obot__class_Obot(tc_fun(_1649945, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1649945, tc_fun(_1649947, tc_HOL_Obool)), _1649943), hAPP(hAPP(c_COMBC(_1649945, tc_fun(_1649947, tc_HOL_Obool), tc_fun(_1649947, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649947, tc_HOL_Obool), tc_fun(tc_fun(_1649947, tc_HOL_Obool), tc_fun(_1649947, tc_HOL_Obool)), _1649945), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1649947, tc_HOL_Obool))), _1649949)), _1649951)) = c_Orderings_Otop__class_Otop(tc_fun(_1649947, tc_HOL_Obool)))], (44368 ^ _780461) ^ [_1650150, _1650152, _1650154, _1650156, _1650158] : [-(_1650150 = c_Orderings_Obot__class_Obot(tc_fun(_1650152, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650152, tc_fun(_1650154, tc_HOL_Obool)), _1650150), hAPP(hAPP(c_COMBC(_1650152, tc_fun(_1650154, tc_HOL_Obool), tc_fun(_1650154, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650154, tc_HOL_Obool), tc_fun(tc_fun(_1650154, tc_HOL_Obool), tc_fun(_1650154, tc_HOL_Obool)), _1650152), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1650154, tc_HOL_Obool))), _1650156)), _1650158)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1650154, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650152, tc_fun(_1650154, tc_HOL_Obool)), _1650150), _1650156)), _1650158))], (44374 ^ _780461) ^ [_1650295, _1650297, _1650299, _1650301, _1650303] : [_1650295 = c_Orderings_Obot__class_Obot(tc_fun(_1650297, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650297, tc_fun(_1650299, tc_HOL_Obool)), _1650295), hAPP(hAPP(c_COMBC(_1650297, tc_fun(_1650299, tc_HOL_Obool), tc_fun(_1650299, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650299, tc_HOL_Obool), tc_fun(tc_fun(_1650299, tc_HOL_Obool), tc_fun(_1650299, tc_HOL_Obool)), _1650297), c_Groups_Ominus__class_Ominus(tc_fun(_1650299, tc_HOL_Obool))), _1650301)), _1650303)) = c_Orderings_Otop__class_Otop(tc_fun(_1650299, tc_HOL_Obool)))], (44380 ^ _780461) ^ [_1650502, _1650504, _1650506, _1650508, _1650510] : [-(_1650502 = c_Orderings_Obot__class_Obot(tc_fun(_1650504, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650504, tc_fun(_1650506, tc_HOL_Obool)), _1650502), hAPP(hAPP(c_COMBC(_1650504, tc_fun(_1650506, tc_HOL_Obool), tc_fun(_1650506, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650506, tc_HOL_Obool), tc_fun(tc_fun(_1650506, tc_HOL_Obool), tc_fun(_1650506, tc_HOL_Obool)), _1650504), c_Groups_Ominus__class_Ominus(tc_fun(_1650506, tc_HOL_Obool))), _1650508)), _1650510)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650506, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650504, tc_fun(_1650506, tc_HOL_Obool)), _1650502), _1650508)), _1650510))], (44386 ^ _780461) ^ [_1650647, _1650649, _1650651, _1650653, _1650655] : [_1650647 = c_Orderings_Obot__class_Obot(tc_fun(_1650649, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650651, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650649, tc_fun(_1650651, tc_HOL_Obool)), _1650647), _1650653)), _1650655) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650651, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1650651, tc_HOL_Obool))), _1650655))], (44392 ^ _780461) ^ [_1650812, _1650814, _1650816, _1650818, _1650820] : [-(_1650812 = c_Orderings_Obot__class_Obot(tc_fun(_1650814, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650816, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650814, tc_fun(_1650816, tc_HOL_Obool)), _1650812), _1650818)), _1650820) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1650814, tc_fun(_1650816, tc_HOL_Obool)), _1650812), hAPP(hAPP(c_COMBC(_1650814, tc_fun(_1650816, tc_HOL_Obool), tc_fun(_1650816, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650816, tc_HOL_Obool), tc_fun(tc_fun(_1650816, tc_HOL_Obool), tc_fun(_1650816, tc_HOL_Obool)), _1650814), c_Groups_Ominus__class_Ominus(tc_fun(_1650816, tc_HOL_Obool))), _1650818)), _1650820)))], (44398 ^ _780461) ^ [_1650957, _1650959, _1650961, _1650963, _1650965] : [_1650957 = c_Orderings_Obot__class_Obot(tc_fun(_1650959, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1650961, tc_HOL_Obool)), _1650963), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1650959, tc_fun(_1650961, tc_HOL_Obool)), _1650957), _1650965)) = _1650963)], (44404 ^ _780461) ^ [_1651090, _1651092, _1651094, _1651096, _1651098] : [-(_1651090 = c_Orderings_Obot__class_Obot(tc_fun(_1651092, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1651094, tc_HOL_Obool)), _1651096), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1651092, tc_fun(_1651094, tc_HOL_Obool)), _1651090), _1651098)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1651092, tc_fun(_1651094, tc_HOL_Obool)), _1651090), hAPP(hAPP(c_COMBB(tc_fun(_1651094, tc_HOL_Obool), tc_fun(_1651094, tc_HOL_Obool), _1651092), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1651094, tc_HOL_Obool)), _1651096)), _1651098)))], (44410 ^ _780461) ^ [_1651198, _1651200, _1651202, _1651204] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651198, _1651198)), hAPP(hAPP(c_Product__Type_OPair(_1651198, _1651198), _1651200), _1651202)), c_Transitive__Closure_Ortrancl(_1651198, hAPP(c_Relation_Oconverse(_1651198, _1651198), _1651204)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651198, _1651198)), hAPP(hAPP(c_Product__Type_OPair(_1651198, _1651198), _1651202), _1651200)), c_Transitive__Closure_Ortrancl(_1651198, _1651204))))], (44416 ^ _780461) ^ [_1651379, _1651381, _1651383, _1651385] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651379, _1651379)), hAPP(hAPP(c_Product__Type_OPair(_1651379, _1651379), _1651381), _1651383)), c_Transitive__Closure_Ortrancl(_1651379, _1651385))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651379, _1651379)), hAPP(hAPP(c_Product__Type_OPair(_1651379, _1651379), _1651383), _1651381)), c_Transitive__Closure_Ortrancl(_1651379, hAPP(c_Relation_Oconverse(_1651379, _1651379), _1651385)))))], (44422 ^ _780461) ^ [_1651560, _1651562, _1651564, _1651566] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651560, _1651560)), hAPP(hAPP(c_Product__Type_OPair(_1651560, _1651560), _1651562), _1651564)), c_Transitive__Closure_Otrancl(_1651560, hAPP(c_Relation_Oconverse(_1651560, _1651560), _1651566)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651560, _1651560)), hAPP(hAPP(c_Product__Type_OPair(_1651560, _1651560), _1651562), _1651564)), hAPP(c_Relation_Oconverse(_1651560, _1651560), c_Transitive__Closure_Otrancl(_1651560, _1651566)))))], (44428 ^ _780461) ^ [_1651753, _1651755, _1651757, _1651759] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651753, _1651753)), hAPP(hAPP(c_Product__Type_OPair(_1651753, _1651753), _1651755), _1651757)), hAPP(c_Relation_Oconverse(_1651753, _1651753), c_Transitive__Closure_Otrancl(_1651753, _1651759)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1651753, _1651753)), hAPP(hAPP(c_Product__Type_OPair(_1651753, _1651753), _1651755), _1651757)), c_Transitive__Closure_Otrancl(_1651753, hAPP(c_Relation_Oconverse(_1651753, _1651753), _1651759)))))], (44434 ^ _780461) ^ [_1651970, _1651972, _1651974, _1651976, _1651978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1651970, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1651972, _1651970, _1651974), _1651976)), _1651978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1651972, tc_HOL_Obool)), _1651976), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1651972, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1651970, _1651972, hAPP(c_Relation_Oconverse(_1651972, _1651970), _1651974)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1651970, tc_HOL_Obool)), _1651978))))))], (44440 ^ _780461) ^ [_1652161, _1652163, _1652165, _1652167, _1652169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1652163, tc_HOL_Obool)), _1652167), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1652163, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1652161, _1652163, hAPP(c_Relation_Oconverse(_1652163, _1652161), _1652165)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1652161, tc_HOL_Obool)), _1652169))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1652161, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1652163, _1652161, _1652165), _1652167)), _1652169)))], (44446 ^ _780461) ^ [_1652358, _1652360, _1652362, _1652364, _1652366] : [class_Complete__Lattice_Ocomplete__lattice(_1652358), hBOOL(hAPP(hAPP(c_member(_1652360), _1652362), _1652364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1652358), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1652360, _1652358), _1652364), _1652366)), hAPP(_1652366, _1652362))))], (44456 ^ _780461) ^ [_1652549, _1652551, _1652553] : [c_Relation_Orefl__on(_1652549, _1652551, _1652553), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1652549, _1652549), tc_HOL_Obool)), _1652553), hAPP(hAPP(c_Relation_Orel__comp(_1652549, _1652549, _1652549), hAPP(c_Relation_Oconverse(_1652549, _1652549), _1652553)), _1652553))))], (44462 ^ _780461) ^ [_1652688, _1652690, _1652692] : [hAPP(hAPP(c_Relation_Orel__comp(_1652688, _1652688, _1652688), hAPP(c_Relation_Oconverse(_1652688, _1652688), _1652690)), _1652690) = _1652690, hAPP(c_Relation_ODomain(_1652688, _1652688), _1652690) = _1652692, -(c_Equiv__Relations_Oequiv(_1652688, _1652692, _1652690))], (44472 ^ _780461) ^ [_1652867, _1652869] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1652867, _1652867)), _1652869)), c_Wellfounded_Oacyclic(_1652867, _1652869), -(c_Wellfounded_Owf(_1652867, hAPP(c_Relation_Oconverse(_1652867, _1652867), _1652869)))], (44482 ^ _780461) ^ [] : [-(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)))], (44484 ^ _780461) ^ [_1653058, _1653060, _1653062, _1653064, _1653066] : [_1653058 = c_Orderings_Obot__class_Obot(tc_fun(_1653060, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653060, tc_fun(_1653062, tc_HOL_Obool)), _1653058), hAPP(hAPP(c_COMBB(tc_fun(_1653062, tc_HOL_Obool), tc_fun(_1653062, tc_HOL_Obool), _1653060), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1653062, tc_HOL_Obool)), _1653064)), _1653066)) = c_Orderings_Otop__class_Otop(tc_fun(_1653062, tc_HOL_Obool)))], (44490 ^ _780461) ^ [_1653227, _1653229, _1653231, _1653233, _1653235] : [-(_1653227 = c_Orderings_Obot__class_Obot(tc_fun(_1653229, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653229, tc_fun(_1653231, tc_HOL_Obool)), _1653227), hAPP(hAPP(c_COMBB(tc_fun(_1653231, tc_HOL_Obool), tc_fun(_1653231, tc_HOL_Obool), _1653229), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1653231, tc_HOL_Obool)), _1653233)), _1653235)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1653231, tc_HOL_Obool)), _1653233), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1653229, tc_fun(_1653231, tc_HOL_Obool)), _1653227), _1653235)))], (44496 ^ _780461) ^ [_1653335, _1653337, _1653339] : [-(hAPP(c_Relation_Oconverse(_1653335, _1653337), _1653339) = hAPP(c_Set_OCollect(tc_prod(_1653337, _1653335)), hAPP(c_Product__Type_Oprod_Oprod__case(_1653337, _1653335, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1653337, tc_fun(tc_prod(_1653335, _1653337), tc_HOL_Obool), tc_fun(_1653335, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1653335, tc_fun(tc_fun(tc_prod(_1653335, _1653337), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1653335, _1653337), tc_HOL_Obool), tc_fun(_1653335, tc_HOL_Obool)), _1653337), c_COMBC(_1653335, tc_fun(tc_prod(_1653335, _1653337), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1653335, tc_prod(_1653335, _1653337)), tc_fun(_1653335, tc_fun(tc_fun(tc_prod(_1653335, _1653337), tc_HOL_Obool), tc_HOL_Obool)), _1653337), hAPP(c_COMBB(tc_prod(_1653335, _1653337), tc_fun(tc_fun(tc_prod(_1653335, _1653337), tc_HOL_Obool), tc_HOL_Obool), _1653335), c_member(tc_prod(_1653335, _1653337)))), hAPP(c_COMBC(_1653335, _1653337, tc_prod(_1653335, _1653337)), c_Product__Type_OPair(_1653335, _1653337))))), _1653339))))], (44498 ^ _780461) ^ [_1653511, _1653513, _1653515, _1653517, _1653519] : [class_Complete__Lattice_Ocomplete__lattice(_1653511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1653513), _1653515)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1653511), _1653517), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1653513, _1653511), _1653515), _1653519)) = hAPP(hAPP(c_Finite__Set_Ofold(_1653513, _1653511, hAPP(hAPP(c_COMBB(_1653511, tc_fun(_1653511, _1653511), _1653513), c_Lattices_Osemilattice__inf__class_Oinf(_1653511)), _1653519)), _1653517), _1653515))], (44508 ^ _780461) ^ [_1653742, _1653744, _1653746, _1653748, _1653750] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653742, _1653742)), hAPP(hAPP(c_Product__Type_OPair(_1653742, _1653742), hAPP(_1653744, hAPP(c_Nat_OSuc, 44509 ^ [_1653742, _1653744, _1653746, _1653748, _1653750]))), hAPP(_1653744, 44509 ^ [_1653742, _1653744, _1653746, _1653748, _1653750]))), c_Transitive__Closure_Ortrancl(_1653742, _1653746))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1653742, _1653742)), hAPP(hAPP(c_Product__Type_OPair(_1653742, _1653742), hAPP(_1653744, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653748), _1653750))), hAPP(_1653744, _1653748))), c_Transitive__Closure_Ortrancl(_1653742, _1653746))))], (44515 ^ _780461) ^ [_1654056, _1654058, _1654060, _1654062] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1654056, tc_fun(_1654056, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1654056, tc_fun(tc_prod(_1654056, _1654056), tc_HOL_Obool), tc_fun(_1654056, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1654056, tc_fun(tc_fun(tc_prod(_1654056, _1654056), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1654056, _1654056), tc_HOL_Obool), tc_fun(_1654056, tc_HOL_Obool)), _1654056), c_COMBC(_1654056, tc_fun(tc_prod(_1654056, _1654056), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1654056, tc_prod(_1654056, _1654056)), tc_fun(_1654056, tc_fun(tc_fun(tc_prod(_1654056, _1654056), tc_HOL_Obool), tc_HOL_Obool)), _1654056), hAPP(c_COMBB(tc_prod(_1654056, _1654056), tc_fun(tc_fun(tc_prod(_1654056, _1654056), tc_HOL_Obool), tc_HOL_Obool), _1654056), c_member(tc_prod(_1654056, _1654056)))), c_Product__Type_OPair(_1654056, _1654056)))), _1654058)), c_fequal), _1654060), _1654062)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654056, _1654056)), hAPP(hAPP(c_Product__Type_OPair(_1654056, _1654056), _1654060), _1654062)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1654056, _1654056), tc_HOL_Obool)), _1654058), c_Relation_OId(_1654056)))))], (44521 ^ _780461) ^ [_1654477, _1654479, _1654481, _1654483] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654477, _1654477)), hAPP(hAPP(c_Product__Type_OPair(_1654477, _1654477), _1654481), _1654483)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1654477, _1654477), tc_HOL_Obool)), _1654479), c_Relation_OId(_1654477)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1654477, tc_fun(_1654477, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1654477, tc_fun(tc_prod(_1654477, _1654477), tc_HOL_Obool), tc_fun(_1654477, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1654477, tc_fun(tc_fun(tc_prod(_1654477, _1654477), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1654477, _1654477), tc_HOL_Obool), tc_fun(_1654477, tc_HOL_Obool)), _1654477), c_COMBC(_1654477, tc_fun(tc_prod(_1654477, _1654477), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1654477, tc_prod(_1654477, _1654477)), tc_fun(_1654477, tc_fun(tc_fun(tc_prod(_1654477, _1654477), tc_HOL_Obool), tc_HOL_Obool)), _1654477), hAPP(c_COMBB(tc_prod(_1654477, _1654477), tc_fun(tc_fun(tc_prod(_1654477, _1654477), tc_HOL_Obool), tc_HOL_Obool), _1654477), c_member(tc_prod(_1654477, _1654477)))), c_Product__Type_OPair(_1654477, _1654477)))), _1654479)), c_fequal), _1654481), _1654483)))], (44527 ^ _780461) ^ [_1654904, _1654906] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1654904, _1654904)), hAPP(hAPP(c_Product__Type_OPair(_1654904, _1654904), _1654906), _1654906)), c_Relation_OId(_1654904))))], (44539 ^ _780461) ^ [_1655192, _1655194, _1655196, _1655198, _1655200] : [44541 ^ _780461 : [(44542 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655192), 44540 ^ [_1655192, _1655194, _1655196, _1655198, _1655200]), _1655196)))], (44544 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1655198, 44540 ^ [_1655192, _1655194, _1655196, _1655198, _1655200]), _1655200))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655192, tc_fun(_1655194, tc_HOL_Obool)), _1655196), _1655198), _1655200)))], (44529 ^ _780461) ^ [_1654974, _1654976, _1654978, _1654980, _1654982] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1654974, tc_fun(_1654976, tc_HOL_Obool)), _1654978), _1654980), _1654982)), 44532 ^ _780461 : [(44533 ^ _780461) ^ [_1655083] : [hBOOL(hAPP(hAPP(c_member(_1654974), _1655083), _1654978)), -(hBOOL(hAPP(hAPP(_1654980, _1655083), _1654982)))]]], (44558 ^ _780461) ^ [_1655692, _1655694, _1655696, _1655698, _1655700, _1655702, _1655704] : [44560 ^ _780461 : [(44561 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655692), 44559 ^ [_1655692, _1655694, _1655696, _1655698, _1655700, _1655702, _1655704]), _1655698)))], (44563 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1655700, 44559 ^ [_1655692, _1655694, _1655696, _1655698, _1655700, _1655702, _1655704]), _1655702), _1655704))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655692, tc_fun(_1655694, tc_fun(_1655696, tc_HOL_Obool))), _1655698), _1655700), _1655702), _1655704)))], (44548 ^ _780461) ^ [_1655445, _1655447, _1655449, _1655451, _1655453, _1655455, _1655457] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1655445, tc_fun(_1655447, tc_fun(_1655449, tc_HOL_Obool))), _1655451), _1655453), _1655455), _1655457)), 44551 ^ _780461 : [(44552 ^ _780461) ^ [_1655573] : [hBOOL(hAPP(hAPP(c_member(_1655445), _1655573), _1655451)), -(hBOOL(hAPP(hAPP(hAPP(_1655453, _1655573), _1655455), _1655457)))]]], (44567 ^ _780461) ^ [_1655952] : [-(hAPP(c_Relation_Oconverse(_1655952, _1655952), c_Relation_OId(_1655952)) = c_Relation_OId(_1655952))], (44569 ^ _780461) ^ [_1655985, _1655987] : [-(hAPP(c_Relation_OImage(_1655985, _1655985, c_Relation_OId(_1655985)), _1655987) = _1655987)], (44571 ^ _780461) ^ [_1656019, _1656021, _1656023] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1656019, _1656021, _1656021), _1656023), c_Relation_OId(_1656021)) = _1656023)], (44573 ^ _780461) ^ [_1656058, _1656060, _1656062] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1656058, _1656058, _1656060), c_Relation_OId(_1656058)), _1656062) = _1656062)], (44575 ^ _780461) ^ [_1656115, _1656117, _1656119] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656115, _1656115)), hAPP(hAPP(c_Product__Type_OPair(_1656115, _1656115), _1656117), _1656119)), c_Relation_OId(_1656115))), -(_1656117 = _1656119)], (44581 ^ _780461) ^ [_1656232, _1656234, _1656236] : [_1656234 = _1656236, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1656232, _1656232)), hAPP(hAPP(c_Product__Type_OPair(_1656232, _1656232), _1656234), _1656236)), c_Relation_OId(_1656232))))], (44587 ^ _780461) ^ [_1656355] : [-(hAPP(c_Relation_ODomain(_1656355, _1656355), c_Relation_OId(_1656355)) = c_Orderings_Otop__class_Otop(tc_fun(_1656355, tc_HOL_Obool)))], (44589 ^ _780461) ^ [_1656391] : [-(c_Transitive__Closure_Ortrancl(_1656391, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1656391, _1656391), tc_HOL_Obool))) = c_Relation_OId(_1656391))], (44591 ^ _780461) ^ [_1656427] : [-(hAPP(c_Relation_ORange(_1656427, _1656427), c_Relation_OId(_1656427)) = c_Orderings_Otop__class_Otop(tc_fun(_1656427, tc_HOL_Obool)))], (44593 ^ _780461) ^ [_1656463, _1656465] : [-(c_Transitive__Closure_Ortrancl(_1656463, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1656463, _1656463), tc_HOL_Obool)), _1656465), c_Relation_OId(_1656463))) = c_Transitive__Closure_Ortrancl(_1656463, _1656465))], (44595 ^ _780461) ^ [_1656510, _1656512] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1656510, _1656510), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1656510, _1656512)), c_Relation_OId(_1656510)) = c_Transitive__Closure_Ortrancl(_1656510, _1656512))], (44597 ^ _780461) ^ [_1656557] : [-(c_Relation_Orefl__on(_1656557, c_Orderings_Otop__class_Otop(tc_fun(_1656557, tc_HOL_Obool)), c_Relation_OId(_1656557)))], (44599 ^ _780461) ^ [_1656588, _1656590] : [-(c_Transitive__Closure_Ortrancl(_1656588, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1656588, _1656588), tc_HOL_Obool)), _1656590), c_Relation_OId(_1656588))) = c_Transitive__Closure_Ortrancl(_1656588, _1656590))], (44601 ^ _780461) ^ [] : [-(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))))], (44603 ^ _780461) ^ [_1656653, _1656655] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1656653, _1656653), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1656653, _1656655)), c_Relation_OId(_1656653)) = c_Transitive__Closure_Ortrancl(_1656653, _1656655))], (44605 ^ _780461) ^ [_1656700, _1656702] : [-(c_Transitive__Closure_Otrancl(_1656700, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1656700, _1656700), tc_HOL_Obool)), _1656702), c_Relation_OId(_1656700))) = c_Transitive__Closure_Ortrancl(_1656700, _1656702))], (44607 ^ _780461) ^ [_1656747, _1656749] : [-(c_Transitive__Closure_Ortrancl(_1656747, _1656749) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1656747, _1656747), tc_HOL_Obool)), c_Relation_OId(_1656747)), hAPP(hAPP(c_Relation_Orel__comp(_1656747, _1656747, _1656747), c_Transitive__Closure_Ortrancl(_1656747, _1656749)), _1656749)))], (44609 ^ _780461) ^ [_1656804, _1656806] : [-(c_Relation_Orefl__on(_1656804, c_Orderings_Otop__class_Otop(tc_fun(_1656804, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1656804, _1656804), tc_HOL_Obool)), _1656806), c_Relation_OId(_1656804))))], (44611 ^ _780461) ^ [_1656851] : [-(c_Relation_OId(_1656851) = hAPP(c_Set_OCollect(tc_prod(_1656851, _1656851)), hAPP(hAPP(c_COMBB(tc_fun(_1656851, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1656851, _1656851)), c_HOL_OEx(_1656851)), hAPP(hAPP(c_COMBC(tc_prod(_1656851, _1656851), tc_fun(_1656851, tc_prod(_1656851, _1656851)), tc_fun(_1656851, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1656851, _1656851), tc_HOL_Obool), tc_fun(tc_fun(_1656851, tc_prod(_1656851, _1656851)), tc_fun(_1656851, tc_HOL_Obool)), tc_prod(_1656851, _1656851)), c_COMBB(tc_prod(_1656851, _1656851), tc_HOL_Obool, _1656851)), c_fequal)), hAPP(hAPP(c_COMBS(_1656851, _1656851, tc_prod(_1656851, _1656851)), c_Product__Type_OPair(_1656851, _1656851)), c_COMBI(_1656851))))))], (44613 ^ _780461) ^ [_1656980, _1656982] : [-(c_Relation_Oirrefl(_1656980, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1656980, _1656980), tc_HOL_Obool)), _1656982), c_Relation_OId(_1656980))))], (44615 ^ _780461) ^ [_1657021, _1657023, _1657025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1657021, _1657021), tc_HOL_Obool)), c_Relation_OId(_1657021)), _1657023)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1657021, _1657021), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1657021, _1657021, _1657021), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1657021, _1657021), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1657021, _1657025)), _1657023)), _1657025)), _1657023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1657021, _1657021), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1657021, _1657025)), _1657023)))], (44625 ^ _780461) ^ [_1657296, _1657298, _1657300, _1657302, _1657304, _1657306] : [c_Relation_Osingle__valued(_1657296, _1657298, hAPP(c_Relation_Oconverse(_1657298, _1657296), _1657300)), -(_1657302 = c_Orderings_Obot__class_Obot(tc_fun(_1657304, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1657298, _1657296, _1657300), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657304, tc_fun(_1657298, tc_HOL_Obool)), _1657302), _1657306)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657304, tc_fun(_1657296, tc_HOL_Obool)), _1657302), hAPP(hAPP(c_COMBB(tc_fun(_1657298, tc_HOL_Obool), tc_fun(_1657296, tc_HOL_Obool), _1657304), c_Relation_OImage(_1657298, _1657296, _1657300)), _1657306)))], (44635 ^ _780461) ^ [_1657522, _1657524, _1657526, _1657528, _1657530, _1657532, _1657534, _1657536] : [c_Fun_Oinj__on(_1657522, _1657524, _1657526, _1657528), 44641 ^ _780461 : [(44642 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1657530), 44640 ^ [_1657522, _1657524, _1657526, _1657528, _1657530, _1657532, _1657534, _1657536]), _1657532)))], (44644 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657522, tc_HOL_Obool)), hAPP(_1657534, 44640 ^ [_1657522, _1657524, _1657526, _1657528, _1657530, _1657532, _1657534, _1657536])), _1657528))]], hBOOL(hAPP(hAPP(c_member(_1657530), _1657536), _1657532)), -(hAPP(c_Set_Oimage(_1657522, _1657524, _1657526), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657530, tc_fun(_1657522, tc_HOL_Obool)), _1657532), _1657534)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657530, tc_fun(_1657524, tc_HOL_Obool)), _1657532), hAPP(hAPP(c_COMBB(tc_fun(_1657522, tc_HOL_Obool), tc_fun(_1657524, tc_HOL_Obool), _1657530), c_Set_Oimage(_1657522, _1657524, _1657526)), _1657534)))], (44652 ^ _780461) ^ [_1658011] : [-(c_Relation_Osingle__valued(_1658011, _1658011, c_Relation_OId(_1658011)))], (44654 ^ _780461) ^ [_1658037, _1658039, _1658041, _1658043, _1658045] : [c_Relation_Osingle__valued(_1658037, _1658039, _1658041), c_Relation_Osingle__valued(_1658039, _1658043, _1658045), -(c_Relation_Osingle__valued(_1658037, _1658043, hAPP(hAPP(c_Relation_Orel__comp(_1658037, _1658039, _1658043), _1658041), _1658045)))], (44664 ^ _780461) ^ [_1658204, _1658206, _1658208, _1658210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1658204, _1658206), tc_HOL_Obool)), _1658208), _1658210)), c_Relation_Osingle__valued(_1658204, _1658206, _1658210), -(c_Relation_Osingle__valued(_1658204, _1658206, _1658208))], (44674 ^ _780461) ^ [_1658371, _1658373] : [-(c_Relation_Osingle__valued(_1658371, _1658371, c_Relation_OId__on(_1658371, _1658373)))], (44690 ^ _780461) ^ [_1658792, _1658794, _1658796] : [44693 ^ _780461 : [(44694 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658792, _1658794)), hAPP(hAPP(c_Product__Type_OPair(_1658792, _1658794), 44691 ^ [_1658792, _1658794, _1658796]), 44692 ^ [_1658792, _1658794, _1658796])), _1658796)))], (44697 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658792, _1658794)), hAPP(hAPP(c_Product__Type_OPair(_1658792, _1658794), 44691 ^ [_1658792, _1658794, _1658796]), 44695 ^ [_1658792, _1658794, _1658796])), _1658796)))], (44699 ^ _780461) ^ [] : [44692 ^ [_1658792, _1658794, _1658796] = 44695 ^ [_1658792, _1658794, _1658796]]], -(c_Relation_Osingle__valued(_1658792, _1658794, _1658796))], (44676 ^ _780461) ^ [_1658418, _1658420, _1658422] : [c_Relation_Osingle__valued(_1658418, _1658420, _1658422), 44679 ^ _780461 : [(44680 ^ _780461) ^ [_1658539, _1658541] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1658418, _1658420)), hAPP(hAPP(c_Product__Type_OPair(_1658418, _1658420), _1658541), _1658539)), _1658422)), 44683 ^ _780461 : [(44684 ^ _780461) ^ [_1658665] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1658418, _1658420)), hAPP(hAPP(c_Product__Type_OPair(_1658418, _1658420), _1658541), _1658665)), _1658422)), -(_1658539 = _1658665)]]]]], (44703 ^ _780461) ^ [_1659162, _1659164, _1659166, _1659168, _1659170, _1659172] : [c_Relation_Osingle__valued(_1659162, _1659164, _1659166), hBOOL(hAPP(hAPP(c_member(tc_prod(_1659162, _1659164)), hAPP(hAPP(c_Product__Type_OPair(_1659162, _1659164), _1659168), _1659170)), _1659166)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1659162, _1659164)), hAPP(hAPP(c_Product__Type_OPair(_1659162, _1659164), _1659168), _1659172)), _1659166)), -(_1659170 = _1659172)], (44717 ^ _780461) ^ [_1659445, _1659447, _1659449, _1659451, _1659453] : [c_Relation_Osingle__valued(_1659445, _1659445, _1659447), hBOOL(hAPP(hAPP(c_member(tc_prod(_1659445, _1659445)), hAPP(hAPP(c_Product__Type_OPair(_1659445, _1659445), _1659449), _1659451)), c_Transitive__Closure_Ortrancl(_1659445, _1659447))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1659445, _1659445)), hAPP(hAPP(c_Product__Type_OPair(_1659445, _1659445), _1659449), _1659453)), c_Transitive__Closure_Ortrancl(_1659445, _1659447))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1659445, _1659445)), hAPP(hAPP(c_Product__Type_OPair(_1659445, _1659445), _1659451), _1659453)), c_Transitive__Closure_Ortrancl(_1659445, _1659447)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1659445, _1659445)), hAPP(hAPP(c_Product__Type_OPair(_1659445, _1659445), _1659453), _1659451)), c_Transitive__Closure_Ortrancl(_1659445, _1659447))))], (44735 ^ _780461) ^ [_1659835, _1659837, _1659839, _1659841, _1659843] : [c_Relation_Osingle__valued(_1659835, _1659837, hAPP(c_Relation_Oconverse(_1659837, _1659835), _1659839)), -(hAPP(c_Relation_OImage(_1659837, _1659835, _1659839), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659837, tc_HOL_Obool)), _1659841), _1659843)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1659835, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1659837, _1659835, _1659839), _1659841)), hAPP(c_Relation_OImage(_1659837, _1659835, _1659839), _1659843)))], (44741 ^ _780461) ^ [_1660036, _1660038, _1660040] : [c_Relation_Ototal__on(_1660036, _1660038, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1660036, _1660036), tc_HOL_Obool)), _1660040), c_Relation_OId(_1660036))), -(c_Relation_Ototal__on(_1660036, _1660038, _1660040))], (44747 ^ _780461) ^ [_1660147, _1660149, _1660151] : [c_Relation_Ototal__on(_1660147, _1660149, _1660151), -(c_Relation_Ototal__on(_1660147, _1660149, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1660147, _1660147), tc_HOL_Obool)), _1660151), c_Relation_OId(_1660147))))], (44753 ^ _780461) ^ [_1660264, _1660266, _1660268] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1660264, _1660264)), _1660266), c_Transitive__Closure_Ortrancl(_1660264, _1660268))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1660264, _1660264)), _1660266), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1660264, _1660264), 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(_1660264, _1660264), tc_HOL_Obool), tc_fun(tc_prod(_1660264, _1660264), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1660264, _1660264), tc_HOL_Obool)), _1660268)))))], (44759 ^ _780461) ^ [_1660475, _1660477] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1660475, _1660475), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1660477) = c_Relation_OId(_1660475))], (44761 ^ _780461) ^ [_1660514, _1660516, _1660518] : [c_Relation_Osingle__valued(_1660514, _1660514, _1660516), -(c_Relation_Osingle__valued(_1660514, _1660514, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1660514, _1660514), tc_HOL_Obool), _1660518), _1660516)))], (44767 ^ _780461) ^ [_1660639, _1660641, _1660643] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1660639, _1660639)), _1660641), c_Transitive__Closure_Ortrancl(_1660639, _1660643))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1660639, _1660639)), _1660641), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1660639, _1660639), tc_HOL_Obool), 44770 ^ [_1660639, _1660641, _1660643]), _1660643))))], (44774 ^ _780461) ^ [_1660798, _1660800, _1660802] : [44775 ^ _780461 : [(44776 ^ _780461) ^ [_1660874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1660798, _1660798)), _1660800), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1660798, _1660798), tc_HOL_Obool), _1660874), _1660802)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1660798, _1660798)), _1660800), c_Transitive__Closure_Ortrancl(_1660798, _1660802))))], (44780 ^ _780461) ^ [_1660962, _1660964, _1660966, _1660968] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1660962, _1660962)), _1660964), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1660962, _1660962), tc_HOL_Obool), _1660966), _1660968))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1660962, _1660962)), _1660964), c_Transitive__Closure_Ortrancl(_1660962, _1660968))))], (44786 ^ _780461) ^ [_1661113, _1661115, _1661117] : [c_Wellfounded_Owf(_1661113, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661113, _1661113), tc_HOL_Obool), _1661115), _1661117)), -(c_Wellfounded_Owf(_1661113, _1661117))], (44792 ^ _780461) ^ [_1661216, _1661218, _1661220, _1661222] : [-(hAPP(hAPP(c_Nat_Ocompow(_1661216, _1661216), _1661218), hAPP(hAPP(c_Nat_Ocompow(_1661216, _1661216), _1661220), _1661222)) = hAPP(hAPP(c_Nat_Ocompow(_1661216, _1661216), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1661220), _1661218)), _1661222))], (44794 ^ _780461) ^ [_1661278, _1661280, _1661282, _1661284] : [-(hAPP(_1661278, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1661280, _1661280), _1661282), _1661278), _1661284)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1661280, _1661280), _1661282), _1661278), hAPP(_1661278, _1661284)))], (44796 ^ _780461) ^ [_1661337, _1661339, _1661341, _1661343] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1661337, _1661339), tc_fun(_1661337, _1661339)), _1661341), c_Fun_Ocomp(_1661339, _1661339, _1661337, _1661343)) = c_Fun_Ocomp(_1661339, _1661339, _1661337, hAPP(hAPP(c_Nat_Ocompow(_1661339, _1661339), _1661341), _1661343)))], (44798 ^ _780461) ^ [_1661400, _1661402, _1661404, _1661406] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661400, _1661400), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1661402), _1661404)), _1661406) = hAPP(hAPP(c_Relation_Orel__comp(_1661400, _1661400, _1661400), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661400, _1661400), tc_HOL_Obool), _1661402), _1661406)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661400, _1661400), tc_HOL_Obool), _1661404), _1661406)))], (44800 ^ _780461) ^ [_1661481, _1661483, _1661485] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661481, _1661481), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1661483)), _1661485) = hAPP(hAPP(c_Relation_Orel__comp(_1661481, _1661481, _1661481), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661481, _1661481), tc_HOL_Obool), _1661483), _1661485)), _1661485))], (44802 ^ _780461) ^ [_1661545, _1661547, _1661549] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1661545, _1661545, _1661545), _1661547), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661545, _1661545), tc_HOL_Obool), _1661549), _1661547)) = hAPP(hAPP(c_Relation_Orel__comp(_1661545, _1661545, _1661545), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661545, _1661545), tc_HOL_Obool), _1661549), _1661547)), _1661547))], (44804 ^ _780461) ^ [_1661616, _1661618] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661616, _1661616), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1661618) = _1661618)], (44806 ^ _780461) ^ [_1661653, _1661655] : [-(c_Relation_Ototal__on(_1661653, c_Orderings_Obot__class_Obot(tc_fun(_1661653, tc_HOL_Obool)), _1661655))], (44808 ^ _780461) ^ [_1661702, _1661704, _1661706] : [c_Relation_Ototal__on(_1661702, _1661704, hAPP(c_Relation_Oconverse(_1661702, _1661702), _1661706)), -(c_Relation_Ototal__on(_1661702, _1661704, _1661706))], (44814 ^ _780461) ^ [_1661793, _1661795, _1661797] : [c_Relation_Ototal__on(_1661793, _1661795, _1661797), -(c_Relation_Ototal__on(_1661793, _1661795, hAPP(c_Relation_Oconverse(_1661793, _1661793), _1661797)))], (44820 ^ _780461) ^ [_1661890, _1661892, _1661894, _1661896] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1661890, _1661890)), hAPP(hAPP(c_Product__Type_OPair(_1661890, _1661890), _1661892), _1661894)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1661890, _1661890), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1661896))), -(_1661892 = _1661894)], (44826 ^ _780461) ^ [_1662033, _1662035, _1662037] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1662033, _1662033)), hAPP(hAPP(c_Product__Type_OPair(_1662033, _1662033), _1662035), _1662035)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1662033, _1662033), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1662037))))], (44828 ^ _780461) ^ [_1662091, _1662093, _1662095, _1662097, _1662099, _1662101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1662091, _1662091)), hAPP(hAPP(c_Product__Type_OPair(_1662091, _1662091), _1662093), _1662095)), _1662097)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1662091, _1662091)), hAPP(hAPP(c_Product__Type_OPair(_1662091, _1662091), _1662095), _1662099)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1662091, _1662091), tc_HOL_Obool), _1662101), _1662097))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1662091, _1662091)), hAPP(hAPP(c_Product__Type_OPair(_1662091, _1662091), _1662093), _1662099)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1662091, _1662091), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1662101)), _1662097))))], (44838 ^ _780461) ^ [_1662404, _1662406, _1662408, _1662410, _1662412, _1662414] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1662404, _1662404)), hAPP(hAPP(c_Product__Type_OPair(_1662404, _1662404), _1662406), _1662408)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1662404, _1662404), tc_HOL_Obool), _1662410), _1662412))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1662404, _1662404)), hAPP(hAPP(c_Product__Type_OPair(_1662404, _1662404), _1662408), _1662414)), _1662412)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1662404, _1662404)), hAPP(hAPP(c_Product__Type_OPair(_1662404, _1662404), _1662406), _1662414)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1662404, _1662404), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1662410)), _1662412))))], (44848 ^ _780461) ^ [_1662717, _1662719, _1662721] : [-(hAPP(hAPP(c_Nat_Ocompow(_1662717, _1662717), hAPP(c_Nat_OSuc, _1662719)), _1662721) = hAPP(c_Fun_Ocomp(_1662717, _1662717, _1662717, _1662721), hAPP(hAPP(c_Nat_Ocompow(_1662717, _1662717), _1662719), _1662721)))], (44850 ^ _780461) ^ [_1662773, _1662775, _1662777, _1662779] : [-(hAPP(hAPP(c_Nat_Ocompow(_1662773, _1662773), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1662775), _1662777)), _1662779) = hAPP(c_Fun_Ocomp(_1662773, _1662773, _1662773, hAPP(hAPP(c_Nat_Ocompow(_1662773, _1662773), _1662775), _1662779)), hAPP(hAPP(c_Nat_Ocompow(_1662773, _1662773), _1662777), _1662779)))], (44852 ^ _780461) ^ [_1662843, _1662845] : [-(hAPP(hAPP(c_Nat_Ocompow(_1662843, _1662843), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1662845) = c_Fun_Oid(_1662843))], (44854 ^ _780461) ^ [_1662897, _1662899, _1662901] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1662897, _1662897)), _1662899), c_Transitive__Closure_Otrancl(_1662897, _1662901))), 44858 ^ _780461 : [(44859 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 44857 ^ [_1662897, _1662899, _1662901])))], (44861 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1662897, _1662897)), _1662899), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1662897, _1662897), tc_HOL_Obool), 44857 ^ [_1662897, _1662899, _1662901]), _1662901))))]]], (44863 ^ _780461) ^ [_1663095, _1663097, _1663099] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1663095, _1663095)), _1663097), c_Transitive__Closure_Otrancl(_1663095, _1663099)))), 44864 ^ _780461 : [(44865 ^ _780461) ^ [_1663174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1663174)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1663095, _1663095)), _1663097), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1663095, _1663095), tc_HOL_Obool), _1663174), _1663099)))]]], (44895 ^ _780461) ^ [_1663852, _1663854, _1663856] : [44897 ^ _780461 : [(44898 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1663852), 44896 ^ [_1663852, _1663854, _1663856]), _1663854)))], (44901 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1663852), 44899 ^ [_1663852, _1663854, _1663856]), _1663854)))], (44903 ^ _780461) ^ [] : [44896 ^ [_1663852, _1663854, _1663856] = 44899 ^ [_1663852, _1663854, _1663856]], (44905 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1663852, _1663852)), hAPP(hAPP(c_Product__Type_OPair(_1663852, _1663852), 44896 ^ [_1663852, _1663854, _1663856]), 44899 ^ [_1663852, _1663854, _1663856])), _1663856))], (44907 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1663852, _1663852)), hAPP(hAPP(c_Product__Type_OPair(_1663852, _1663852), 44899 ^ [_1663852, _1663854, _1663856]), 44896 ^ [_1663852, _1663854, _1663856])), _1663856))]], -(c_Relation_Ototal__on(_1663852, _1663854, _1663856))], (44873 ^ _780461) ^ [_1663363, _1663365, _1663367] : [c_Relation_Ototal__on(_1663363, _1663365, _1663367), 44876 ^ _780461 : [(44877 ^ _780461) ^ [_1663507] : [hBOOL(hAPP(hAPP(c_member(_1663363), _1663507), _1663365)), 44880 ^ _780461 : [(44881 ^ _780461) ^ [_1663647] : [hBOOL(hAPP(hAPP(c_member(_1663363), _1663647), _1663365)), -(_1663507 = _1663647), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1663363, _1663363)), hAPP(hAPP(c_Product__Type_OPair(_1663363, _1663363), _1663507), _1663647)), _1663367))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1663363, _1663363)), hAPP(hAPP(c_Product__Type_OPair(_1663363, _1663363), _1663647), _1663507)), _1663367)))]]]]], (44911 ^ _780461) ^ [_1664434, _1664436] : [-(c_Transitive__Closure_Ortrancl(_1664434, _1664436) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1664434, _1664434), 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(_1664434, _1664434), tc_HOL_Obool), tc_fun(tc_prod(_1664434, _1664434), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1664434, _1664434), tc_HOL_Obool)), _1664436)))], (44913 ^ _780461) ^ [_1664505] : [-(c_Nat_Ofunpow(_1664505) = c_Nat_Ocompow(_1664505, _1664505))], (44915 ^ _780461) ^ [_1664533, _1664535, _1664537, _1664539, _1664541] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1664533, _1664533)), hAPP(hAPP(c_Product__Type_OPair(_1664533, _1664533), _1664535), _1664537)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1664533, _1664533), tc_HOL_Obool), _1664539), _1664541))), 44920 ^ _780461 : [(44921 ^ _780461) ^ [] : [-(_1664539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44923 ^ _780461) ^ [] : [-(_1664535 = _1664537)]], 44926 ^ _780461 : [(44927 ^ _780461) ^ [] : [-(_1664539 = hAPP(c_Nat_OSuc, 44925 ^ [_1664533, _1664535, _1664537, _1664539, _1664541]))], (44929 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1664533, _1664533)), hAPP(hAPP(c_Product__Type_OPair(_1664533, _1664533), _1664535), 44924 ^ [_1664533, _1664535, _1664537, _1664539, _1664541])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1664533, _1664533), tc_HOL_Obool), 44925 ^ [_1664533, _1664535, _1664537, _1664539, _1664541]), _1664541))))], (44931 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1664533, _1664533)), hAPP(hAPP(c_Product__Type_OPair(_1664533, _1664533), 44924 ^ [_1664533, _1664535, _1664537, _1664539, _1664541]), _1664537)), _1664541)))]]], (44933 ^ _780461) ^ [_1664975, _1664977, _1664979, _1664981, _1664983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1664975, _1664975)), hAPP(hAPP(c_Product__Type_OPair(_1664975, _1664975), _1664977), _1664979)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1664975, _1664975), tc_HOL_Obool), _1664981), _1664983))), 44938 ^ _780461 : [(44939 ^ _780461) ^ [] : [-(_1664981 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44941 ^ _780461) ^ [] : [-(_1664977 = _1664979)]], 44944 ^ _780461 : [(44945 ^ _780461) ^ [] : [-(_1664981 = hAPP(c_Nat_OSuc, 44943 ^ [_1664975, _1664977, _1664979, _1664981, _1664983]))], (44947 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1664975, _1664975)), hAPP(hAPP(c_Product__Type_OPair(_1664975, _1664975), _1664977), 44942 ^ [_1664975, _1664977, _1664979, _1664981, _1664983])), _1664983)))], (44949 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1664975, _1664975)), hAPP(hAPP(c_Product__Type_OPair(_1664975, _1664975), 44942 ^ [_1664975, _1664977, _1664979, _1664981, _1664983]), _1664979)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1664975, _1664975), tc_HOL_Obool), 44943 ^ [_1664975, _1664977, _1664979, _1664981, _1664983]), _1664983))))]]], (44951 ^ _780461) ^ [_1665417, _1665419] : [class_Complete__Lattice_Ocomplete__lattice(_1665417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1665417), _1665419)), -(c_Complete__Lattice_OInf__class_OInf(_1665417, _1665419) = hAPP(hAPP(c_Finite__Set_Ofold(_1665417, _1665417, c_Lattices_Osemilattice__inf__class_Oinf(_1665417)), c_Orderings_Otop__class_Otop(_1665417)), _1665419))], (44961 ^ _780461) ^ [_1665586, _1665588] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1665586), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1665586, tc_HOL_Obool), _1665588)))), 44962 ^ _780461 : [(44963 ^ _780461) ^ [_1665650] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1665586, tc_HOL_Obool)), _1665650), _1665588)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1665586), _1665650))]]], (44971 ^ _780461) ^ [_1665794, _1665796, _1665798, _1665800] : [hBOOL(hAPP(hAPP(c_member(_1665794), _1665796), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1665794, tc_HOL_Obool), _1665798))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1665794, tc_HOL_Obool)), _1665800), _1665798)), -(hBOOL(hAPP(hAPP(c_member(_1665794), _1665796), _1665800)))], (44981 ^ _780461) ^ [_1665991, _1665993, _1665995, _1665997] : [hBOOL(hAPP(hAPP(c_member(_1665991), _1665993), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1665991, tc_HOL_Obool), _1665995))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1665991, tc_HOL_Obool)), _1665997), _1665995)), -(hBOOL(hAPP(hAPP(c_member(_1665991), _1665993), _1665997)))], (44991 ^ _780461) ^ [_1666188, _1666190, _1666192] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1666188, tc_HOL_Obool)), _1666190), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1666188, tc_HOL_Obool), _1666192)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1666188, tc_HOL_Obool), tc_fun(_1666188, tc_HOL_Obool)), _1666192), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1666188, tc_HOL_Obool)), _1666190)))], (44993 ^ _780461) ^ [_1666255, _1666257, _1666259] : [class_Complete__Lattice_Ocomplete__lattice(_1666255), class_Orderings_Olinorder(_1666255), 45000 ^ _780461 : [(45001 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1666255), c_Complete__Lattice_OInf__class_OInf(_1666255, _1666257)), _1666259)), 45005 ^ _780461 : [(45006 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666255), 45004 ^ [_1666255, _1666257, _1666259]), _1666257)))], (45008 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1666255), 45004 ^ [_1666255, _1666257, _1666259]), _1666259)))]]], (45010 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1666255), c_Complete__Lattice_OInf__class_OInf(_1666255, _1666257)), _1666259))), 45011 ^ _780461 : [(45012 ^ _780461) ^ [_1666561] : [hBOOL(hAPP(hAPP(c_member(_1666255), _1666561), _1666257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1666255), _1666561), _1666259))]]]]], (45020 ^ _780461) ^ [_1666715, _1666717, _1666719] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1666715, tc_HOL_Obool)), _1666717), _1666719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1666715, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1666715, tc_HOL_Obool), _1666719)), _1666717)))], (45026 ^ _780461) ^ [_1666846, _1666848, _1666850] : [class_Complete__Lattice_Ocomplete__lattice(_1666846), 45029 ^ _780461 : [(45040 ^ _780461) ^ [] : [45042 ^ _780461 : [(45043 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666846), 45041 ^ [_1666846, _1666848, _1666850]), _1666850)))], (45045 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666846), _1666848), 45041 ^ [_1666846, _1666848, _1666850]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666846), _1666848), c_Complete__Lattice_OInf__class_OInf(_1666846, _1666850))))], (45030 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666846), _1666848), c_Complete__Lattice_OInf__class_OInf(_1666846, _1666850))), 45033 ^ _780461 : [(45034 ^ _780461) ^ [_1667004] : [hBOOL(hAPP(hAPP(c_member(_1666846), _1667004), _1666850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1666846), _1666848), _1667004)))]]]]], (45049 ^ _780461) ^ [_1667280, _1667282, _1667284] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667280, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1667280, tc_HOL_Obool)), _1667282), _1667284)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667280, tc_HOL_Obool)), _1667282), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667280, tc_HOL_Obool), _1667284)))], (45051 ^ _780461) ^ [_1667341, _1667343] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667341, tc_HOL_Obool), _1667343) = hAPP(c_Set_OCollect(_1667341), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1667341, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1667341), c_HOL_OAll(tc_fun(_1667341, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1667341, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1667341, tc_HOL_Obool), tc_HOL_Obool), _1667341), hAPP(c_COMBS(tc_fun(_1667341, 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(_1667341, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1667341, tc_HOL_Obool), tc_fun(tc_fun(_1667341, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1667341, tc_HOL_Obool))), _1667343)))), c_member(_1667341)))))], (45053 ^ _780461) ^ [_1667469] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667469, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1667469, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1667469, tc_HOL_Obool)))], (45055 ^ _780461) ^ [_1667511, _1667513, _1667515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1667511, tc_HOL_Obool), tc_HOL_Obool)), _1667513), _1667515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1667511, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667511, tc_HOL_Obool), _1667515)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667511, tc_HOL_Obool), _1667513))))], (45061 ^ _780461) ^ [_1667660] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667660, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1667660, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1667660, tc_HOL_Obool)))], (45063 ^ _780461) ^ [_1667702, _1667704, _1667706] : [class_Complete__Lattice_Ocomplete__lattice(_1667702), hBOOL(hAPP(hAPP(c_member(_1667702), _1667704), _1667706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1667702), c_Complete__Lattice_OInf__class_OInf(_1667702, _1667706)), _1667704)))], (45073 ^ _780461) ^ [_1667867, _1667869, _1667871] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667867, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1667867, tc_HOL_Obool), tc_HOL_Obool)), _1667869), _1667871)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667867, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667867, tc_HOL_Obool), _1667869)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1667867, tc_HOL_Obool), _1667871)))], (45075 ^ _780461) ^ [_1667937, _1667939] : [class_Complete__Lattice_Ocomplete__lattice(_1667937), -(c_Complete__Lattice_OInf__class_OInf(_1667937, hAPP(hAPP(c_Set_Oinsert(_1667937), _1667939), c_Orderings_Obot__class_Obot(tc_fun(_1667937, tc_HOL_Obool)))) = _1667939)], (45081 ^ _780461) ^ [_1668044] : [class_Complete__Lattice_Ocomplete__lattice(_1668044), -(c_Complete__Lattice_OInf__class_OInf(_1668044, c_Orderings_Obot__class_Obot(tc_fun(_1668044, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1668044))], (45087 ^ _780461) ^ [_1668137] : [class_Complete__Lattice_Ocomplete__lattice(_1668137), -(c_Complete__Lattice_OInf__class_OInf(_1668137, c_Orderings_Otop__class_Otop(tc_fun(_1668137, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1668137))], (45093 ^ _780461) ^ [_1668230, _1668232, _1668234] : [class_Complete__Lattice_Ocomplete__lattice(_1668230), -(c_Complete__Lattice_OInf__class_OInf(_1668230, hAPP(hAPP(c_Set_Oinsert(_1668230), _1668232), _1668234)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1668230), _1668232), c_Complete__Lattice_OInf__class_OInf(_1668230, _1668234)))], (45099 ^ _780461) ^ [_1668351, _1668353, _1668355, _1668357] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668351, tc_fun(_1668353, tc_HOL_Obool)), _1668355), _1668357) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668353, tc_HOL_Obool), hAPP(c_Set_Oimage(_1668351, tc_fun(_1668353, tc_HOL_Obool), _1668357), _1668355)))], (45101 ^ _780461) ^ [_1668408, _1668410, _1668412, _1668414] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668408, tc_HOL_Obool), hAPP(c_Set_Oimage(_1668410, tc_fun(_1668408, tc_HOL_Obool), _1668412), _1668414)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668410, tc_fun(_1668408, tc_HOL_Obool)), _1668414), _1668412))], (45103 ^ _780461) ^ [_1668465, _1668467, _1668469] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668465, tc_HOL_Obool)), _1668467), _1668469) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668465, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1668465, tc_HOL_Obool)), _1668467), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1668465, tc_HOL_Obool)), _1668469), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1668465, tc_HOL_Obool), tc_HOL_Obool))))))], (45105 ^ _780461) ^ [_1668539, _1668541, _1668543, _1668545, _1668547] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668539, tc_fun(_1668541, tc_HOL_Obool)), _1668543), hAPP(hAPP(c_COMBS(_1668539, tc_fun(_1668541, tc_HOL_Obool), tc_fun(_1668541, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1668541, tc_HOL_Obool), tc_fun(tc_fun(_1668541, tc_HOL_Obool), tc_fun(_1668541, tc_HOL_Obool)), _1668539), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668541, tc_HOL_Obool))), _1668545)), _1668547)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668541, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668541, tc_HOL_Obool), hAPP(c_Set_Oimage(_1668539, tc_fun(_1668541, tc_HOL_Obool), _1668545), _1668543))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668541, tc_HOL_Obool), hAPP(c_Set_Oimage(_1668539, tc_fun(_1668541, tc_HOL_Obool), _1668547), _1668543))))], (45107 ^ _780461) ^ [_1668668, _1668670, _1668672] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1668668, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1668668, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668668, tc_HOL_Obool), _1668670)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668668, tc_HOL_Obool), _1668672))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1668668, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1668668, tc_HOL_Obool), tc_HOL_Obool)), _1668670), _1668672)))))], (45109 ^ _780461) ^ [_1668748, _1668750, _1668752] : [class_Complete__Lattice_Ocomplete__lattice(_1668748), -(c_Complete__Lattice_OInf__class_OInf(_1668748, hAPP(hAPP(c_Set_Oinsert(_1668748), _1668750), hAPP(hAPP(c_Set_Oinsert(_1668748), _1668752), c_Orderings_Obot__class_Obot(tc_fun(_1668748, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1668748), _1668750), _1668752))], (45115 ^ _780461) ^ [_1668889, _1668891, _1668893] : [class_Complete__Lattice_Ocomplete__lattice(_1668889), hBOOL(hAPP(c_Finite__Set_Ofinite(_1668889), _1668891)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1668889), _1668893), c_Complete__Lattice_OInf__class_OInf(_1668889, _1668891)) = hAPP(hAPP(c_Finite__Set_Ofold(_1668889, _1668889, c_Lattices_Osemilattice__inf__class_Oinf(_1668889)), _1668893), _1668891))], (45125 ^ _780461) ^ [_1669074, _1669076] : [class_Complete__Lattice_Ocomplete__lattice(_1669074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1669074), _1669076)), -(_1669076 = c_Orderings_Obot__class_Obot(tc_fun(_1669074, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1669074, _1669076) = c_Complete__Lattice_OInf__class_OInf(_1669074, _1669076))], (45139 ^ _780461) ^ [_1669246, _1669248] : [class_Complete__Lattice_Ocomplete__lattice(_1669246), -(c_Complete__Lattice_OInf__class_OInf(_1669246, _1669248) = c_Complete__Lattice_OSup__class_OSup(_1669246, hAPP(c_Set_OCollect(_1669246), hAPP(hAPP(c_COMBB(tc_fun(_1669246, tc_HOL_Obool), tc_HOL_Obool, _1669246), c_HOL_OAll(_1669246)), hAPP(hAPP(c_COMBB(tc_fun(_1669246, tc_HOL_Obool), tc_fun(_1669246, tc_HOL_Obool), _1669246), hAPP(c_COMBS(_1669246, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1669246), c_fimplies), hAPP(hAPP(c_COMBC(_1669246, tc_fun(_1669246, tc_HOL_Obool), tc_HOL_Obool), c_member(_1669246)), _1669248)))), c_Orderings_Oord__class_Oless__eq(_1669246))))))], (45145 ^ _780461) ^ [_1669473, _1669475] : [class_Complete__Lattice_Ocomplete__lattice(_1669473), -(c_Complete__Lattice_OSup__class_OSup(_1669473, _1669475) = c_Complete__Lattice_OInf__class_OInf(_1669473, hAPP(c_Set_OCollect(_1669473), hAPP(hAPP(c_COMBB(tc_fun(_1669473, tc_HOL_Obool), tc_HOL_Obool, _1669473), c_HOL_OAll(_1669473)), hAPP(hAPP(c_COMBB(tc_fun(_1669473, tc_HOL_Obool), tc_fun(_1669473, tc_HOL_Obool), _1669473), hAPP(c_COMBS(_1669473, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1669473), c_fimplies), hAPP(hAPP(c_COMBC(_1669473, tc_fun(_1669473, tc_HOL_Obool), tc_HOL_Obool), c_member(_1669473)), _1669475)))), hAPP(c_COMBC(_1669473, _1669473, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1669473)))))))], (45151 ^ _780461) ^ [_1669714, _1669716, _1669718, _1669720] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1669714, tc_HOL_Obool)), _1669716), _1669718)), hBOOL(hAPP(hAPP(c_member(_1669714), _1669720), _1669716)), -(hBOOL(hAPP(hAPP(c_member(_1669714), _1669720), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669714, tc_HOL_Obool), _1669718))))], (45161 ^ _780461) ^ [_1669911, _1669913] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1669911, tc_HOL_Obool), _1669913) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1669911, tc_HOL_Obool), tc_fun(_1669911, tc_HOL_Obool)), _1669913), c_COMBI(tc_fun(_1669911, tc_HOL_Obool))))], (45163 ^ _780461) ^ [_1669962, _1669964, _1669966, _1669968] : [-(hAPP(c_Set_Oimage(_1669962, _1669964, _1669966), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1669962, tc_HOL_Obool), _1669968)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1669962, tc_HOL_Obool), tc_fun(_1669964, tc_HOL_Obool)), _1669968), c_Set_Oimage(_1669962, _1669964, _1669966)))], (45165 ^ _780461) ^ [_1670023, _1670025, _1670027, _1670029] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1670023, _1670025), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670023, tc_HOL_Obool), _1670027)), _1670029) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1670023, tc_HOL_Obool), tc_fun(tc_prod(_1670023, _1670025), tc_HOL_Obool)), _1670027), hAPP(hAPP(c_COMBC(tc_fun(_1670023, tc_HOL_Obool), tc_fun(_1670023, tc_fun(_1670025, tc_HOL_Obool)), tc_fun(tc_prod(_1670023, _1670025), tc_HOL_Obool)), c_Product__Type_OSigma(_1670023, _1670025)), _1670029)))], (45167 ^ _780461) ^ [_1670113, _1670115, _1670117, _1670119] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1670113, tc_fun(_1670115, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670113, tc_HOL_Obool), _1670117)), _1670119) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1670113, tc_HOL_Obool), tc_fun(_1670115, tc_HOL_Obool)), _1670117), hAPP(hAPP(c_COMBC(tc_fun(_1670113, tc_HOL_Obool), tc_fun(_1670113, tc_fun(_1670115, tc_HOL_Obool)), tc_fun(_1670115, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1670113, tc_fun(_1670115, tc_HOL_Obool))), _1670119)))], (45169 ^ _780461) ^ [_1670203, _1670205, _1670207, _1670209] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1670203, tc_HOL_Obool), tc_fun(_1670205, tc_HOL_Obool)), _1670207), hAPP(hAPP(c_COMBC(tc_fun(_1670203, tc_HOL_Obool), tc_fun(_1670203, tc_fun(_1670205, tc_HOL_Obool)), tc_fun(_1670205, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1670203, tc_fun(_1670205, tc_HOL_Obool))), _1670209)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1670203, tc_fun(_1670205, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670203, tc_HOL_Obool), _1670207)), _1670209))], (45171 ^ _780461) ^ [_1670293, _1670295, _1670297] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670293, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670293, tc_HOL_Obool), _1670295)), _1670297) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1670293, tc_HOL_Obool), tc_fun(_1670293, tc_HOL_Obool)), _1670295), hAPP(hAPP(c_COMBC(tc_fun(_1670293, tc_HOL_Obool), tc_fun(_1670293, tc_HOL_Obool), tc_fun(_1670293, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670293, tc_HOL_Obool))), _1670297)))], (45173 ^ _780461) ^ [_1670376, _1670378, _1670380] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670376, tc_HOL_Obool)), _1670378), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670376, tc_HOL_Obool), _1670380)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1670376, tc_HOL_Obool), tc_fun(_1670376, tc_HOL_Obool)), _1670380), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670376, tc_HOL_Obool)), _1670378)))], (45175 ^ _780461) ^ [_1670443, _1670445, _1670447, _1670449] : [-(hAPP(c_Set_Ovimage(_1670443, _1670445, _1670447), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670445, tc_HOL_Obool), _1670449)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1670445, tc_HOL_Obool), tc_fun(_1670443, tc_HOL_Obool)), _1670449), c_Set_Ovimage(_1670443, _1670445, _1670447)))], (45177 ^ _780461) ^ [_1670504, _1670506, _1670508] : [-(hAPP(c_Relation_ORange(_1670504, _1670506), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1670504, _1670506), tc_HOL_Obool), _1670508)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1670504, _1670506), tc_HOL_Obool), tc_fun(_1670506, tc_HOL_Obool)), _1670508), c_Relation_ORange(_1670504, _1670506)))], (45179 ^ _780461) ^ [_1670567, _1670569, _1670571] : [-(hAPP(c_Relation_ODomain(_1670567, _1670569), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1670567, _1670569), tc_HOL_Obool), _1670571)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1670567, _1670569), tc_HOL_Obool), tc_fun(_1670567, tc_HOL_Obool)), _1670571), c_Relation_ODomain(_1670567, _1670569)))], (45181 ^ _780461) ^ [_1670630, _1670632, _1670634, _1670636] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1670630, tc_HOL_Obool), tc_fun(_1670632, tc_HOL_Obool)), _1670634), hAPP(hAPP(c_COMBC(tc_fun(_1670630, tc_HOL_Obool), tc_fun(_1670630, tc_fun(_1670632, tc_HOL_Obool)), tc_fun(_1670632, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670630, tc_fun(_1670632, tc_HOL_Obool))), _1670636)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670630, tc_fun(_1670632, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670630, tc_HOL_Obool), _1670634)), _1670636))], (45183 ^ _780461) ^ [_1670720, _1670722, _1670724, _1670726] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670720, tc_fun(_1670722, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670720, tc_HOL_Obool), _1670724)), _1670726) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1670720, tc_HOL_Obool), tc_fun(_1670722, tc_HOL_Obool)), _1670724), hAPP(hAPP(c_COMBC(tc_fun(_1670720, tc_HOL_Obool), tc_fun(_1670720, tc_fun(_1670722, tc_HOL_Obool)), tc_fun(_1670722, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670720, tc_fun(_1670722, tc_HOL_Obool))), _1670726)))], (45185 ^ _780461) ^ [_1670810] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670810, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1670810, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1670810, tc_HOL_Obool)))], (45187 ^ _780461) ^ [_1670852, _1670854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1670852, tc_HOL_Obool), tc_HOL_Obool)), _1670854), hAPP(c_Set_OPow(_1670852), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670852, tc_HOL_Obool), _1670854)))))], (45189 ^ _780461) ^ [_1670901, _1670903] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1670901), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670901, tc_HOL_Obool), _1670903))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1670901, tc_HOL_Obool)), _1670903)))], (45205 ^ _780461) ^ [_1671298, _1671300, _1671302] : [45207 ^ _780461 : [(45208 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1671298, tc_HOL_Obool)), 45206 ^ [_1671298, _1671300, _1671302]), _1671300)))], (45210 ^ _780461) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1671298, tc_HOL_Obool)), 45206 ^ [_1671298, _1671300, _1671302]), _1671302) = c_Orderings_Obot__class_Obot(tc_fun(_1671298, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1671298, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671298, tc_HOL_Obool), _1671300)), _1671302) = c_Orderings_Obot__class_Obot(tc_fun(_1671298, tc_HOL_Obool)))], (45195 ^ _780461) ^ [_1671030, _1671032, _1671034] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1671030, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671030, tc_HOL_Obool), _1671032)), _1671034) = c_Orderings_Obot__class_Obot(tc_fun(_1671030, tc_HOL_Obool)), 45198 ^ _780461 : [(45199 ^ _780461) ^ [_1671165] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1671030, tc_HOL_Obool)), _1671165), _1671032)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1671030, tc_HOL_Obool)), _1671165), _1671034) = c_Orderings_Obot__class_Obot(tc_fun(_1671030, tc_HOL_Obool)))]]], (45214 ^ _780461) ^ [_1671561] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671561, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1671561, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1671561, tc_HOL_Obool)))], (45216 ^ _780461) ^ [_1671603, _1671605, _1671607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1671603, tc_HOL_Obool), tc_HOL_Obool)), _1671605), _1671607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1671603, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671603, tc_HOL_Obool), _1671605)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671603, tc_HOL_Obool), _1671607))))], (45222 ^ _780461) ^ [_1671752, _1671754, _1671756] : [class_Complete__Lattice_Ocomplete__lattice(_1671752), 45225 ^ _780461 : [(45236 ^ _780461) ^ [] : [45238 ^ _780461 : [(45239 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1671752), 45237 ^ [_1671752, _1671754, _1671756]), _1671754)))], (45241 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1671752), 45237 ^ [_1671752, _1671754, _1671756]), _1671756))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1671752), c_Complete__Lattice_OSup__class_OSup(_1671752, _1671754)), _1671756)))], (45226 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1671752), c_Complete__Lattice_OSup__class_OSup(_1671752, _1671754)), _1671756)), 45229 ^ _780461 : [(45230 ^ _780461) ^ [_1671910] : [hBOOL(hAPP(hAPP(c_member(_1671752), _1671910), _1671754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1671752), _1671910), _1671756)))]]]]], (45245 ^ _780461) ^ [_1672186, _1672188, _1672190] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1672186, tc_HOL_Obool)), _1672188), _1672190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1672186, tc_HOL_Obool)), _1672188), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672186, tc_HOL_Obool), _1672190))))], (45251 ^ _780461) ^ [_1672317, _1672319] : [-(hAPP(c_Relation_OField(_1672317), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1672317, _1672317), tc_HOL_Obool), _1672319)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672317, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1672317, _1672317), tc_HOL_Obool), tc_fun(_1672317, tc_HOL_Obool), c_Relation_OField(_1672317)), _1672319)))], (45253 ^ _780461) ^ [_1672380, _1672382, _1672384] : [class_Complete__Lattice_Ocomplete__lattice(_1672380), class_Orderings_Olinorder(_1672380), 45260 ^ _780461 : [(45261 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1672380), _1672382), c_Complete__Lattice_OSup__class_OSup(_1672380, _1672384))), 45265 ^ _780461 : [(45266 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1672380), 45264 ^ [_1672380, _1672382, _1672384]), _1672384)))], (45268 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1672380), _1672382), 45264 ^ [_1672380, _1672382, _1672384])))]]], (45270 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1672380), _1672382), c_Complete__Lattice_OSup__class_OSup(_1672380, _1672384)))), 45271 ^ _780461 : [(45272 ^ _780461) ^ [_1672686] : [hBOOL(hAPP(hAPP(c_member(_1672380), _1672686), _1672384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1672380), _1672382), _1672686))]]]]], (45280 ^ _780461) ^ [_1672840, _1672842] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672840, tc_HOL_Obool), hAPP(c_Set_OPow(_1672840), _1672842)) = _1672842)], (45282 ^ _780461) ^ [_1672876, _1672878, _1672880] : [c_Equiv__Relations_Oequiv(_1672876, _1672878, _1672880), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672876, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1672876), _1672878), _1672880)) = _1672878)], (45288 ^ _780461) ^ [_1672985, _1672987, _1672989] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672985, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1672985, tc_HOL_Obool)), _1672987), _1672989)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1672985, tc_HOL_Obool)), _1672987), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1672985, tc_HOL_Obool), _1672989)))], (45290 ^ _780461) ^ [_1673046, _1673048, _1673050] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673046, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1673046, tc_HOL_Obool), tc_HOL_Obool)), _1673048), _1673050)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1673046, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673046, tc_HOL_Obool), _1673048)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673046, tc_HOL_Obool), _1673050)))], (45292 ^ _780461) ^ [_1673116, _1673118, _1673120, _1673122] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673116, tc_HOL_Obool), hAPP(c_Set_Oimage(_1673118, tc_fun(_1673116, tc_HOL_Obool), _1673120), _1673122)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1673118, tc_fun(_1673116, tc_HOL_Obool)), _1673122), _1673120))], (45294 ^ _780461) ^ [_1673173, _1673175, _1673177, _1673179] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1673173, tc_fun(_1673175, tc_HOL_Obool)), _1673177), _1673179) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673175, tc_HOL_Obool), hAPP(c_Set_Oimage(_1673173, tc_fun(_1673175, tc_HOL_Obool), _1673179), _1673177)))], (45296 ^ _780461) ^ [_1673230, _1673232, _1673234] : [class_Complete__Lattice_Ocomplete__lattice(_1673230), hBOOL(hAPP(hAPP(c_member(_1673230), _1673232), _1673234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1673230), _1673232), c_Complete__Lattice_OSup__class_OSup(_1673230, _1673234))))], (45306 ^ _780461) ^ [_1673395] : [class_Complete__Lattice_Ocomplete__lattice(_1673395), -(c_Complete__Lattice_OSup__class_OSup(_1673395, c_Orderings_Obot__class_Obot(tc_fun(_1673395, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1673395))], (45312 ^ _780461) ^ [_1673488, _1673490] : [class_Complete__Lattice_Ocomplete__lattice(_1673488), -(c_Complete__Lattice_OSup__class_OSup(_1673488, hAPP(hAPP(c_Set_Oinsert(_1673488), _1673490), c_Orderings_Obot__class_Obot(tc_fun(_1673488, tc_HOL_Obool)))) = _1673490)], (45318 ^ _780461) ^ [_1673595, _1673597, _1673599] : [class_Complete__Lattice_Ocomplete__lattice(_1673595), -(c_Complete__Lattice_OSup__class_OSup(_1673595, hAPP(hAPP(c_Set_Oinsert(_1673595), _1673597), _1673599)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1673595), _1673597), c_Complete__Lattice_OSup__class_OSup(_1673595, _1673599)))], (45324 ^ _780461) ^ [_1673716] : [class_Complete__Lattice_Ocomplete__lattice(_1673716), -(c_Complete__Lattice_OSup__class_OSup(_1673716, c_Orderings_Otop__class_Otop(tc_fun(_1673716, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1673716))], (45330 ^ _780461) ^ [_1673809, _1673811, _1673813] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1673809, tc_HOL_Obool)), _1673811), _1673813) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673809, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1673809, tc_HOL_Obool)), _1673811), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1673809, tc_HOL_Obool)), _1673813), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1673809, tc_HOL_Obool), tc_HOL_Obool))))))], (45332 ^ _780461) ^ [_1673883, _1673885, _1673887, _1673889, _1673891] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1673883, tc_fun(_1673885, tc_HOL_Obool)), _1673887), hAPP(hAPP(c_COMBS(_1673883, tc_fun(_1673885, tc_HOL_Obool), tc_fun(_1673885, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1673885, tc_HOL_Obool), tc_fun(tc_fun(_1673885, tc_HOL_Obool), tc_fun(_1673885, tc_HOL_Obool)), _1673883), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1673885, tc_HOL_Obool))), _1673889)), _1673891)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1673885, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673885, tc_HOL_Obool), hAPP(c_Set_Oimage(_1673883, tc_fun(_1673885, tc_HOL_Obool), _1673889), _1673887))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1673885, tc_HOL_Obool), hAPP(c_Set_Oimage(_1673883, tc_fun(_1673885, tc_HOL_Obool), _1673891), _1673887))))], (45334 ^ _780461) ^ [_1674012, _1674014, _1674016] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1674012, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1674012, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1674012, tc_HOL_Obool), tc_HOL_Obool)), _1674014), _1674016))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1674012, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1674012, tc_HOL_Obool), _1674014)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1674012, tc_HOL_Obool), _1674016)))))], (45336 ^ _780461) ^ [_1674092, _1674094, _1674096] : [class_Complete__Lattice_Ocomplete__lattice(_1674092), -(c_Complete__Lattice_OSup__class_OSup(_1674092, hAPP(hAPP(c_Set_Oinsert(_1674092), _1674094), hAPP(hAPP(c_Set_Oinsert(_1674092), _1674096), c_Orderings_Obot__class_Obot(tc_fun(_1674092, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1674092), _1674094), _1674096))], (45342 ^ _780461) ^ [_1674233, _1674235, _1674237] : [class_Complete__Lattice_Ocomplete__lattice(_1674233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1674233), _1674235)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1674233), _1674237), c_Complete__Lattice_OSup__class_OSup(_1674233, _1674235)) = hAPP(hAPP(c_Finite__Set_Ofold(_1674233, _1674233, c_Lattices_Osemilattice__sup__class_Osup(_1674233)), _1674237), _1674235))], (45352 ^ _780461) ^ [_1674418, _1674420] : [class_Complete__Lattice_Ocomplete__lattice(_1674418), hBOOL(hAPP(c_Finite__Set_Ofinite(_1674418), _1674420)), -(_1674420 = c_Orderings_Obot__class_Obot(tc_fun(_1674418, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1674418, _1674420) = c_Complete__Lattice_OSup__class_OSup(_1674418, _1674420))], (45366 ^ _780461) ^ [_1674590, _1674592] : [class_Complete__Lattice_Ocomplete__lattice(_1674590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1674590), _1674592)), -(c_Complete__Lattice_OSup__class_OSup(_1674590, _1674592) = hAPP(hAPP(c_Finite__Set_Ofold(_1674590, _1674590, c_Lattices_Osemilattice__sup__class_Osup(_1674590)), c_Orderings_Obot__class_Obot(_1674590)), _1674592))], (45376 ^ _780461) ^ [_1674758, _1674760, _1674762, _1674764] : [-(_1674758 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1674760, tc_HOL_Obool), tc_HOL_Obool))), 45382 ^ _780461 : [(45383 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1674760, tc_HOL_Obool)), 45381 ^ [_1674758, _1674760, _1674762, _1674764]), _1674758)))], (45385 ^ _780461) ^ [] : [c_Fun_Oinj__on(_1674760, _1674762, _1674764, 45381 ^ [_1674758, _1674760, _1674762, _1674764])]], -(c_Fun_Oinj__on(_1674760, _1674762, _1674764, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1674760, tc_HOL_Obool), _1674758)))], (45389 ^ _780461) ^ [_1675019, _1675021, _1675023] : [45391 ^ _780461 : [(45392 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1675019, tc_HOL_Obool)), 45390 ^ [_1675019, _1675021, _1675023]), _1675021)))], (45394 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1675019, tc_HOL_Obool)), 45390 ^ [_1675019, _1675021, _1675023]), _1675023))]], -(_1675021 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1675019, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1675019, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1675019, tc_HOL_Obool), _1675021)), _1675023)))], (45402 ^ _780461) ^ [_1675281, _1675283] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1675281, tc_HOL_Obool), _1675283) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1675281, tc_HOL_Obool), tc_fun(_1675281, tc_HOL_Obool)), _1675283), c_COMBI(tc_fun(_1675281, tc_HOL_Obool))))], (45404 ^ _780461) ^ [_1675332, _1675334] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1675332, tc_HOL_Obool)), _1675334)), 45410 ^ _780461 : [(45411 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1675332, tc_HOL_Obool)), 45409 ^ [_1675332, _1675334]), _1675334)))], (45413 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1675332), 45409 ^ [_1675332, _1675334]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1675332), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1675332, tc_HOL_Obool), _1675334))))], (45417 ^ _780461) ^ [_1675590, _1675592, _1675594] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1675590, tc_HOL_Obool)), _1675592), _1675594))), 45423 ^ _780461 : [(45424 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1675590, tc_HOL_Obool)), 45422 ^ [_1675590, _1675592, _1675594]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1675590, tc_HOL_Obool)), _1675592), _1675594))))], (45427 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1675590, tc_HOL_Obool)), 45425 ^ [_1675590, _1675592, _1675594]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1675590, tc_HOL_Obool)), _1675592), _1675594))))], (45429 ^ _780461) ^ [] : [45422 ^ [_1675590, _1675592, _1675594] = 45425 ^ [_1675590, _1675592, _1675594]], (45431 ^ _780461) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1675590, tc_HOL_Obool)), 45422 ^ [_1675590, _1675592, _1675594]), 45425 ^ [_1675590, _1675592, _1675594]) = c_Orderings_Obot__class_Obot(tc_fun(_1675590, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1675590, tc_HOL_Obool)), _1675592), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1675590, tc_HOL_Obool), _1675594)) = c_Orderings_Obot__class_Obot(tc_fun(_1675590, tc_HOL_Obool)))], (45435 ^ _780461) ^ [_1676184, _1676186, _1676188] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1676184, tc_HOL_Obool)), _1676186)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1676184), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1676184, tc_HOL_Obool), _1676186))), 45445 ^ _780461 : [(45446 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1676184, tc_HOL_Obool)), 45444 ^ [_1676184, _1676186, _1676188]), _1676186)))], (45448 ^ _780461) ^ [] : [hAPP(c_Finite__Set_Ocard(_1676184), 45444 ^ [_1676184, _1676186, _1676188]) = _1676188]], 45452 ^ _780461 : [(45453 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1676184, tc_HOL_Obool)), 45451 ^ [_1676184, _1676186, _1676188]), _1676186)))], (45456 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1676184, tc_HOL_Obool)), 45454 ^ [_1676184, _1676186, _1676188]), _1676186)))], (45458 ^ _780461) ^ [] : [45451 ^ [_1676184, _1676186, _1676188] = 45454 ^ [_1676184, _1676186, _1676188]], (45460 ^ _780461) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1676184, tc_HOL_Obool)), 45451 ^ [_1676184, _1676186, _1676188]), 45454 ^ [_1676184, _1676186, _1676188]) = c_Orderings_Obot__class_Obot(tc_fun(_1676184, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1676188), hAPP(c_Finite__Set_Ocard(tc_fun(_1676184, tc_HOL_Obool)), _1676186)) = hAPP(c_Finite__Set_Ocard(_1676184), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1676184, tc_HOL_Obool), _1676186)))], (45464 ^ _780461) ^ [_1676965, _1676967, _1676969, _1676971, _1676973, _1676975] : [-(_1676965 = c_Orderings_Obot__class_Obot(tc_fun(_1676967, tc_HOL_Obool))), 45470 ^ _780461 : [(45471 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676967), 45469 ^ [_1676965, _1676967, _1676969, _1676971, _1676973, _1676975]), _1676965)))], (45473 ^ _780461) ^ [] : [c_Fun_Oinj__on(_1676969, _1676971, _1676973, hAPP(_1676975, 45469 ^ [_1676965, _1676967, _1676969, _1676971, _1676973, _1676975]))]], -(c_Fun_Oinj__on(_1676969, _1676971, _1676973, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1676967, tc_fun(_1676969, tc_HOL_Obool)), _1676965), _1676975)))], (45477 ^ _780461) ^ [_1677257, _1677259, _1677261, _1677263, _1677265, _1677267, _1677269] : [c_Finite__Set_Ofun__left__comm(_1677257, _1677259, _1677261), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1677257, _1677259, _1677261, _1677263, hAPP(hAPP(c_Set_Oinsert(_1677257), _1677265), _1677267)), _1677269)), -(hBOOL(hAPP(hAPP(c_member(_1677257), _1677265), _1677267))), 45489 ^ _780461 : [(45490 ^ _780461) ^ [] : [-(_1677269 = hAPP(hAPP(_1677261, _1677265), 45488 ^ [_1677257, _1677259, _1677261, _1677263, _1677265, _1677267, _1677269]))], (45492 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1677257, _1677259, _1677261, _1677263, _1677267), 45488 ^ [_1677257, _1677259, _1677261, _1677263, _1677265, _1677267, _1677269])))]]], (45494 ^ _780461) ^ [_1677579, _1677581] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1677579, _1677579)), hAPP(hAPP(c_Product__Type_OPair(_1677579, _1677579), 45495 ^ [_1677579, _1677581]), 45495 ^ [_1677579, _1677581])), c_Transitive__Closure_Otrancl(_1677579, _1677581)))), -(c_Wellfounded_Oacyclic(_1677579, _1677581))], (45501 ^ _780461) ^ [_1677651, _1677653, _1677655, _1677657, _1677659] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1677651, _1677651)), hAPP(hAPP(c_Product__Type_OPair(_1677651, _1677651), _1677653), _1677655)), c_Transitive__Closure_Ortrancl(_1677651, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1677651, _1677651), tc_HOL_Obool)), _1677657), _1677659)))), 45507 ^ _780461 : [(45508 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1677651, _1677651)), hAPP(hAPP(c_Product__Type_OPair(_1677651, _1677651), 45506 ^ [_1677651, _1677653, _1677655, _1677657, _1677659]), _1677655)), c_Transitive__Closure_Ortrancl(_1677651, _1677657))))], (45511 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1677651, _1677651)), hAPP(hAPP(c_Product__Type_OPair(_1677651, _1677651), 45509 ^ [_1677651, _1677653, _1677655, _1677657, _1677659]), 45506 ^ [_1677651, _1677653, _1677655, _1677657, _1677659])), _1677659)))], (45513 ^ _780461) ^ [] : [45509 ^ [_1677651, _1677653, _1677655, _1677657, _1677659] = 45506 ^ [_1677651, _1677653, _1677655, _1677657, _1677659]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1677651, _1677651)), hAPP(hAPP(c_Product__Type_OPair(_1677651, _1677651), _1677653), _1677655)), c_Transitive__Closure_Ortrancl(_1677651, _1677657))))], (45517 ^ _780461) ^ [_1678210, _1678212, _1678214, _1678216, _1678218] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1678210, _1678210)), hAPP(hAPP(c_Product__Type_OPair(_1678210, _1678210), _1678212), _1678214)), c_Transitive__Closure_Ortrancl(_1678210, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1678210, _1678210), tc_HOL_Obool)), _1678216), _1678218)))), 45523 ^ _780461 : [(45524 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1678210, _1678210)), hAPP(hAPP(c_Product__Type_OPair(_1678210, _1678210), _1678212), 45522 ^ [_1678210, _1678212, _1678214, _1678216, _1678218])), c_Transitive__Closure_Ortrancl(_1678210, _1678216))))], (45527 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1678210, _1678210)), hAPP(hAPP(c_Product__Type_OPair(_1678210, _1678210), 45522 ^ [_1678210, _1678212, _1678214, _1678216, _1678218]), 45525 ^ [_1678210, _1678212, _1678214, _1678216, _1678218])), _1678218)))], (45529 ^ _780461) ^ [] : [45522 ^ [_1678210, _1678212, _1678214, _1678216, _1678218] = 45525 ^ [_1678210, _1678212, _1678214, _1678216, _1678218]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1678210, _1678210)), hAPP(hAPP(c_Product__Type_OPair(_1678210, _1678210), _1678212), _1678214)), c_Transitive__Closure_Ortrancl(_1678210, _1678216))))], (45533 ^ _780461) ^ [_1678769, _1678771, _1678773, _1678775, _1678777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1678769, _1678769)), hAPP(hAPP(c_Product__Type_OPair(_1678769, _1678769), _1678771), _1678773)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1678769, _1678769), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1678775)), _1678777))), 45537 ^ _780461 : [(45538 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1678769, _1678769)), hAPP(hAPP(c_Product__Type_OPair(_1678769, _1678769), _1678771), 45536 ^ [_1678769, _1678771, _1678773, _1678775, _1678777])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1678769, _1678769), tc_HOL_Obool), _1678775), _1678777))))], (45540 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1678769, _1678769)), hAPP(hAPP(c_Product__Type_OPair(_1678769, _1678769), 45536 ^ [_1678769, _1678771, _1678773, _1678775, _1678777]), _1678773)), _1678777)))]]], (45542 ^ _780461) ^ [_1679081, _1679083, _1679085, _1679087, _1679089] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1679081, _1679081)), hAPP(hAPP(c_Product__Type_OPair(_1679081, _1679081), _1679083), _1679085)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1679081, _1679081), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1679087)), _1679089))), 45546 ^ _780461 : [(45547 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679081, _1679081)), hAPP(hAPP(c_Product__Type_OPair(_1679081, _1679081), _1679083), 45545 ^ [_1679081, _1679083, _1679085, _1679087, _1679089])), _1679089)))], (45549 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679081, _1679081)), hAPP(hAPP(c_Product__Type_OPair(_1679081, _1679081), 45545 ^ [_1679081, _1679083, _1679085, _1679087, _1679089]), _1679085)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1679081, _1679081), tc_HOL_Obool), _1679087), _1679089))))]]], (45551 ^ _780461) ^ [_1679393, _1679395, _1679397, _1679399, _1679401] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1679393, _1679393)), hAPP(hAPP(c_Product__Type_OPair(_1679393, _1679393), _1679395), _1679397)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1679393, _1679393), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1679399)), _1679401))), 45555 ^ _780461 : [(45556 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679393, _1679393)), hAPP(hAPP(c_Product__Type_OPair(_1679393, _1679393), _1679395), 45554 ^ [_1679393, _1679395, _1679397, _1679399, _1679401])), _1679401)))], (45558 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679393, _1679393)), hAPP(hAPP(c_Product__Type_OPair(_1679393, _1679393), 45554 ^ [_1679393, _1679395, _1679397, _1679399, _1679401]), _1679397)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1679393, _1679393), tc_HOL_Obool), _1679399), _1679401))))]]], (45560 ^ _780461) ^ [_1679701, _1679703, _1679705, _1679707] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1679701, _1679701)), hAPP(hAPP(c_Product__Type_OPair(_1679701, _1679701), _1679703), _1679705)), c_Transitive__Closure_Otrancl(_1679701, _1679707))), 45564 ^ _780461 : [(45565 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679701, _1679701)), hAPP(hAPP(c_Product__Type_OPair(_1679701, _1679701), _1679703), 45563 ^ [_1679701, _1679703, _1679705, _1679707])), _1679707)))], (45567 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679701, _1679701)), hAPP(hAPP(c_Product__Type_OPair(_1679701, _1679701), 45563 ^ [_1679701, _1679703, _1679705, _1679707]), _1679705)), c_Transitive__Closure_Ortrancl(_1679701, _1679707))))]]], (45569 ^ _780461) ^ [_1679961, _1679963, _1679965, _1679967] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1679961, _1679961)), hAPP(hAPP(c_Product__Type_OPair(_1679961, _1679961), _1679963), _1679965)), c_Transitive__Closure_Otrancl(_1679961, _1679967))), 45573 ^ _780461 : [(45574 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679961, _1679961)), hAPP(hAPP(c_Product__Type_OPair(_1679961, _1679961), _1679963), 45572 ^ [_1679961, _1679963, _1679965, _1679967])), c_Transitive__Closure_Ortrancl(_1679961, _1679967))))], (45576 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1679961, _1679961)), hAPP(hAPP(c_Product__Type_OPair(_1679961, _1679961), 45572 ^ [_1679961, _1679963, _1679965, _1679967]), _1679965)), _1679967)))]]], (45578 ^ _780461) ^ [_1680221, _1680223, _1680225, _1680227] : [class_Orderings_Olinorder(_1680221), hBOOL(hAPP(c_Finite__Set_Ofinite(_1680221), _1680223)), 45588 ^ _780461 : [(45589 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1680221), 45587 ^ [_1680221, _1680223, _1680225, _1680227]), _1680223)))], (45591 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1680221), 45587 ^ [_1680221, _1680223, _1680225, _1680227]), _1680225))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1680221), hAPP(hAPP(c_Finite__Set_Ofold(_1680221, _1680221, c_Orderings_Oord__class_Omax(_1680221)), _1680227), _1680223)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1680221), _1680225), _1680227))))], (45595 ^ _780461) ^ [_1680585, _1680587, _1680589, _1680591] : [class_Orderings_Olinorder(_1680585), hBOOL(hAPP(c_Finite__Set_Ofinite(_1680585), _1680587)), 45605 ^ _780461 : [(45606 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1680585), 45604 ^ [_1680585, _1680587, _1680589, _1680591]), _1680587)))], (45608 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1680585), _1680589), 45604 ^ [_1680585, _1680587, _1680589, _1680591]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1680585), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1680585), _1680589), _1680591)), hAPP(hAPP(c_Finite__Set_Ofold(_1680585, _1680585, c_Orderings_Oord__class_Omin(_1680585)), _1680591), _1680587))))], (45612 ^ _780461) ^ [_1680949, _1680951, _1680953] : [45614 ^ _780461 : [(45615 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1680949, tc_HOL_Obool)), 45613 ^ [_1680949, _1680951, _1680953]), _1680951)))], (45617 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1680949), _1680953), 45613 ^ [_1680949, _1680951, _1680953]))]], -(hBOOL(hAPP(hAPP(c_member(_1680949), _1680953), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1680949, tc_HOL_Obool), _1680951))))], (45621 ^ _780461) ^ [_1681165, _1681167, _1681169, _1681171] : [class_Lattices_Osemilattice__inf(_1681165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1681165), _1681167)), 45631 ^ _780461 : [(45632 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1681165), 45630 ^ [_1681165, _1681167, _1681169, _1681171]), _1681167)))], (45634 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1681165), _1681169), 45630 ^ [_1681165, _1681167, _1681169, _1681171]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1681165), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1681165), _1681169), _1681171)), hAPP(hAPP(c_Finite__Set_Ofold(_1681165, _1681165, c_Lattices_Osemilattice__inf__class_Oinf(_1681165)), _1681171), _1681167))))], (45638 ^ _780461) ^ [_1681529, _1681531, _1681533, _1681535] : [class_Lattices_Osemilattice__sup(_1681529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1681529), _1681531)), 45648 ^ _780461 : [(45649 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1681529), 45647 ^ [_1681529, _1681531, _1681533, _1681535]), _1681531)))], (45651 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1681529), 45647 ^ [_1681529, _1681531, _1681533, _1681535]), _1681533))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1681529), hAPP(hAPP(c_Finite__Set_Ofold(_1681529, _1681529, c_Lattices_Osemilattice__sup__class_Osup(_1681529)), _1681535), _1681531)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1681529), _1681533), _1681535))))], (45655 ^ _780461) ^ [_1681893, _1681895] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681893, _1681893)), _1681895), c_Relation_OId(_1681893))), -(_1681895 = hAPP(hAPP(c_Product__Type_OPair(_1681893, _1681893), 45658 ^ [_1681893, _1681895]), 45658 ^ [_1681893, _1681895]))], (45679 ^ _780461) ^ [_1682569, _1682571] : [-(c_Wellfounded_Owf(_1682569, _1682571)), 45682 ^ _780461 : [(45683 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1682569), 45681 ^ [_1682569, _1682571]), 45680 ^ [_1682569, _1682571])))], (45685 ^ _780461) ^ [_1682789] : [hBOOL(hAPP(hAPP(c_member(_1682569), _1682789), 45680 ^ [_1682569, _1682571])), 45689 ^ _780461 : [(45690 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682569, _1682569)), hAPP(hAPP(c_Product__Type_OPair(_1682569, _1682569), 45688 ^ [_1682569, _1682571, _1682789]), _1682789)), _1682571)))], (45692 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1682569), 45688 ^ [_1682569, _1682571, _1682789]), 45680 ^ [_1682569, _1682571])))]]]]], (45662 ^ _780461) ^ [_1682050, _1682052] : [c_Wellfounded_Owf(_1682050, _1682052), 45665 ^ _780461 : [(45666 ^ _780461) ^ [_1682182] : [45667 ^ _780461 : [(45668 ^ _780461) ^ [_1682287] : [hBOOL(hAPP(hAPP(c_member(_1682050), _1682287), _1682182))]], 45670 ^ _780461 : [(45671 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1682050), 45669 ^ [_1682050, _1682052, _1682182]), _1682182)))], (45673 ^ _780461) ^ [_1682409] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1682050, _1682050)), hAPP(hAPP(c_Product__Type_OPair(_1682050, _1682050), _1682409), 45669 ^ [_1682050, _1682052, _1682182])), _1682052)), hBOOL(hAPP(hAPP(c_member(_1682050), _1682409), _1682182))]]]]], (45696 ^ _780461) ^ [_1683045, _1683047, _1683049, _1683051, _1683053, _1683055, _1683057, _1683059] : [c_Finite__Set_Ofolding__image__simple__idem(_1683045, _1683047, _1683049, _1683051, _1683053, _1683055), hBOOL(hAPP(c_Finite__Set_Ofinite(_1683047), _1683057)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1683047), _1683059)), -(hAPP(_1683055, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1683047, tc_HOL_Obool)), _1683057), _1683059)) = hAPP(hAPP(_1683049, hAPP(_1683055, _1683057)), hAPP(_1683055, _1683059)))], (45710 ^ _780461) ^ [_1683338, _1683340] : [-(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)))), _1683338)) = 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)))), _1683340))), 45712 ^ _780461 : [(45713 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 45711 ^ [_1683338, _1683340])))], (45715 ^ _780461) ^ [] : [45716 ^ _780461 : [(45717 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1683338, 45711 ^ [_1683338, _1683340])))], (45719 ^ _780461) ^ [] : [hBOOL(hAPP(_1683340, 45711 ^ [_1683338, _1683340]))]], 45720 ^ _780461 : [(45721 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1683340, 45711 ^ [_1683338, _1683340])))], (45723 ^ _780461) ^ [] : [hBOOL(hAPP(_1683338, 45711 ^ [_1683338, _1683340]))]]]]], (45727 ^ _780461) ^ [_1683659, _1683661, _1683663, _1683665, _1683667, _1683669, _1683671] : [c_Finite__Set_Ofolding__image__simple__idem(_1683659, _1683661, _1683663, _1683665, _1683667, _1683669), -(hAPP(hAPP(_1683663, _1683671), _1683671) = _1683671)], (45733 ^ _780461) ^ [_1683766, _1683768, _1683770, _1683772, _1683774, _1683776, _1683778, _1683780] : [c_Finite__Set_Ofolding__image__simple__idem(_1683766, _1683768, _1683770, _1683772, _1683774, _1683776), hBOOL(hAPP(c_Finite__Set_Ofinite(_1683768), _1683778)), hBOOL(hAPP(hAPP(c_member(_1683768), _1683780), _1683778)), -(hAPP(hAPP(_1683770, hAPP(_1683774, _1683780)), hAPP(_1683776, _1683778)) = hAPP(_1683776, _1683778))], (45747 ^ _780461) ^ [_1684043, _1684045, _1684047, _1684049, _1684051, _1684053, _1684055, _1684057] : [c_Finite__Set_Ofolding__image__simple__idem(_1684043, _1684045, _1684047, _1684049, _1684051, _1684053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1684045), _1684055)), -(hAPP(_1684053, hAPP(hAPP(c_Set_Oinsert(_1684045), _1684057), _1684055)) = hAPP(hAPP(_1684047, hAPP(_1684051, _1684057)), hAPP(_1684053, _1684055)))], (45757 ^ _780461) ^ [_1684258, _1684260, _1684262, _1684264, _1684266, _1684268, _1684270, _1684272] : [c_Finite__Set_Ofolding__image__simple__idem(_1684258, _1684260, _1684262, _1684264, _1684266, _1684268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1684260), _1684270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684260, tc_HOL_Obool)), _1684272), _1684270)), -(hAPP(hAPP(_1684262, hAPP(_1684268, _1684272)), hAPP(_1684268, _1684270)) = hAPP(_1684268, _1684270))], (45771 ^ _780461) ^ [_1684541, _1684543, _1684545, _1684547, _1684549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684541, tc_HOL_Obool)), _1684543), _1684545)), 45777 ^ _780461 : [(45778 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1684541), 45776 ^ [_1684541, _1684543, _1684545, _1684547, _1684549]), _1684543)))], (45780 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1684547, 45776 ^ [_1684541, _1684543, _1684545, _1684547, _1684549])))], (45782 ^ _780461) ^ [] : [hBOOL(hAPP(_1684549, 45776 ^ [_1684541, _1684543, _1684545, _1684547, _1684549]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684541, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1684541, tc_HOL_Obool)), _1684543), hAPP(c_Set_OCollect(_1684541), _1684547))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1684541, tc_HOL_Obool)), _1684545), hAPP(c_Set_OCollect(_1684541), _1684549)))))], (45786 ^ _780461) ^ [_1684941, _1684943, _1684945] : [hBOOL(hAPP(hAPP(c_member(_1684941), _1684943), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1684941, tc_HOL_Obool), _1684945))), 45790 ^ _780461 : [(45791 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1684941), _1684943), 45789 ^ [_1684941, _1684943, _1684945])))], (45793 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1684941, tc_HOL_Obool)), 45789 ^ [_1684941, _1684943, _1684945]), _1684945)))]]], (45795 ^ _780461) ^ [_1685129, _1685131, _1685133, _1685135, _1685137, _1685139] : [-(hBOOL(hAPP(hAPP(c_member(_1685129), _1685131), c_Map_Odom(_1685129, _1685133, _1685135)))), -(c_Map_Omap__add(_1685129, _1685133, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1685129, tc_Option_Ooption(_1685133)), _1685137), _1685131), hAPP(c_Option_Ooption_OSome(_1685133), _1685139)), _1685135) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1685129, tc_Option_Ooption(_1685133)), c_Map_Omap__add(_1685129, _1685133, _1685137, _1685135)), _1685131), hAPP(c_Option_Ooption_OSome(_1685133), _1685139)))], (45801 ^ _780461) ^ [_1685232, _1685234, _1685236, _1685238, _1685240, _1685242] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685232, _1685234)), _1685236), hAPP(hAPP(c_Relation_Orel__comp(_1685232, _1685238, _1685234), _1685240), _1685242))), 45807 ^ _780461 : [(45808 ^ _780461) ^ [] : [-(_1685236 = hAPP(hAPP(c_Product__Type_OPair(_1685232, _1685234), 45804 ^ [_1685232, _1685234, _1685236, _1685238, _1685240, _1685242]), 45806 ^ [_1685232, _1685234, _1685236, _1685238, _1685240, _1685242]))], (45810 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1685232, _1685238)), hAPP(hAPP(c_Product__Type_OPair(_1685232, _1685238), 45804 ^ [_1685232, _1685234, _1685236, _1685238, _1685240, _1685242]), 45805 ^ [_1685232, _1685234, _1685236, _1685238, _1685240, _1685242])), _1685240)))], (45812 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1685238, _1685234)), hAPP(hAPP(c_Product__Type_OPair(_1685238, _1685234), 45805 ^ [_1685232, _1685234, _1685236, _1685238, _1685240, _1685242]), 45806 ^ [_1685232, _1685234, _1685236, _1685238, _1685240, _1685242])), _1685242)))]]], (45814 ^ _780461) ^ [_1685610, _1685612, _1685614, _1685616, _1685618, _1685620] : [-(c_Map_Omap__add(_1685610, _1685612, _1685614, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1685610, tc_Option_Ooption(_1685612)), _1685616), _1685618), hAPP(c_Option_Ooption_OSome(_1685612), _1685620))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1685610, tc_Option_Ooption(_1685612)), c_Map_Omap__add(_1685610, _1685612, _1685614, _1685616)), _1685618), hAPP(c_Option_Ooption_OSome(_1685612), _1685620)))], (45816 ^ _780461) ^ [_1685691, _1685693, _1685695, _1685697, _1685699, _1685701] : [hAPP(c_Map_Omap__add(_1685691, _1685693, _1685695, _1685697), _1685699) = hAPP(c_Option_Ooption_OSome(_1685693), _1685701), -(hAPP(_1685697, _1685699) = hAPP(c_Option_Ooption_OSome(_1685693), _1685701)), 45823 ^ _780461 : [(45824 ^ _780461) ^ [] : [-(hAPP(_1685697, _1685699) = c_Option_Ooption_ONone(_1685693))], (45826 ^ _780461) ^ [] : [-(hAPP(_1685695, _1685699) = hAPP(c_Option_Ooption_OSome(_1685693), _1685701))]]], (45828 ^ _780461) ^ [_1685927, _1685929, _1685931, _1685933, _1685935, _1685937] : [hAPP(c_Map_Omap__add(_1685927, _1685929, _1685931, _1685933), _1685935) = hAPP(c_Option_Ooption_OSome(_1685929), _1685937), -(hAPP(_1685933, _1685935) = hAPP(c_Option_Ooption_OSome(_1685929), _1685937)), 45835 ^ _780461 : [(45836 ^ _780461) ^ [] : [-(hAPP(_1685933, _1685935) = c_Option_Ooption_ONone(_1685929))], (45838 ^ _780461) ^ [] : [-(hAPP(_1685931, _1685935) = hAPP(c_Option_Ooption_OSome(_1685929), _1685937))]]], (45840 ^ _780461) ^ [_1686132, _1686134, _1686136, _1686138, _1686140, _1686142] : [-(hAPP(c_Map_Omap__add(_1686132, _1686134, _1686136, _1686138), _1686140) = hAPP(c_Option_Ooption_OSome(_1686134), _1686142)), 45841 ^ _780461 : [(45842 ^ _780461) ^ [] : [hAPP(_1686138, _1686140) = hAPP(c_Option_Ooption_OSome(_1686134), _1686142)], (45844 ^ _780461) ^ [] : [hAPP(_1686138, _1686140) = c_Option_Ooption_ONone(_1686134), hAPP(_1686136, _1686140) = hAPP(c_Option_Ooption_OSome(_1686134), _1686142)]]], (45852 ^ _780461) ^ [_1686383, _1686385, _1686387, _1686389, _1686391] : [-(hAPP(c_Map_Omap__add(_1686383, _1686385, _1686387, _1686389), _1686391) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1686385), _1686385, hAPP(_1686387, _1686391), c_Option_Ooption_OSome(_1686385)), hAPP(_1686389, _1686391)))], (45854 ^ _780461) ^ [_1686440, _1686442, _1686444] : [-(c_Map_Omap__add(_1686440, _1686442, _1686444, hAPP(c_COMBK(tc_Option_Ooption(_1686442), _1686440), c_Option_Ooption_ONone(_1686442))) = _1686444)], (45856 ^ _780461) ^ [_1686482, _1686484, _1686486] : [-(c_Map_Omap__add(_1686482, _1686484, hAPP(c_COMBK(tc_Option_Ooption(_1686484), _1686482), c_Option_Ooption_ONone(_1686484)), _1686486) = _1686486)], (45858 ^ _780461) ^ [_1686548, _1686550, _1686552, _1686554, _1686556] : [hAPP(c_Map_Omap__add(_1686548, _1686550, _1686552, _1686554), _1686556) = c_Option_Ooption_ONone(_1686550), 45861 ^ _780461 : [(45862 ^ _780461) ^ [] : [-(hAPP(_1686554, _1686556) = c_Option_Ooption_ONone(_1686550))], (45864 ^ _780461) ^ [] : [-(hAPP(_1686552, _1686556) = c_Option_Ooption_ONone(_1686550))]]], (45866 ^ _780461) ^ [_1686693, _1686695, _1686697, _1686699, _1686701] : [-(hAPP(c_Map_Omap__add(_1686693, _1686695, _1686697, _1686699), _1686701) = c_Option_Ooption_ONone(_1686695)), hAPP(_1686699, _1686701) = c_Option_Ooption_ONone(_1686695), hAPP(_1686697, _1686701) = c_Option_Ooption_ONone(_1686695)], (45876 ^ _780461) ^ [_1686876, _1686878, _1686880, _1686882, _1686884, _1686886] : [hAPP(_1686876, _1686878) = hAPP(c_Option_Ooption_OSome(_1686880), _1686882), -(hAPP(c_Map_Omap__add(_1686884, _1686880, _1686886, _1686876), _1686878) = hAPP(c_Option_Ooption_OSome(_1686880), _1686882))], (45882 ^ _780461) ^ [_1687003, _1687005, _1687007, _1687009, _1687011] : [-(c_Map_Omap__add(_1687003, _1687005, _1687007, c_Map_Omap__add(_1687003, _1687005, _1687009, _1687011)) = c_Map_Omap__add(_1687003, _1687005, c_Map_Omap__add(_1687003, _1687005, _1687007, _1687009), _1687011))], (45884 ^ _780461) ^ [_1687054, _1687056, _1687058, _1687060, _1687062] : [hBOOL(hAPP(hAPP(c_member(_1687054), _1687056), c_Map_Odom(_1687054, _1687058, _1687060))), -(hAPP(c_Map_Omap__add(_1687054, _1687058, _1687062, _1687060), _1687056) = hAPP(_1687060, _1687056))], (45890 ^ _780461) ^ [_1687177, _1687179, _1687181, _1687183, _1687185] : [-(hBOOL(hAPP(hAPP(c_member(_1687177), _1687179), c_Map_Odom(_1687177, _1687181, _1687183)))), -(hAPP(c_Map_Omap__add(_1687177, _1687181, _1687185, _1687183), _1687179) = hAPP(_1687185, _1687179))], (45896 ^ _780461) ^ [_1687237, _1687239, _1687241, _1687243, _1687245] : [-(hBOOL(hAPP(hAPP(c_member(_1687237), _1687239), c_Map_Odom(_1687237, _1687241, _1687243)))), -(hAPP(c_Map_Omap__add(_1687237, _1687241, _1687243, _1687245), _1687239) = hAPP(_1687245, _1687239))], (45902 ^ _780461) ^ [_1687301, _1687303, _1687305, _1687307] : [-(c_Map_Odom(_1687301, _1687303, c_Map_Omap__add(_1687301, _1687303, _1687305, _1687307)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1687301, tc_HOL_Obool)), c_Map_Odom(_1687301, _1687303, _1687307)), c_Map_Odom(_1687301, _1687303, _1687305)))], (45904 ^ _780461) ^ [_1687379, _1687381, _1687383, _1687385] : [c_Fun_Oinj__on(_1687379, tc_Option_Ooption(_1687381), c_Map_Omap__add(_1687379, _1687381, _1687383, _1687385), c_Map_Odom(_1687379, _1687381, _1687385)), -(c_Fun_Oinj__on(_1687379, tc_Option_Ooption(_1687381), _1687385, c_Map_Odom(_1687379, _1687381, _1687385)))], (45910 ^ _780461) ^ [_1687498, _1687500, _1687502, _1687504] : [c_Fun_Oinj__on(_1687498, tc_Option_Ooption(_1687500), _1687504, c_Map_Odom(_1687498, _1687500, _1687504)), -(c_Fun_Oinj__on(_1687498, tc_Option_Ooption(_1687500), c_Map_Omap__add(_1687498, _1687500, _1687502, _1687504), c_Map_Odom(_1687498, _1687500, _1687504)))], (45916 ^ _780461) ^ [_1687623, _1687625, _1687627, _1687629] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1687623, tc_HOL_Obool)), c_Map_Odom(_1687623, _1687625, _1687627)), c_Map_Odom(_1687623, _1687625, _1687629)) = c_Orderings_Obot__class_Obot(tc_fun(_1687623, tc_HOL_Obool)), -(c_Map_Omap__add(_1687623, _1687625, _1687627, _1687629) = c_Map_Omap__add(_1687623, _1687625, _1687629, _1687627))], (45922 ^ _780461) ^ [_1687772, _1687774, _1687776, _1687778] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1687772)), hAPP(c_Set_Oimage(_1687774, tc_Option_Ooption(_1687772), _1687776), c_Orderings_Otop__class_Otop(tc_fun(_1687774, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1687772)), hAPP(c_Set_Oimage(_1687774, tc_Option_Ooption(_1687772), c_Map_Omap__add(_1687774, _1687772, _1687776, c_Map_Omap__of(_1687774, _1687772, _1687778))), c_Orderings_Otop__class_Otop(tc_fun(_1687774, tc_HOL_Obool))))))], (45928 ^ _780461) ^ [_1687951, _1687953, _1687955, _1687957] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1687951, _1687953)), _1687955), hAPP(c_Relation_Oconverse(_1687953, _1687951), _1687957))), 45933 ^ _780461 : [(45934 ^ _780461) ^ [] : [-(_1687955 = hAPP(hAPP(c_Product__Type_OPair(_1687951, _1687953), 45932 ^ [_1687951, _1687953, _1687955, _1687957]), 45931 ^ [_1687951, _1687953, _1687955, _1687957]))], (45936 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1687953, _1687951)), hAPP(hAPP(c_Product__Type_OPair(_1687953, _1687951), 45931 ^ [_1687951, _1687953, _1687955, _1687957]), 45932 ^ [_1687951, _1687953, _1687955, _1687957])), _1687957)))]]], (45938 ^ _780461) ^ [_1688204, _1688206, _1688208] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1688204), c_Map_Odom(_1688204, _1688206, c_Map_Omap__of(_1688204, _1688206, _1688208)))))], (45940 ^ _780461) ^ [_1688243, _1688245, _1688247] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1688243)), hAPP(c_Set_Oimage(_1688245, tc_Option_Ooption(_1688243), c_Map_Omap__of(_1688245, _1688243, _1688247)), c_Orderings_Otop__class_Otop(tc_fun(_1688245, tc_HOL_Obool))))))], (45942 ^ _780461) ^ [_1688294, _1688296, _1688298, _1688300] : [-(c_Map_Omap__add(_1688294, _1688296, _1688298, c_Map_Omap__of(_1688294, _1688296, _1688300)) = c_List_Ofoldr(tc_prod(_1688294, _1688296), tc_fun(_1688294, tc_Option_Ooption(_1688296)), hAPP(c_Product__Type_Oprod_Oprod__case(_1688294, _1688296, tc_fun(tc_fun(_1688294, tc_Option_Ooption(_1688296)), tc_fun(_1688294, tc_Option_Ooption(_1688296)))), hAPP(hAPP(c_COMBC(_1688294, tc_fun(_1688296, tc_Option_Ooption(_1688296)), tc_fun(_1688296, tc_fun(tc_fun(_1688294, tc_Option_Ooption(_1688296)), tc_fun(_1688294, tc_Option_Ooption(_1688296))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1688296), tc_fun(tc_fun(_1688294, tc_Option_Ooption(_1688296)), tc_fun(_1688294, tc_Option_Ooption(_1688296)))), tc_fun(tc_fun(_1688296, tc_Option_Ooption(_1688296)), tc_fun(_1688296, tc_fun(tc_fun(_1688294, tc_Option_Ooption(_1688296)), tc_fun(_1688294, tc_Option_Ooption(_1688296))))), _1688294), c_COMBB(tc_Option_Ooption(_1688296), tc_fun(tc_fun(_1688294, tc_Option_Ooption(_1688296)), tc_fun(_1688294, tc_Option_Ooption(_1688296))), _1688296)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1688294, tc_Option_Ooption(_1688296)), tc_fun(tc_Option_Ooption(_1688296), tc_fun(_1688294, tc_Option_Ooption(_1688296)))), tc_fun(tc_Option_Ooption(_1688296), tc_fun(tc_fun(_1688294, tc_Option_Ooption(_1688296)), tc_fun(_1688294, tc_Option_Ooption(_1688296)))), _1688294), c_COMBC(tc_fun(_1688294, tc_Option_Ooption(_1688296)), tc_Option_Ooption(_1688296), tc_fun(_1688294, tc_Option_Ooption(_1688296)))), hAPP(c_COMBC(tc_fun(_1688294, tc_Option_Ooption(_1688296)), _1688294, tc_fun(tc_Option_Ooption(_1688296), tc_fun(_1688294, tc_Option_Ooption(_1688296)))), c_Fun_Ofun__upd(_1688294, tc_Option_Ooption(_1688296)))))), c_Option_Ooption_OSome(_1688296))), _1688300, _1688298))], (45944 ^ _780461) ^ [_1688559, _1688561, _1688563] : [-(c_Smallcheck_Oorelse(_1688559, _1688561, _1688563) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1688559), _1688559, _1688563, c_Option_Ooption_OSome(_1688559)), _1688561))], (45946 ^ _780461) ^ [_1688602, _1688604] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1688602, _1688604) = c_Smallcheck_Ofull__small_H(_1688602, hAPP(c_Code__Numeral_Oint__of, _1688604), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1688604))))], (45948 ^ _780461) ^ [_1688656, _1688658, _1688660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1688656), _1688658)), -(c_Smallcheck_Osmall_H(_1688660, _1688656, _1688658) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (45954 ^ _780461) ^ [_1688747, _1688749, _1688751] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1688747), _1688749))), -(c_Smallcheck_Osmall_H(_1688751, _1688747, _1688749) = 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(_1688751, _1688747, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1688749), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1688751, _1688749)))], (45960 ^ _780461) ^ [_1688817, _1688819, _1688821] : [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)), _1688817), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1688819), _1688821)))), 45963 ^ _780461 : [(45964 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1688819), _1688821)), -(c_Smallcheck_Osmall_H(_1688817, _1688819, _1688821) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (45970 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1688819), _1688821))), -(c_Smallcheck_Osmall_H(_1688817, _1688819, _1688821) = 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(_1688817, _1688819, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1688821), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1688817, _1688821)))]]], (45976 ^ _780461) ^ [_1689103, _1689105] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1689103), _1689105) = c_Smallcheck_Osmall_H(_1689103, hAPP(c_Code__Numeral_Oint__of, _1689105), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1689105))))], (45978 ^ _780461) ^ [_1689147, _1689149, _1689151, _1689153] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1689149, _1689147)), _1689151), _1689153) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1689149), hAPP(hAPP(c_COMBC(_1689149, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1689147, 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))), _1689149), c_Smallcheck_Osmall__class_Osmall(_1689147)), hAPP(hAPP(c_COMBB(tc_fun(_1689147, tc_prod(_1689149, _1689147)), tc_fun(_1689147, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1689149), hAPP(c_COMBB(tc_prod(_1689149, _1689147), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1689147), _1689151)), c_Product__Type_OPair(_1689149, _1689147)))), _1689153)), _1689153)), class_Smallcheck_Osmall(_1689147), class_Smallcheck_Osmall(_1689149)], (45988 ^ _780461) ^ [_1689432, _1689434, _1689436, _1689438] : [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)), _1689432), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1689434), _1689436)))), -(hBOOL(hAPP(hAPP(hAPP(_1689438, _1689432), _1689434), _1689436))), 45996 ^ _780461 : [(45997 ^ _780461) ^ [] : [-(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)), 45993 ^ [_1689432, _1689434, _1689436, _1689438]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 45994 ^ [_1689432, _1689434, _1689436, _1689438]), 45995 ^ [_1689432, _1689434, _1689436, _1689438])))))], (46009 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1689438, 45993 ^ [_1689432, _1689434, _1689436, _1689438]), 45994 ^ [_1689432, _1689434, _1689436, _1689438]), 45995 ^ [_1689432, _1689434, _1689436, _1689438]))], (45999 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 45994 ^ [_1689432, _1689434, _1689436, _1689438]), 45995 ^ [_1689432, _1689434, _1689436, _1689438]))), hAPP(45993 ^ [_1689432, _1689434, _1689436, _1689438], 45995 ^ [_1689432, _1689434, _1689436, _1689438]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1689438, 45993 ^ [_1689432, _1689434, _1689436, _1689438]), 45994 ^ [_1689432, _1689434, _1689436, _1689438]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 45995 ^ [_1689432, _1689434, _1689436, _1689438]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (46013 ^ _780461) ^ [] : [-(c_Com_Obody = c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom, c_Com_Obodies))], (46015 ^ _780461) ^ [_1690189, _1690191, _1690193, _1690195, _1690197, _1690199, _1690201] : [c_Fun_Oinj__on(_1690189, _1690191, _1690193, c_Orderings_Otop__class_Otop(tc_fun(_1690189, tc_HOL_Obool))), hAPP(c_Map_Omap__of(_1690189, _1690195, _1690197), _1690199) = hAPP(c_Option_Ooption_OSome(_1690195), _1690201), -(hAPP(c_Map_Omap__of(_1690191, _1690195, hAPP(hAPP(c_List_Omap(tc_prod(_1690189, _1690195), tc_prod(_1690191, _1690195)), hAPP(c_Product__Type_Oprod_Oprod__case(_1690189, _1690195, tc_prod(_1690191, _1690195)), hAPP(hAPP(c_COMBB(_1690191, tc_fun(_1690195, tc_prod(_1690191, _1690195)), _1690189), c_Product__Type_OPair(_1690191, _1690195)), _1690193))), _1690197)), hAPP(_1690193, _1690199)) = hAPP(c_Option_Ooption_OSome(_1690195), _1690201))], (46025 ^ _780461) ^ [_1690494, _1690496, _1690498, _1690500, _1690502, _1690504] : [-(c_Map_Omap__comp(_1690494, _1690496, _1690498, _1690500, _1690502, _1690504) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1690496), _1690494, c_Option_Ooption_ONone(_1690496), _1690500), hAPP(_1690502, _1690504)))], (46027 ^ _780461) ^ [_1690549, _1690551, _1690553] : [c_Fun_Oinj__on(_1690549, _1690551, _1690553, c_Orderings_Otop__class_Otop(tc_fun(_1690549, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1690549), tc_List_Olist(_1690551), hAPP(c_List_Omap(_1690549, _1690551), _1690553), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1690549), tc_HOL_Obool))))], (46033 ^ _780461) ^ [_1690710, _1690712, _1690714, _1690716, _1690718, _1690720, _1690722] : [c_Map_Omap__comp(_1690710, _1690712, _1690714, _1690716, _1690718, _1690720) = hAPP(c_Option_Ooption_OSome(_1690712), _1690722), 46037 ^ _780461 : [(46038 ^ _780461) ^ [] : [-(hAPP(_1690718, _1690720) = hAPP(c_Option_Ooption_OSome(_1690710), 46036 ^ [_1690710, _1690712, _1690714, _1690716, _1690718, _1690720, _1690722]))], (46040 ^ _780461) ^ [] : [-(hAPP(_1690716, 46036 ^ [_1690710, _1690712, _1690714, _1690716, _1690718, _1690720, _1690722]) = hAPP(c_Option_Ooption_OSome(_1690712), _1690722))]]], (46042 ^ _780461) ^ [_1690914, _1690916, _1690918, _1690920, _1690922, _1690924, _1690926] : [-(c_Map_Omap__comp(_1690914, _1690916, _1690918, _1690920, _1690922, _1690924) = hAPP(c_Option_Ooption_OSome(_1690916), _1690926)), 46043 ^ _780461 : [(46044 ^ _780461) ^ [_1690992] : [hAPP(_1690922, _1690924) = hAPP(c_Option_Ooption_OSome(_1690914), _1690992), hAPP(_1690920, _1690992) = hAPP(c_Option_Ooption_OSome(_1690916), _1690926)]]], (46052 ^ _780461) ^ [_1691154, _1691156, _1691158, _1691160, _1691162, _1691164, _1691166] : [hAPP(_1691154, _1691156) = hAPP(c_Option_Ooption_OSome(_1691158), _1691160), -(c_Map_Omap__comp(_1691158, _1691162, _1691164, _1691166, _1691154, _1691156) = hAPP(_1691166, _1691160))], (46058 ^ _780461) ^ [_1691277, _1691279, _1691281, _1691283, _1691285, _1691287] : [hAPP(_1691277, _1691279) = c_Option_Ooption_ONone(_1691281), -(c_Map_Omap__comp(_1691281, _1691283, _1691285, _1691287, _1691277, _1691279) = c_Option_Ooption_ONone(_1691283))], (46064 ^ _780461) ^ [_1691390, _1691392, _1691394, _1691396, _1691398, _1691400] : [-(hAPP(hAPP(c_List_Omap(_1691390, _1691392), _1691394), hAPP(hAPP(c_List_Omap(_1691396, _1691390), _1691398), _1691400)) = hAPP(hAPP(c_List_Omap(_1691396, _1691392), hAPP(c_Fun_Ocomp(_1691390, _1691392, _1691396, _1691394), _1691398)), _1691400))], (46066 ^ _780461) ^ [_1691458, _1691460, _1691462, _1691464, _1691466, _1691468] : [-(hAPP(hAPP(c_List_Omap(_1691458, _1691460), _1691462), hAPP(hAPP(c_List_Omap(_1691464, _1691458), _1691466), _1691468)) = hAPP(hAPP(c_List_Omap(_1691464, _1691460), hAPP(c_Fun_Ocomp(_1691458, _1691460, _1691464, _1691462), _1691466)), _1691468))], (46068 ^ _780461) ^ [_1691526, _1691528, _1691530, _1691532, _1691534] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1691526), tc_List_Olist(_1691528), tc_List_Olist(_1691530), hAPP(c_List_Omap(_1691526, _1691528), _1691532)), hAPP(c_List_Omap(_1691530, _1691526), _1691534)) = hAPP(c_List_Omap(_1691530, _1691528), hAPP(c_Fun_Ocomp(_1691526, _1691528, _1691530, _1691532), _1691534)))], (46070 ^ _780461) ^ [_1691597, _1691599, _1691601, _1691603, _1691605] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1691597), tc_List_Olist(_1691599), tc_List_Olist(_1691601), hAPP(c_List_Omap(_1691597, _1691599), _1691603)), hAPP(c_List_Omap(_1691601, _1691597), _1691605)) = hAPP(c_List_Omap(_1691601, _1691599), hAPP(c_Fun_Ocomp(_1691597, _1691599, _1691601, _1691603), _1691605)))], (46072 ^ _780461) ^ [_1691668, _1691670, _1691672, _1691674, _1691676] : [hAPP(hAPP(c_List_Omap(_1691668, _1691670), _1691672), _1691674) = hAPP(hAPP(c_List_Omap(_1691668, _1691670), _1691672), _1691676), c_Fun_Oinj__on(_1691668, _1691670, _1691672, c_Orderings_Otop__class_Otop(tc_fun(_1691668, tc_HOL_Obool))), -(_1691674 = _1691676)], (46082 ^ _780461) ^ [_1691859, _1691861, _1691863] : [c_Fun_Oinj__on(tc_List_Olist(_1691859), tc_List_Olist(_1691861), hAPP(c_List_Omap(_1691859, _1691861), _1691863), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1691859), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1691859, _1691861, _1691863, c_Orderings_Otop__class_Otop(tc_fun(_1691859, tc_HOL_Obool))))], (46088 ^ _780461) ^ [_1691990, _1691992, _1691994, _1691996, _1691998] : [c_Fun_Oinj__on(_1691990, _1691992, _1691994, c_Orderings_Otop__class_Otop(tc_fun(_1691990, tc_HOL_Obool))), 46091 ^ _780461 : [(46092 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Omap(_1691990, _1691992), _1691994), _1691996) = hAPP(hAPP(c_List_Omap(_1691990, _1691992), _1691994), _1691998), -(_1691996 = _1691998)], (46098 ^ _780461) ^ [] : [_1691996 = _1691998, -(hAPP(hAPP(c_List_Omap(_1691990, _1691992), _1691994), _1691996) = hAPP(hAPP(c_List_Omap(_1691990, _1691992), _1691994), _1691998))]]], (46104 ^ _780461) ^ [_1692301, _1692303, _1692305] : [c_Fun_Oinj__on(tc_List_Olist(_1692301), tc_List_Olist(_1692303), hAPP(c_List_Omap(_1692301, _1692303), _1692305), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1692301), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1692301, _1692303, _1692305, c_Orderings_Otop__class_Otop(tc_fun(_1692301, tc_HOL_Obool))))], (46110 ^ _780461) ^ [_1692428, _1692430, _1692432] : [c_Fun_Oinj__on(_1692428, _1692430, _1692432, c_Orderings_Otop__class_Otop(tc_fun(_1692428, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1692428), tc_List_Olist(_1692430), hAPP(c_List_Omap(_1692428, _1692430), _1692432), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1692428), tc_HOL_Obool))))], (46116 ^ _780461) ^ [_1692561, _1692563] : [-(hAPP(hAPP(c_List_Omap(_1692561, _1692561), c_COMBI(_1692561)), _1692563) = _1692563)], (46118 ^ _780461) ^ [_1692597] : [-(hAPP(c_List_Omap(_1692597, _1692597), c_COMBI(_1692597)) = c_Fun_Oid(tc_List_Olist(_1692597)))], (46120 ^ _780461) ^ [_1692632] : [-(hAPP(c_List_Omap(_1692632, _1692632), c_Fun_Oid(_1692632)) = c_Fun_Oid(tc_List_Olist(_1692632)))], (46122 ^ _780461) ^ [_1692667, _1692669, _1692671, _1692673, _1692675, _1692677, _1692679] : [-(c_List_Ofoldr(_1692667, _1692669, _1692671, hAPP(hAPP(c_List_Omap(_1692673, _1692667), _1692675), _1692677), _1692679) = c_List_Ofoldr(_1692673, _1692669, hAPP(c_Fun_Ocomp(_1692667, tc_fun(_1692669, _1692669), _1692673, _1692671), _1692675), _1692677, _1692679))], (46124 ^ _780461) ^ [_1692734, _1692736, _1692738, _1692740, _1692742] : [-(c_Map_Omap__comp(_1692734, _1692736, _1692738, _1692740, hAPP(c_COMBK(tc_Option_Ooption(_1692734), _1692738), c_Option_Ooption_ONone(_1692734)), _1692742) = c_Option_Ooption_ONone(_1692736))], (46126 ^ _780461) ^ [_1692784, _1692786, _1692788, _1692790, _1692792] : [-(c_Map_Omap__comp(_1692784, _1692786, _1692788, hAPP(c_COMBK(tc_Option_Ooption(_1692786), _1692784), c_Option_Ooption_ONone(_1692786)), _1692790, _1692792) = c_Option_Ooption_ONone(_1692786))], (46128 ^ _780461) ^ [_1692861, _1692863, _1692865, _1692867, _1692869, _1692871] : [c_Map_Omap__comp(_1692861, _1692863, _1692865, _1692867, _1692869, _1692871) = c_Option_Ooption_ONone(_1692863), -(hAPP(_1692869, _1692871) = c_Option_Ooption_ONone(_1692861)), 46136 ^ _780461 : [(46137 ^ _780461) ^ [] : [-(hAPP(_1692869, _1692871) = hAPP(c_Option_Ooption_OSome(_1692861), 46135 ^ [_1692861, _1692863, _1692865, _1692867, _1692869, _1692871]))], (46139 ^ _780461) ^ [] : [-(hAPP(_1692867, 46135 ^ [_1692861, _1692863, _1692865, _1692867, _1692869, _1692871]) = c_Option_Ooption_ONone(_1692863))]]], (46141 ^ _780461) ^ [_1693087, _1693089, _1693091, _1693093, _1693095, _1693097] : [-(c_Map_Omap__comp(_1693087, _1693089, _1693091, _1693093, _1693095, _1693097) = c_Option_Ooption_ONone(_1693089)), 46142 ^ _780461 : [(46143 ^ _780461) ^ [] : [hAPP(_1693095, _1693097) = c_Option_Ooption_ONone(_1693087)], (46145 ^ _780461) ^ [_1693199] : [hAPP(_1693095, _1693097) = hAPP(c_Option_Ooption_OSome(_1693087), _1693199), hAPP(_1693093, _1693199) = c_Option_Ooption_ONone(_1693089)]]], (46153 ^ _780461) ^ [_1693352, _1693354, _1693356, _1693358, _1693360] : [-(c_Map_Omap__of(_1693352, _1693354, hAPP(hAPP(c_List_Omap(tc_prod(_1693352, _1693356), tc_prod(_1693352, _1693354)), hAPP(c_Product__Type_Oprod_Oprod__case(_1693352, _1693356, tc_prod(_1693352, _1693354)), hAPP(hAPP(c_COMBC(_1693352, tc_fun(_1693356, _1693354), tc_fun(_1693356, tc_prod(_1693352, _1693354))), hAPP(hAPP(c_COMBB(tc_fun(_1693354, tc_prod(_1693352, _1693354)), tc_fun(tc_fun(_1693356, _1693354), tc_fun(_1693356, tc_prod(_1693352, _1693354))), _1693352), c_COMBB(_1693354, tc_prod(_1693352, _1693354), _1693356)), c_Product__Type_OPair(_1693352, _1693354))), _1693358))), _1693360)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1693356), tc_Option_Ooption(_1693354), _1693352, hAPP(c_Option_Omap(_1693356, _1693354), _1693358)), c_Map_Omap__of(_1693352, _1693356, _1693360)))], (46155 ^ _780461) ^ [_1693491, _1693493, _1693495, _1693497] : [hAPP(c_List_Oset(_1693491), _1693493) = c_Map_Odom(_1693491, _1693495, _1693497), -(c_Map_Omap__of(_1693491, _1693495, hAPP(hAPP(c_List_Omap(_1693491, tc_prod(_1693491, _1693495)), hAPP(hAPP(c_COMBS(_1693491, _1693495, tc_prod(_1693491, _1693495)), c_Product__Type_OPair(_1693491, _1693495)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1693495), _1693495, _1693491), c_Option_Othe(_1693495)), _1693497))), _1693493)) = _1693497)], (46161 ^ _780461) ^ [_1693682, _1693684] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1693682), hAPP(c_List_Oset(_1693682), _1693684))))], (46163 ^ _780461) ^ [_1693716, _1693718, _1693720, _1693722] : [-(hAPP(c_List_Oset(_1693716), hAPP(hAPP(c_List_Omap(_1693718, _1693716), _1693720), _1693722)) = hAPP(c_Set_Oimage(_1693718, _1693716, _1693720), hAPP(c_List_Oset(_1693718), _1693722)))], (46175 ^ _780461) ^ [_1694039, _1694041, _1694043, _1694045, _1694047] : [46177 ^ _780461 : [(46178 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1694039), 46176 ^ [_1694039, _1694041, _1694043, _1694045, _1694047]), hAPP(c_List_Oset(_1694039), _1694045))))], (46180 ^ _780461) ^ [] : [hAPP(_1694043, 46176 ^ [_1694039, _1694041, _1694043, _1694045, _1694047]) = hAPP(_1694047, 46176 ^ [_1694039, _1694041, _1694043, _1694045, _1694047])]], -(hAPP(hAPP(c_List_Omap(_1694039, _1694041), _1694043), _1694045) = hAPP(hAPP(c_List_Omap(_1694039, _1694041), _1694047), _1694045))], (46165 ^ _780461) ^ [_1693795, _1693797, _1693799, _1693801, _1693803] : [hAPP(hAPP(c_List_Omap(_1693795, _1693797), _1693799), _1693801) = hAPP(hAPP(c_List_Omap(_1693795, _1693797), _1693803), _1693801), 46168 ^ _780461 : [(46169 ^ _780461) ^ [_1693918] : [hBOOL(hAPP(hAPP(c_member(_1693795), _1693918), hAPP(c_List_Oset(_1693795), _1693801))), -(hAPP(_1693799, _1693918) = hAPP(_1693803, _1693918))]]], (46184 ^ _780461) ^ [_1694296] : [-(hAPP(c_Option_Omap(_1694296, _1694296), c_COMBI(_1694296)) = c_Fun_Oid(tc_Option_Ooption(_1694296)))], (46186 ^ _780461) ^ [_1694331] : [-(hAPP(c_Option_Omap(_1694331, _1694331), c_Fun_Oid(_1694331)) = c_Fun_Oid(tc_Option_Ooption(_1694331)))], (46188 ^ _780461) ^ [_1694366, _1694368, _1694370, _1694372, _1694374] : [-(c_Map_Odom(_1694366, _1694368, hAPP(hAPP(c_COMBS(_1694366, tc_Option_Ooption(_1694370), tc_Option_Ooption(_1694368)), hAPP(hAPP(c_COMBB(tc_fun(_1694370, _1694368), tc_fun(tc_Option_Ooption(_1694370), tc_Option_Ooption(_1694368)), _1694366), c_Option_Omap(_1694370, _1694368)), _1694372)), _1694374)) = c_Map_Odom(_1694366, _1694370, _1694374))], (46190 ^ _780461) ^ [_1694451] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1694451)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1694451), tc_HOL_Obool))))], (46192 ^ _780461) ^ [_1694487, _1694489, _1694491, _1694493, _1694495] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1694487), tc_Option_Ooption(_1694489), tc_Option_Ooption(_1694491), hAPP(c_Option_Omap(_1694487, _1694489), _1694493)), hAPP(c_Option_Omap(_1694491, _1694487), _1694495)) = hAPP(c_Option_Omap(_1694491, _1694489), hAPP(c_Fun_Ocomp(_1694487, _1694489, _1694491, _1694493), _1694495)))], (46194 ^ _780461) ^ [_1694558, _1694560, _1694562, _1694564, _1694566, _1694568] : [-(hAPP(hAPP(c_Option_Omap(_1694558, _1694560), _1694562), hAPP(hAPP(c_Option_Omap(_1694564, _1694558), _1694566), _1694568)) = hAPP(hAPP(c_Option_Omap(_1694564, _1694560), hAPP(c_Fun_Ocomp(_1694558, _1694560, _1694564, _1694562), _1694566)), _1694568))], (46196 ^ _780461) ^ [_1694626, _1694628, _1694630, _1694632, _1694634, _1694636] : [-(hAPP(hAPP(c_Option_Omap(_1694626, _1694628), _1694630), hAPP(hAPP(c_Option_Omap(_1694632, _1694626), _1694634), _1694636)) = hAPP(hAPP(c_Option_Omap(_1694632, _1694628), hAPP(c_Fun_Ocomp(_1694626, _1694628, _1694632, _1694630), _1694634)), _1694636))], (46198 ^ _780461) ^ [_1694694, _1694696, _1694698, _1694700, _1694702, _1694704, _1694706] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1694694), tc_Option_Ooption(_1694696), tc_sum(_1694698, _1694700), hAPP(c_Option_Omap(_1694694, _1694696), _1694702)), c_Sum__Type_Osum_Osum__case(_1694698, tc_Option_Ooption(_1694694), _1694700, _1694704, _1694706)) = c_Sum__Type_Osum_Osum__case(_1694698, tc_Option_Ooption(_1694696), _1694700, hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1694694), tc_Option_Ooption(_1694696), _1694698, hAPP(c_Option_Omap(_1694694, _1694696), _1694702)), _1694704), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1694694), tc_Option_Ooption(_1694696), _1694700, hAPP(c_Option_Omap(_1694694, _1694696), _1694702)), _1694706)))], (46200 ^ _780461) ^ [_1694802, _1694804, _1694806, _1694808, _1694810] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1694802), tc_Option_Ooption(_1694804), _1694806, hAPP(c_Option_Omap(_1694802, _1694804), _1694808)), hAPP(c_COMBK(tc_Option_Ooption(_1694802), _1694806), c_Option_Ooption_ONone(_1694802))), _1694810) = c_Option_Ooption_ONone(_1694804))], (46202 ^ _780461) ^ [_1694866, _1694868, _1694870, _1694872] : [-(hAPP(hAPP(c_Option_Omap(_1694866, _1694868), _1694870), hAPP(c_Option_Ooption_OSome(_1694866), _1694872)) = hAPP(c_Option_Ooption_OSome(_1694868), hAPP(_1694870, _1694872)))], (46204 ^ _780461) ^ [_1694941, _1694943, _1694945, _1694947, _1694949] : [hAPP(hAPP(c_Option_Omap(_1694941, _1694943), _1694945), _1694947) = hAPP(c_Option_Ooption_OSome(_1694943), _1694949), 46208 ^ _780461 : [(46209 ^ _780461) ^ [] : [-(_1694947 = hAPP(c_Option_Ooption_OSome(_1694941), 46207 ^ [_1694941, _1694943, _1694945, _1694947, _1694949]))], (46211 ^ _780461) ^ [] : [-(hAPP(_1694945, 46207 ^ [_1694941, _1694943, _1694945, _1694947, _1694949]) = _1694949)]]], (46213 ^ _780461) ^ [_1695121, _1695123, _1695125, _1695127, _1695129] : [-(hAPP(hAPP(c_Option_Omap(_1695121, _1695123), _1695125), _1695127) = hAPP(c_Option_Ooption_OSome(_1695123), _1695129)), 46214 ^ _780461 : [(46215 ^ _780461) ^ [_1695189] : [_1695127 = hAPP(c_Option_Ooption_OSome(_1695121), _1695189), hAPP(_1695125, _1695189) = _1695129]]], (46223 ^ _780461) ^ [_1695333, _1695335, _1695337] : [-(hAPP(hAPP(c_Option_Omap(_1695333, _1695335), _1695337), c_Option_Ooption_ONone(_1695333)) = c_Option_Ooption_ONone(_1695335))], (46225 ^ _780461) ^ [_1695394, _1695396, _1695398, _1695400] : [hAPP(hAPP(c_Option_Omap(_1695394, _1695396), _1695398), _1695400) = c_Option_Ooption_ONone(_1695396), -(_1695400 = c_Option_Ooption_ONone(_1695394))], (46231 ^ _780461) ^ [_1695497, _1695499, _1695501, _1695503] : [_1695503 = c_Option_Ooption_ONone(_1695497), -(hAPP(hAPP(c_Option_Omap(_1695497, _1695499), _1695501), _1695503) = c_Option_Ooption_ONone(_1695499))], (46237 ^ _780461) ^ [_1695606, _1695608, _1695610, _1695612, _1695614, _1695616, _1695618] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1695606), tc_Option_Ooption(_1695608), _1695610, hAPP(c_Option_Omap(_1695606, _1695608), _1695612)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1695610, tc_Option_Ooption(_1695606)), _1695614), _1695616), hAPP(c_Option_Ooption_OSome(_1695606), _1695618))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1695610, tc_Option_Ooption(_1695608)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1695606), tc_Option_Ooption(_1695608), _1695610, hAPP(c_Option_Omap(_1695606, _1695608), _1695612)), _1695614)), _1695616), hAPP(c_Option_Ooption_OSome(_1695608), hAPP(_1695612, _1695618))))], (46239 ^ _780461) ^ [_1695718, _1695720, _1695722, _1695724, _1695726] : [c_Fun_Oinj__on(_1695718, _1695720, _1695722, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1695718, tc_HOL_Obool)), hAPP(c_List_Oset(_1695718), _1695724)), hAPP(c_List_Oset(_1695718), _1695726))), 46242 ^ _780461 : [(46243 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Omap(_1695718, _1695720), _1695722), _1695724) = hAPP(hAPP(c_List_Omap(_1695718, _1695720), _1695722), _1695726), -(_1695724 = _1695726)], (46249 ^ _780461) ^ [] : [_1695724 = _1695726, -(hAPP(hAPP(c_List_Omap(_1695718, _1695720), _1695722), _1695724) = hAPP(hAPP(c_List_Omap(_1695718, _1695720), _1695722), _1695726))]]], (46255 ^ _780461) ^ [_1696043, _1696045, _1696047, _1696049, _1696051] : [hAPP(hAPP(c_List_Omap(_1696043, _1696045), _1696047), _1696049) = hAPP(hAPP(c_List_Omap(_1696043, _1696045), _1696047), _1696051), c_Fun_Oinj__on(_1696043, _1696045, _1696047, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1696043, tc_HOL_Obool)), hAPP(c_List_Oset(_1696043), _1696049)), hAPP(c_List_Oset(_1696043), _1696051))), -(_1696049 = _1696051)], (46265 ^ _780461) ^ [_1696262, _1696264, _1696266, _1696268, _1696270, _1696272] : [-(hBOOL(hAPP(hAPP(c_member(_1696262), _1696264), hAPP(c_List_Oset(_1696262), _1696266)))), -(hAPP(hAPP(c_List_Omap(_1696262, _1696268), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1696262, _1696268), _1696270), _1696264), _1696272)), _1696266) = hAPP(hAPP(c_List_Omap(_1696262, _1696268), _1696270), _1696266))], (46271 ^ _780461) ^ [_1696348, _1696350, _1696352, _1696354] : [c_Fun_Oinj__on(_1696348, _1696350, _1696352, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1696348, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1696348), tc_fun(_1696348, tc_HOL_Obool), c_List_Oset(_1696348)), _1696354))), -(c_Fun_Oinj__on(tc_List_Olist(_1696348), tc_List_Olist(_1696350), hAPP(c_List_Omap(_1696348, _1696350), _1696352), _1696354))], (46277 ^ _780461) ^ [_1696497, _1696499, _1696501, _1696503] : [c_Map_Omap__of(_1696497, _1696499, _1696501) = c_Map_Omap__of(_1696497, _1696499, _1696503), -(hAPP(c_Set_Oimage(tc_prod(_1696497, _1696499), _1696497, c_Product__Type_Ofst(_1696497, _1696499)), hAPP(c_List_Oset(tc_prod(_1696497, _1696499)), _1696501)) = hAPP(c_Set_Oimage(tc_prod(_1696497, _1696499), _1696497, c_Product__Type_Ofst(_1696497, _1696499)), hAPP(c_List_Oset(tc_prod(_1696497, _1696499)), _1696503)))], (46283 ^ _780461) ^ [_1696678, _1696680, _1696682, _1696684, _1696686] : [hAPP(c_Map_Omap__of(_1696678, _1696680, _1696682), _1696684) = hAPP(c_Option_Ooption_OSome(_1696680), _1696686), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1696678, _1696680)), hAPP(hAPP(c_Product__Type_OPair(_1696678, _1696680), _1696684), _1696686)), hAPP(c_List_Oset(tc_prod(_1696678, _1696680)), _1696682))))], (46289 ^ _780461) ^ [_1696839, _1696841, _1696843, _1696845, _1696847] : [hAPP(c_Map_Omap__of(_1696839, _1696841, _1696843), _1696845) = hAPP(c_Option_Ooption_OSome(_1696841), _1696847), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1696839, _1696841)), hAPP(hAPP(c_Product__Type_OPair(_1696839, _1696841), _1696845), _1696847)), hAPP(c_List_Oset(tc_prod(_1696839, _1696841)), _1696843))))], (46295 ^ _780461) ^ [_1697000, _1697002, _1697004] : [-(c_Map_Odom(_1697000, _1697002, c_Map_Omap__of(_1697000, _1697002, _1697004)) = hAPP(c_Set_Oimage(tc_prod(_1697000, _1697002), _1697000, c_Product__Type_Ofst(_1697000, _1697002)), hAPP(c_List_Oset(tc_prod(_1697000, _1697002)), _1697004)))], (46297 ^ _780461) ^ [_1697077, _1697079, _1697081, _1697083] : [hAPP(c_Map_Omap__of(_1697077, _1697079, _1697081), _1697083) = c_Option_Ooption_ONone(_1697079), hBOOL(hAPP(hAPP(c_member(_1697077), _1697083), hAPP(c_Set_Oimage(tc_prod(_1697077, _1697079), _1697077, c_Product__Type_Ofst(_1697077, _1697079)), hAPP(c_List_Oset(tc_prod(_1697077, _1697079)), _1697081))))], (46303 ^ _780461) ^ [_1697227, _1697229, _1697231, _1697233] : [-(hBOOL(hAPP(hAPP(c_member(_1697227), _1697233), hAPP(c_Set_Oimage(tc_prod(_1697227, _1697229), _1697227, c_Product__Type_Ofst(_1697227, _1697229)), hAPP(c_List_Oset(tc_prod(_1697227, _1697229)), _1697231))))), -(hAPP(c_Map_Omap__of(_1697227, _1697229, _1697231), _1697233) = c_Option_Ooption_ONone(_1697229))], (46309 ^ _780461) ^ [_1697306, _1697308, _1697310] : [-(hAPP(c_Option_Omap(_1697306, _1697308), _1697310) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1697308), _1697306, c_Option_Ooption_ONone(_1697308), hAPP(hAPP(c_COMBB(_1697308, tc_Option_Ooption(_1697308), _1697306), c_Option_Ooption_OSome(_1697308)), _1697310)))], (46321 ^ _780461) ^ [] : [46323 ^ _780461 : [(46324 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 46322 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))], (46326 ^ _780461) ^ [] : [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)), 46322 ^ []))]], -(c_Com_OWT__bodies)], (46311 ^ _780461) ^ [] : [c_Com_OWT__bodies, 46314 ^ _780461 : [(46315 ^ _780461) ^ [_1697408] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1697408), 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)), _1697408)))]]], (46330 ^ _780461) ^ [_1697599, _1697601, _1697603, _1697605] : [-(c_Map_Omap__of(_1697599, _1697601, hAPP(hAPP(c_List_Omap(_1697599, tc_prod(_1697599, _1697601)), hAPP(hAPP(c_COMBS(_1697599, _1697601, tc_prod(_1697599, _1697601)), c_Product__Type_OPair(_1697599, _1697601)), _1697603)), _1697605)) = c_Map_Orestrict__map(_1697599, _1697601, hAPP(c_Fun_Ocomp(_1697601, tc_Option_Ooption(_1697601), _1697599, c_Option_Ooption_OSome(_1697601)), _1697603), hAPP(c_List_Oset(_1697599), _1697605)))], (46332 ^ _780461) ^ [_1697682, _1697684, _1697686] : [hBOOL(hAPP(c_List_Odistinct(_1697682), hAPP(hAPP(c_List_Omap(tc_prod(_1697682, _1697684), _1697682), c_Product__Type_Ofst(_1697682, _1697684)), _1697686))), -(c_Map_Oran(_1697682, _1697684, c_Map_Omap__of(_1697682, _1697684, _1697686)) = hAPP(c_Set_Oimage(tc_prod(_1697682, _1697684), _1697684, c_Product__Type_Osnd(_1697682, _1697684)), hAPP(c_List_Oset(tc_prod(_1697682, _1697684)), _1697686)))], (46338 ^ _780461) ^ [_1697857, _1697859, _1697861] : [hBOOL(hAPP(c_List_Odistinct(_1697857), hAPP(hAPP(c_List_Omap(tc_prod(_1697857, _1697859), _1697857), c_Product__Type_Ofst(_1697857, _1697859)), _1697861))), -(hAPP(c_List_Oset(tc_prod(_1697857, _1697859)), _1697861) = hAPP(c_Set_OCollect(tc_prod(_1697857, _1697859)), hAPP(c_Product__Type_Oprod_Oprod__case(_1697857, _1697859, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1697857, tc_fun(_1697859, tc_Option_Ooption(_1697859)), tc_fun(_1697859, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1697859), tc_HOL_Obool), tc_fun(tc_fun(_1697859, tc_Option_Ooption(_1697859)), tc_fun(_1697859, tc_HOL_Obool)), _1697857), c_COMBB(tc_Option_Ooption(_1697859), tc_HOL_Obool, _1697859)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1697859), tc_fun(tc_Option_Ooption(_1697859), tc_HOL_Obool), _1697857), c_fequal), c_Map_Omap__of(_1697857, _1697859, _1697861)))), c_Option_Ooption_OSome(_1697859)))))], (46344 ^ _780461) ^ [_1698187, _1698189, _1698191, _1698193] : [hBOOL(hAPP(c_List_Odistinct(_1698187), hAPP(hAPP(c_List_Omap(_1698189, _1698187), _1698191), _1698193))), 46347 ^ _780461 : [(46348 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1698189), _1698193)))], (46350 ^ _780461) ^ [] : [-(c_Fun_Oinj__on(_1698189, _1698187, _1698191, hAPP(c_List_Oset(_1698189), _1698193)))]]], (46352 ^ _780461) ^ [_1698338, _1698340, _1698342, _1698344] : [-(hBOOL(hAPP(c_List_Odistinct(_1698338), hAPP(hAPP(c_List_Omap(_1698340, _1698338), _1698342), _1698344)))), hBOOL(hAPP(c_List_Odistinct(_1698340), _1698344)), c_Fun_Oinj__on(_1698340, _1698338, _1698342, hAPP(c_List_Oset(_1698340), _1698344))], (46362 ^ _780461) ^ [_1698525, _1698527, _1698529, _1698531] : [hBOOL(hAPP(c_List_Odistinct(_1698525), hAPP(hAPP(c_List_Omap(tc_prod(_1698525, _1698527), _1698525), c_Product__Type_Ofst(_1698525, _1698527)), _1698529))), hBOOL(hAPP(c_List_Odistinct(_1698525), hAPP(hAPP(c_List_Omap(tc_prod(_1698525, _1698527), _1698525), c_Product__Type_Ofst(_1698525, _1698527)), _1698531))), 46369 ^ _780461 : [(46370 ^ _780461) ^ [] : [c_Map_Omap__of(_1698525, _1698527, _1698529) = c_Map_Omap__of(_1698525, _1698527, _1698531), -(hAPP(c_List_Oset(tc_prod(_1698525, _1698527)), _1698529) = hAPP(c_List_Oset(tc_prod(_1698525, _1698527)), _1698531))], (46376 ^ _780461) ^ [] : [hAPP(c_List_Oset(tc_prod(_1698525, _1698527)), _1698529) = hAPP(c_List_Oset(tc_prod(_1698525, _1698527)), _1698531), -(c_Map_Omap__of(_1698525, _1698527, _1698529) = c_Map_Omap__of(_1698525, _1698527, _1698531))]]], (46382 ^ _780461) ^ [_1698948, _1698950, _1698952, _1698954, _1698956] : [hBOOL(hAPP(c_List_Odistinct(_1698948), hAPP(hAPP(c_List_Omap(tc_prod(_1698948, _1698950), _1698948), c_Product__Type_Ofst(_1698948, _1698950)), _1698952))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1698948, _1698950)), hAPP(hAPP(c_Product__Type_OPair(_1698948, _1698950), _1698954), _1698956)), hAPP(c_List_Oset(tc_prod(_1698948, _1698950)), _1698952))), -(hAPP(c_Map_Omap__of(_1698948, _1698950, _1698952), _1698954) = hAPP(c_Option_Ooption_OSome(_1698950), _1698956))], (46392 ^ _780461) ^ [_1699205, _1699207, _1699209, _1699211, _1699213] : [hBOOL(hAPP(c_List_Odistinct(_1699205), hAPP(hAPP(c_List_Omap(tc_prod(_1699205, _1699207), _1699205), c_Product__Type_Ofst(_1699205, _1699207)), _1699209))), 46395 ^ _780461 : [(46396 ^ _780461) ^ [] : [hAPP(c_Map_Omap__of(_1699205, _1699207, _1699209), _1699211) = hAPP(c_Option_Ooption_OSome(_1699207), _1699213), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1699205, _1699207)), hAPP(hAPP(c_Product__Type_OPair(_1699205, _1699207), _1699211), _1699213)), hAPP(c_List_Oset(tc_prod(_1699205, _1699207)), _1699209))))], (46402 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1699205, _1699207)), hAPP(hAPP(c_Product__Type_OPair(_1699205, _1699207), _1699211), _1699213)), hAPP(c_List_Oset(tc_prod(_1699205, _1699207)), _1699209))), -(hAPP(c_Map_Omap__of(_1699205, _1699207, _1699209), _1699211) = hAPP(c_Option_Ooption_OSome(_1699207), _1699213))]]], (46408 ^ _780461) ^ [_1699585, _1699587, _1699589, _1699591, _1699593] : [hBOOL(hAPP(c_List_Odistinct(_1699585), hAPP(hAPP(c_List_Omap(tc_prod(_1699585, _1699587), _1699585), c_Product__Type_Ofst(_1699585, _1699587)), _1699589))), 46411 ^ _780461 : [(46412 ^ _780461) ^ [] : [hAPP(c_Option_Ooption_OSome(_1699587), _1699591) = hAPP(c_Map_Omap__of(_1699585, _1699587, _1699589), _1699593), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1699585, _1699587)), hAPP(hAPP(c_Product__Type_OPair(_1699585, _1699587), _1699593), _1699591)), hAPP(c_List_Oset(tc_prod(_1699585, _1699587)), _1699589))))], (46418 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1699585, _1699587)), hAPP(hAPP(c_Product__Type_OPair(_1699585, _1699587), _1699593), _1699591)), hAPP(c_List_Oset(tc_prod(_1699585, _1699587)), _1699589))), -(hAPP(c_Option_Ooption_OSome(_1699587), _1699591) = hAPP(c_Map_Omap__of(_1699585, _1699587, _1699589), _1699593))]]], (46424 ^ _780461) ^ [_1699965, _1699967] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1699965, _1699967) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1699965), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1699967), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (46426 ^ _780461) ^ [_1700012, _1700014, _1700016, _1700018, _1700020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1700012, _1700014)), hAPP(hAPP(c_Product__Type_OPair(_1700012, _1700014), _1700016), _1700018)), hAPP(c_List_Oset(tc_prod(_1700012, _1700014)), _1700020))), -(hAPP(c_Map_Omap__of(_1700012, _1700014, _1700020), _1700016) = hAPP(c_Option_Ooption_OSome(_1700014), 46429 ^ [_1700012, _1700014, _1700016, _1700018, _1700020]))], (46433 ^ _780461) ^ [_1700191, _1700193] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1700191, _1700193) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1700191, _1700193)))], (46435 ^ _780461) ^ [_1700226, _1700228] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1700226, _1700228)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1700226, _1700228))], (46437 ^ _780461) ^ [_1700261, _1700263] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1700261, _1700263))))], (46439 ^ _780461) ^ [_1700291, _1700293] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1700291), _1700293) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1700291, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1700293), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (46441 ^ _780461) ^ [_1700334, _1700336] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1700334, _1700336) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1700334), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1700336)))], (46443 ^ _780461) ^ [_1700387] : [c_List_Onat__list(_1700387), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1700387)))], (46449 ^ _780461) ^ [_1700460] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1700460)), -(c_List_Onat__list(_1700460))], (46455 ^ _780461) ^ [_1700539, _1700541, _1700543] : [hBOOL(hAPP(c_List_Odistinct(_1700539), _1700541)), -(hAPP(c_List_Oset(_1700539), c_List_Oremove1(_1700539, _1700543, _1700541)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1700539, tc_HOL_Obool)), hAPP(c_List_Oset(_1700539), _1700541)), hAPP(hAPP(c_Set_Oinsert(_1700539), _1700543), c_Orderings_Obot__class_Obot(tc_fun(_1700539, tc_HOL_Obool)))))], (46461 ^ _780461) ^ [_1700701, _1700703, _1700705, _1700707] : [-(_1700701 = _1700703), 46464 ^ _780461 : [(46465 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1700705), _1700701), hAPP(c_List_Oset(_1700705), c_List_Oremove1(_1700705, _1700703, _1700707)))), -(hBOOL(hAPP(hAPP(c_member(_1700705), _1700701), hAPP(c_List_Oset(_1700705), _1700707))))], (46471 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1700705), _1700701), hAPP(c_List_Oset(_1700705), _1700707))), -(hBOOL(hAPP(hAPP(c_member(_1700705), _1700701), hAPP(c_List_Oset(_1700705), c_List_Oremove1(_1700705, _1700703, _1700707)))))]]], (46477 ^ _780461) ^ [_1701001, _1701003, _1701005, _1701007] : [-(hBOOL(hAPP(hAPP(c_member(_1701001), _1701003), hAPP(c_List_Oset(_1701001), _1701005)))), hBOOL(hAPP(hAPP(c_member(_1701001), _1701003), hAPP(c_List_Oset(_1701001), c_List_Oremove1(_1701001, _1701007, _1701005))))], (46483 ^ _780461) ^ [_1701121, _1701123, _1701125] : [-(hBOOL(hAPP(hAPP(c_member(_1701121), _1701123), hAPP(c_List_Oset(_1701121), _1701125)))), -(c_List_Oremove1(_1701121, _1701123, _1701125) = _1701125)], (46489 ^ _780461) ^ [_1701175, _1701177, _1701179] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1701175, tc_HOL_Obool)), hAPP(c_List_Oset(_1701175), c_List_Oremove1(_1701175, _1701177, _1701179))), hAPP(c_List_Oset(_1701175), _1701179))))], (46491 ^ _780461) ^ [_1701226, _1701228, _1701230, _1701232] : [-(c_List_Oremove1(_1701226, _1701228, c_List_Oremove1(_1701226, _1701230, _1701232)) = c_List_Oremove1(_1701226, _1701230, c_List_Oremove1(_1701226, _1701228, _1701232)))], (46493 ^ _780461) ^ [_1701271, _1701273, _1701275] : [hBOOL(hAPP(c_List_Odistinct(_1701271), _1701273)), -(hBOOL(hAPP(c_List_Odistinct(_1701271), c_List_Oremove1(_1701271, _1701275, _1701273))))], (46499 ^ _780461) ^ [_1701374, _1701376, _1701378] : [class_Orderings_Olinorder(_1701374), hBOOL(hAPP(c_Finite__Set_Ofinite(_1701374), _1701376)), -(c_List_Olinorder__class_Osorted__list__of__set(_1701374, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1701374, tc_HOL_Obool)), _1701376), hAPP(hAPP(c_Set_Oinsert(_1701374), _1701378), c_Orderings_Obot__class_Obot(tc_fun(_1701374, tc_HOL_Obool))))) = c_List_Oremove1(_1701374, _1701378, c_List_Olinorder__class_Osorted__list__of__set(_1701374, _1701376)))], (46509 ^ _780461) ^ [_1701599, _1701601, _1701603, _1701605, _1701607] : [hBOOL(hAPP(hAPP(c_member(_1701599), _1701601), hAPP(c_List_Oset(_1701599), _1701603))), -(hAPP(c_Map_Omap__of(_1701599, _1701605, hAPP(hAPP(c_List_Ozip(_1701599, _1701605), _1701603), hAPP(hAPP(c_List_Omap(_1701599, _1701605), _1701607), _1701603))), _1701601) = hAPP(c_Option_Ooption_OSome(_1701605), hAPP(_1701607, _1701601)))], (46515 ^ _780461) ^ [_1701766, _1701768, _1701770, _1701772, _1701774] : [-(hBOOL(hAPP(hAPP(c_member(_1701766), _1701768), hAPP(c_List_Oset(_1701766), _1701770)))), -(hAPP(c_Map_Omap__of(_1701766, _1701772, hAPP(hAPP(c_List_Ozip(_1701766, _1701772), _1701770), hAPP(hAPP(c_List_Omap(_1701766, _1701772), _1701774), _1701770))), _1701768) = c_Option_Ooption_ONone(_1701772))], (46521 ^ _780461) ^ [_1701849, _1701851, _1701853, _1701855] : [hBOOL(hAPP(c_List_Odistinct(_1701849), _1701851)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1701853, _1701849)), hAPP(hAPP(c_List_Ozip(_1701853, _1701849), _1701855), _1701851))))], (46527 ^ _780461) ^ [_1701970, _1701972, _1701974, _1701976] : [hBOOL(hAPP(c_List_Odistinct(_1701970), _1701972)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1701970, _1701974)), hAPP(hAPP(c_List_Ozip(_1701970, _1701974), _1701972), _1701976))))], (46533 ^ _780461) ^ [_1702091, _1702093] : [-(hAPP(hAPP(c_List_Ozip(_1702091, _1702091), _1702093), _1702093) = hAPP(hAPP(c_List_Omap(_1702091, tc_prod(_1702091, _1702091)), hAPP(hAPP(c_COMBS(_1702091, _1702091, tc_prod(_1702091, _1702091)), c_Product__Type_OPair(_1702091, _1702091)), c_COMBI(_1702091))), _1702093))], (46535 ^ _780461) ^ [_1702155, _1702157, _1702159] : [-(hAPP(hAPP(c_List_Ozip(_1702155, _1702157), hAPP(hAPP(c_List_Omap(tc_prod(_1702155, _1702157), _1702155), c_Product__Type_Ofst(_1702155, _1702157)), _1702159)), hAPP(hAPP(c_List_Omap(tc_prod(_1702155, _1702157), _1702157), c_Product__Type_Osnd(_1702155, _1702157)), _1702159)) = _1702159)], (46537 ^ _780461) ^ [_1702221, _1702223, _1702225, _1702227, _1702229, _1702231, _1702233, _1702235] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1702221, _1702223), _1702225), _1702227), hAPP(hAPP(c_List_Ozip(_1702221, _1702223), _1702229), hAPP(hAPP(c_List_Omap(_1702231, _1702223), _1702233), _1702235))) = hAPP(hAPP(c_List_Omap(tc_prod(_1702221, _1702231), _1702225), hAPP(c_Product__Type_Oprod_Oprod__case(_1702221, _1702231, _1702225), hAPP(hAPP(c_COMBB(tc_fun(_1702231, tc_prod(_1702221, _1702223)), tc_fun(_1702231, _1702225), _1702221), hAPP(c_COMBB(tc_prod(_1702221, _1702223), _1702225, _1702231), _1702227)), hAPP(hAPP(c_COMBC(_1702221, tc_fun(_1702231, _1702223), tc_fun(_1702231, tc_prod(_1702221, _1702223))), hAPP(hAPP(c_COMBB(tc_fun(_1702223, tc_prod(_1702221, _1702223)), tc_fun(tc_fun(_1702231, _1702223), tc_fun(_1702231, tc_prod(_1702221, _1702223))), _1702221), c_COMBB(_1702223, tc_prod(_1702221, _1702223), _1702231)), c_Product__Type_OPair(_1702221, _1702223))), _1702233)))), hAPP(hAPP(c_List_Ozip(_1702221, _1702231), _1702229), _1702235)))], (46539 ^ _780461) ^ [_1702402, _1702404, _1702406, _1702408, _1702410, _1702412, _1702414, _1702416] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1702402, _1702404), _1702406), _1702408), hAPP(hAPP(c_List_Ozip(_1702402, _1702404), hAPP(hAPP(c_List_Omap(_1702410, _1702402), _1702412), _1702414)), _1702416)) = hAPP(hAPP(c_List_Omap(tc_prod(_1702410, _1702404), _1702406), hAPP(c_Product__Type_Oprod_Oprod__case(_1702410, _1702404, _1702406), hAPP(hAPP(c_COMBB(tc_fun(_1702404, tc_prod(_1702402, _1702404)), tc_fun(_1702404, _1702406), _1702410), hAPP(c_COMBB(tc_prod(_1702402, _1702404), _1702406, _1702404), _1702408)), hAPP(hAPP(c_COMBB(_1702402, tc_fun(_1702404, tc_prod(_1702402, _1702404)), _1702410), c_Product__Type_OPair(_1702402, _1702404)), _1702412)))), hAPP(hAPP(c_List_Ozip(_1702410, _1702404), _1702414), _1702416)))], (46541 ^ _780461) ^ [_1702545, _1702547, _1702549, _1702551, _1702553, _1702555] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1702545, _1702547)), hAPP(hAPP(c_Product__Type_OPair(_1702545, _1702547), _1702549), _1702551)), hAPP(c_List_Oset(tc_prod(_1702545, _1702547)), hAPP(hAPP(c_List_Ozip(_1702545, _1702547), _1702553), _1702555)))), 46544 ^ _780461 : [(46545 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1702545), _1702549), hAPP(c_List_Oset(_1702545), _1702553))))], (46547 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1702547), _1702551), hAPP(c_List_Oset(_1702547), _1702555))))]]], (46549 ^ _780461) ^ [_1702780, _1702782, _1702784, _1702786, _1702788, _1702790] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1702780, _1702782)), hAPP(hAPP(c_Product__Type_OPair(_1702780, _1702782), _1702784), _1702786)), hAPP(c_List_Oset(tc_prod(_1702780, _1702782)), hAPP(hAPP(c_List_Ozip(_1702780, _1702782), _1702788), _1702790)))), -(hBOOL(hAPP(hAPP(c_member(_1702782), _1702786), hAPP(c_List_Oset(_1702782), _1702790))))], (46555 ^ _780461) ^ [_1702961, _1702963, _1702965, _1702967, _1702969, _1702971] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1702961, _1702963)), hAPP(hAPP(c_Product__Type_OPair(_1702961, _1702963), _1702965), _1702967)), hAPP(c_List_Oset(tc_prod(_1702961, _1702963)), hAPP(hAPP(c_List_Ozip(_1702961, _1702963), _1702969), _1702971)))), -(hBOOL(hAPP(hAPP(c_member(_1702961), _1702965), hAPP(c_List_Oset(_1702961), _1702969))))], (46561 ^ _780461) ^ [_1703163, _1703165, _1703167, _1703169] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1703163, _1703163)), hAPP(hAPP(c_Product__Type_OPair(_1703163, _1703163), _1703165), _1703167)), hAPP(c_List_Oset(tc_prod(_1703163, _1703163)), hAPP(hAPP(c_List_Ozip(_1703163, _1703163), _1703169), _1703169)))), 46564 ^ _780461 : [(46565 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703163), _1703165), hAPP(c_List_Oset(_1703163), _1703169))))], (46567 ^ _780461) ^ [] : [-(_1703165 = _1703167)]]], (46569 ^ _780461) ^ [_1703362, _1703364, _1703366, _1703368] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1703362, _1703362)), hAPP(hAPP(c_Product__Type_OPair(_1703362, _1703362), _1703364), _1703366)), hAPP(c_List_Oset(tc_prod(_1703362, _1703362)), hAPP(hAPP(c_List_Ozip(_1703362, _1703362), _1703368), _1703368))))), hBOOL(hAPP(hAPP(c_member(_1703362), _1703364), hAPP(c_List_Oset(_1703362), _1703368))), _1703364 = _1703366], (46579 ^ _780461) ^ [_1703597, _1703599, _1703601, _1703603, _1703605, _1703607] : [-(hAPP(hAPP(c_List_Ozip(_1703597, _1703599), _1703601), hAPP(hAPP(c_List_Omap(_1703603, _1703599), _1703605), _1703607)) = hAPP(hAPP(c_List_Omap(tc_prod(_1703597, _1703603), tc_prod(_1703597, _1703599)), hAPP(c_Product__Type_Oprod_Oprod__case(_1703597, _1703603, tc_prod(_1703597, _1703599)), hAPP(hAPP(c_COMBC(_1703597, tc_fun(_1703603, _1703599), tc_fun(_1703603, tc_prod(_1703597, _1703599))), hAPP(hAPP(c_COMBB(tc_fun(_1703599, tc_prod(_1703597, _1703599)), tc_fun(tc_fun(_1703603, _1703599), tc_fun(_1703603, tc_prod(_1703597, _1703599))), _1703597), c_COMBB(_1703599, tc_prod(_1703597, _1703599), _1703603)), c_Product__Type_OPair(_1703597, _1703599))), _1703605))), hAPP(hAPP(c_List_Ozip(_1703597, _1703603), _1703601), _1703607)))], (46581 ^ _780461) ^ [_1703739, _1703741, _1703743, _1703745, _1703747, _1703749] : [-(hAPP(hAPP(c_List_Ozip(_1703739, _1703741), hAPP(hAPP(c_List_Omap(_1703743, _1703739), _1703745), _1703747)), _1703749) = hAPP(hAPP(c_List_Omap(tc_prod(_1703743, _1703741), tc_prod(_1703739, _1703741)), hAPP(c_Product__Type_Oprod_Oprod__case(_1703743, _1703741, tc_prod(_1703739, _1703741)), hAPP(hAPP(c_COMBB(_1703739, tc_fun(_1703741, tc_prod(_1703739, _1703741)), _1703743), c_Product__Type_OPair(_1703739, _1703741)), _1703745))), hAPP(hAPP(c_List_Ozip(_1703743, _1703741), _1703747), _1703749)))], (46583 ^ _780461) ^ [_1703843, _1703845, _1703847, _1703849, _1703851, _1703853, _1703855, _1703857] : [-(hAPP(hAPP(c_List_Ozip(_1703843, _1703845), hAPP(hAPP(c_List_Omap(_1703847, _1703843), _1703849), _1703851)), hAPP(hAPP(c_List_Omap(_1703853, _1703845), _1703855), _1703857)) = hAPP(hAPP(c_List_Omap(tc_prod(_1703847, _1703853), tc_prod(_1703843, _1703845)), hAPP(c_Product__Type_Oprod_Oprod__case(_1703847, _1703853, tc_prod(_1703843, _1703845)), hAPP(hAPP(c_COMBC(_1703847, tc_fun(_1703853, _1703845), tc_fun(_1703853, tc_prod(_1703843, _1703845))), hAPP(hAPP(c_COMBB(tc_fun(_1703845, tc_prod(_1703843, _1703845)), tc_fun(tc_fun(_1703853, _1703845), tc_fun(_1703853, tc_prod(_1703843, _1703845))), _1703847), c_COMBB(_1703845, tc_prod(_1703843, _1703845), _1703853)), hAPP(hAPP(c_COMBB(_1703843, tc_fun(_1703845, tc_prod(_1703843, _1703845)), _1703847), c_Product__Type_OPair(_1703843, _1703845)), _1703849))), _1703855))), hAPP(hAPP(c_List_Ozip(_1703847, _1703853), _1703851), _1703857)))], (46585 ^ _780461) ^ [_1704014, _1704016, _1704018] : [class_Orderings_Olinorder(_1704014), hBOOL(hAPP(c_Finite__Set_Ofinite(_1704014), _1704016)), -(c_List_Olinorder__class_Osorted__list__of__set(_1704014, hAPP(hAPP(c_Set_Oinsert(_1704014), _1704018), _1704016)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1704014, _1704014, c_COMBI(_1704014)), _1704018), c_List_Olinorder__class_Osorted__list__of__set(_1704014, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1704014, tc_HOL_Obool)), _1704016), hAPP(hAPP(c_Set_Oinsert(_1704014), _1704018), c_Orderings_Obot__class_Obot(tc_fun(_1704014, tc_HOL_Obool)))))))], (46595 ^ _780461) ^ [_1704253, _1704255, _1704257, _1704259, _1704261, _1704263, _1704265, _1704267] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704253)), _1704255) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704257)), _1704259), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704253)), _1704261) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704257)), _1704259), -(hBOOL(hAPP(hAPP(c_member(_1704257), _1704263), hAPP(c_List_Oset(_1704257), _1704259)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1704257, tc_Option_Ooption(_1704253)), c_Map_Omap__of(_1704257, _1704253, hAPP(hAPP(c_List_Ozip(_1704257, _1704253), _1704259), _1704255))), _1704263), hAPP(c_Option_Ooption_OSome(_1704253), _1704265)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1704257, tc_Option_Ooption(_1704253)), c_Map_Omap__of(_1704257, _1704253, hAPP(hAPP(c_List_Ozip(_1704257, _1704253), _1704259), _1704261))), _1704263), hAPP(c_Option_Ooption_OSome(_1704253), _1704267)), -(c_Map_Omap__of(_1704257, _1704253, hAPP(hAPP(c_List_Ozip(_1704257, _1704253), _1704259), _1704255)) = c_Map_Omap__of(_1704257, _1704253, hAPP(hAPP(c_List_Ozip(_1704257, _1704253), _1704259), _1704261)))], (46613 ^ _780461) ^ [_1704797, _1704799, _1704801, _1704803] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1704797, _1704799))), hAPP(hAPP(c_List_Ozip(_1704797, _1704799), _1704801), _1704803)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704797)), _1704801)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704799)), _1704803)))], (46615 ^ _780461) ^ [_1704865, _1704867, _1704869, _1704871, _1704873] : [class_Orderings_Olinorder(_1704865), -(hAPP(c_List_Oset(_1704867), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1704867, _1704865, _1704869), _1704871), _1704873)) = hAPP(hAPP(c_Set_Oinsert(_1704867), _1704871), hAPP(c_List_Oset(_1704867), _1704873)))], (46621 ^ _780461) ^ [_1705002, _1705004, _1705006, _1705008] : [class_Orderings_Olinorder(_1705002), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705002, _1705002, c_COMBI(_1705002)), _1705004), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705002, _1705002, c_COMBI(_1705002)), _1705006), _1705008)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705002, _1705002, c_COMBI(_1705002)), _1705006), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705002, _1705002, c_COMBI(_1705002)), _1705004), _1705008)))], (46627 ^ _780461) ^ [_1705177, _1705179, _1705181, _1705183, _1705185, _1705187] : [class_Orderings_Olinorder(_1705177), -(hAPP(_1705179, _1705181) = hAPP(_1705179, _1705183)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705185, _1705177, _1705179), _1705183), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705185, _1705177, _1705179), _1705181), _1705187)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705185, _1705177, _1705179), _1705181), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705185, _1705177, _1705179), _1705183), _1705187)))], (46637 ^ _780461) ^ [_1705366, _1705368, _1705370] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705366)), _1705368) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705366)), _1705370)), _1705368 = _1705370], (46643 ^ _780461) ^ [_1705458, _1705460, _1705462, _1705464, _1705466] : [class_Orderings_Olinorder(_1705458), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705460)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705460, _1705458, _1705462), _1705464), _1705466)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705460)), _1705466)))], (46649 ^ _780461) ^ [_1705593] : [class_Orderings_Olinorder(_1705593), -(c_Finite__Set_Ofun__left__comm(_1705593, tc_List_Olist(_1705593), c_List_Olinorder__class_Oinsort__key(_1705593, _1705593, c_COMBI(_1705593))))], (46655 ^ _780461) ^ [_1705684, _1705686, _1705688, _1705690, _1705692] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1705684), tc_List_Olist(_1705684))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1705684), tc_List_Olist(_1705684)), _1705686), _1705688)), hAPP(c_List_Olexn(_1705684, _1705690), _1705692))), 46658 ^ _780461 : [(46659 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705684)), _1705686) = _1705692)], (46661 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705684)), _1705688) = _1705692)]]], (46663 ^ _780461) ^ [_1705887, _1705889, _1705891, _1705893, _1705895, _1705897, _1705899] : [hAPP(hAPP(c_List_Omap(_1705887, _1705889), _1705891), _1705893) = hAPP(hAPP(c_List_Omap(_1705895, _1705889), _1705897), _1705899), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705887)), _1705893) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705895)), _1705899))], (46669 ^ _780461) ^ [_1706038, _1706040, _1706042, _1706044] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706038)), hAPP(hAPP(c_List_Omap(_1706040, _1706038), _1706042), _1706044)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706040)), _1706044))], (46671 ^ _780461) ^ [_1706090, _1706092, _1706094] : [class_Orderings_Olinorder(_1706090), -(c_List_Oremove1(_1706090, _1706092, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706090, _1706090, c_COMBI(_1706090)), _1706092), _1706094)) = _1706094)], (46677 ^ _780461) ^ [_1706199, _1706201] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1706199), hAPP(c_List_Oset(_1706199), _1706201))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706199)), _1706201))))], (46679 ^ _780461) ^ [_1706246, _1706248] : [hAPP(c_Finite__Set_Ocard(_1706246), hAPP(c_List_Oset(_1706246), _1706248)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706246)), _1706248), -(hBOOL(hAPP(c_List_Odistinct(_1706246), _1706248)))], (46685 ^ _780461) ^ [_1706365, _1706367] : [hBOOL(hAPP(c_List_Odistinct(_1706365), _1706367)), -(hAPP(c_Finite__Set_Ocard(_1706365), hAPP(c_List_Oset(_1706365), _1706367)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706365)), _1706367))], (46691 ^ _780461) ^ [_1706484, _1706486, _1706488, _1706490, _1706492] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706484)), _1706486) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706488)), _1706490), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706484)), _1706492) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706488)), _1706490), hBOOL(hAPP(c_List_Odistinct(_1706488), _1706490)), c_Map_Omap__of(_1706488, _1706484, hAPP(hAPP(c_List_Ozip(_1706488, _1706484), _1706490), _1706486)) = c_Map_Omap__of(_1706488, _1706484, hAPP(hAPP(c_List_Ozip(_1706488, _1706484), _1706490), _1706492)), -(_1706486 = _1706492)], (46709 ^ _780461) ^ [_1706857, _1706859, _1706861, _1706863] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706857)), _1706859) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706861)), _1706863), -(hAPP(hAPP(c_List_Omap(tc_prod(_1706857, _1706861), _1706857), c_Product__Type_Ofst(_1706857, _1706861)), hAPP(hAPP(c_List_Ozip(_1706857, _1706861), _1706859), _1706863)) = _1706859)], (46715 ^ _780461) ^ [_1707014, _1707016, _1707018, _1707020] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707014)), _1707016) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707018)), _1707020), -(hAPP(hAPP(c_List_Omap(tc_prod(_1707014, _1707018), _1707018), c_Product__Type_Osnd(_1707014, _1707018)), hAPP(hAPP(c_List_Ozip(_1707014, _1707018), _1707016), _1707020)) = _1707020)], (46721 ^ _780461) ^ [_1707171, _1707173, _1707175, _1707177, _1707179] : [class_Orderings_Olinorder(_1707171), 46724 ^ _780461 : [(46725 ^ _780461) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1707173), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1707173, _1707171, _1707175), _1707177), _1707179))), 46728 ^ _780461 : [(46729 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1707173), _1707177), hAPP(c_List_Oset(_1707173), _1707179)))], (46731 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1707173), _1707179)))]]], (46733 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1707173), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1707173, _1707171, _1707175), _1707177), _1707179)))), -(hBOOL(hAPP(hAPP(c_member(_1707173), _1707177), hAPP(c_List_Oset(_1707173), _1707179)))), hBOOL(hAPP(c_List_Odistinct(_1707173), _1707179))]]], (46743 ^ _780461) ^ [_1707573, _1707575, _1707577] : [hBOOL(hAPP(hAPP(c_member(_1707573), _1707575), hAPP(c_List_Oset(_1707573), _1707577))), -(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(_1707573)), _1707577))))], (46749 ^ _780461) ^ [_1707694, _1707696, _1707698, _1707700, _1707702] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707694)), _1707696) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707698)), _1707700), 46752 ^ _780461 : [(46753 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Ozip(_1707694, _1707698), _1707696), _1707700) = _1707702, 46756 ^ _780461 : [(46757 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1707694, _1707698), _1707694), c_Product__Type_Ofst(_1707694, _1707698)), _1707702) = _1707696)], (46759 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1707694, _1707698), _1707698), c_Product__Type_Osnd(_1707694, _1707698)), _1707702) = _1707700)]]], (46761 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1707694, _1707698), _1707696), _1707700) = _1707702), hAPP(hAPP(c_List_Omap(tc_prod(_1707694, _1707698), _1707694), c_Product__Type_Ofst(_1707694, _1707698)), _1707702) = _1707696, hAPP(hAPP(c_List_Omap(tc_prod(_1707694, _1707698), _1707698), c_Product__Type_Osnd(_1707694, _1707698)), _1707702) = _1707700]]], (46771 ^ _780461) ^ [_1708142, _1708144] : [-(c_List_Olenlex(_1708142, _1708144) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1708142), tc_List_Olist(_1708142), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1708142), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708142), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), tc_List_Olist(_1708142)), c_COMBS(tc_List_Olist(_1708142), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708142), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1708142)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1708142)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708142), tc_fun(tc_List_Olist(_1708142), tc_Nat_Onat), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1708142), tc_Nat_Onat), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), tc_List_Olist(_1708142)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1708142))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1708142)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1708142))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1708142)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1708142), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708142), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), tc_List_Olist(_1708142)), c_COMBS(tc_List_Olist(_1708142), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708142), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1708142)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1708142)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708142), tc_fun(tc_List_Olist(_1708142), tc_Nat_Onat), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1708142), tc_Nat_Onat), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), tc_List_Olist(_1708142)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1708142))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1708142)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1708142))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1708142)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708142), tc_fun(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708142), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1708142), tc_HOL_Obool)), tc_List_Olist(_1708142)), c_COMBC(tc_List_Olist(_1708142), tc_fun(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1708142), tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142))), tc_fun(tc_List_Olist(_1708142), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1708142)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1708142)), c_member(tc_prod(tc_List_Olist(_1708142), tc_List_Olist(_1708142))))), c_Product__Type_OPair(tc_List_Olist(_1708142), tc_List_Olist(_1708142))))), c_List_Olex(_1708142, _1708144)))))))], (46773 ^ _780461) ^ [_1708698, _1708700] : [-(c_List_Olenlex(_1708698, _1708700) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1708698)), tc_List_Olist(_1708698)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1708698), c_Wellfounded_Oless__than, c_List_Olex(_1708698, _1708700))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1708698), tc_List_Olist(_1708698), tc_prod(tc_Nat_Onat, tc_List_Olist(_1708698))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1708698), tc_prod(tc_Nat_Onat, tc_List_Olist(_1708698))), tc_List_Olist(_1708698)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1708698))), c_Nat_Osize__class_Osize(tc_List_Olist(_1708698)))), c_COMBI(tc_List_Olist(_1708698)))))], (46775 ^ _780461) ^ [_1708806, _1708808, _1708810] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1708806), _1708808)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1708806)), hAPP(c_Set_OCollect(tc_List_Olist(_1708806)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1708806), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1708806)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708806), tc_fun(_1708806, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1708806, tc_HOL_Obool), tc_fun(tc_fun(_1708806, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1708806)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1708806, tc_HOL_Obool))), c_List_Oset(_1708806))), _1708808))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708806), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1708806)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1708806)))), _1708810))))))], (46781 ^ _780461) ^ [_1709127, _1709129, _1709131] : [_1709127 = _1709129, 46784 ^ _780461 : [(46785 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709131)), _1709127) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709131)), _1709129))], (46787 ^ _780461) ^ [_1709283] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1709131, _1709131)), _1709283), hAPP(c_List_Oset(tc_prod(_1709131, _1709131)), hAPP(hAPP(c_List_Ozip(_1709131, _1709131), _1709127), _1709129)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1709131, _1709131, tc_HOL_Obool), c_fequal), _1709283)))]]], (46793 ^ _780461) ^ [_1709438, _1709440, _1709442] : [-(_1709438 = _1709440), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709442)), _1709438) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709442)), _1709440), 46799 ^ _780461 : [(46800 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1709442, _1709442)), 46798 ^ [_1709438, _1709440, _1709442]), hAPP(c_List_Oset(tc_prod(_1709442, _1709442)), hAPP(hAPP(c_List_Ozip(_1709442, _1709442), _1709438), _1709440)))))], (46802 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1709442, _1709442, tc_HOL_Obool), c_fequal), 46798 ^ [_1709438, _1709440, _1709442]))]]], (46806 ^ _780461) ^ [_1709752, _1709754, _1709756, _1709758, _1709760] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709752)), _1709754) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709756)), _1709758), 46809 ^ _780461 : [(46810 ^ _780461) ^ [] : [hAPP(c_Map_Omap__of(_1709752, _1709756, hAPP(hAPP(c_List_Ozip(_1709752, _1709756), _1709754), _1709758)), _1709760) = c_Option_Ooption_ONone(_1709756), hBOOL(hAPP(hAPP(c_member(_1709752), _1709760), hAPP(c_List_Oset(_1709752), _1709754)))], (46816 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709752), _1709760), hAPP(c_List_Oset(_1709752), _1709754)))), -(hAPP(c_Map_Omap__of(_1709752, _1709756, hAPP(hAPP(c_List_Ozip(_1709752, _1709756), _1709754), _1709758)), _1709760) = c_Option_Ooption_ONone(_1709756))]]], (46822 ^ _780461) ^ [_1710051, _1710053, _1710055, _1710057, _1710059] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710051)), _1710053) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710055)), _1710057), 46825 ^ _780461 : [(46826 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1710051), _1710059), hAPP(c_List_Oset(_1710051), _1710053))), -(hAPP(c_Map_Omap__of(_1710051, _1710055, hAPP(hAPP(c_List_Ozip(_1710051, _1710055), _1710053), _1710057)), _1710059) = hAPP(c_Option_Ooption_OSome(_1710055), 46829 ^ [_1710051, _1710053, _1710055, _1710057, _1710059]))], (46833 ^ _780461) ^ [] : [46834 ^ _780461 : [(46835 ^ _780461) ^ [_1710339] : [hAPP(c_Map_Omap__of(_1710051, _1710055, hAPP(hAPP(c_List_Ozip(_1710051, _1710055), _1710053), _1710057)), _1710059) = hAPP(c_Option_Ooption_OSome(_1710055), _1710339)]], -(hBOOL(hAPP(hAPP(c_member(_1710051), _1710059), hAPP(c_List_Oset(_1710051), _1710053))))]]], (46839 ^ _780461) ^ [_1710441, _1710443, _1710445] : [hBOOL(hAPP(hAPP(c_member(_1710441), _1710443), hAPP(c_List_Oset(_1710441), _1710445))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710441)), c_List_Oremove1(_1710441, _1710443, _1710445)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710441)), _1710445)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46845 ^ _780461) ^ [_1710586, _1710588, _1710590] : [-(hBOOL(hAPP(hAPP(c_member(_1710586), _1710588), hAPP(c_List_Oset(_1710586), _1710590)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710586)), c_List_Oremove1(_1710586, _1710588, _1710590)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710586)), _1710590))], (46851 ^ _780461) ^ [_1710656, _1710658, _1710660, _1710662] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710656)), _1710658) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710660)), _1710662), hBOOL(hAPP(c_List_Odistinct(_1710656), _1710658)), -(c_Map_Odom(_1710656, _1710660, c_Map_Omap__of(_1710656, _1710660, hAPP(hAPP(c_List_Ozip(_1710656, _1710660), _1710658), _1710662))) = hAPP(c_List_Oset(_1710656), _1710658))], (46861 ^ _780461) ^ [_1710873, _1710875, _1710877] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1710873), _1710875)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1710873)), hAPP(c_Set_OCollect(tc_List_Olist(_1710873)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1710873), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1710873)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710873), tc_fun(_1710873, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1710873, tc_HOL_Obool), tc_fun(tc_fun(_1710873, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1710873)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1710873, tc_HOL_Obool))), c_List_Oset(_1710873))), _1710875))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710873), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1710873)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1710873)))), _1710877))))))], (46867 ^ _780461) ^ [_1711185, _1711187] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1711185), _1711187)), -(c_Nitpick_Ocard_H(_1711185, _1711187) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711185)), c_Hilbert__Choice_OEps(tc_List_Olist(_1711185), hAPP(hAPP(c_COMBS(tc_List_Olist(_1711185), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1711185)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1711185), tc_fun(_1711185, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1711185, tc_HOL_Obool), tc_fun(tc_fun(_1711185, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1711185)), c_fequal), c_List_Oset(_1711185))), _1711187))), c_List_Odistinct(_1711185)))))], (46873 ^ _780461) ^ [_1711422, _1711424] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1711422), _1711424))), -(c_Nitpick_Ocard_H(_1711422, _1711424) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46879 ^ _780461) ^ [_1711488, _1711490, _1711492, _1711494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711488), tc_List_Olist(_1711488))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711488), tc_List_Olist(_1711488)), _1711490), _1711492)), c_List_Olistrel(_1711488, _1711494))), 46882 ^ _780461 : [(46883 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711488)), _1711490) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711488)), _1711492))], (46885 ^ _780461) ^ [_1711824] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1711488, _1711488)), _1711824), hAPP(c_List_Oset(tc_prod(_1711488, _1711488)), hAPP(hAPP(c_List_Ozip(_1711488, _1711488), _1711490), _1711492)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1711488, _1711488, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1711488, tc_fun(tc_prod(_1711488, _1711488), tc_HOL_Obool), tc_fun(_1711488, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711488, tc_fun(tc_fun(tc_prod(_1711488, _1711488), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1711488, _1711488), tc_HOL_Obool), tc_fun(_1711488, tc_HOL_Obool)), _1711488), c_COMBC(_1711488, tc_fun(tc_prod(_1711488, _1711488), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711488, tc_prod(_1711488, _1711488)), tc_fun(_1711488, tc_fun(tc_fun(tc_prod(_1711488, _1711488), tc_HOL_Obool), tc_HOL_Obool)), _1711488), hAPP(c_COMBB(tc_prod(_1711488, _1711488), tc_fun(tc_fun(tc_prod(_1711488, _1711488), tc_HOL_Obool), tc_HOL_Obool), _1711488), c_member(tc_prod(_1711488, _1711488)))), c_Product__Type_OPair(_1711488, _1711488)))), _1711494)), _1711824)))]]], (46891 ^ _780461) ^ [_1712217, _1712219, _1712221, _1712223] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712217), tc_List_Olist(_1712217))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712217), tc_List_Olist(_1712217)), _1712219), _1712221)), c_List_Olistrel(_1712217, _1712223)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712217)), _1712219) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712217)), _1712221), 46897 ^ _780461 : [(46898 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1712217, _1712217)), 46896 ^ [_1712217, _1712219, _1712221, _1712223]), hAPP(c_List_Oset(tc_prod(_1712217, _1712217)), hAPP(hAPP(c_List_Ozip(_1712217, _1712217), _1712219), _1712221)))))], (46900 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1712217, _1712217, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1712217, tc_fun(tc_prod(_1712217, _1712217), tc_HOL_Obool), tc_fun(_1712217, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1712217, tc_fun(tc_fun(tc_prod(_1712217, _1712217), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1712217, _1712217), tc_HOL_Obool), tc_fun(_1712217, tc_HOL_Obool)), _1712217), c_COMBC(_1712217, tc_fun(tc_prod(_1712217, _1712217), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1712217, tc_prod(_1712217, _1712217)), tc_fun(_1712217, tc_fun(tc_fun(tc_prod(_1712217, _1712217), tc_HOL_Obool), tc_HOL_Obool)), _1712217), hAPP(c_COMBB(tc_prod(_1712217, _1712217), tc_fun(tc_fun(tc_prod(_1712217, _1712217), tc_HOL_Obool), tc_HOL_Obool), _1712217), c_member(tc_prod(_1712217, _1712217)))), c_Product__Type_OPair(_1712217, _1712217)))), _1712223)), 46896 ^ [_1712217, _1712219, _1712221, _1712223]))]]], (46904 ^ _780461) ^ [_1712955, _1712957, _1712959] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712955), tc_List_Olist(_1712955))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712955), tc_List_Olist(_1712955)), _1712957), _1712957)), c_List_Olistrel(_1712955, c_Transitive__Closure_Ortrancl(_1712955, _1712959)))))], (46906 ^ _780461) ^ [_1713015, _1713017, _1713019, _1713021] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713015), tc_List_Olist(_1713015))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713015), tc_List_Olist(_1713015)), _1713017), _1713019)), c_List_Olistrel(_1713015, _1713021))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713015)), _1713017) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713015)), _1713019))], (46912 ^ _780461) ^ [_1713184, _1713186, _1713188, _1713190, _1713192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713184), tc_List_Olist(_1713184))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713184), tc_List_Olist(_1713184)), _1713186), _1713188)), c_List_Olistrel(_1713184, c_Transitive__Closure_Ortrancl(_1713184, _1713190)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713184), tc_List_Olist(_1713184))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713184), tc_List_Olist(_1713184)), _1713188), _1713192)), c_List_Olistrel(_1713184, c_Transitive__Closure_Ortrancl(_1713184, _1713190)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713184), tc_List_Olist(_1713184))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713184), tc_List_Olist(_1713184)), _1713186), _1713192)), c_List_Olistrel(_1713184, c_Transitive__Closure_Ortrancl(_1713184, _1713190)))))], (46922 ^ _780461) ^ [_1713523, _1713525, _1713527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1713523, _1713523), tc_HOL_Obool)), _1713525), _1713527)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1713523), tc_List_Olist(_1713523)), tc_HOL_Obool)), c_List_Olistrel(_1713523, _1713525)), c_List_Olistrel(_1713523, _1713527))))], (46928 ^ _780461) ^ [_1713695, _1713697, _1713699, _1713701] : [c_List_Olistrelp(_1713695, hAPP(hAPP(c_COMBC(_1713695, tc_fun(tc_prod(_1713695, _1713695), tc_HOL_Obool), tc_fun(_1713695, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1713695, tc_fun(tc_fun(tc_prod(_1713695, _1713695), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1713695, _1713695), tc_HOL_Obool), tc_fun(_1713695, tc_HOL_Obool)), _1713695), c_COMBC(_1713695, tc_fun(tc_prod(_1713695, _1713695), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1713695, tc_prod(_1713695, _1713695)), tc_fun(_1713695, tc_fun(tc_fun(tc_prod(_1713695, _1713695), tc_HOL_Obool), tc_HOL_Obool)), _1713695), hAPP(c_COMBB(tc_prod(_1713695, _1713695), tc_fun(tc_fun(tc_prod(_1713695, _1713695), tc_HOL_Obool), tc_HOL_Obool), _1713695), c_member(tc_prod(_1713695, _1713695)))), c_Product__Type_OPair(_1713695, _1713695)))), _1713697), _1713699, _1713701), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713695), tc_List_Olist(_1713695))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713695), tc_List_Olist(_1713695)), _1713699), _1713701)), c_List_Olistrel(_1713695, _1713697))))], (46934 ^ _780461) ^ [_1714072, _1714074, _1714076, _1714078] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714072), tc_List_Olist(_1714072))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714072), tc_List_Olist(_1714072)), _1714076), _1714078)), c_List_Olistrel(_1714072, _1714074))), -(c_List_Olistrelp(_1714072, hAPP(hAPP(c_COMBC(_1714072, tc_fun(tc_prod(_1714072, _1714072), tc_HOL_Obool), tc_fun(_1714072, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1714072, tc_fun(tc_fun(tc_prod(_1714072, _1714072), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1714072, _1714072), tc_HOL_Obool), tc_fun(_1714072, tc_HOL_Obool)), _1714072), c_COMBC(_1714072, tc_fun(tc_prod(_1714072, _1714072), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1714072, tc_prod(_1714072, _1714072)), tc_fun(_1714072, tc_fun(tc_fun(tc_prod(_1714072, _1714072), tc_HOL_Obool), tc_HOL_Obool)), _1714072), hAPP(c_COMBB(tc_prod(_1714072, _1714072), tc_fun(tc_fun(tc_prod(_1714072, _1714072), tc_HOL_Obool), tc_HOL_Obool), _1714072), c_member(tc_prod(_1714072, _1714072)))), c_Product__Type_OPair(_1714072, _1714072)))), _1714074), _1714076, _1714078))], (46940 ^ _780461) ^ [_1714455, _1714457, _1714459] : [-(hAPP(c_List_Olexn(_1714455, _1714457), hAPP(c_Nat_OSuc, _1714459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1714455), tc_List_Olist(_1714455)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1714455, tc_List_Olist(_1714455)), tc_prod(_1714455, tc_List_Olist(_1714455))), tc_prod(tc_List_Olist(_1714455), tc_List_Olist(_1714455)), c_Product__Type_Omap__pair(tc_prod(_1714455, tc_List_Olist(_1714455)), tc_List_Olist(_1714455), tc_prod(_1714455, tc_List_Olist(_1714455)), tc_List_Olist(_1714455), hAPP(c_Product__Type_Oprod_Oprod__case(_1714455, tc_List_Olist(_1714455), tc_List_Olist(_1714455)), c_List_Olist_OCons(_1714455)), hAPP(c_Product__Type_Oprod_Oprod__case(_1714455, tc_List_Olist(_1714455), tc_List_Olist(_1714455)), c_List_Olist_OCons(_1714455)))), c_Wellfounded_Olex__prod(_1714455, tc_List_Olist(_1714455), _1714457, hAPP(c_List_Olexn(_1714455, _1714457), _1714459)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1714455), tc_List_Olist(_1714455))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1714455), tc_List_Olist(_1714455), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714455), tc_fun(tc_List_Olist(_1714455), tc_HOL_Obool), tc_fun(tc_List_Olist(_1714455), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1714455), tc_HOL_Obool), tc_fun(tc_List_Olist(_1714455), tc_HOL_Obool)), tc_List_Olist(_1714455)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1714455))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1714455)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714455), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1714455)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1714455)))), hAPP(c_Nat_OSuc, _1714459))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714455), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1714455)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1714455)))), hAPP(c_Nat_OSuc, _1714459)))))))], (46942 ^ _780461) ^ [_1714746, _1714748, _1714750, _1714752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714746)), _1714748)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714746)), _1714750))), _1714748 = hAPP(hAPP(c_List_Olist_OCons(_1714746), _1714752), _1714750)], (46948 ^ _780461) ^ [_1714882, _1714884, _1714886, _1714888] : [hBOOL(hAPP(hAPP(c_member(_1714882), _1714884), hAPP(c_List_Oset(_1714882), hAPP(hAPP(c_List_Olist_OCons(_1714882), _1714886), _1714888)))), -(_1714884 = _1714886), -(hBOOL(hAPP(hAPP(c_member(_1714882), _1714884), hAPP(c_List_Oset(_1714882), _1714888))))], (46958 ^ _780461) ^ [_1715040, _1715042, _1715044, _1715046, _1715048, _1715050] : [-(hAPP(hAPP(c_List_Ozip(_1715040, _1715042), hAPP(hAPP(c_List_Olist_OCons(_1715040), _1715044), _1715046)), hAPP(hAPP(c_List_Olist_OCons(_1715042), _1715048), _1715050)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1715040, _1715042)), hAPP(hAPP(c_Product__Type_OPair(_1715040, _1715042), _1715044), _1715048)), hAPP(hAPP(c_List_Ozip(_1715040, _1715042), _1715046), _1715050)))], (46960 ^ _780461) ^ [_1715127, _1715129, _1715131] : [-(hAPP(c_List_Oset(_1715127), hAPP(hAPP(c_List_Olist_OCons(_1715127), _1715129), _1715131)) = hAPP(hAPP(c_Set_Oinsert(_1715127), _1715129), hAPP(c_List_Oset(_1715127), _1715131)))], (46962 ^ _780461) ^ [_1715180, _1715182, _1715184] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1715180, tc_HOL_Obool)), hAPP(c_List_Oset(_1715180), _1715182)), hAPP(c_List_Oset(_1715180), hAPP(hAPP(c_List_Olist_OCons(_1715180), _1715184), _1715182)))))], (46964 ^ _780461) ^ [_1715235, _1715237, _1715239, _1715241, _1715243, _1715245] : [-(c_List_Ofoldr(_1715235, _1715237, _1715239, hAPP(hAPP(c_List_Olist_OCons(_1715235), _1715241), _1715243), _1715245) = hAPP(hAPP(_1715239, _1715241), c_List_Ofoldr(_1715235, _1715237, _1715239, _1715243, _1715245)))], (46966 ^ _780461) ^ [_1715309, _1715311, _1715313] : [_1715309 = hAPP(hAPP(c_List_Olist_OCons(_1715311), _1715313), _1715309)], (46968 ^ _780461) ^ [_1715359, _1715361, _1715363] : [hAPP(hAPP(c_List_Olist_OCons(_1715359), _1715361), _1715363) = _1715363], (46970 ^ _780461) ^ [_1715418, _1715420, _1715422, _1715424, _1715426] : [hAPP(hAPP(c_List_Olist_OCons(_1715418), _1715420), _1715422) = hAPP(hAPP(c_List_Olist_OCons(_1715418), _1715424), _1715426), 46973 ^ _780461 : [(46974 ^ _780461) ^ [] : [-(_1715420 = _1715424)], (46976 ^ _780461) ^ [] : [-(_1715422 = _1715426)]]], (46978 ^ _780461) ^ [_1715555, _1715557, _1715559, _1715561, _1715563] : [-(hAPP(hAPP(c_List_Olist_OCons(_1715555), _1715557), _1715559) = hAPP(hAPP(c_List_Olist_OCons(_1715555), _1715561), _1715563)), _1715557 = _1715561, _1715559 = _1715563], (46988 ^ _780461) ^ [_1715757, _1715759, _1715761, _1715763, _1715765, _1715767] : [c_List_Olistrelp(_1715757, _1715759, hAPP(hAPP(c_List_Olist_OCons(_1715757), _1715761), _1715763), hAPP(hAPP(c_List_Olist_OCons(_1715757), _1715765), _1715767)), 46991 ^ _780461 : [(46992 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(_1715759, _1715761), _1715765)))], (46994 ^ _780461) ^ [] : [-(c_List_Olistrelp(_1715757, _1715759, _1715763, _1715767))]]], (46996 ^ _780461) ^ [_1715914, _1715916, _1715918, _1715920, _1715922, _1715924] : [-(c_List_Olistrelp(_1715914, _1715916, hAPP(hAPP(c_List_Olist_OCons(_1715914), _1715918), _1715920), hAPP(hAPP(c_List_Olist_OCons(_1715914), _1715922), _1715924))), hBOOL(hAPP(hAPP(_1715916, _1715918), _1715922)), c_List_Olistrelp(_1715914, _1715916, _1715920, _1715924)], (47006 ^ _780461) ^ [_1716111, _1716113, _1716115, _1716117, _1716119, _1716121] : [hBOOL(hAPP(hAPP(_1716111, _1716113), _1716115)), c_List_Olistrelp(_1716117, _1716111, _1716119, _1716121), -(c_List_Olistrelp(_1716117, _1716111, hAPP(hAPP(c_List_Olist_OCons(_1716117), _1716113), _1716119), hAPP(hAPP(c_List_Olist_OCons(_1716117), _1716115), _1716121)))], (47016 ^ _780461) ^ [_1716306, _1716308, _1716310, _1716312, _1716314] : [-(hAPP(hAPP(c_List_Omap(_1716306, _1716308), _1716310), hAPP(hAPP(c_List_Olist_OCons(_1716306), _1716312), _1716314)) = hAPP(hAPP(c_List_Olist_OCons(_1716308), hAPP(_1716310, _1716312)), hAPP(hAPP(c_List_Omap(_1716306, _1716308), _1716310), _1716314)))], (47018 ^ _780461) ^ [_1716389, _1716391, _1716393, _1716395] : [_1716389 = _1716391, -(c_List_Oremove1(_1716393, _1716389, hAPP(hAPP(c_List_Olist_OCons(_1716393), _1716391), _1716395)) = _1716395)], (47024 ^ _780461) ^ [_1716488, _1716490, _1716492, _1716494] : [-(_1716488 = _1716490), -(c_List_Oremove1(_1716492, _1716488, hAPP(hAPP(c_List_Olist_OCons(_1716492), _1716490), _1716494)) = hAPP(hAPP(c_List_Olist_OCons(_1716492), _1716490), c_List_Oremove1(_1716492, _1716488, _1716494)))], (47030 ^ _780461) ^ [_1716554, _1716556, _1716558, _1716560, _1716562, _1716564] : [class_Orderings_Olinorder(_1716554), 47033 ^ _780461 : [(47034 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716554), hAPP(_1716556, _1716558)), hAPP(_1716556, _1716560))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716562, _1716554, _1716556), _1716558), hAPP(hAPP(c_List_Olist_OCons(_1716562), _1716560), _1716564)) = hAPP(hAPP(c_List_Olist_OCons(_1716562), _1716558), hAPP(hAPP(c_List_Olist_OCons(_1716562), _1716560), _1716564)))], (47040 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716554), hAPP(_1716556, _1716558)), hAPP(_1716556, _1716560)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716562, _1716554, _1716556), _1716558), hAPP(hAPP(c_List_Olist_OCons(_1716562), _1716560), _1716564)) = hAPP(hAPP(c_List_Olist_OCons(_1716562), _1716560), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716562, _1716554, _1716556), _1716558), _1716564)))]]], (47046 ^ _780461) ^ [_1716954, _1716956, _1716958] : [hBOOL(hAPP(c_List_Odistinct(_1716954), hAPP(hAPP(c_List_Olist_OCons(_1716954), _1716956), _1716958))), 47049 ^ _780461 : [(47050 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1716954), _1716956), hAPP(c_List_Oset(_1716954), _1716958)))], (47052 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1716954), _1716958)))]]], (47054 ^ _780461) ^ [_1717121, _1717123, _1717125] : [-(hBOOL(hAPP(c_List_Odistinct(_1717121), hAPP(hAPP(c_List_Olist_OCons(_1717121), _1717123), _1717125)))), -(hBOOL(hAPP(hAPP(c_member(_1717121), _1717123), hAPP(c_List_Oset(_1717121), _1717125)))), hBOOL(hAPP(c_List_Odistinct(_1717121), _1717125))], (47064 ^ _780461) ^ [_1717336, _1717338, _1717340, _1717342, _1717344, _1717346] : [_1717336 = _1717338, -(hAPP(c_Map_Omap__of(_1717340, _1717342, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1717340, _1717342)), hAPP(hAPP(c_Product__Type_OPair(_1717340, _1717342), _1717336), _1717344)), _1717346)), _1717338) = hAPP(c_Option_Ooption_OSome(_1717342), _1717344))], (47070 ^ _780461) ^ [_1717479, _1717481, _1717483, _1717485, _1717487, _1717489] : [-(_1717479 = _1717481), -(hAPP(c_Map_Omap__of(_1717483, _1717485, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1717483, _1717485)), hAPP(hAPP(c_Product__Type_OPair(_1717483, _1717485), _1717479), _1717487)), _1717489)), _1717481) = hAPP(c_Map_Omap__of(_1717483, _1717485, _1717489), _1717481))], (47076 ^ _780461) ^ [_1717559, _1717561, _1717563] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717559)), hAPP(hAPP(c_List_Olist_OCons(_1717559), _1717561), _1717563)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717559)), _1717563)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47078 ^ _780461) ^ [_1717614, _1717616, _1717618, _1717620, _1717622, _1717624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1717614, _1717614)), hAPP(hAPP(c_Product__Type_OPair(_1717614, _1717614), _1717616), _1717618)), _1717620)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1717614), tc_List_Olist(_1717614))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1717614), tc_List_Olist(_1717614)), _1717622), _1717624)), c_List_Olistrel(_1717614, _1717620))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1717614), tc_List_Olist(_1717614))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1717614), tc_List_Olist(_1717614)), hAPP(hAPP(c_List_Olist_OCons(_1717614), _1717616), _1717622)), hAPP(hAPP(c_List_Olist_OCons(_1717614), _1717618), _1717624))), c_List_Olistrel(_1717614, _1717620))))], (47088 ^ _780461) ^ [_1717949, _1717951, _1717953, _1717955] : [-(c_Map_Omap__of(_1717949, _1717951, hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1717949, _1717951)), _1717953), _1717955)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1717949, tc_Option_Ooption(_1717951)), c_Map_Omap__of(_1717949, _1717951, _1717955)), hAPP(c_Product__Type_Ofst(_1717949, _1717951), _1717953)), hAPP(c_Option_Ooption_OSome(_1717951), hAPP(c_Product__Type_Osnd(_1717949, _1717951), _1717953))))], (47090 ^ _780461) ^ [_1718055, _1718057, _1718059, _1718061, _1718063, _1718065] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1718055), tc_List_Olist(_1718055))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718055), tc_List_Olist(_1718055)), hAPP(hAPP(c_List_Olist_OCons(_1718055), _1718057), _1718059)), hAPP(hAPP(c_List_Olist_OCons(_1718055), _1718061), _1718063))), c_List_Olex(_1718055, _1718065))), 47095 ^ _780461 : [(47096 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718055, _1718055)), hAPP(hAPP(c_Product__Type_OPair(_1718055, _1718055), _1718057), _1718061)), _1718065)))], (47098 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718055)), _1718059) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718055)), _1718063))]], 47099 ^ _780461 : [(47100 ^ _780461) ^ [] : [-(_1718057 = _1718061)], (47102 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1718055), tc_List_Olist(_1718055))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718055), tc_List_Olist(_1718055)), _1718059), _1718063)), c_List_Olex(_1718055, _1718065))))]]], (47104 ^ _780461) ^ [_1718453, _1718455, _1718457, _1718459, _1718461, _1718463] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1718453), tc_List_Olist(_1718453))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718453), tc_List_Olist(_1718453)), hAPP(hAPP(c_List_Olist_OCons(_1718453), _1718455), _1718457)), hAPP(hAPP(c_List_Olist_OCons(_1718453), _1718459), _1718461))), c_List_Olex(_1718453, _1718463)))), 47105 ^ _780461 : [(47106 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1718453, _1718453)), hAPP(hAPP(c_Product__Type_OPair(_1718453, _1718453), _1718455), _1718459)), _1718463)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718453)), _1718457) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718453)), _1718461)], (47112 ^ _780461) ^ [] : [_1718455 = _1718459, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1718453), tc_List_Olist(_1718453))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1718453), tc_List_Olist(_1718453)), _1718457), _1718461)), c_List_Olex(_1718453, _1718463)))]]], (47120 ^ _780461) ^ [_1718909, _1718911, _1718913, _1718915] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1718909), tc_List_Olist(_1718909), c_List_Olistrel(_1718909, _1718911)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1718909)), hAPP(hAPP(c_List_Olist_OCons(_1718909), _1718913), _1718915)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1718909), tc_HOL_Obool)))) = c_List_Oset__Cons(_1718909, hAPP(c_Relation_OImage(_1718909, _1718909, _1718911), hAPP(hAPP(c_Set_Oinsert(_1718909), _1718913), c_Orderings_Obot__class_Obot(tc_fun(_1718909, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1718909), tc_List_Olist(_1718909), c_List_Olistrel(_1718909, _1718911)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1718909)), _1718915), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1718909), tc_HOL_Obool))))))], (47122 ^ _780461) ^ [_1719032, _1719034, _1719036] : [-(c_List_Oset__Cons(_1719032, _1719034, _1719036) = hAPP(c_Set_OCollect(tc_List_Olist(_1719032)), hAPP(hAPP(c_COMBB(tc_fun(_1719032, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1719032)), c_HOL_OEx(_1719032)), hAPP(hAPP(c_COMBB(tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), tc_fun(_1719032, tc_HOL_Obool), tc_List_Olist(_1719032)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_HOL_Obool, _1719032), c_HOL_OEx(tc_List_Olist(_1719032)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719032), tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1719032, tc_fun(tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool))), tc_fun(tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool))), tc_List_Olist(_1719032)), c_COMBS(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1719032, tc_fun(tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool))), tc_List_Olist(_1719032)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1719032), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), _1719032), c_COMBS(tc_List_Olist(_1719032), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1719032)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_fun(tc_List_Olist(_1719032), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1719032), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1719032)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719032), tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_List_Olist(_1719032))), tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1719032), tc_List_Olist(_1719032)), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), tc_fun(tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_List_Olist(_1719032))), tc_fun(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool))), tc_List_Olist(_1719032)), c_COMBB(tc_fun(tc_List_Olist(_1719032), tc_List_Olist(_1719032)), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), _1719032)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1719032), tc_List_Olist(_1719032)), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), tc_List_Olist(_1719032)), c_COMBB(tc_List_Olist(_1719032), tc_HOL_Obool, tc_List_Olist(_1719032))), c_fequal))), c_List_Olist_OCons(_1719032)))))), hAPP(hAPP(c_COMBC(_1719032, tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool)), _1719032), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1719032))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1719032), c_fconj), hAPP(hAPP(c_COMBC(_1719032, tc_fun(_1719032, tc_HOL_Obool), tc_HOL_Obool), c_member(_1719032)), _1719034)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719032), tc_fun(tc_List_Olist(_1719032), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1719032))), _1719036)))))))], (47124 ^ _780461) ^ [_1719567, _1719569, _1719571, _1719573, _1719575] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1719567), tc_List_Olist(_1719567))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1719567), tc_List_Olist(_1719567)), hAPP(hAPP(c_List_Olist_OCons(_1719567), _1719569), _1719571)), _1719573)), c_List_Olistrel(_1719567, _1719575))), 47129 ^ _780461 : [(47130 ^ _780461) ^ [] : [-(_1719573 = hAPP(hAPP(c_List_Olist_OCons(_1719567), 47127 ^ [_1719567, _1719569, _1719571, _1719573, _1719575]), 47128 ^ [_1719567, _1719569, _1719571, _1719573, _1719575]))], (47132 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1719567, _1719567)), hAPP(hAPP(c_Product__Type_OPair(_1719567, _1719567), _1719569), 47127 ^ [_1719567, _1719569, _1719571, _1719573, _1719575])), _1719575)))], (47134 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1719567), tc_List_Olist(_1719567))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1719567), tc_List_Olist(_1719567)), _1719571), 47128 ^ [_1719567, _1719569, _1719571, _1719573, _1719575])), c_List_Olistrel(_1719567, _1719575))))]]], (47136 ^ _780461) ^ [_1719956, _1719958, _1719960, _1719962, _1719964] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1719956), tc_List_Olist(_1719956))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1719956), tc_List_Olist(_1719956)), _1719958), hAPP(hAPP(c_List_Olist_OCons(_1719956), _1719960), _1719962))), c_List_Olistrel(_1719956, _1719964))), 47141 ^ _780461 : [(47142 ^ _780461) ^ [] : [-(_1719958 = hAPP(hAPP(c_List_Olist_OCons(_1719956), 47139 ^ [_1719956, _1719958, _1719960, _1719962, _1719964]), 47140 ^ [_1719956, _1719958, _1719960, _1719962, _1719964]))], (47144 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1719956, _1719956)), hAPP(hAPP(c_Product__Type_OPair(_1719956, _1719956), 47139 ^ [_1719956, _1719958, _1719960, _1719962, _1719964]), _1719960)), _1719964)))], (47146 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1719956), tc_List_Olist(_1719956))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1719956), tc_List_Olist(_1719956)), 47140 ^ [_1719956, _1719958, _1719960, _1719962, _1719964]), _1719962)), c_List_Olistrel(_1719956, _1719964))))]]], (47148 ^ _780461) ^ [_1720345, _1720347, _1720349] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720345)), c_List_Osublist(_1720345, _1720347, _1720349)) = 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(_1720345)), _1720347)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1720349)))))], (47150 ^ _780461) ^ [_1720426, _1720428, _1720430, _1720432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1720426), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1720428), _1720430))), -(hAPP(c_Random_Opick(_1720428, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1720428)), _1720430), _1720432)), _1720426) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1720428), _1720430))], (47156 ^ _780461) ^ [_1720569, _1720571, _1720573, _1720575] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1720569), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1720571), _1720573)))), -(hAPP(c_Random_Opick(_1720571, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1720571)), _1720573), _1720575)), _1720569) = hAPP(c_Random_Opick(_1720571, _1720575), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1720569), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1720571), _1720573))))], (47162 ^ _780461) ^ [_1720657, _1720659, _1720661] : [hBOOL(hAPP(c_List_Odistinct(_1720657), _1720659)), -(hBOOL(hAPP(c_List_Odistinct(_1720657), c_List_Osublist(_1720657, _1720659, _1720661))))], (47168 ^ _780461) ^ [_1720759, _1720761, _1720763, _1720765] : [-(hBOOL(hAPP(hAPP(c_member(_1720759), _1720761), hAPP(c_List_Oset(_1720759), _1720763)))), hBOOL(hAPP(hAPP(c_member(_1720759), _1720761), hAPP(c_List_Oset(_1720759), c_List_Osublist(_1720759, _1720763, _1720765))))], (47174 ^ _780461) ^ [_1720883, _1720885, _1720887, _1720889] : [hBOOL(hAPP(hAPP(c_member(_1720883), _1720885), hAPP(c_List_Oset(_1720883), c_List_Osublist(_1720883, _1720887, _1720889)))), -(hBOOL(hAPP(hAPP(c_member(_1720883), _1720885), hAPP(c_List_Oset(_1720883), _1720887))))], (47180 ^ _780461) ^ [_1721020, _1721022, _1721024] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1721020, tc_HOL_Obool)), hAPP(c_List_Oset(_1721020), c_List_Osublist(_1721020, _1721022, _1721024))), hAPP(c_List_Oset(_1721020), _1721022))))], (47182 ^ _780461) ^ [_1721071, _1721073, _1721075] : [-(c_Random_Oselect__weight(_1721071, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1721071)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1721071), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1721073)), _1721075)) = c_Random_Oselect__weight(_1721071, _1721075))], (47184 ^ _780461) ^ [_1721124, _1721126, _1721128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1721124), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1721126), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1721126)), _1721128)))), -(hBOOL(hAPP(hAPP(c_member(_1721126), hAPP(c_Random_Opick(_1721126, _1721128), _1721124)), hAPP(c_List_Oset(_1721126), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1721126), _1721126), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1721126)), _1721128)))))], (47190 ^ _780461) ^ [_1721315, _1721317, _1721319] : [class_Groups_Omonoid__add(_1721315), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1721315), hAPP(hAPP(c_List_Olist_OCons(_1721315), _1721317), _1721319)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1721315), _1721317), hAPP(c_List_Omonoid__add__class_Olistsum(_1721315), _1721319)))], (47196 ^ _780461) ^ [_1721444, _1721446, _1721448, _1721450, _1721452] : [class_Groups_Oab__group__add(_1721444), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1721444), hAPP(hAPP(c_List_Omap(_1721446, _1721444), hAPP(hAPP(c_COMBS(_1721446, _1721444, _1721444), hAPP(hAPP(c_COMBB(_1721444, tc_fun(_1721444, _1721444), _1721446), c_Groups_Ominus__class_Ominus(_1721444)), _1721448)), _1721450)), _1721452)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1721444), hAPP(c_List_Omonoid__add__class_Olistsum(_1721444), hAPP(hAPP(c_List_Omap(_1721446, _1721444), _1721448), _1721452))), hAPP(c_List_Omonoid__add__class_Olistsum(_1721444), hAPP(hAPP(c_List_Omap(_1721446, _1721444), _1721450), _1721452))))], (47202 ^ _780461) ^ [_1721675, _1721677, _1721679, _1721681, _1721683] : [class_Rings_Osemiring__0(_1721675), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1721675), hAPP(hAPP(c_List_Omap(_1721677, _1721675), hAPP(hAPP(c_COMBC(_1721677, _1721675, _1721675), hAPP(hAPP(c_COMBB(_1721675, tc_fun(_1721675, _1721675), _1721677), c_Groups_Otimes__class_Otimes(_1721675)), _1721679)), _1721681)), _1721683)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1721675), hAPP(c_List_Omonoid__add__class_Olistsum(_1721675), hAPP(hAPP(c_List_Omap(_1721677, _1721675), _1721679), _1721683))), _1721681))], (47208 ^ _780461) ^ [_1721878, _1721880, _1721882, _1721884, _1721886] : [class_Rings_Osemiring__0(_1721878), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1721878), hAPP(hAPP(c_List_Omap(_1721880, _1721878), hAPP(hAPP(c_COMBB(_1721878, _1721878, _1721880), hAPP(c_Groups_Otimes__class_Otimes(_1721878), _1721882)), _1721884)), _1721886)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1721878), _1721882), hAPP(c_List_Omonoid__add__class_Olistsum(_1721878), hAPP(hAPP(c_List_Omap(_1721880, _1721878), _1721884), _1721886))))], (47214 ^ _780461) ^ [_1722061, _1722063, _1722065, _1722067, _1722069] : [class_Groups_Ocomm__monoid__add(_1722061), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1722061), hAPP(hAPP(c_List_Omap(_1722063, _1722061), hAPP(hAPP(c_COMBS(_1722063, _1722061, _1722061), hAPP(hAPP(c_COMBB(_1722061, tc_fun(_1722061, _1722061), _1722063), c_Groups_Oplus__class_Oplus(_1722061)), _1722065)), _1722067)), _1722069)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1722061), hAPP(c_List_Omonoid__add__class_Olistsum(_1722061), hAPP(hAPP(c_List_Omap(_1722063, _1722061), _1722065), _1722069))), hAPP(c_List_Omonoid__add__class_Olistsum(_1722061), hAPP(hAPP(c_List_Omap(_1722063, _1722061), _1722067), _1722069))))], (47220 ^ _780461) ^ [_1722292, _1722294, _1722296] : [class_Groups_Omonoid__add(_1722292), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1722292), hAPP(hAPP(c_List_Omap(_1722294, _1722292), hAPP(c_COMBK(_1722292, _1722294), c_Groups_Ozero__class_Ozero(_1722292))), _1722296)) = c_Groups_Ozero__class_Ozero(_1722292))], (47226 ^ _780461) ^ [_1722417, _1722419] : [class_Groups_Oordered__ab__group__add__abs(_1722417), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1722417), hAPP(c_Groups_Oabs__class_Oabs(_1722417), hAPP(c_List_Omonoid__add__class_Olistsum(_1722417), _1722419))), hAPP(c_List_Omonoid__add__class_Olistsum(_1722417), hAPP(hAPP(c_List_Omap(_1722417, _1722417), c_Groups_Oabs__class_Oabs(_1722417)), _1722419)))))], (47232 ^ _780461) ^ [_1722558, _1722560, _1722562, _1722564] : [class_Groups_Oab__group__add(_1722558), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1722558), hAPP(c_List_Omonoid__add__class_Olistsum(_1722558), hAPP(hAPP(c_List_Omap(_1722560, _1722558), _1722562), _1722564))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1722558), hAPP(hAPP(c_List_Omap(_1722560, _1722558), hAPP(c_Fun_Ocomp(_1722558, _1722558, _1722560, c_Groups_Ouminus__class_Ouminus(_1722558)), _1722562)), _1722564)))], (47238 ^ _780461) ^ [_1722723, _1722725] : [class_Groups_Ocomm__monoid__add(_1722723), hBOOL(hAPP(c_List_Odistinct(_1722723), _1722725)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1722723), _1722725) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1722723, _1722723), c_COMBI(_1722723)), hAPP(c_List_Oset(_1722723), _1722725)))], (47248 ^ _780461) ^ [_1722900, _1722902] : [-(c_Random_Oselect__weight(_1722900, _1722902) = 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(_1722900, 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, _1722900), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1722900)), _1722902)))), hAPP(hAPP(c_COMBB(_1722900, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1722900, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1722900, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1722900, _1722902))))], (47250 ^ _780461) ^ [_1722984, _1722986, _1722988, _1722990] : [class_Groups_Ocomm__monoid__add(_1722984), hBOOL(hAPP(c_List_Odistinct(_1722986), _1722988)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1722984), hAPP(hAPP(c_List_Omap(_1722986, _1722984), _1722990), _1722988)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1722986, _1722984), _1722990), hAPP(c_List_Oset(_1722986), _1722988)))], (47260 ^ _780461) ^ [_1723183, _1723185, _1723187, _1723189] : [class_Groups_Ocomm__monoid__add(_1723183), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1723183), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1723183), _1723185), c_List_Oupto(_1723187, _1723189))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1723183), _1723185), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1723187, _1723189))))], (47266 ^ _780461) ^ [_1723326, _1723328, _1723330, _1723332] : [class_Groups_Ocomm__monoid__add(_1723326), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1723326), _1723328), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1723330, _1723332))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1723326), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1723326), _1723328), c_List_Oupto(_1723330, _1723332))))], (47272 ^ _780461) ^ [_1723469, _1723471, _1723473, _1723475] : [class_Rings_Osemiring__1(_1723469), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1723469), hAPP(hAPP(c_List_Omap(_1723471, _1723469), hAPP(c_COMBK(_1723469, _1723471), _1723473)), _1723475)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1723469), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1723469), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723471)), _1723475))), _1723473))], (47278 ^ _780461) ^ [_1723628, _1723630, _1723632, _1723634, _1723636] : [class_Groups_Ocomm__monoid__add(_1723628), hBOOL(hAPP(hAPP(c_member(_1723630), _1723632), hAPP(c_List_Oset(_1723630), _1723634))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1723628), hAPP(hAPP(c_List_Omap(_1723630, _1723628), _1723636), _1723634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1723628), hAPP(_1723636, _1723632)), hAPP(c_List_Omonoid__add__class_Olistsum(_1723628), hAPP(hAPP(c_List_Omap(_1723630, _1723628), _1723636), c_List_Oremove1(_1723630, _1723632, _1723634)))))], (47288 ^ _780461) ^ [_1723877, _1723879, _1723881] : [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, _1723877), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1723877)), _1723879)))), -(hBOOL(hAPP(hAPP(c_member(_1723877), hAPP(c_Product__Type_Ofst(_1723877, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1723877, _1723879), _1723881))), hAPP(c_List_Oset(_1723877), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1723877), _1723877), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1723877)), _1723879)))))], (47294 ^ _780461) ^ [_1724074, _1724076, _1724078, _1724080] : [class_Groups_Ocomm__monoid__add(_1724074), 47297 ^ _780461 : [(47298 ^ _780461) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1724076), _1724078)), -(c_Nitpick_Osetsum_H(_1724076, _1724074, _1724080, _1724078) = hAPP(c_List_Omonoid__add__class_Olistsum(_1724074), hAPP(hAPP(c_List_Omap(_1724076, _1724074), _1724080), c_Hilbert__Choice_OEps(tc_List_Olist(_1724076), hAPP(hAPP(c_COMBS(tc_List_Olist(_1724076), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1724076)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1724076), tc_fun(_1724076, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1724076, tc_HOL_Obool), tc_fun(tc_fun(_1724076, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1724076)), c_fequal), c_List_Oset(_1724076))), _1724078))), c_List_Odistinct(_1724076))))))], (47304 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1724076), _1724078))), -(c_Nitpick_Osetsum_H(_1724076, _1724074, _1724080, _1724078) = c_Groups_Ozero__class_Ozero(_1724074))]]], (47310 ^ _780461) ^ [_1724462, _1724464, _1724466, _1724468, _1724470] : [class_Orderings_Olinorder(_1724462), -(hBOOL(hAPP(hAPP(c_member(_1724462), hAPP(_1724464, _1724466)), hAPP(c_Set_Oimage(_1724468, _1724462, _1724464), hAPP(c_List_Oset(_1724468), _1724470))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1724468, _1724462, _1724464, _1724466, _1724470) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1724468, _1724462, _1724464), _1724466), _1724470))], (47330 ^ _780461) ^ [_1724814] : [47332 ^ _780461 : [(47333 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 47331 ^ [_1724814]), hAPP(c_List_Oset(tc_Nat_Onat), _1724814))))], (47335 ^ _780461) ^ [] : [47331 ^ [_1724814] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1724814) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47320 ^ _780461) ^ [_1724646] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1724646) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 47323 ^ _780461 : [(47324 ^ _780461) ^ [_1724721] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1724721), hAPP(c_List_Oset(tc_Nat_Onat), _1724646))), -(_1724721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (47339 ^ _780461) ^ [_1724970, _1724972, _1724974, _1724976, _1724978] : [class_Orderings_Olinorder(_1724970), hBOOL(hAPP(c_List_Odistinct(_1724972), _1724974)), -(hBOOL(hAPP(c_List_Odistinct(_1724972), c_List_Olinorder__class_Oinsort__insert__key(_1724972, _1724970, _1724976, _1724978, _1724974))))], (47349 ^ _780461) ^ [_1725137, _1725139, _1725141] : [class_Orderings_Olinorder(_1725137), hBOOL(hAPP(hAPP(c_member(_1725137), _1725139), hAPP(c_List_Oset(_1725137), _1725141))), -(c_List_Olinorder__class_Oinsort__insert__key(_1725137, _1725137, c_COMBI(_1725137), _1725139, _1725141) = _1725141)], (47359 ^ _780461) ^ [_1725308, _1725310, _1725312] : [class_Orderings_Olinorder(_1725308), -(hAPP(c_List_Oset(_1725308), c_List_Olinorder__class_Oinsort__insert__key(_1725308, _1725308, c_COMBI(_1725308), _1725310, _1725312)) = hAPP(hAPP(c_Set_Oinsert(_1725308), _1725310), hAPP(c_List_Oset(_1725308), _1725312)))], (47365 ^ _780461) ^ [_1725437, _1725439, _1725441, _1725443, _1725445] : [class_Orderings_Olinorder(_1725437), hBOOL(hAPP(hAPP(c_member(_1725437), hAPP(_1725439, _1725441)), hAPP(c_Set_Oimage(_1725443, _1725437, _1725439), hAPP(c_List_Oset(_1725443), _1725445)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1725443, _1725437, _1725439, _1725441, _1725445) = _1725445)], (47375 ^ _780461) ^ [_1725632, _1725634, _1725636] : [class_Orderings_Olinorder(_1725632), -(hBOOL(hAPP(hAPP(c_member(_1725632), _1725634), hAPP(c_List_Oset(_1725632), _1725636)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1725632, _1725632, c_COMBI(_1725632), _1725634, _1725636) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1725632, _1725632, c_COMBI(_1725632)), _1725634), _1725636))], (47385 ^ _780461) ^ [_1725815, _1725817, _1725819, _1725821, _1725823, _1725825] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1725815), tc_List_Olist(_1725815))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725815), tc_List_Olist(_1725815)), hAPP(hAPP(c_List_Olist_OCons(_1725815), _1725817), _1725819)), hAPP(hAPP(c_List_Olist_OCons(_1725815), _1725821), _1725823))), c_List_Olexord(_1725815, _1725825))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1725815, _1725815)), hAPP(hAPP(c_Product__Type_OPair(_1725815, _1725815), _1725817), _1725821)), _1725825))), 47392 ^ _780461 : [(47393 ^ _780461) ^ [] : [-(_1725817 = _1725821)], (47395 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1725815), tc_List_Olist(_1725815))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1725815), tc_List_Olist(_1725815)), _1725819), _1725823)), c_List_Olexord(_1725815, _1725825))))]]], (47397 ^ _780461) ^ [_1726142, _1726144, _1726146, _1726148, _1726150, _1726152] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1726142), tc_List_Olist(_1726142))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1726142), tc_List_Olist(_1726142)), hAPP(hAPP(c_List_Olist_OCons(_1726142), _1726144), _1726146)), hAPP(hAPP(c_List_Olist_OCons(_1726142), _1726148), _1726150))), c_List_Olexord(_1726142, _1726152)))), 47398 ^ _780461 : [(47399 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1726142, _1726142)), hAPP(hAPP(c_Product__Type_OPair(_1726142, _1726142), _1726144), _1726148)), _1726152))], (47401 ^ _780461) ^ [] : [_1726144 = _1726148, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1726142), tc_List_Olist(_1726142))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1726142), tc_List_Olist(_1726142)), _1726146), _1726150)), c_List_Olexord(_1726142, _1726152)))]]], (47409 ^ _780461) ^ [_1726515, _1726517, _1726519, _1726521] : [-(hAPP(c_List_Oset(tc_prod(_1726515, _1726517)), hAPP(hAPP(c_List_Ozip(_1726515, _1726517), _1726519), _1726521)) = hAPP(c_Set_OCollect(tc_prod(_1726515, _1726517)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1726515, _1726517)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1726515, _1726517), 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(_1726515, _1726517)), 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(_1726515, _1726517)), 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(_1726515, _1726517), tc_fun(tc_Nat_Onat, tc_prod(_1726515, _1726517)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1726515, _1726517), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1726515, _1726517)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1726515, _1726517)), c_COMBB(tc_prod(_1726515, _1726517), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1726517, tc_prod(_1726515, _1726517)), hAPP(hAPP(c_COMBB(_1726515, tc_fun(_1726517, tc_prod(_1726515, _1726517)), tc_Nat_Onat), c_Product__Type_OPair(_1726515, _1726517)), hAPP(c_List_Onth(_1726515), _1726519))), hAPP(c_List_Onth(_1726517), _1726521)))))), 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(_1726515)), _1726519)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726517)), _1726521)))))))], (47411 ^ _780461) ^ [_1726740, _1726742, _1726744, _1726746, _1726748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726740), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726742)), _1726744))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726740), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726746)), _1726748))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1726742, _1726746)), hAPP(hAPP(c_List_Ozip(_1726742, _1726746), _1726744), _1726748)), _1726740) = hAPP(hAPP(c_Product__Type_OPair(_1726742, _1726746), hAPP(hAPP(c_List_Onth(_1726742), _1726744), _1726740)), hAPP(hAPP(c_List_Onth(_1726746), _1726748), _1726740)))], (47421 ^ _780461) ^ [_1727019, _1727021, _1727023, _1727025, _1727027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727019), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727021)), _1727023))), -(hAPP(hAPP(c_List_Onth(_1727025), hAPP(hAPP(c_List_Omap(_1727021, _1727025), _1727027), _1727023)), _1727019) = hAPP(_1727027, hAPP(hAPP(c_List_Onth(_1727021), _1727023), _1727019)))], (47427 ^ _780461) ^ [_1727182, _1727184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727182), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1727184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1727184), _1727182)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1727184))))], (47433 ^ _780461) ^ [_1727303, _1727305, _1727307, _1727309] : [-(hAPP(hAPP(c_List_Onth(_1727303), hAPP(hAPP(c_List_Olist_OCons(_1727303), _1727305), _1727307)), hAPP(c_Nat_OSuc, _1727309)) = hAPP(hAPP(c_List_Onth(_1727303), _1727307), _1727309))], (47435 ^ _780461) ^ [_1727359, _1727361, _1727363] : [-(hAPP(hAPP(c_List_Onth(_1727359), hAPP(hAPP(c_List_Olist_OCons(_1727359), _1727361), _1727363)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1727361)], (47437 ^ _780461) ^ [_1727402, _1727404, _1727406, _1727408] : [-(hAPP(hAPP(c_List_Onth(_1727402), hAPP(hAPP(c_List_Olist_OCons(_1727402), _1727404), _1727406)), _1727408) = c_Nat_Onat_Onat__case(_1727402, _1727404, hAPP(c_List_Onth(_1727402), _1727406), _1727408))], (47439 ^ _780461) ^ [_1727475, _1727477, _1727479] : [47441 ^ _780461 : [(47442 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1727475), 47440 ^ [_1727475, _1727477, _1727479]), hAPP(c_List_Oset(_1727475), _1727477))))], (47444 ^ _780461) ^ [] : [hBOOL(hAPP(_1727479, 47440 ^ [_1727475, _1727477, _1727479]))]], 47445 ^ _780461 : [(47446 ^ _780461) ^ [_1727659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727659), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727475)), _1727477))), -(hBOOL(hAPP(_1727479, hAPP(hAPP(c_List_Onth(_1727475), _1727477), _1727659))))]]], (47452 ^ _780461) ^ [_1727786, _1727788, _1727790] : [47454 ^ _780461 : [(47455 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47453 ^ [_1727786, _1727788, _1727790]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727786)), _1727788))))], (47457 ^ _780461) ^ [] : [hBOOL(hAPP(_1727790, hAPP(hAPP(c_List_Onth(_1727786), _1727788), 47453 ^ [_1727786, _1727788, _1727790])))]], 47458 ^ _780461 : [(47459 ^ _780461) ^ [_1727988] : [hBOOL(hAPP(hAPP(c_member(_1727786), _1727988), hAPP(c_List_Oset(_1727786), _1727788))), -(hBOOL(hAPP(_1727790, _1727988)))]]], (47465 ^ _780461) ^ [_1728123, _1728125, _1728127] : [_1728123 = _1728125, 47468 ^ _780461 : [(47469 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728127)), _1728123) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728127)), _1728125))], (47471 ^ _780461) ^ [_1728271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728271), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728127)), _1728123))), -(hAPP(hAPP(c_List_Onth(_1728127), _1728123), _1728271) = hAPP(hAPP(c_List_Onth(_1728127), _1728125), _1728271))]]], (47477 ^ _780461) ^ [_1728410, _1728412, _1728414] : [-(_1728410 = _1728412), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728414)), _1728410) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728414)), _1728412), 47483 ^ _780461 : [(47484 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47482 ^ [_1728410, _1728412, _1728414]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728414)), _1728410))))], (47486 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Onth(_1728414), _1728410), 47482 ^ [_1728410, _1728412, _1728414]) = hAPP(hAPP(c_List_Onth(_1728414), _1728412), 47482 ^ [_1728410, _1728412, _1728414])]]], (47508 ^ _780461) ^ [_1729200, _1729202] : [47510 ^ _780461 : [(47511 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47509 ^ [_1729200, _1729202]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729200)), _1729202))))], (47514 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47512 ^ [_1729200, _1729202]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729200)), _1729202))))], (47516 ^ _780461) ^ [] : [47509 ^ [_1729200, _1729202] = 47512 ^ [_1729200, _1729202]], (47518 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1729200), _1729202), 47509 ^ [_1729200, _1729202]) = hAPP(hAPP(c_List_Onth(_1729200), _1729202), 47512 ^ [_1729200, _1729202]))]], -(hBOOL(hAPP(c_List_Odistinct(_1729200), _1729202)))], (47490 ^ _780461) ^ [_1728740, _1728742] : [hBOOL(hAPP(c_List_Odistinct(_1728740), _1728742)), 47493 ^ _780461 : [(47494 ^ _780461) ^ [_1728872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728872), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728740)), _1728742))), 47497 ^ _780461 : [(47498 ^ _780461) ^ [_1728999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728999), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728740)), _1728742))), -(_1728872 = _1728999), hAPP(hAPP(c_List_Onth(_1728740), _1728742), _1728872) = hAPP(hAPP(c_List_Onth(_1728740), _1728742), _1728999)]]]]], (47522 ^ _780461) ^ [_1729632, _1729634, _1729636, _1729638] : [hBOOL(hAPP(c_List_Odistinct(_1729632), _1729634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729636), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729632)), _1729634))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729638), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729632)), _1729634))), 47533 ^ _780461 : [(47534 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Onth(_1729632), _1729634), _1729636) = hAPP(hAPP(c_List_Onth(_1729632), _1729634), _1729638), -(_1729636 = _1729638)], (47540 ^ _780461) ^ [] : [_1729636 = _1729638, -(hAPP(hAPP(c_List_Onth(_1729632), _1729634), _1729636) = hAPP(hAPP(c_List_Onth(_1729632), _1729634), _1729638))]]], (47546 ^ _780461) ^ [_1730067, _1730069, _1730071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730067), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730069)), _1730071))), -(hBOOL(hAPP(hAPP(c_member(_1730069), hAPP(hAPP(c_List_Onth(_1730069), _1730071), _1730067)), hAPP(c_List_Oset(_1730069), _1730071))))], (47552 ^ _780461) ^ [_1730228, _1730230, _1730232] : [hBOOL(hAPP(hAPP(c_member(_1730228), _1730230), hAPP(c_List_Oset(_1730228), _1730232))), 47556 ^ _780461 : [(47557 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47555 ^ [_1730228, _1730230, _1730232]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730228)), _1730232))))], (47559 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1730228), _1730232), 47555 ^ [_1730228, _1730230, _1730232]) = _1730230)]]], (47561 ^ _780461) ^ [_1730416, _1730418, _1730420] : [-(hBOOL(hAPP(hAPP(c_member(_1730416), _1730418), hAPP(c_List_Oset(_1730416), _1730420)))), 47562 ^ _780461 : [(47563 ^ _780461) ^ [_1730490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1730490), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730416)), _1730420))), hAPP(hAPP(c_List_Onth(_1730416), _1730420), _1730490) = _1730418]]], (47571 ^ _780461) ^ [_1730667, _1730669, _1730671, _1730673] : [_1730667 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1730669), hAPP(hAPP(c_List_Olist_OCons(_1730669), _1730671), _1730673)), _1730667) = _1730671)], (47577 ^ _780461) ^ [_1730774, _1730776, _1730778, _1730780] : [-(_1730774 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1730776), hAPP(hAPP(c_List_Olist_OCons(_1730776), _1730778), _1730780)), _1730774) = hAPP(hAPP(c_List_Onth(_1730776), _1730780), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1730774), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (47583 ^ _780461) ^ [_1730846, _1730848] : [-(hAPP(c_List_Oset(_1730846), _1730848) = hAPP(c_Set_OCollect(_1730846), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1730846), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1730846, 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)), _1730846), 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)), _1730846), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1730846, tc_fun(tc_Nat_Onat, _1730846), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1730846, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1730846), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1730846), c_COMBB(_1730846, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1730846), _1730848))))), 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(_1730846)), _1730848))))))], (47585 ^ _780461) ^ [_1730987, _1730989, _1730991, _1730993] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730987) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1730989), hAPP(hAPP(c_List_Olist_OCons(_1730989), _1730991), _1730993)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1730987)) = _1730991)], (47591 ^ _780461) ^ [_1731106, _1731108, _1731110, _1731112] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1731106) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1731108), hAPP(hAPP(c_List_Olist_OCons(_1731108), _1731110), _1731112)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1731106)) = hAPP(hAPP(c_List_Onth(_1731108), _1731112), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1731106)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (47597 ^ _780461) ^ [_1731187, _1731189] : [class_Groups_Ocomm__monoid__add(_1731187), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1731187), _1731189) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1731187), hAPP(c_List_Onth(_1731187), _1731189)), 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(_1731187)), _1731189))))], (47603 ^ _780461) ^ [_1731320, _1731322, _1731324] : [-(hAPP(c_List_Oset(_1731320), c_List_Osublist(_1731320, _1731322, _1731324)) = hAPP(c_Set_OCollect(_1731320), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1731320), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1731320, 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)), _1731320), 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)), _1731320), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1731320, tc_fun(tc_Nat_Onat, _1731320), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1731320, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1731320), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1731320), c_COMBB(_1731320, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1731320), _1731322))))), 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(_1731320)), _1731322)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1731324))))))], (47605 ^ _780461) ^ [_1731485, _1731487, _1731489, _1731491] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731485), tc_List_Olist(_1731485))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731485), tc_List_Olist(_1731485)), _1731487), _1731489)), c_List_Olex(_1731485, _1731491))), 47608 ^ _780461 : [(47609 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731485), tc_List_Olist(_1731485))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731485), tc_List_Olist(_1731485)), _1731487), _1731489)), c_List_Olexord(_1731485, _1731491))))], (47611 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731485)), _1731487) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731485)), _1731489))]]], (47613 ^ _780461) ^ [_1731736, _1731738, _1731740, _1731742] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731736), tc_List_Olist(_1731736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731736), tc_List_Olist(_1731736)), _1731738), _1731740)), c_List_Olex(_1731736, _1731742)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1731736), tc_List_Olist(_1731736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731736), tc_List_Olist(_1731736)), _1731738), _1731740)), c_List_Olexord(_1731736, _1731742))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731736)), _1731738) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731736)), _1731740)], (47623 ^ _780461) ^ [_1732044, _1732046, _1732048, _1732050] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1732044), tc_List_Olist(_1732044))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1732044), tc_List_Olist(_1732044)), _1732046), _1732048)), c_List_Olistrel(_1732044, _1732050))), 47626 ^ _780461 : [(47627 ^ _780461) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732044)), _1732046) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732044)), _1732048))], (47629 ^ _780461) ^ [_1732273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732273), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732044)), _1732046))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1732044, _1732044)), hAPP(hAPP(c_Product__Type_OPair(_1732044, _1732044), hAPP(hAPP(c_List_Onth(_1732044), _1732046), _1732273)), hAPP(hAPP(c_List_Onth(_1732044), _1732048), _1732273))), _1732050)))]]], (47635 ^ _780461) ^ [_1732452, _1732454, _1732456, _1732458] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1732452), tc_List_Olist(_1732452))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1732452), tc_List_Olist(_1732452)), _1732454), _1732456)), c_List_Olistrel(_1732452, _1732458)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732452)), _1732454) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732452)), _1732456), 47641 ^ _780461 : [(47642 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47640 ^ [_1732452, _1732454, _1732456, _1732458]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732452)), _1732454))))], (47644 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1732452, _1732452)), hAPP(hAPP(c_Product__Type_OPair(_1732452, _1732452), hAPP(hAPP(c_List_Onth(_1732452), _1732454), 47640 ^ [_1732452, _1732454, _1732456, _1732458])), hAPP(hAPP(c_List_Onth(_1732452), _1732456), 47640 ^ [_1732452, _1732454, _1732456, _1732458]))), _1732458))]]], (47648 ^ _780461) ^ [_1732896, _1732898, _1732900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732896), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732898)), _1732900))), -(hAPP(c_Random_Opick(_1732898, hAPP(hAPP(c_List_Omap(_1732898, tc_prod(tc_Code__Numeral_Ocode__numeral, _1732898)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1732898), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1732900)), hAPP(c_Code__Numeral_Oof__nat, _1732896)) = hAPP(hAPP(c_List_Onth(_1732898), _1732900), _1732896))], (47654 ^ _780461) ^ [_1733069, _1733071] : [-(c_Random_Oselect(_1733069, _1733071) = 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(_1733069, 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(_1733069)), _1733071)))), hAPP(hAPP(c_COMBB(_1733069, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1733069, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1733069, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1733069, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1733069), _1733071)), c_Code__Numeral_Onat__of))))], (47656 ^ _780461) ^ [_1733178, _1733180, _1733182, _1733184] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733178), tc_List_Olist(_1733178))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733178), tc_List_Olist(_1733178)), _1733180), _1733182)), c_List_Olexord(_1733178, _1733184))), 47661 ^ _780461 : [(47662 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733178)), _1733180)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733178)), _1733182))))], (47664 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1733178), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733178)), _1733180)), _1733182) = _1733180)]], 47666 ^ _780461 : [(47667 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47665 ^ [_1733178, _1733180, _1733182, _1733184]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733178)), _1733180)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733178)), _1733182)))))], (47669 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1733178), 47665 ^ [_1733178, _1733180, _1733182, _1733184]), _1733180) = hAPP(hAPP(c_List_Otake(_1733178), 47665 ^ [_1733178, _1733180, _1733182, _1733184]), _1733182))], (47671 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1733178, _1733178)), hAPP(hAPP(c_Product__Type_OPair(_1733178, _1733178), hAPP(hAPP(c_List_Onth(_1733178), _1733180), 47665 ^ [_1733178, _1733180, _1733182, _1733184])), hAPP(hAPP(c_List_Onth(_1733178), _1733182), 47665 ^ [_1733178, _1733180, _1733182, _1733184]))), _1733184)))]]], (47673 ^ _780461) ^ [_1733718, _1733720, _1733722, _1733724] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1733718), tc_List_Olist(_1733718))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1733718), tc_List_Olist(_1733718)), _1733720), _1733722)), c_List_Olexord(_1733718, _1733724)))), 47674 ^ _780461 : [(47675 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733718)), _1733720)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733718)), _1733722))), hAPP(hAPP(c_List_Otake(_1733718), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733718)), _1733720)), _1733722) = _1733720], (47681 ^ _780461) ^ [_1734025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734025), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733718)), _1733720)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733718)), _1733722)))), hAPP(hAPP(c_List_Otake(_1733718), _1734025), _1733720) = hAPP(hAPP(c_List_Otake(_1733718), _1734025), _1733722), hBOOL(hAPP(hAPP(c_member(tc_prod(_1733718, _1733718)), hAPP(hAPP(c_Product__Type_OPair(_1733718, _1733718), hAPP(hAPP(c_List_Onth(_1733718), _1733720), _1734025)), hAPP(hAPP(c_List_Onth(_1733718), _1733722), _1734025))), _1733724))]]], (47693 ^ _780461) ^ [_1734379, _1734381, _1734383, _1734385] : [hBOOL(hAPP(hAPP(c_member(_1734379), _1734381), hAPP(c_List_Oset(_1734379), hAPP(hAPP(c_List_Otake(_1734379), _1734383), _1734385)))), -(hBOOL(hAPP(hAPP(c_member(_1734379), _1734381), hAPP(c_List_Oset(_1734379), _1734385))))], (47699 ^ _780461) ^ [_1734524, _1734526, _1734528, _1734530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734524), _1734526)), -(hAPP(hAPP(c_List_Onth(_1734528), hAPP(hAPP(c_List_Otake(_1734528), _1734526), _1734530)), _1734524) = hAPP(hAPP(c_List_Onth(_1734528), _1734530), _1734524))], (47705 ^ _780461) ^ [_1734663, _1734665, _1734667] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1734663, tc_HOL_Obool)), hAPP(c_List_Oset(_1734663), hAPP(hAPP(c_List_Otake(_1734663), _1734665), _1734667))), hAPP(c_List_Oset(_1734663), _1734667))))], (47707 ^ _780461) ^ [_1734718, _1734720, _1734722, _1734724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1734718), _1734720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1734722, tc_HOL_Obool)), hAPP(c_List_Oset(_1734722), hAPP(hAPP(c_List_Otake(_1734722), _1734718), _1734724))), hAPP(c_List_Oset(_1734722), hAPP(hAPP(c_List_Otake(_1734722), _1734720), _1734724)))))], (47713 ^ _780461) ^ [_1734881, _1734883, _1734885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734881)), _1734883)), _1734885)), -(hAPP(hAPP(c_List_Otake(_1734881), _1734885), _1734883) = _1734883)], (47719 ^ _780461) ^ [_1735000, _1735002, _1735004] : [hBOOL(hAPP(c_List_Odistinct(_1735000), _1735002)), -(hBOOL(hAPP(c_List_Odistinct(_1735000), hAPP(hAPP(c_List_Otake(_1735000), _1735004), _1735002))))], (47725 ^ _780461) ^ [_1735111, _1735113, _1735115, _1735117] : [-(hAPP(hAPP(c_List_Otake(_1735111), _1735113), hAPP(hAPP(c_List_Otake(_1735111), _1735115), _1735117)) = hAPP(hAPP(c_List_Otake(_1735111), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1735113), _1735115)), _1735117))], (47727 ^ _780461) ^ [_1735170, _1735172, _1735174, _1735176, _1735178] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1735170, _1735172)), _1735174), hAPP(hAPP(c_List_Ozip(_1735170, _1735172), _1735176), _1735178)) = hAPP(hAPP(c_List_Ozip(_1735170, _1735172), hAPP(hAPP(c_List_Otake(_1735170), _1735174), _1735176)), hAPP(hAPP(c_List_Otake(_1735172), _1735174), _1735178)))], (47729 ^ _780461) ^ [_1735246, _1735248, _1735250] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735246)), hAPP(hAPP(c_List_Otake(_1735246), _1735248), _1735250)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735246)), _1735250)), _1735248))], (47731 ^ _780461) ^ [_1735301, _1735303, _1735305, _1735307] : [-(hAPP(hAPP(c_List_Otake(_1735301), hAPP(c_Nat_OSuc, _1735303)), hAPP(hAPP(c_List_Olist_OCons(_1735301), _1735305), _1735307)) = hAPP(hAPP(c_List_Olist_OCons(_1735301), _1735305), hAPP(hAPP(c_List_Otake(_1735301), _1735303), _1735307)))], (47733 ^ _780461) ^ [_1735365, _1735367, _1735369] : [-(c_List_Osublist(_1735365, _1735367, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1735369)) = hAPP(hAPP(c_List_Otake(_1735365), _1735369), _1735367))], (47735 ^ _780461) ^ [_1735407, _1735409, _1735411, _1735413, _1735415] : [-(hAPP(hAPP(c_List_Otake(_1735407), _1735409), hAPP(hAPP(c_List_Omap(_1735411, _1735407), _1735413), _1735415)) = hAPP(hAPP(c_List_Omap(_1735411, _1735407), _1735413), hAPP(hAPP(c_List_Otake(_1735411), _1735409), _1735415)))], (47737 ^ _780461) ^ [_1735472, _1735474, _1735476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735472), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1735474))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1735474), _1735472), _1735476)) = 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), _1735474)), _1735476)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1735474), _1735472)))], (47743 ^ _780461) ^ [_1735629, _1735631] : [-(_1735629 = c_List_Olist_ONil(_1735631)), -(c_Random_Oselect__weight(_1735631, hAPP(hAPP(c_List_Omap(_1735631, tc_prod(tc_Code__Numeral_Ocode__numeral, _1735631)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1735631), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1735629)) = c_Random_Oselect(_1735631, _1735629))], (47749 ^ _780461) ^ [_1735691, _1735693, _1735695] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1735691), tc_List_Olist(_1735691))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1735691), tc_List_Olist(_1735691)), c_List_Olist_ONil(_1735691)), _1735693)), c_List_Olistrel(_1735691, _1735695))), -(_1735693 = c_List_Olist_ONil(_1735691))], (47755 ^ _780461) ^ [_1735838, _1735840, _1735842] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1735838), tc_List_Olist(_1735838))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1735838), tc_List_Olist(_1735838)), _1735840), c_List_Olist_ONil(_1735838))), c_List_Olistrel(_1735838, _1735842))), -(_1735840 = c_List_Olist_ONil(_1735838))], (47761 ^ _780461) ^ [_1735985, _1735987, _1735989] : [-(hAPP(hAPP(c_List_Olist__update(_1735985, _1735987), _1735989), hAPP(hAPP(c_List_Onth(_1735985), _1735987), _1735989)) = _1735987)], (47763 ^ _780461) ^ [_1736025, _1736027, _1736029, _1736031, _1736033] : [-(_1736025 = _1736027), -(hAPP(hAPP(c_List_Onth(_1736029), hAPP(hAPP(c_List_Olist__update(_1736029, _1736031), _1736025), _1736033)), _1736027) = hAPP(hAPP(c_List_Onth(_1736029), _1736031), _1736027))], (47769 ^ _780461) ^ [_1736092, _1736094, _1736096, _1736098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736092)), _1736094)), _1736096)), -(hAPP(hAPP(c_List_Olist__update(_1736092, _1736094), _1736096), _1736098) = _1736094)], (47775 ^ _780461) ^ [_1736215, _1736217] : [-(hAPP(hAPP(c_List_Otake(_1736215), _1736217), c_List_Olist_ONil(_1736215)) = c_List_Olist_ONil(_1736215))], (47787 ^ _780461) ^ [_1736382, _1736384, _1736386] : [47788 ^ _780461 : [(47789 ^ _780461) ^ [] : [_1736384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47791 ^ _780461) ^ [] : [_1736386 = c_List_Olist_ONil(_1736382)]], -(hAPP(hAPP(c_List_Otake(_1736382), _1736384), _1736386) = c_List_Olist_ONil(_1736382))], (47777 ^ _780461) ^ [_1736270, _1736272, _1736274] : [hAPP(hAPP(c_List_Otake(_1736270), _1736272), _1736274) = c_List_Olist_ONil(_1736270), -(_1736272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1736274 = c_List_Olist_ONil(_1736270))], (47795 ^ _780461) ^ [_1736525, _1736527] : [-(hAPP(hAPP(c_List_Otake(_1736525), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1736527) = c_List_Olist_ONil(_1736525))], (47797 ^ _780461) ^ [_1736560] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736560)), c_List_Olist_ONil(_1736560)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47799 ^ _780461) ^ [_1736607, _1736609] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736607)), _1736609) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1736609 = c_List_Olist_ONil(_1736607))], (47805 ^ _780461) ^ [_1736698, _1736700] : [_1736700 = c_List_Olist_ONil(_1736698), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736698)), _1736700) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47811 ^ _780461) ^ [_1736795, _1736797, _1736799, _1736801] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736795)), hAPP(hAPP(c_List_Olist__update(_1736795, _1736797), _1736799), _1736801)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736795)), _1736797))], (47813 ^ _780461) ^ [_1736847, _1736849, _1736851, _1736853] : [-(hAPP(hAPP(c_List_Otake(_1736847), _1736849), hAPP(hAPP(c_List_Olist_OCons(_1736847), _1736851), _1736853)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1736847), c_List_Olist_ONil(_1736847), hAPP(hAPP(c_COMBB(tc_List_Olist(_1736847), tc_List_Olist(_1736847), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1736847), _1736851)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1736847), tc_List_Olist(_1736847)), c_List_Otake(_1736847)), _1736853)), _1736849))], (47815 ^ _780461) ^ [_1736957, _1736959, _1736961, _1736963] : [c_List_Olist_ONil(_1736957) = hAPP(hAPP(c_List_Omap(_1736959, _1736957), _1736961), _1736963), -(_1736963 = c_List_Olist_ONil(_1736959))], (47821 ^ _780461) ^ [_1737060, _1737062, _1737064, _1737066] : [_1737066 = c_List_Olist_ONil(_1737062), -(c_List_Olist_ONil(_1737060) = hAPP(hAPP(c_List_Omap(_1737062, _1737060), _1737064), _1737066))], (47827 ^ _780461) ^ [_1737169, _1737171, _1737173] : [-(hAPP(hAPP(c_List_Omap(_1737169, _1737171), _1737173), c_List_Olist_ONil(_1737169)) = c_List_Olist_ONil(_1737171))], (47829 ^ _780461) ^ [_1737209, _1737211, _1737213, _1737215, _1737217, _1737219] : [-(hAPP(hAPP(c_List_Omap(_1737209, _1737211), _1737213), hAPP(hAPP(c_List_Olist__update(_1737209, _1737215), _1737217), _1737219)) = hAPP(hAPP(c_List_Olist__update(_1737211, hAPP(hAPP(c_List_Omap(_1737209, _1737211), _1737213), _1737215)), _1737217), hAPP(_1737213, _1737219)))], (47831 ^ _780461) ^ [_1737302, _1737304, _1737306, _1737308] : [hAPP(hAPP(c_List_Omap(_1737302, _1737304), _1737306), _1737308) = c_List_Olist_ONil(_1737304), -(_1737308 = c_List_Olist_ONil(_1737302))], (47837 ^ _780461) ^ [_1737405, _1737407, _1737409, _1737411] : [_1737411 = c_List_Olist_ONil(_1737405), -(hAPP(hAPP(c_List_Omap(_1737405, _1737407), _1737409), _1737411) = c_List_Olist_ONil(_1737407))], (47843 ^ _780461) ^ [_1737514, _1737516, _1737518, _1737520, _1737522, _1737524, _1737526] : [-(hAPP(hAPP(c_List_Ozip(_1737514, _1737516), hAPP(hAPP(c_List_Olist__update(_1737514, _1737518), _1737520), _1737522)), hAPP(hAPP(c_List_Olist__update(_1737516, _1737524), _1737520), _1737526)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1737514, _1737516), hAPP(hAPP(c_List_Ozip(_1737514, _1737516), _1737518), _1737524)), _1737520), hAPP(hAPP(c_Product__Type_OPair(_1737514, _1737516), _1737522), _1737526)))], (47845 ^ _780461) ^ [_1737606, _1737608, _1737610, _1737612, _1737614, _1737616] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1737606, _1737608), hAPP(hAPP(c_List_Ozip(_1737606, _1737608), _1737610), _1737612)), _1737614), _1737616) = hAPP(hAPP(c_List_Ozip(_1737606, _1737608), hAPP(hAPP(c_List_Olist__update(_1737606, _1737610), _1737614), hAPP(c_Product__Type_Ofst(_1737606, _1737608), _1737616))), hAPP(hAPP(c_List_Olist__update(_1737608, _1737612), _1737614), hAPP(c_Product__Type_Osnd(_1737606, _1737608), _1737616))))], (47847 ^ _780461) ^ [_1737699, _1737701] : [-(c_List_Osublist(_1737699, c_List_Olist_ONil(_1737699), _1737701) = c_List_Olist_ONil(_1737699))], (47849 ^ _780461) ^ [_1737732, _1737734] : [-(c_List_Osublist(_1737732, _1737734, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1737732))], (47851 ^ _780461) ^ [_1737763, _1737765, _1737767, _1737769] : [class_Orderings_Olinorder(_1737763), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1737765, _1737763, _1737767), _1737769), c_List_Olist_ONil(_1737765)) = hAPP(hAPP(c_List_Olist_OCons(_1737765), _1737769), c_List_Olist_ONil(_1737765)))], (47857 ^ _780461) ^ [_1737886, _1737888, _1737890, _1737892, _1737894] : [-(hAPP(hAPP(c_List_Olist__update(_1737886, hAPP(hAPP(c_List_Olist_OCons(_1737886), _1737888), _1737890)), hAPP(c_Nat_OSuc, _1737892)), _1737894) = hAPP(hAPP(c_List_Olist_OCons(_1737886), _1737888), hAPP(hAPP(c_List_Olist__update(_1737886, _1737890), _1737892), _1737894)))], (47859 ^ _780461) ^ [_1737969, _1737971, _1737973] : [hAPP(hAPP(c_List_Olist_OCons(_1737969), _1737971), _1737973) = c_List_Olist_ONil(_1737969)], (47861 ^ _780461) ^ [_1738021, _1738023, _1738025] : [c_List_Olist_ONil(_1738021) = hAPP(hAPP(c_List_Olist_OCons(_1738021), _1738023), _1738025)], (47863 ^ _780461) ^ [_1738058, _1738060, _1738062, _1738064] : [-(hAPP(hAPP(c_List_Olist__update(_1738058, hAPP(hAPP(c_List_Olist_OCons(_1738058), _1738060), _1738062)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1738064) = hAPP(hAPP(c_List_Olist_OCons(_1738058), _1738064), _1738062))], (47865 ^ _780461) ^ [_1738112, _1738114, _1738116, _1738118, _1738120] : [-(hAPP(hAPP(c_List_Olist__update(_1738112, hAPP(hAPP(c_List_Olist_OCons(_1738112), _1738114), _1738116)), _1738118), _1738120) = c_Nat_Onat_Onat__case(tc_List_Olist(_1738112), hAPP(hAPP(c_List_Olist_OCons(_1738112), _1738120), _1738116), hAPP(hAPP(c_COMBB(tc_List_Olist(_1738112), tc_List_Olist(_1738112), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1738112), _1738114)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1738112, tc_List_Olist(_1738112)), c_List_Olist__update(_1738112, _1738116)), _1738120)), _1738118))], (47867 ^ _780461) ^ [_1738209] : [class_Orderings_Olinorder(_1738209), -(c_List_Olinorder__class_Osorted__list__of__set(_1738209, c_Orderings_Obot__class_Obot(tc_fun(_1738209, tc_HOL_Obool))) = c_List_Olist_ONil(_1738209))], (47873 ^ _780461) ^ [_1738302, _1738304, _1738306] : [-(hAPP(hAPP(c_List_Ozip(_1738302, _1738304), _1738306), c_List_Olist_ONil(_1738304)) = c_List_Olist_ONil(tc_prod(_1738302, _1738304)))], (47875 ^ _780461) ^ [_1738345, _1738347, _1738349] : [-(hAPP(hAPP(c_List_Ozip(_1738345, _1738347), c_List_Olist_ONil(_1738345)), _1738349) = c_List_Olist_ONil(tc_prod(_1738345, _1738347)))], (47877 ^ _780461) ^ [_1738388, _1738390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1738388), _1738390)), -(c_List_Oupto(_1738390, _1738388) = c_List_Olist_ONil(tc_Int_Oint))], (47883 ^ _780461) ^ [_1738481, _1738483, _1738485, _1738487] : [-(c_List_Ofoldr(_1738481, _1738483, _1738485, c_List_Olist_ONil(_1738481), _1738487) = _1738487)], (47885 ^ _780461) ^ [_1738518, _1738520, _1738522] : [-(hAPP(c_Map_Omap__of(_1738518, _1738520, c_List_Olist_ONil(tc_prod(_1738518, _1738520))), _1738522) = c_Option_Ooption_ONone(_1738520))], (47887 ^ _780461) ^ [_1738559, _1738561, _1738563] : [-(hAPP(c_Map_Omap__of(_1738559, _1738561, c_List_Olist_ONil(tc_prod(_1738559, _1738561))), _1738563) = c_Option_Ooption_ONone(_1738561))], (47889 ^ _780461) ^ [_1738621, _1738623, _1738625, _1738627] : [hAPP(hAPP(c_List_Olist__update(_1738621, _1738623), _1738625), _1738627) = c_List_Olist_ONil(_1738621), -(_1738623 = c_List_Olist_ONil(_1738621))], (47895 ^ _780461) ^ [_1738724, _1738726, _1738728, _1738730] : [_1738726 = c_List_Olist_ONil(_1738724), -(hAPP(hAPP(c_List_Olist__update(_1738724, _1738726), _1738728), _1738730) = c_List_Olist_ONil(_1738724))], (47901 ^ _780461) ^ [_1738833, _1738835, _1738837] : [-(hAPP(hAPP(c_List_Olist__update(_1738833, c_List_Olist_ONil(_1738833)), _1738835), _1738837) = c_List_Olist_ONil(_1738833))], (47903 ^ _780461) ^ [_1738873, _1738875, _1738877] : [-(hAPP(hAPP(c_List_Olist__update(_1738873, c_List_Olist_ONil(_1738873)), _1738875), _1738877) = c_List_Olist_ONil(_1738873))], (47905 ^ _780461) ^ [_1738913, _1738915, _1738917, _1738919, _1738921] : [-(hAPP(hAPP(c_List_Olist__update(_1738913, hAPP(hAPP(c_List_Olist__update(_1738913, _1738915), _1738917), _1738919)), _1738917), _1738921) = hAPP(hAPP(c_List_Olist__update(_1738913, _1738915), _1738917), _1738921))], (47907 ^ _780461) ^ [_1738967, _1738969, _1738971, _1738973, _1738975, _1738977] : [-(_1738967 = _1738969), -(hAPP(hAPP(c_List_Olist__update(_1738971, hAPP(hAPP(c_List_Olist__update(_1738971, _1738973), _1738967), _1738975)), _1738969), _1738977) = hAPP(hAPP(c_List_Olist__update(_1738971, hAPP(hAPP(c_List_Olist__update(_1738971, _1738973), _1738969), _1738977)), _1738967), _1738975))], (47913 ^ _780461) ^ [_1739047, _1739049] : [-(c_List_Oremove1(_1739047, _1739049, c_List_Olist_ONil(_1739047)) = c_List_Olist_ONil(_1739047))], (47915 ^ _780461) ^ [_1739080] : [-(hBOOL(hAPP(c_List_Odistinct(_1739080), c_List_Olist_ONil(_1739080))))], (47917 ^ _780461) ^ [_1739109, _1739111, _1739113, _1739115, _1739117] : [class_Orderings_Olinorder(_1739109), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739111, _1739109, _1739113), _1739115), _1739117) = c_List_Olist_ONil(_1739111)], (47923 ^ _780461) ^ [_1739215, _1739217] : [-(c_List_Olistrelp(_1739215, _1739217, c_List_Olist_ONil(_1739215), c_List_Olist_ONil(_1739215)))], (47925 ^ _780461) ^ [_1739246, _1739248] : [-(c_List_Olistrelp(_1739246, _1739248, c_List_Olist_ONil(_1739246), c_List_Olist_ONil(_1739246)))], (47927 ^ _780461) ^ [_1739277] : [-(hAPP(c_List_Oset(_1739277), c_List_Olist_ONil(_1739277)) = c_Orderings_Obot__class_Obot(tc_fun(_1739277, tc_HOL_Obool)))], (47929 ^ _780461) ^ [_1739327, _1739329] : [c_Orderings_Obot__class_Obot(tc_fun(_1739327, tc_HOL_Obool)) = hAPP(c_List_Oset(_1739327), _1739329), -(_1739329 = c_List_Olist_ONil(_1739327))], (47935 ^ _780461) ^ [_1739424, _1739426] : [_1739426 = c_List_Olist_ONil(_1739424), -(c_Orderings_Obot__class_Obot(tc_fun(_1739424, tc_HOL_Obool)) = hAPP(c_List_Oset(_1739424), _1739426))], (47941 ^ _780461) ^ [_1739542, _1739544] : [hAPP(c_List_Oset(_1739542), _1739544) = c_Orderings_Obot__class_Obot(tc_fun(_1739542, tc_HOL_Obool)), -(_1739544 = c_List_Olist_ONil(_1739542))], (47947 ^ _780461) ^ [_1739639, _1739641] : [_1739641 = c_List_Olist_ONil(_1739639), -(hAPP(c_List_Oset(_1739639), _1739641) = c_Orderings_Obot__class_Obot(tc_fun(_1739639, tc_HOL_Obool)))], (47953 ^ _780461) ^ [_1739742] : [class_Groups_Omonoid__add(_1739742), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1739742), c_List_Olist_ONil(_1739742)) = c_Groups_Ozero__class_Ozero(_1739742))], (47959 ^ _780461) ^ [_1739848, _1739850] : [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(_1739848)), _1739850))), _1739850 = c_List_Olist_ONil(_1739848)], (47965 ^ _780461) ^ [_1739942, _1739944] : [-(_1739944 = c_List_Olist_ONil(_1739942)), -(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(_1739942)), _1739944))))], (47971 ^ _780461) ^ [_1739991, _1739993, _1739995, _1739997, _1739999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1739991, tc_HOL_Obool)), hAPP(c_List_Oset(_1739991), _1739993)), _1739995)), hBOOL(hAPP(hAPP(c_member(_1739991), _1739997), _1739995)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1739991, tc_HOL_Obool)), hAPP(c_List_Oset(_1739991), hAPP(hAPP(c_List_Olist__update(_1739991, _1739993), _1739999), _1739997))), _1739995)))], (47981 ^ _780461) ^ [_1740224, _1740226, _1740228] : [-(hAPP(hAPP(c_List_Otake(_1740224), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1740224), _1740226), _1740228)) = hAPP(hAPP(c_List_Olist_OCons(_1740224), _1740226), c_List_Olist_ONil(_1740224)))], (47983 ^ _780461) ^ [_1740277, _1740279, _1740281, _1740283] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1740277, tc_HOL_Obool)), hAPP(c_List_Oset(_1740277), hAPP(hAPP(c_List_Olist__update(_1740277, _1740279), _1740281), _1740283))), hAPP(hAPP(c_Set_Oinsert(_1740277), _1740283), hAPP(c_List_Oset(_1740277), _1740279)))))], (47985 ^ _780461) ^ [_1740343, _1740345, _1740347, _1740349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740343), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740345)), _1740347))), -(hAPP(hAPP(c_List_Onth(_1740345), hAPP(hAPP(c_List_Olist__update(_1740345, _1740347), _1740343), _1740349)), _1740343) = _1740349)], (47991 ^ _780461) ^ [_1740482, _1740484, _1740486, _1740488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740482), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740484)), _1740486))), 47994 ^ _780461 : [(47995 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1740484, _1740486), _1740482), _1740488) = _1740486, -(hAPP(hAPP(c_List_Onth(_1740484), _1740486), _1740482) = _1740488)], (48001 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Onth(_1740484), _1740486), _1740482) = _1740488, -(hAPP(hAPP(c_List_Olist__update(_1740484, _1740486), _1740482), _1740488) = _1740486)]]], (48007 ^ _780461) ^ [_1740776, _1740778, _1740780, _1740782, _1740784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1740776), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740778)), _1740780))), 48010 ^ _780461 : [(48011 ^ _780461) ^ [] : [_1740776 = _1740782, -(hAPP(hAPP(c_List_Onth(_1740778), hAPP(hAPP(c_List_Olist__update(_1740778, _1740780), _1740776), _1740784)), _1740782) = _1740784)], (48017 ^ _780461) ^ [] : [-(_1740776 = _1740782), -(hAPP(hAPP(c_List_Onth(_1740778), hAPP(hAPP(c_List_Olist__update(_1740778, _1740780), _1740776), _1740784)), _1740782) = hAPP(hAPP(c_List_Onth(_1740778), _1740780), _1740782))]]], (48023 ^ _780461) ^ [_1741072, _1741074] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741072), tc_List_Olist(_1741072))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741072), tc_List_Olist(_1741072)), c_List_Olist_ONil(_1741072)), c_List_Olist_ONil(_1741072))), c_List_Olistrel(_1741072, _1741074))))], (48025 ^ _780461) ^ [_1741146, _1741148, _1741150] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741146), tc_List_Olist(_1741146))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741146), tc_List_Olist(_1741146)), _1741148), c_List_Olist_ONil(_1741146))), c_List_Olexord(_1741146, _1741150)))], (48027 ^ _780461) ^ [_1741220, _1741222, _1741224] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741220), tc_List_Olist(_1741220))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741220), tc_List_Olist(_1741220)), _1741222), c_List_Olist_ONil(_1741220))), c_List_Olex(_1741220, _1741224)))], (48029 ^ _780461) ^ [_1741294, _1741296, _1741298] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1741294), tc_List_Olist(_1741294))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1741294), tc_List_Olist(_1741294)), c_List_Olist_ONil(_1741294)), _1741296)), c_List_Olex(_1741294, _1741298)))], (48031 ^ _780461) ^ [_1741353, _1741355, _1741357, _1741359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741353), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741355)), _1741357))), -(hBOOL(hAPP(hAPP(c_member(_1741355), _1741359), hAPP(c_List_Oset(_1741355), hAPP(hAPP(c_List_Olist__update(_1741355, _1741357), _1741353), _1741359)))))], (48037 ^ _780461) ^ [_1741509, _1741511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1741509), _1741511)), -(c_List_Oupto(_1741509, _1741511) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1741509), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1741509), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1741511)))], (48043 ^ _780461) ^ [_1741626, _1741628] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1741626), _1741628))), -(c_List_Oupto(_1741626, _1741628) = c_List_Olist_ONil(tc_Int_Oint))], (48049 ^ _780461) ^ [_1741684, _1741686, _1741688] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1741684)), -(c_List_Osublist(_1741686, hAPP(hAPP(c_List_Olist_OCons(_1741686), _1741688), c_List_Olist_ONil(_1741686)), _1741684) = hAPP(hAPP(c_List_Olist_OCons(_1741686), _1741688), c_List_Olist_ONil(_1741686)))], (48055 ^ _780461) ^ [_1741809, _1741811, _1741813] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1741809))), -(c_List_Osublist(_1741811, hAPP(hAPP(c_List_Olist_OCons(_1741811), _1741813), c_List_Olist_ONil(_1741811)), _1741809) = c_List_Olist_ONil(_1741811))], (48061 ^ _780461) ^ [_1741882, _1741884, _1741886, _1741888] : [_1741882 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1741884), _1741882), hAPP(hAPP(c_List_Olist_OCons(_1741884), _1741886), _1741888)) = c_List_Olist_ONil(_1741884))], (48067 ^ _780461) ^ [_1741993, _1741995, _1741997, _1741999] : [-(_1741993 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1741995), _1741993), hAPP(hAPP(c_List_Olist_OCons(_1741995), _1741997), _1741999)) = hAPP(hAPP(c_List_Olist_OCons(_1741995), _1741997), hAPP(hAPP(c_List_Otake(_1741995), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1741993), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1741999)))], (48073 ^ _780461) ^ [_1742082, _1742084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742082)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742084))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742082), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742084)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742082)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742082)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742084))))], (48079 ^ _780461) ^ [_1742241, _1742243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742241)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742243)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742241), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1742243)) = c_List_Olist_ONil(tc_Int_Oint))], (48085 ^ _780461) ^ [_1742295, _1742297, _1742299] : [-(_1742295 = c_List_Olist_ONil(_1742297)), -(hBOOL(hAPP(hAPP(c_member(_1742297), hAPP(c_Product__Type_Ofst(_1742297, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1742297, _1742295), _1742299))), hAPP(c_List_Oset(_1742297), _1742295))))], (48091 ^ _780461) ^ [_1742359, _1742361] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1742359), tc_List_Olist(_1742359), c_List_Olistrel(_1742359, _1742361)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1742359)), c_List_Olist_ONil(_1742359)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1742359), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1742359)), c_List_Olist_ONil(_1742359)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1742359), tc_HOL_Obool))))], (48093 ^ _780461) ^ [_1742436, _1742438] : [-(c_List_Oset__Cons(_1742436, _1742438, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1742436)), c_List_Olist_ONil(_1742436)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1742436), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1742436, tc_List_Olist(_1742436), hAPP(hAPP(c_COMBC(_1742436, tc_List_Olist(_1742436), tc_List_Olist(_1742436)), c_List_Olist_OCons(_1742436)), c_List_Olist_ONil(_1742436))), _1742438))], (48095 ^ _780461) ^ [_1742526, _1742528, _1742530, _1742532] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1742526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1742528), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1742526)), hAPP(hAPP(c_List_Olist_OCons(_1742528), _1742530), _1742532)) = c_List_Olist_ONil(_1742528))], (48101 ^ _780461) ^ [_1742649, _1742651, _1742653, _1742655] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1742649) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1742651), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1742649)), hAPP(hAPP(c_List_Olist_OCons(_1742651), _1742653), _1742655)) = hAPP(hAPP(c_List_Olist_OCons(_1742651), _1742653), hAPP(hAPP(c_List_Otake(_1742651), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1742649)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1742655)))], (48107 ^ _780461) ^ [_1742738, _1742740, _1742742, _1742744] : [hBOOL(hAPP(c_List_Odistinct(_1742738), _1742740)), -(hBOOL(hAPP(hAPP(c_member(_1742738), _1742742), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1742738, tc_HOL_Obool)), hAPP(c_List_Oset(_1742738), _1742740)), hAPP(hAPP(c_Set_Oinsert(_1742738), hAPP(hAPP(c_List_Onth(_1742738), _1742740), _1742744)), c_Orderings_Obot__class_Obot(tc_fun(_1742738, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1742738), hAPP(hAPP(c_List_Olist__update(_1742738, _1742740), _1742744), _1742742))))], (48117 ^ _780461) ^ [_1742956, _1742958] : [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), _1742956), _1742958))), 48120 ^ _780461 : [(48121 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1742956), _1742958)), -(c_List_Oupto(_1742956, _1742958) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1742956), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1742956), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1742958)))], (48127 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1742956), _1742958))), -(c_List_Oupto(_1742956, _1742958) = c_List_Olist_ONil(tc_Int_Oint))]]], (48133 ^ _780461) ^ [_1743228, _1743230, _1743232, _1743234, _1743236] : [_1743228 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Lazy__Sequence_Oanamorph(_1743230, _1743232, _1743234, _1743228), _1743236) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743232), _1743230), c_List_Olist_ONil(_1743232)), _1743236))], (48139 ^ _780461) ^ [_1743347, _1743349, _1743351, _1743353, _1743355] : [-(_1743347 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Lazy__Sequence_Oanamorph(_1743349, _1743351, _1743353, _1743347), _1743355) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1743351), _1743349), tc_prod(_1743351, _1743349), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1743351), _1743349), c_List_Olist_ONil(_1743351)), _1743355), hAPP(c_Product__Type_Oprod_Oprod__case(_1743351, _1743349, tc_prod(tc_List_Olist(_1743351), _1743349)), hAPP(hAPP(c_COMBC(_1743351, tc_fun(_1743349, tc_prod(tc_List_Olist(_1743351), _1743349)), tc_fun(_1743349, tc_prod(tc_List_Olist(_1743351), _1743349))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1743351), _1743349), tc_prod(tc_List_Olist(_1743351), _1743349)), tc_fun(tc_fun(_1743349, tc_prod(tc_List_Olist(_1743351), _1743349)), tc_fun(_1743349, tc_prod(tc_List_Olist(_1743351), _1743349))), _1743351), c_COMBB(tc_prod(tc_List_Olist(_1743351), _1743349), tc_prod(tc_List_Olist(_1743351), _1743349), _1743349)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1743351), tc_fun(_1743349, tc_prod(tc_List_Olist(_1743351), _1743349))), tc_fun(tc_prod(tc_List_Olist(_1743351), _1743349), tc_prod(tc_List_Olist(_1743351), _1743349)), _1743351), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1743351), _1743349, tc_prod(tc_List_Olist(_1743351), _1743349))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1743351), tc_List_Olist(_1743351)), tc_fun(tc_List_Olist(_1743351), tc_fun(_1743349, tc_prod(tc_List_Olist(_1743351), _1743349))), _1743351), hAPP(c_COMBB(tc_List_Olist(_1743351), tc_fun(_1743349, tc_prod(tc_List_Olist(_1743351), _1743349)), tc_List_Olist(_1743351)), c_Product__Type_OPair(tc_List_Olist(_1743351), _1743349))), c_List_Olist_OCons(_1743351))))), c_Lazy__Sequence_Oanamorph(_1743349, _1743351, _1743353, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1743347), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1743353, _1743355)))], (48145 ^ _780461) ^ [_1743639] : [-(c_List_Olistset(_1743639, c_List_Olist_ONil(tc_fun(_1743639, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1743639)), c_List_Olist_ONil(_1743639)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1743639), tc_HOL_Obool))))], (48147 ^ _780461) ^ [_1743689, _1743691, _1743693, _1743695, _1743697] : [-(hAPP(hAPP(c_List_Ozip(_1743689, _1743691), hAPP(hAPP(c_List_Olist_OCons(_1743689), _1743693), _1743695)), _1743697) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1743689, _1743691)), _1743691, c_List_Olist_ONil(tc_prod(_1743689, _1743691)), hAPP(hAPP(c_COMBC(_1743691, tc_fun(tc_List_Olist(_1743691), tc_List_Olist(tc_prod(_1743689, _1743691))), tc_fun(tc_List_Olist(_1743691), tc_List_Olist(tc_prod(_1743689, _1743691)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1743689, _1743691)), tc_List_Olist(tc_prod(_1743689, _1743691))), tc_fun(tc_fun(tc_List_Olist(_1743691), tc_List_Olist(tc_prod(_1743689, _1743691))), tc_fun(tc_List_Olist(_1743691), tc_List_Olist(tc_prod(_1743689, _1743691)))), _1743691), c_COMBB(tc_List_Olist(tc_prod(_1743689, _1743691)), tc_List_Olist(tc_prod(_1743689, _1743691)), tc_List_Olist(_1743691))), hAPP(hAPP(c_COMBB(tc_prod(_1743689, _1743691), tc_fun(tc_List_Olist(tc_prod(_1743689, _1743691)), tc_List_Olist(tc_prod(_1743689, _1743691))), _1743691), c_List_Olist_OCons(tc_prod(_1743689, _1743691))), hAPP(c_Product__Type_OPair(_1743689, _1743691), _1743693)))), hAPP(c_List_Ozip(_1743689, _1743691), _1743695))), _1743697))], (48149 ^ _780461) ^ [_1743890, _1743892, _1743894, _1743896, _1743898, _1743900] : [-(hAPP(c_List_Olist_Olist__case(_1743890, _1743892, _1743894, _1743896), hAPP(hAPP(c_List_Olist_OCons(_1743892), _1743898), _1743900)) = hAPP(hAPP(_1743896, _1743898), _1743900))], (48151 ^ _780461) ^ [_1743945, _1743947, _1743949, _1743951] : [-(hAPP(c_List_Olist_Olist__case(_1743945, _1743947, _1743949, _1743951), c_List_Olist_ONil(_1743947)) = _1743949)], (48153 ^ _780461) ^ [_1743984, _1743986, _1743988] : [-(c_List_Olistset(_1743984, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1743984, tc_HOL_Obool)), _1743986), _1743988)) = c_List_Oset__Cons(_1743984, _1743986, c_List_Olistset(_1743984, _1743988)))], (48155 ^ _780461) ^ [_1744032, _1744034, _1744036, _1744038, _1744040] : [-(hAPP(hAPP(c_List_Ozip(_1744032, _1744034), _1744036), hAPP(hAPP(c_List_Olist_OCons(_1744034), _1744038), _1744040)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1744032, _1744034)), _1744032, c_List_Olist_ONil(tc_prod(_1744032, _1744034)), hAPP(hAPP(c_COMBC(_1744032, tc_fun(tc_List_Olist(_1744032), tc_List_Olist(tc_prod(_1744032, _1744034))), tc_fun(tc_List_Olist(_1744032), tc_List_Olist(tc_prod(_1744032, _1744034)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1744032, _1744034)), tc_List_Olist(tc_prod(_1744032, _1744034))), tc_fun(tc_fun(tc_List_Olist(_1744032), tc_List_Olist(tc_prod(_1744032, _1744034))), tc_fun(tc_List_Olist(_1744032), tc_List_Olist(tc_prod(_1744032, _1744034)))), _1744032), c_COMBB(tc_List_Olist(tc_prod(_1744032, _1744034)), tc_List_Olist(tc_prod(_1744032, _1744034)), tc_List_Olist(_1744032))), hAPP(hAPP(c_COMBB(tc_prod(_1744032, _1744034), tc_fun(tc_List_Olist(tc_prod(_1744032, _1744034)), tc_List_Olist(tc_prod(_1744032, _1744034))), _1744032), c_List_Olist_OCons(tc_prod(_1744032, _1744034))), hAPP(hAPP(c_COMBC(_1744032, _1744034, tc_prod(_1744032, _1744034)), c_Product__Type_OPair(_1744032, _1744034)), _1744038)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1744032), tc_List_Olist(_1744034), tc_List_Olist(tc_prod(_1744032, _1744034))), c_List_Ozip(_1744032, _1744034)), _1744040))), _1744036))], (48157 ^ _780461) ^ [_1744259, _1744261, _1744263] : [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), _1744259), _1744261))), -(hBOOL(hAPP(hAPP(_1744263, _1744259), _1744261))), 48164 ^ _780461 : [(48165 ^ _780461) ^ [] : [-(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), 48162 ^ [_1744259, _1744261, _1744263]), 48163 ^ [_1744259, _1744261, _1744263]))))], (48173 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(_1744263, 48162 ^ [_1744259, _1744261, _1744263]), 48163 ^ [_1744259, _1744261, _1744263]))], (48167 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 48162 ^ [_1744259, _1744261, _1744263]), 48163 ^ [_1744259, _1744261, _1744263])), -(hBOOL(hAPP(hAPP(_1744263, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48162 ^ [_1744259, _1744261, _1744263]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 48163 ^ [_1744259, _1744261, _1744263])))]]], (48177 ^ _780461) ^ [_1744774, _1744776, _1744778, _1744780, _1744782, _1744784, _1744786] : [hBOOL(hAPP(hAPP(c_member(_1744774), _1744776), hAPP(c_List_Oset(_1744774), hAPP(hAPP(c_List_Otake(_1744774), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744778)), _1744780)), _1744782)))), -(c_Map_Omap__upds(_1744774, _1744778, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1744774, tc_Option_Ooption(_1744778)), _1744784), _1744776), hAPP(c_Option_Ooption_OSome(_1744778), _1744786)), _1744782, _1744780) = c_Map_Omap__upds(_1744774, _1744778, _1744784, _1744782, _1744780))], (48183 ^ _780461) ^ [_1744971, _1744973, _1744975, _1744977, _1744979, _1744981, _1744983] : [-(hBOOL(hAPP(hAPP(c_member(_1744971), _1744973), hAPP(c_List_Oset(_1744971), hAPP(hAPP(c_List_Otake(_1744971), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1744975)), _1744977)), _1744979))))), -(c_Map_Omap__upds(_1744971, _1744975, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1744971, tc_Option_Ooption(_1744975)), _1744981), _1744973), hAPP(c_Option_Ooption_OSome(_1744975), _1744983)), _1744979, _1744977) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1744971, tc_Option_Ooption(_1744975)), c_Map_Omap__upds(_1744971, _1744975, _1744981, _1744979, _1744977)), _1744973), hAPP(c_Option_Ooption_OSome(_1744975), _1744983)))], (48189 ^ _780461) ^ [_1745096, _1745098, _1745100, _1745102] : [-(c_Map_Omap__upds(_1745096, _1745098, _1745100, c_List_Olist_ONil(_1745096), _1745102) = _1745100)], (48191 ^ _780461) ^ [_1745133, _1745135, _1745137, _1745139] : [-(c_Map_Omap__upds(_1745133, _1745135, _1745137, _1745139, c_List_Olist_ONil(_1745135)) = _1745137)], (48193 ^ _780461) ^ [_1745166, _1745168, _1745170, _1745172, _1745174, _1745176] : [-(hBOOL(hAPP(hAPP(c_member(_1745166), _1745168), hAPP(c_List_Oset(_1745166), _1745170)))), -(hAPP(c_Map_Omap__upds(_1745166, _1745172, _1745174, _1745170, _1745176), _1745168) = hAPP(_1745174, _1745168))], (48199 ^ _780461) ^ [_1745234, _1745236, _1745238, _1745240, _1745242, _1745244] : [-(c_Map_Omap__add(_1745234, _1745236, _1745238, c_Map_Omap__upds(_1745234, _1745236, _1745240, _1745242, _1745244)) = c_Map_Omap__upds(_1745234, _1745236, c_Map_Omap__add(_1745234, _1745236, _1745238, _1745240), _1745242, _1745244))], (48201 ^ _780461) ^ [_1745289, _1745291, _1745293, _1745295, _1745297, _1745299, _1745301] : [-(c_Map_Omap__upds(_1745289, _1745291, _1745293, hAPP(hAPP(c_List_Olist_OCons(_1745289), _1745295), _1745297), hAPP(hAPP(c_List_Olist_OCons(_1745291), _1745299), _1745301)) = c_Map_Omap__upds(_1745289, _1745291, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1745289, tc_Option_Ooption(_1745291)), _1745293), _1745295), hAPP(c_Option_Ooption_OSome(_1745291), _1745299)), _1745297, _1745301))], (48203 ^ _780461) ^ [_1745371, _1745373, _1745375, _1745377, _1745379, _1745381, _1745383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745371)), _1745373)), _1745375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745375), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745377)), _1745379))), -(c_Map_Omap__upds(_1745371, _1745377, _1745381, _1745373, hAPP(hAPP(c_List_Olist__update(_1745377, _1745379), _1745375), _1745383)) = c_Map_Omap__upds(_1745371, _1745377, _1745381, _1745373, _1745379))], (48213 ^ _780461) ^ [_1745606, _1745608, _1745610, _1745612, _1745614, _1745616, _1745618] : [-(hBOOL(hAPP(hAPP(c_member(_1745606), _1745608), hAPP(c_List_Oset(_1745606), _1745610)))), -(c_Map_Omap__upds(_1745606, _1745612, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1745606, tc_Option_Ooption(_1745612)), _1745614), _1745608), hAPP(c_Option_Ooption_OSome(_1745612), _1745616)), _1745610, _1745618) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1745606, tc_Option_Ooption(_1745612)), c_Map_Omap__upds(_1745606, _1745612, _1745614, _1745610, _1745618)), _1745608), hAPP(c_Option_Ooption_OSome(_1745612), _1745616)))], (48219 ^ _780461) ^ [_1745714, _1745716, _1745718, _1745720, _1745722, _1745724] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745714)), _1745716) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745718)), _1745720), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1745714, tc_HOL_Obool)), hAPP(c_List_Oset(_1745714), _1745716)), _1745722)), -(c_Map_Orestrict__map(_1745714, _1745718, c_Map_Omap__upds(_1745714, _1745718, _1745724, _1745716, _1745720), _1745722) = c_Map_Omap__upds(_1745714, _1745718, c_Map_Orestrict__map(_1745714, _1745718, _1745724, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1745714, tc_HOL_Obool)), _1745722), hAPP(c_List_Oset(_1745714), _1745716))), _1745716, _1745720))], (48229 ^ _780461) ^ [_1745993, _1745995, _1745997, _1745999, _1746001] : [-(c_Map_Odom(_1745993, _1745995, c_Map_Omap__upds(_1745993, _1745995, _1745997, _1745999, _1746001)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1745993, tc_HOL_Obool)), hAPP(c_List_Oset(_1745993), hAPP(hAPP(c_List_Otake(_1745993), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745995)), _1746001)), _1745999))), c_Map_Odom(_1745993, _1745995, _1745997)))], (48231 ^ _780461) ^ [_1746069, _1746071, _1746073, _1746075, _1746077, _1746079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746069)), _1746071)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746073)), _1746075))), -(c_Map_Omap__upds(_1746069, _1746073, _1746077, hAPP(hAPP(c_List_Oappend(_1746069), _1746071), hAPP(hAPP(c_List_Olist_OCons(_1746069), _1746079), c_List_Olist_ONil(_1746069))), _1746075) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1746069, tc_Option_Ooption(_1746073)), c_Map_Omap__upds(_1746069, _1746073, _1746077, _1746071, _1746075)), _1746079), hAPP(c_Option_Ooption_OSome(_1746073), hAPP(hAPP(c_List_Onth(_1746073), _1746075), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746069)), _1746071)))))], (48237 ^ _780461) ^ [_1746320, _1746322, _1746324, _1746326] : [-(c_List_Osublist(_1746320, hAPP(hAPP(c_List_Olist_OCons(_1746320), _1746322), _1746324), _1746326) = hAPP(hAPP(c_List_Oappend(_1746320), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1746320)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1746326)), hAPP(hAPP(c_List_Olist_OCons(_1746320), _1746322), c_List_Olist_ONil(_1746320))), c_List_Olist_ONil(_1746320))), c_List_Osublist(_1746320, _1746324, 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)), _1746326)))))], (48239 ^ _780461) ^ [_1746431, _1746433, _1746435, _1746437, _1746439] : [hAPP(hAPP(c_List_Oappend(_1746431), _1746433), hAPP(hAPP(c_List_Olist_OCons(_1746431), _1746435), c_List_Olist_ONil(_1746431))) = hAPP(hAPP(c_List_Oappend(_1746431), _1746437), hAPP(hAPP(c_List_Olist_OCons(_1746431), _1746439), c_List_Olist_ONil(_1746431))), 48242 ^ _780461 : [(48243 ^ _780461) ^ [] : [-(_1746433 = _1746437)], (48245 ^ _780461) ^ [] : [-(_1746435 = _1746439)]]], (48247 ^ _780461) ^ [_1746608, _1746610, _1746612, _1746614, _1746616] : [-(hAPP(hAPP(c_List_Oappend(_1746608), _1746610), hAPP(hAPP(c_List_Olist_OCons(_1746608), _1746612), c_List_Olist_ONil(_1746608))) = hAPP(hAPP(c_List_Oappend(_1746608), _1746614), hAPP(hAPP(c_List_Olist_OCons(_1746608), _1746616), c_List_Olist_ONil(_1746608)))), _1746610 = _1746614, _1746612 = _1746616], (48257 ^ _780461) ^ [_1746847, _1746849, _1746851, _1746853, _1746855] : [hAPP(hAPP(c_List_Olist_OCons(_1746847), _1746849), _1746851) = hAPP(hAPP(c_List_Oappend(_1746847), _1746853), _1746855), 48262 ^ _780461 : [(48263 ^ _780461) ^ [] : [-(_1746853 = c_List_Olist_ONil(_1746847))], (48265 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1746847), _1746849), _1746851) = _1746855)]], 48267 ^ _780461 : [(48268 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1746847), _1746849), 48266 ^ [_1746847, _1746849, _1746851, _1746853, _1746855]) = _1746853)], (48270 ^ _780461) ^ [] : [-(_1746851 = hAPP(hAPP(c_List_Oappend(_1746847), 48266 ^ [_1746847, _1746849, _1746851, _1746853, _1746855]), _1746855))]]], (48272 ^ _780461) ^ [_1747140, _1747142, _1747144, _1747146, _1747148] : [-(hAPP(hAPP(c_List_Olist_OCons(_1747140), _1747142), _1747144) = hAPP(hAPP(c_List_Oappend(_1747140), _1747146), _1747148)), 48273 ^ _780461 : [(48274 ^ _780461) ^ [] : [_1747146 = c_List_Olist_ONil(_1747140), hAPP(hAPP(c_List_Olist_OCons(_1747140), _1747142), _1747144) = _1747148], (48280 ^ _780461) ^ [_1747323] : [hAPP(hAPP(c_List_Olist_OCons(_1747140), _1747142), _1747323) = _1747146, _1747144 = hAPP(hAPP(c_List_Oappend(_1747140), _1747323), _1747148)]]], (48288 ^ _780461) ^ [_1747511, _1747513, _1747515, _1747517, _1747519] : [hAPP(hAPP(c_List_Oappend(_1747511), _1747513), _1747515) = hAPP(hAPP(c_List_Olist_OCons(_1747511), _1747517), _1747519), 48293 ^ _780461 : [(48294 ^ _780461) ^ [] : [-(_1747513 = c_List_Olist_ONil(_1747511))], (48296 ^ _780461) ^ [] : [-(_1747515 = hAPP(hAPP(c_List_Olist_OCons(_1747511), _1747517), _1747519))]], 48298 ^ _780461 : [(48299 ^ _780461) ^ [] : [-(_1747513 = hAPP(hAPP(c_List_Olist_OCons(_1747511), _1747517), 48297 ^ [_1747511, _1747513, _1747515, _1747517, _1747519]))], (48301 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1747511), 48297 ^ [_1747511, _1747513, _1747515, _1747517, _1747519]), _1747515) = _1747519)]]], (48303 ^ _780461) ^ [_1747804, _1747806, _1747808, _1747810, _1747812] : [-(hAPP(hAPP(c_List_Oappend(_1747804), _1747806), _1747808) = hAPP(hAPP(c_List_Olist_OCons(_1747804), _1747810), _1747812)), 48304 ^ _780461 : [(48305 ^ _780461) ^ [] : [_1747806 = c_List_Olist_ONil(_1747804), _1747808 = hAPP(hAPP(c_List_Olist_OCons(_1747804), _1747810), _1747812)], (48311 ^ _780461) ^ [_1747987] : [_1747806 = hAPP(hAPP(c_List_Olist_OCons(_1747804), _1747810), _1747987), hAPP(hAPP(c_List_Oappend(_1747804), _1747987), _1747808) = _1747812]]], (48319 ^ _780461) ^ [_1748151, _1748153, _1748155, _1748157, _1748159, _1748161] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748151)), _1748153) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748155)), _1748157), -(c_Map_Omap__upds(_1748151, _1748155, _1748159, _1748153, hAPP(hAPP(c_List_Oappend(_1748155), _1748157), _1748161)) = c_Map_Omap__upds(_1748151, _1748155, _1748159, _1748153, _1748157))], (48325 ^ _780461) ^ [_1748304, _1748306, _1748308, _1748310, _1748312, _1748314] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748304)), _1748306) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748308)), _1748310), -(c_Map_Omap__upds(_1748304, _1748308, _1748312, hAPP(hAPP(c_List_Oappend(_1748304), _1748306), _1748314), _1748310) = c_Map_Omap__upds(_1748304, _1748308, _1748312, _1748306, _1748310))], (48331 ^ _780461) ^ [_1748457, _1748459, _1748461, _1748463] : [-(hAPP(hAPP(c_List_Onth(_1748457), hAPP(hAPP(c_List_Oappend(_1748457), _1748459), hAPP(hAPP(c_List_Olist_OCons(_1748457), _1748461), _1748463))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748457)), _1748459)) = _1748461)], (48333 ^ _780461) ^ [_1748517, _1748519, _1748521, _1748523, _1748525, _1748527] : [hAPP(hAPP(c_List_Olist_OCons(_1748517), _1748519), _1748521) = _1748523, _1748525 = hAPP(hAPP(c_List_Oappend(_1748517), _1748521), _1748527), -(hAPP(hAPP(c_List_Olist_OCons(_1748517), _1748519), _1748525) = hAPP(hAPP(c_List_Oappend(_1748517), _1748523), _1748527))], (48343 ^ _780461) ^ [_1748726, _1748728, _1748730, _1748732] : [-(hAPP(hAPP(c_List_Oappend(_1748726), hAPP(hAPP(c_List_Olist_OCons(_1748726), _1748728), _1748730)), _1748732) = hAPP(hAPP(c_List_Olist_OCons(_1748726), _1748728), hAPP(hAPP(c_List_Oappend(_1748726), _1748730), _1748732)))], (48345 ^ _780461) ^ [_1748787, _1748789, _1748791, _1748793, _1748795] : [-(hAPP(hAPP(c_List_Olist__update(_1748787, hAPP(hAPP(c_List_Oappend(_1748787), _1748789), hAPP(hAPP(c_List_Olist_OCons(_1748787), _1748791), _1748793))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748787)), _1748789)), _1748795) = hAPP(hAPP(c_List_Oappend(_1748787), _1748789), hAPP(hAPP(c_List_Olist_OCons(_1748787), _1748795), _1748793)))], (48347 ^ _780461) ^ [_1748866, _1748868, _1748870, _1748872, _1748874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748866), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748868)), _1748870))), -(hAPP(hAPP(c_List_Olist__update(_1748868, hAPP(hAPP(c_List_Oappend(_1748868), _1748870), _1748872)), _1748866), _1748874) = hAPP(hAPP(c_List_Oappend(_1748868), hAPP(hAPP(c_List_Olist__update(_1748868, _1748870), _1748866), _1748874)), _1748872))], (48353 ^ _780461) ^ [_1749041, _1749043, _1749045, _1749047] : [-(hAPP(hAPP(c_List_Onth(_1749041), hAPP(hAPP(c_List_Oappend(_1749041), _1749043), _1749045)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749041)), _1749043)), _1749047)) = hAPP(hAPP(c_List_Onth(_1749041), _1749045), _1749047))], (48355 ^ _780461) ^ [_1749107, _1749109, _1749111] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749107)), hAPP(hAPP(c_List_Oappend(_1749107), _1749109), _1749111)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749107)), _1749109)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749107)), _1749111)))], (48357 ^ _780461) ^ [_1749169, _1749171, _1749173, _1749175, _1749177, _1749179] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749169)), _1749171) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749173)), _1749175), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749169)), _1749177) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749173)), _1749179), -(hAPP(hAPP(c_List_Ozip(_1749169, _1749173), hAPP(hAPP(c_List_Oappend(_1749169), _1749171), _1749177)), hAPP(hAPP(c_List_Oappend(_1749173), _1749175), _1749179)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1749169, _1749173)), hAPP(hAPP(c_List_Ozip(_1749169, _1749173), _1749171), _1749175)), hAPP(hAPP(c_List_Ozip(_1749169, _1749173), _1749177), _1749179)))], (48367 ^ _780461) ^ [_1749478, _1749480, _1749482, _1749484, _1749486] : [-(hAPP(hAPP(c_List_Omap(_1749478, _1749480), _1749482), hAPP(hAPP(c_List_Oappend(_1749478), _1749484), _1749486)) = hAPP(hAPP(c_List_Oappend(_1749480), hAPP(hAPP(c_List_Omap(_1749478, _1749480), _1749482), _1749484)), hAPP(hAPP(c_List_Omap(_1749478, _1749480), _1749482), _1749486)))], (48369 ^ _780461) ^ [_1749567, _1749569, _1749571, _1749573] : [hBOOL(hAPP(hAPP(c_member(_1749567), _1749569), hAPP(c_List_Oset(_1749567), _1749571))), -(c_List_Oremove1(_1749567, _1749569, hAPP(hAPP(c_List_Oappend(_1749567), _1749571), _1749573)) = hAPP(hAPP(c_List_Oappend(_1749567), c_List_Oremove1(_1749567, _1749569, _1749571)), _1749573))], (48375 ^ _780461) ^ [_1749714, _1749716, _1749718, _1749720] : [-(hBOOL(hAPP(hAPP(c_member(_1749714), _1749716), hAPP(c_List_Oset(_1749714), _1749718)))), -(c_List_Oremove1(_1749714, _1749716, hAPP(hAPP(c_List_Oappend(_1749714), _1749718), _1749720)) = hAPP(hAPP(c_List_Oappend(_1749714), _1749718), c_List_Oremove1(_1749714, _1749716, _1749720)))], (48381 ^ _780461) ^ [_1749792, _1749794, _1749796, _1749798, _1749800, _1749802] : [-(c_List_Ofoldr(_1749792, _1749794, _1749796, hAPP(hAPP(c_List_Oappend(_1749792), _1749798), _1749800), _1749802) = c_List_Ofoldr(_1749792, _1749794, _1749796, _1749798, c_List_Ofoldr(_1749792, _1749794, _1749796, _1749800, _1749802)))], (48383 ^ _780461) ^ [_1749851, _1749853, _1749855, _1749857] : [-(c_Map_Omap__of(_1749851, _1749853, hAPP(hAPP(c_List_Oappend(tc_prod(_1749851, _1749853)), _1749855), _1749857)) = c_Map_Omap__add(_1749851, _1749853, c_Map_Omap__of(_1749851, _1749853, _1749857), c_Map_Omap__of(_1749851, _1749853, _1749855)))], (48385 ^ _780461) ^ [_1749908, _1749910, _1749912, _1749914] : [-(hAPP(hAPP(c_List_Oappend(_1749908), hAPP(hAPP(c_List_Oappend(_1749908), _1749910), _1749912)), _1749914) = hAPP(hAPP(c_List_Oappend(_1749908), _1749910), hAPP(hAPP(c_List_Oappend(_1749908), _1749912), _1749914)))], (48387 ^ _780461) ^ [_1749993, _1749995, _1749997, _1749999, _1750001] : [hAPP(hAPP(c_List_Oappend(_1749993), _1749995), _1749997) = hAPP(hAPP(c_List_Oappend(_1749993), _1749999), _1750001), 48393 ^ _780461 : [(48394 ^ _780461) ^ [] : [-(_1749995 = hAPP(hAPP(c_List_Oappend(_1749993), _1749999), 48390 ^ [_1749993, _1749995, _1749997, _1749999, _1750001]))], (48396 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1749993), 48390 ^ [_1749993, _1749995, _1749997, _1749999, _1750001]), _1749997) = _1750001)]], 48397 ^ _780461 : [(48398 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1749993), _1749995), 48390 ^ [_1749993, _1749995, _1749997, _1749999, _1750001]) = _1749999)], (48400 ^ _780461) ^ [] : [-(_1749997 = hAPP(hAPP(c_List_Oappend(_1749993), 48390 ^ [_1749993, _1749995, _1749997, _1749999, _1750001]), _1750001))]]], (48402 ^ _780461) ^ [_1750324, _1750326, _1750328, _1750330, _1750332] : [-(hAPP(hAPP(c_List_Oappend(_1750324), _1750326), _1750328) = hAPP(hAPP(c_List_Oappend(_1750324), _1750330), _1750332)), 48403 ^ _780461 : [(48404 ^ _780461) ^ [_1750436] : [_1750326 = hAPP(hAPP(c_List_Oappend(_1750324), _1750330), _1750436), hAPP(hAPP(c_List_Oappend(_1750324), _1750436), _1750328) = _1750332], (48410 ^ _780461) ^ [_1750548] : [hAPP(hAPP(c_List_Oappend(_1750324), _1750326), _1750548) = _1750330, _1750328 = hAPP(hAPP(c_List_Oappend(_1750324), _1750548), _1750332)]]], (48418 ^ _780461) ^ [_1750733, _1750735, _1750737, _1750739] : [hAPP(hAPP(c_List_Oappend(_1750733), _1750735), _1750737) = hAPP(hAPP(c_List_Oappend(_1750733), _1750735), _1750739), -(_1750737 = _1750739)], (48424 ^ _780461) ^ [_1750842, _1750844, _1750846, _1750848] : [_1750846 = _1750848, -(hAPP(hAPP(c_List_Oappend(_1750842), _1750844), _1750846) = hAPP(hAPP(c_List_Oappend(_1750842), _1750844), _1750848))], (48430 ^ _780461) ^ [_1750978, _1750980, _1750982, _1750984] : [hAPP(hAPP(c_List_Oappend(_1750978), _1750980), _1750982) = hAPP(hAPP(c_List_Oappend(_1750978), _1750984), _1750982), -(_1750980 = _1750984)], (48436 ^ _780461) ^ [_1751087, _1751089, _1751091, _1751093] : [_1751089 = _1751093, -(hAPP(hAPP(c_List_Oappend(_1751087), _1751089), _1751091) = hAPP(hAPP(c_List_Oappend(_1751087), _1751093), _1751091))], (48442 ^ _780461) ^ [_1751202, _1751204, _1751206, _1751208, _1751210, _1751212] : [hAPP(hAPP(c_List_Oappend(_1751202), _1751204), _1751206) = _1751208, _1751210 = hAPP(hAPP(c_List_Oappend(_1751202), _1751206), _1751212), -(hAPP(hAPP(c_List_Oappend(_1751202), _1751204), _1751210) = hAPP(hAPP(c_List_Oappend(_1751202), _1751208), _1751212))], (48452 ^ _780461) ^ [_1751411, _1751413, _1751415] : [-(hAPP(c_List_Oset(_1751411), hAPP(hAPP(c_List_Oappend(_1751411), _1751413), _1751415)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1751411, tc_HOL_Obool)), hAPP(c_List_Oset(_1751411), _1751413)), hAPP(c_List_Oset(_1751411), _1751415)))], (48454 ^ _780461) ^ [_1751472, _1751474, _1751476] : [class_Groups_Omonoid__add(_1751472), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1751472), hAPP(hAPP(c_List_Oappend(_1751472), _1751474), _1751476)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1751472), hAPP(c_List_Omonoid__add__class_Olistsum(_1751472), _1751474)), hAPP(c_List_Omonoid__add__class_Olistsum(_1751472), _1751476)))], (48460 ^ _780461) ^ [_1751611, _1751613, _1751615, _1751617] : [-(hAPP(hAPP(c_List_Otake(_1751611), _1751613), hAPP(hAPP(c_List_Oappend(_1751611), _1751615), _1751617)) = hAPP(hAPP(c_List_Oappend(_1751611), hAPP(hAPP(c_List_Otake(_1751611), _1751613), _1751615)), hAPP(hAPP(c_List_Otake(_1751611), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1751613), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751611)), _1751615))), _1751617)))], (48462 ^ _780461) ^ [_1751693, _1751695, _1751697] : [_1751693 = _1751695, -(_1751693 = hAPP(hAPP(c_List_Oappend(_1751697), c_List_Olist_ONil(_1751697)), _1751695))], (48468 ^ _780461) ^ [_1751810, _1751812, _1751814] : [hAPP(hAPP(c_List_Oappend(_1751810), _1751812), _1751814) = _1751814, -(_1751812 = c_List_Olist_ONil(_1751810))], (48474 ^ _780461) ^ [_1751905, _1751907, _1751909] : [_1751907 = c_List_Olist_ONil(_1751905), -(hAPP(hAPP(c_List_Oappend(_1751905), _1751907), _1751909) = _1751909)], (48480 ^ _780461) ^ [_1752024, _1752026, _1752028] : [hAPP(hAPP(c_List_Oappend(_1752024), _1752026), _1752028) = _1752026, -(_1752028 = c_List_Olist_ONil(_1752024))], (48486 ^ _780461) ^ [_1752119, _1752121, _1752123] : [_1752123 = c_List_Olist_ONil(_1752119), -(hAPP(hAPP(c_List_Oappend(_1752119), _1752121), _1752123) = _1752121)], (48492 ^ _780461) ^ [_1752238, _1752240, _1752242] : [hAPP(hAPP(c_List_Oappend(_1752238), _1752240), _1752242) = c_List_Olist_ONil(_1752238), 48495 ^ _780461 : [(48496 ^ _780461) ^ [] : [-(_1752240 = c_List_Olist_ONil(_1752238))], (48498 ^ _780461) ^ [] : [-(_1752242 = c_List_Olist_ONil(_1752238))]]], (48500 ^ _780461) ^ [_1752367, _1752369, _1752371] : [-(hAPP(hAPP(c_List_Oappend(_1752367), _1752369), _1752371) = c_List_Olist_ONil(_1752367)), _1752369 = c_List_Olist_ONil(_1752367), _1752371 = c_List_Olist_ONil(_1752367)], (48510 ^ _780461) ^ [_1752548, _1752550, _1752552] : [_1752548 = hAPP(hAPP(c_List_Oappend(_1752550), _1752552), _1752548), -(_1752552 = c_List_Olist_ONil(_1752550))], (48516 ^ _780461) ^ [_1752643, _1752645, _1752647] : [_1752647 = c_List_Olist_ONil(_1752645), -(_1752643 = hAPP(hAPP(c_List_Oappend(_1752645), _1752647), _1752643))], (48522 ^ _780461) ^ [_1752762, _1752764, _1752766] : [_1752762 = hAPP(hAPP(c_List_Oappend(_1752764), _1752762), _1752766), -(_1752766 = c_List_Olist_ONil(_1752764))], (48528 ^ _780461) ^ [_1752857, _1752859, _1752861] : [_1752861 = c_List_Olist_ONil(_1752859), -(_1752857 = hAPP(hAPP(c_List_Oappend(_1752859), _1752857), _1752861))], (48534 ^ _780461) ^ [_1752958, _1752960] : [-(hAPP(hAPP(c_List_Oappend(_1752958), _1752960), c_List_Olist_ONil(_1752958)) = _1752960)], (48536 ^ _780461) ^ [_1753011, _1753013, _1753015] : [c_List_Olist_ONil(_1753011) = hAPP(hAPP(c_List_Oappend(_1753011), _1753013), _1753015), 48539 ^ _780461 : [(48540 ^ _780461) ^ [] : [-(_1753013 = c_List_Olist_ONil(_1753011))], (48542 ^ _780461) ^ [] : [-(_1753015 = c_List_Olist_ONil(_1753011))]]], (48544 ^ _780461) ^ [_1753140, _1753142, _1753144] : [-(c_List_Olist_ONil(_1753140) = hAPP(hAPP(c_List_Oappend(_1753140), _1753142), _1753144)), _1753142 = c_List_Olist_ONil(_1753140), _1753144 = c_List_Olist_ONil(_1753140)], (48554 ^ _780461) ^ [_1753303, _1753305] : [-(hAPP(hAPP(c_List_Oappend(_1753303), c_List_Olist_ONil(_1753303)), _1753305) = _1753305)], (48556 ^ _780461) ^ [_1753338, _1753340, _1753342, _1753344, _1753346] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753338), tc_List_Olist(_1753338))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753338), tc_List_Olist(_1753338)), _1753340), _1753342)), c_List_Olexord(_1753338, _1753344))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1753338), tc_List_Olist(_1753338))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1753338), tc_List_Olist(_1753338)), hAPP(hAPP(c_List_Oappend(_1753338), _1753346), _1753340)), hAPP(hAPP(c_List_Oappend(_1753338), _1753346), _1753342))), c_List_Olexord(_1753338, _1753344))))], (48562 ^ _780461) ^ [_1753591, _1753593, _1753595] : [hBOOL(hAPP(c_List_Odistinct(_1753591), hAPP(hAPP(c_List_Oappend(_1753591), _1753593), _1753595))), 48565 ^ _780461 : [(48566 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1753591), _1753593)))], (48568 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1753591), _1753595)))], (48570 ^ _780461) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1753591, tc_HOL_Obool)), hAPP(c_List_Oset(_1753591), _1753593)), hAPP(c_List_Oset(_1753591), _1753595)) = c_Orderings_Obot__class_Obot(tc_fun(_1753591, tc_HOL_Obool)))]]], (48572 ^ _780461) ^ [_1753808, _1753810, _1753812] : [-(hBOOL(hAPP(c_List_Odistinct(_1753808), hAPP(hAPP(c_List_Oappend(_1753808), _1753810), _1753812)))), hBOOL(hAPP(c_List_Odistinct(_1753808), _1753810)), hBOOL(hAPP(c_List_Odistinct(_1753808), _1753812)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1753808, tc_HOL_Obool)), hAPP(c_List_Oset(_1753808), _1753810)), hAPP(c_List_Oset(_1753808), _1753812)) = c_Orderings_Obot__class_Obot(tc_fun(_1753808, tc_HOL_Obool))], (48586 ^ _780461) ^ [_1754104, _1754106, _1754108, _1754110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754104), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754106)), _1754108))), -(hAPP(hAPP(c_List_Onth(_1754106), hAPP(hAPP(c_List_Oappend(_1754106), _1754108), _1754110)), _1754104) = hAPP(hAPP(c_List_Onth(_1754106), _1754108), _1754104))], (48592 ^ _780461) ^ [_1754251, _1754253, _1754255, _1754257] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754251), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754253)), _1754255)))), -(hAPP(hAPP(c_List_Onth(_1754253), hAPP(hAPP(c_List_Oappend(_1754253), _1754255), _1754257)), _1754251) = hAPP(hAPP(c_List_Onth(_1754253), _1754257), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1754251), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754253)), _1754255))))], (48598 ^ _780461) ^ [_1754360, _1754362, _1754364, _1754366, _1754368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754360), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754362)), _1754364))), -(hAPP(hAPP(c_List_Olist__update(_1754362, hAPP(hAPP(c_List_Oappend(_1754362), _1754364), _1754366)), _1754360), _1754368) = hAPP(hAPP(c_List_Oappend(_1754362), hAPP(hAPP(c_List_Olist__update(_1754362, _1754364), _1754360), _1754368)), _1754366))], (48604 ^ _780461) ^ [_1754529, _1754531, _1754533, _1754535, _1754537] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754529), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754531)), _1754533)))), -(hAPP(hAPP(c_List_Olist__update(_1754531, hAPP(hAPP(c_List_Oappend(_1754531), _1754533), _1754535)), _1754529), _1754537) = hAPP(hAPP(c_List_Oappend(_1754531), _1754533), hAPP(hAPP(c_List_Olist__update(_1754531, _1754535), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1754529), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754531)), _1754533))), _1754537)))], (48610 ^ _780461) ^ [_1754632, _1754634, _1754636, _1754638] : [-(c_List_Osublist(_1754632, hAPP(hAPP(c_List_Oappend(_1754632), _1754634), _1754636), _1754638) = hAPP(hAPP(c_List_Oappend(_1754632), c_List_Osublist(_1754632, _1754634, _1754638)), c_List_Osublist(_1754632, _1754636, 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(_1754632)), _1754634)))), _1754638)))))], (48612 ^ _780461) ^ [_1754711, _1754713, _1754715, _1754717, _1754719, _1754721, _1754723] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1754711, _1754711)), hAPP(hAPP(c_Product__Type_OPair(_1754711, _1754711), _1754713), _1754715)), _1754717)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1754711), tc_List_Olist(_1754711))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1754711), tc_List_Olist(_1754711)), hAPP(hAPP(c_List_Oappend(_1754711), _1754719), hAPP(hAPP(c_List_Olist_OCons(_1754711), _1754713), _1754721))), hAPP(hAPP(c_List_Oappend(_1754711), _1754719), hAPP(hAPP(c_List_Olist_OCons(_1754711), _1754715), _1754723)))), c_List_Olexord(_1754711, _1754717))))], (48618 ^ _780461) ^ [_1754960, _1754962, _1754964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754960), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754962)), _1754964))), -(hAPP(hAPP(c_List_Otake(_1754962), hAPP(c_Nat_OSuc, _1754960)), _1754964) = hAPP(hAPP(c_List_Oappend(_1754962), hAPP(hAPP(c_List_Otake(_1754962), _1754960), _1754964)), hAPP(hAPP(c_List_Olist_OCons(_1754962), hAPP(hAPP(c_List_Onth(_1754962), _1754964), _1754960)), c_List_Olist_ONil(_1754962))))], (48624 ^ _780461) ^ [_1755180, _1755182, _1755184, _1755186, _1755188, _1755190] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755180), tc_List_Olist(_1755180))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755180), tc_List_Olist(_1755180)), hAPP(hAPP(c_List_Oappend(_1755180), _1755182), hAPP(hAPP(c_List_Olist_OCons(_1755180), _1755184), c_List_Olist_ONil(_1755180)))), hAPP(hAPP(c_List_Oappend(_1755180), _1755186), hAPP(hAPP(c_List_Olist_OCons(_1755180), _1755188), c_List_Olist_ONil(_1755180))))), c_List_Olistrel1(_1755180, _1755190))), 48629 ^ _780461 : [(48630 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755180), tc_List_Olist(_1755180))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755180), tc_List_Olist(_1755180)), _1755182), _1755186)), c_List_Olistrel1(_1755180, _1755190))))], (48632 ^ _780461) ^ [] : [-(_1755184 = _1755188)]], 48633 ^ _780461 : [(48634 ^ _780461) ^ [] : [-(_1755182 = _1755186)], (48636 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1755180, _1755180)), hAPP(hAPP(c_Product__Type_OPair(_1755180, _1755180), _1755184), _1755188)), _1755190)))]]], (48638 ^ _780461) ^ [_1755590, _1755592, _1755594, _1755596, _1755598, _1755600] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755590), tc_List_Olist(_1755590))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755590), tc_List_Olist(_1755590)), hAPP(hAPP(c_List_Oappend(_1755590), _1755592), hAPP(hAPP(c_List_Olist_OCons(_1755590), _1755594), c_List_Olist_ONil(_1755590)))), hAPP(hAPP(c_List_Oappend(_1755590), _1755596), hAPP(hAPP(c_List_Olist_OCons(_1755590), _1755598), c_List_Olist_ONil(_1755590))))), c_List_Olistrel1(_1755590, _1755600)))), 48639 ^ _780461 : [(48640 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755590), tc_List_Olist(_1755590))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755590), tc_List_Olist(_1755590)), _1755592), _1755596)), c_List_Olistrel1(_1755590, _1755600))), _1755594 = _1755598], (48646 ^ _780461) ^ [] : [_1755592 = _1755596, hBOOL(hAPP(hAPP(c_member(tc_prod(_1755590, _1755590)), hAPP(hAPP(c_Product__Type_OPair(_1755590, _1755590), _1755594), _1755598)), _1755600))]]], (48654 ^ _780461) ^ [_1756058, _1756060, _1756062, _1756064, _1756066] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756058), tc_List_Olist(_1756058))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756058), tc_List_Olist(_1756058)), hAPP(hAPP(c_List_Oappend(_1756058), _1756060), _1756062)), hAPP(hAPP(c_List_Oappend(_1756058), _1756060), _1756064))), c_List_Olexord(_1756058, _1756066))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756058, _1756058)), hAPP(hAPP(c_Product__Type_OPair(_1756058, _1756058), 48659 ^ [_1756058, _1756060, _1756062, _1756064, _1756066]), 48659 ^ [_1756058, _1756060, _1756062, _1756064, _1756066])), _1756066))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756058), tc_List_Olist(_1756058))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756058), tc_List_Olist(_1756058)), _1756062), _1756064)), c_List_Olexord(_1756058, _1756066))))], (48665 ^ _780461) ^ [_1756377, _1756379, _1756381, _1756383] : [hBOOL(hAPP(hAPP(c_member(_1756377), _1756379), c_Wellfounded_Oacc(_1756377, _1756381))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1756377)), _1756383), c_Wellfounded_Oacc(tc_List_Olist(_1756377), c_List_Olistrel1(_1756377, _1756381)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1756377)), hAPP(hAPP(c_List_Olist_OCons(_1756377), _1756379), _1756383)), c_Wellfounded_Oacc(tc_List_Olist(_1756377), c_List_Olistrel1(_1756377, _1756381)))))], (48675 ^ _780461) ^ [_1756618, _1756620, _1756622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1756618, _1756618), tc_HOL_Obool)), _1756620), _1756622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1756618), tc_List_Olist(_1756618)), tc_HOL_Obool)), c_List_Olistrel1(_1756618, _1756620)), c_List_Olistrel1(_1756618, _1756622))))], (48681 ^ _780461) ^ [_1756769, _1756771] : [-(c_List_Olistrel1(_1756769, hAPP(c_Relation_Oconverse(_1756769, _1756769), _1756771)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1756769), tc_List_Olist(_1756769)), c_List_Olistrel1(_1756769, _1756771)))], (48683 ^ _780461) ^ [_1756816, _1756818] : [-(c_List_Olistrel(_1756816, c_Transitive__Closure_Ortrancl(_1756816, _1756818)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756816), c_List_Olistrel1(_1756816, _1756818)))], (48685 ^ _780461) ^ [_1756855, _1756857] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1756855), tc_List_Olist(_1756855)), tc_HOL_Obool)), c_List_Olistrel1(_1756855, c_Transitive__Closure_Ortrancl(_1756855, _1756857))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756855), c_List_Olistrel1(_1756855, _1756857)))))], (48687 ^ _780461) ^ [_1756911, _1756913] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1756911), tc_List_Olist(_1756911)), tc_HOL_Obool)), c_List_Olistrel(_1756911, _1756913)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756911), c_List_Olistrel1(_1756911, _1756913)))))], (48689 ^ _780461) ^ [_1756964, _1756966, _1756968, _1756970, _1756972] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756964), tc_List_Olist(_1756964))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756964), tc_List_Olist(_1756964)), _1756966), _1756968)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756964), c_List_Olistrel1(_1756964, _1756970)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1756964), tc_List_Olist(_1756964))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1756964), tc_List_Olist(_1756964)), hAPP(hAPP(c_List_Olist_OCons(_1756964), _1756972), _1756966)), hAPP(hAPP(c_List_Olist_OCons(_1756964), _1756972), _1756968))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1756964), c_List_Olistrel1(_1756964, _1756970)))))], (48695 ^ _780461) ^ [_1757219, _1757221, _1757223, _1757225, _1757227] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757219), tc_List_Olist(_1757219))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757219), tc_List_Olist(_1757219)), _1757221), _1757223)), c_List_Olistrel1(_1757219, _1757225))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757219), tc_List_Olist(_1757219))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757219), tc_List_Olist(_1757219)), hAPP(hAPP(c_List_Olist_OCons(_1757219), _1757227), _1757221)), hAPP(hAPP(c_List_Olist_OCons(_1757219), _1757227), _1757223))), c_List_Olistrel1(_1757219, _1757225))))], (48701 ^ _780461) ^ [_1757454, _1757456, _1757458, _1757460] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757454), tc_List_Olist(_1757454))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757454), tc_List_Olist(_1757454)), _1757456), _1757458)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1757454), c_List_Olistrel1(_1757454, _1757460)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757454)), _1757456) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757454)), _1757458))], (48707 ^ _780461) ^ [_1757633, _1757635, _1757637, _1757639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757633), tc_List_Olist(_1757633))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757633), tc_List_Olist(_1757633)), _1757635), _1757637)), c_List_Olistrel1(_1757633, _1757639))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757633)), _1757635) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757633)), _1757637))], (48713 ^ _780461) ^ [_1757817, _1757819, _1757821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757817), tc_List_Olist(_1757817))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757817), tc_List_Olist(_1757817)), _1757819), c_List_Olist_ONil(_1757817))), c_List_Olistrel1(_1757817, _1757821)))], (48715 ^ _780461) ^ [_1757891, _1757893, _1757895] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757891), tc_List_Olist(_1757891))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757891), tc_List_Olist(_1757891)), c_List_Olist_ONil(_1757891)), _1757893)), c_List_Olistrel1(_1757891, _1757895)))], (48717 ^ _780461) ^ [_1757950, _1757952, _1757954, _1757956, _1757958, _1757960] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757950), tc_List_Olist(_1757950))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757950), tc_List_Olist(_1757950)), hAPP(hAPP(c_List_Oappend(_1757950), _1757952), _1757958)), hAPP(hAPP(c_List_Oappend(_1757950), _1757954), _1757960))), c_List_Olistrel1(_1757950, _1757956)))), 48718 ^ _780461 : [(48719 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757950), tc_List_Olist(_1757950))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757950), tc_List_Olist(_1757950)), _1757952), _1757954)), c_List_Olistrel1(_1757950, _1757956))), _1757958 = _1757960], (48725 ^ _780461) ^ [] : [_1757952 = _1757954, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1757950), tc_List_Olist(_1757950))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1757950), tc_List_Olist(_1757950)), _1757958), _1757960)), c_List_Olistrel1(_1757950, _1757956)))]]], (48733 ^ _780461) ^ [_1758419, _1758421, _1758423, _1758425] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1758419), tc_List_Olist(_1758419))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1758419), tc_List_Olist(_1758419)), _1758421), _1758423)), c_List_Olistrel1(_1758419, hAPP(c_Relation_Oconverse(_1758419, _1758419), _1758425)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1758419), tc_List_Olist(_1758419))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1758419), tc_List_Olist(_1758419)), _1758421), _1758423)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1758419), tc_List_Olist(_1758419)), c_List_Olistrel1(_1758419, _1758425)))))], (48739 ^ _780461) ^ [_1758648, _1758650, _1758652, _1758654] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1758648), tc_List_Olist(_1758648))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1758648), tc_List_Olist(_1758648)), _1758650), _1758652)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1758648), tc_List_Olist(_1758648)), c_List_Olistrel1(_1758648, _1758654)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1758648), tc_List_Olist(_1758648))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1758648), tc_List_Olist(_1758648)), _1758650), _1758652)), c_List_Olistrel1(_1758648, hAPP(c_Relation_Oconverse(_1758648, _1758648), _1758654)))))], (48745 ^ _780461) ^ [_1758883, _1758885, _1758887, _1758889] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1758883), tc_List_Olist(_1758883))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1758883), tc_List_Olist(_1758883)), _1758885), _1758887)), c_List_Olistrel(_1758883, _1758889))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1758883), tc_List_Olist(_1758883))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1758883), tc_List_Olist(_1758883)), _1758885), _1758887)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1758883), c_List_Olistrel1(_1758883, _1758889)))))], (48751 ^ _780461) ^ [_1759094, _1759096, _1759098, _1759100] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1759094), tc_List_Olist(_1759094))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1759094), tc_List_Olist(_1759094)), _1759096), _1759098)), c_List_Olistrel1(_1759094, _1759100))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1759094), tc_List_Olist(_1759094))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1759094), tc_List_Olist(_1759094)), _1759096), _1759098)), c_List_Olistrel(_1759094, c_Transitive__Closure_Ortrancl(_1759094, _1759100)))))], (48757 ^ _780461) ^ [_1759328, _1759330, _1759332, _1759334, _1759336, _1759338] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1759328), tc_List_Olist(_1759328))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1759328), tc_List_Olist(_1759328)), hAPP(hAPP(c_List_Olist_OCons(_1759328), _1759330), _1759332)), hAPP(hAPP(c_List_Olist_OCons(_1759328), _1759334), _1759336))), c_List_Olistrel1(_1759328, _1759338))), 48762 ^ _780461 : [(48763 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1759328, _1759328)), hAPP(hAPP(c_Product__Type_OPair(_1759328, _1759328), _1759330), _1759334)), _1759338)))], (48765 ^ _780461) ^ [] : [-(_1759332 = _1759336)]], 48766 ^ _780461 : [(48767 ^ _780461) ^ [] : [-(_1759330 = _1759334)], (48769 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1759328), tc_List_Olist(_1759328))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1759328), tc_List_Olist(_1759328)), _1759332), _1759336)), c_List_Olistrel1(_1759328, _1759338))))]]], (48771 ^ _780461) ^ [_1759698, _1759700, _1759702, _1759704, _1759706, _1759708] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1759698), tc_List_Olist(_1759698))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1759698), tc_List_Olist(_1759698)), hAPP(hAPP(c_List_Olist_OCons(_1759698), _1759700), _1759702)), hAPP(hAPP(c_List_Olist_OCons(_1759698), _1759704), _1759706))), c_List_Olistrel1(_1759698, _1759708)))), 48772 ^ _780461 : [(48773 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1759698, _1759698)), hAPP(hAPP(c_Product__Type_OPair(_1759698, _1759698), _1759700), _1759704)), _1759708)), _1759702 = _1759706], (48779 ^ _780461) ^ [] : [_1759700 = _1759704, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1759698), tc_List_Olist(_1759698))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1759698), tc_List_Olist(_1759698)), _1759702), _1759706)), c_List_Olistrel1(_1759698, _1759708)))]]], (48787 ^ _780461) ^ [_1760126, _1760128, _1760130, _1760132, _1760134] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760126, _1760126)), hAPP(hAPP(c_Product__Type_OPair(_1760126, _1760126), _1760128), _1760130)), _1760132)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760126), tc_List_Olist(_1760126))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760126), tc_List_Olist(_1760126)), hAPP(hAPP(c_List_Olist_OCons(_1760126), _1760128), _1760134)), hAPP(hAPP(c_List_Olist_OCons(_1760126), _1760130), _1760134))), c_List_Olistrel1(_1760126, _1760132))))], (48793 ^ _780461) ^ [_1760339, _1760341, _1760343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760339, _1760339), tc_HOL_Obool)), _1760341), _1760343)), c_Relation_Orefl__on(_1760339, c_Orderings_Otop__class_Otop(tc_fun(_1760339, tc_HOL_Obool)), _1760343), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1760339), tc_List_Olist(_1760339)), tc_HOL_Obool)), c_List_Olistrel1(_1760339, _1760341)), c_List_Olistrel(_1760339, _1760343))))], (48803 ^ _780461) ^ [_1760556, _1760558, _1760560, _1760562, _1760564, _1760566, _1760568, _1760570] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760556, _1760556)), hAPP(hAPP(c_Product__Type_OPair(_1760556, _1760556), _1760558), _1760560)), _1760562)), _1760564 = hAPP(hAPP(c_List_Oappend(_1760556), _1760566), hAPP(hAPP(c_List_Olist_OCons(_1760556), _1760558), _1760568)), _1760570 = hAPP(hAPP(c_List_Oappend(_1760556), _1760566), hAPP(hAPP(c_List_Olist_OCons(_1760556), _1760560), _1760568)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760556), tc_List_Olist(_1760556))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760556), tc_List_Olist(_1760556)), _1760564), _1760570)), c_List_Olistrel1(_1760556, _1760562))))], (48817 ^ _780461) ^ [_1760935, _1760937, _1760939, _1760941, _1760943, _1760945] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760935, _1760935)), hAPP(hAPP(c_Product__Type_OPair(_1760935, _1760935), _1760937), _1760939)), c_Transitive__Closure_Ortrancl(_1760935, _1760941))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760935), tc_List_Olist(_1760935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760935), tc_List_Olist(_1760935)), _1760943), _1760945)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1760935), c_List_Olistrel1(_1760935, _1760941)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760935), tc_List_Olist(_1760935))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760935), tc_List_Olist(_1760935)), hAPP(hAPP(c_List_Olist_OCons(_1760935), _1760937), _1760943)), hAPP(hAPP(c_List_Olist_OCons(_1760935), _1760939), _1760945))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1760935), c_List_Olistrel1(_1760935, _1760941)))))], (48827 ^ _780461) ^ [_1761317, _1761319, _1761321, _1761323] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1761317), tc_List_Olist(_1761317))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1761317), tc_List_Olist(_1761317)), _1761319), _1761321)), c_List_Olistrel1(_1761317, _1761323))), 48832 ^ _780461 : [(48833 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1761317, _1761317)), hAPP(hAPP(c_Product__Type_OPair(_1761317, _1761317), hAPP(hAPP(c_List_Onth(_1761317), _1761319), 48831 ^ [_1761317, _1761319, _1761321, _1761323])), 48830 ^ [_1761317, _1761319, _1761321, _1761323])), _1761323)))], (48835 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48831 ^ [_1761317, _1761319, _1761321, _1761323]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761317)), _1761319))))], (48837 ^ _780461) ^ [] : [-(_1761321 = hAPP(hAPP(c_List_Olist__update(_1761317, _1761319), 48831 ^ [_1761317, _1761319, _1761321, _1761323]), 48830 ^ [_1761317, _1761319, _1761321, _1761323]))]]], (48839 ^ _780461) ^ [_1761665, _1761667, _1761669, _1761671] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1761665), tc_List_Olist(_1761665))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1761665), tc_List_Olist(_1761665)), _1761667), _1761669)), c_List_Olistrel1(_1761665, _1761671)))), 48840 ^ _780461 : [(48841 ^ _780461) ^ [_1761798, _1761800] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761665, _1761665)), hAPP(hAPP(c_Product__Type_OPair(_1761665, _1761665), hAPP(hAPP(c_List_Onth(_1761665), _1761667), _1761798)), _1761800)), _1761671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1761665)), _1761667))), _1761669 = hAPP(hAPP(c_List_Olist__update(_1761665, _1761667), _1761798), _1761800)]]], (48853 ^ _780461) ^ [_1762098, _1762100, _1762102, _1762104] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762098), tc_List_Olist(_1762098))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762098), tc_List_Olist(_1762098)), _1762100), _1762102)), c_List_Olistrel1(_1762098, _1762104))), 48858 ^ _780461 : [(48859 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1762098, _1762098)), hAPP(hAPP(c_Product__Type_OPair(_1762098, _1762098), 48856 ^ [_1762098, _1762100, _1762102, _1762104]), 48857 ^ [_1762098, _1762100, _1762102, _1762104])), _1762104)))], (48863 ^ _780461) ^ [] : [-(_1762100 = hAPP(hAPP(c_List_Oappend(_1762098), 48860 ^ [_1762098, _1762100, _1762102, _1762104]), hAPP(hAPP(c_List_Olist_OCons(_1762098), 48856 ^ [_1762098, _1762100, _1762102, _1762104]), 48861 ^ [_1762098, _1762100, _1762102, _1762104])))], (48865 ^ _780461) ^ [] : [-(_1762102 = hAPP(hAPP(c_List_Oappend(_1762098), 48860 ^ [_1762098, _1762100, _1762102, _1762104]), hAPP(hAPP(c_List_Olist_OCons(_1762098), 48857 ^ [_1762098, _1762100, _1762102, _1762104]), 48861 ^ [_1762098, _1762100, _1762102, _1762104])))]]], (48867 ^ _780461) ^ [_1762503, _1762505] : [-(hAPP(c_List_Orotate1(_1762503), _1762505) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1762503), _1762503, c_List_Olist_ONil(_1762503), hAPP(hAPP(c_COMBB(tc_List_Olist(_1762503), tc_fun(tc_List_Olist(_1762503), tc_List_Olist(_1762503)), _1762503), hAPP(c_COMBC(tc_List_Olist(_1762503), tc_List_Olist(_1762503), tc_List_Olist(_1762503)), c_List_Oappend(_1762503))), hAPP(hAPP(c_COMBC(_1762503, tc_List_Olist(_1762503), tc_List_Olist(_1762503)), c_List_Olist_OCons(_1762503)), c_List_Olist_ONil(_1762503)))), _1762505))], (48869 ^ _780461) ^ [_1762597, _1762599, _1762601, _1762603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762597), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1762599)), _1762601))), -(hAPP(hAPP(c_List_Olist__update(_1762599, _1762601), _1762597), _1762603) = hAPP(hAPP(c_List_Oappend(_1762599), hAPP(hAPP(c_List_Otake(_1762599), _1762597), _1762601)), hAPP(hAPP(c_List_Olist_OCons(_1762599), _1762603), hAPP(hAPP(c_List_Odrop(_1762599), hAPP(c_Nat_OSuc, _1762597)), _1762601))))], (48875 ^ _780461) ^ [_1762790, _1762792] : [-(hAPP(hAPP(c_List_Odrop(_1762790), _1762792), c_List_Olist_ONil(_1762790)) = c_List_Olist_ONil(_1762790))], (48877 ^ _780461) ^ [_1762842, _1762844] : [hAPP(c_List_Orotate1(_1762842), _1762844) = c_List_Olist_ONil(_1762842), -(_1762844 = c_List_Olist_ONil(_1762842))], (48883 ^ _780461) ^ [_1762933, _1762935] : [_1762935 = c_List_Olist_ONil(_1762933), -(hAPP(c_List_Orotate1(_1762933), _1762935) = c_List_Olist_ONil(_1762933))], (48889 ^ _780461) ^ [_1763030, _1763032, _1763034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763030)), _1763032)), _1763034)), -(hAPP(hAPP(c_List_Odrop(_1763030), _1763034), _1763032) = c_List_Olist_ONil(_1763030))], (48895 ^ _780461) ^ [_1763171, _1763173, _1763175] : [hAPP(hAPP(c_List_Odrop(_1763171), _1763173), _1763175) = c_List_Olist_ONil(_1763171), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763171)), _1763175)), _1763173)))], (48901 ^ _780461) ^ [_1763290, _1763292, _1763294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763290)), _1763294)), _1763292)), -(hAPP(hAPP(c_List_Odrop(_1763290), _1763292), _1763294) = c_List_Olist_ONil(_1763290))], (48907 ^ _780461) ^ [_1763415, _1763417, _1763419, _1763421] : [-(hAPP(hAPP(c_List_Otake(_1763415), _1763417), hAPP(hAPP(c_List_Odrop(_1763415), _1763419), _1763421)) = hAPP(hAPP(c_List_Odrop(_1763415), _1763419), hAPP(hAPP(c_List_Otake(_1763415), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1763417), _1763419)), _1763421)))], (48909 ^ _780461) ^ [_1763482, _1763484, _1763486, _1763488] : [-(hAPP(hAPP(c_List_Odrop(_1763482), _1763484), hAPP(hAPP(c_List_Otake(_1763482), _1763486), _1763488)) = hAPP(hAPP(c_List_Otake(_1763482), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1763486), _1763484)), hAPP(hAPP(c_List_Odrop(_1763482), _1763484), _1763488)))], (48911 ^ _780461) ^ [_1763549, _1763551, _1763553, _1763555] : [hBOOL(hAPP(hAPP(c_member(_1763549), _1763551), hAPP(c_List_Oset(_1763549), hAPP(hAPP(c_List_Odrop(_1763549), _1763553), _1763555)))), -(hBOOL(hAPP(hAPP(c_member(_1763549), _1763551), hAPP(c_List_Oset(_1763549), _1763555))))], (48917 ^ _780461) ^ [_1763694, _1763696] : [-(hAPP(c_List_Oset(_1763694), hAPP(c_List_Orotate1(_1763694), _1763696)) = hAPP(c_List_Oset(_1763694), _1763696))], (48919 ^ _780461) ^ [_1763734, _1763736, _1763738] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1763734, tc_HOL_Obool)), hAPP(c_List_Oset(_1763734), hAPP(hAPP(c_List_Odrop(_1763734), _1763736), _1763738))), hAPP(c_List_Oset(_1763734), _1763738))))], (48921 ^ _780461) ^ [_1763804, _1763806] : [hBOOL(hAPP(c_List_Odistinct(_1763804), hAPP(c_List_Orotate1(_1763804), _1763806))), -(hBOOL(hAPP(c_List_Odistinct(_1763804), _1763806)))], (48927 ^ _780461) ^ [_1763903, _1763905] : [hBOOL(hAPP(c_List_Odistinct(_1763903), _1763905)), -(hBOOL(hAPP(c_List_Odistinct(_1763903), hAPP(c_List_Orotate1(_1763903), _1763905))))], (48933 ^ _780461) ^ [_1764008, _1764010, _1764012] : [hBOOL(hAPP(c_List_Odistinct(_1764008), _1764010)), -(hBOOL(hAPP(c_List_Odistinct(_1764008), hAPP(hAPP(c_List_Odrop(_1764008), _1764012), _1764010))))], (48939 ^ _780461) ^ [_1764119, _1764121, _1764123, _1764125] : [-(hAPP(hAPP(c_List_Odrop(_1764119), _1764121), hAPP(hAPP(c_List_Odrop(_1764119), _1764123), _1764125)) = hAPP(hAPP(c_List_Odrop(_1764119), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1764121), _1764123)), _1764125))], (48941 ^ _780461) ^ [_1764178, _1764180] : [-(hAPP(hAPP(c_List_Odrop(_1764178), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1764180) = _1764180)], (48943 ^ _780461) ^ [_1764211, _1764213, _1764215, _1764217, _1764219] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1764211, _1764213)), _1764215), hAPP(hAPP(c_List_Ozip(_1764211, _1764213), _1764217), _1764219)) = hAPP(hAPP(c_List_Ozip(_1764211, _1764213), hAPP(hAPP(c_List_Odrop(_1764211), _1764215), _1764217)), hAPP(hAPP(c_List_Odrop(_1764213), _1764215), _1764219)))], (48945 ^ _780461) ^ [_1764287, _1764289, _1764291, _1764293, _1764295] : [-(hAPP(hAPP(c_List_Odrop(_1764287), _1764289), hAPP(hAPP(c_List_Omap(_1764291, _1764287), _1764293), _1764295)) = hAPP(hAPP(c_List_Omap(_1764291, _1764287), _1764293), hAPP(hAPP(c_List_Odrop(_1764291), _1764289), _1764295)))], (48947 ^ _780461) ^ [_1764352, _1764354, _1764356] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764352)), hAPP(hAPP(c_List_Odrop(_1764352), _1764354), _1764356)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764352)), _1764356)), _1764354))], (48949 ^ _780461) ^ [_1764407, _1764409] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764407)), hAPP(c_List_Orotate1(_1764407), _1764409)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764407)), _1764409))], (48951 ^ _780461) ^ [_1764451, _1764453, _1764455, _1764457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764451), _1764453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1764455, tc_HOL_Obool)), hAPP(c_List_Oset(_1764455), hAPP(hAPP(c_List_Odrop(_1764455), _1764453), _1764457))), hAPP(c_List_Oset(_1764455), hAPP(hAPP(c_List_Odrop(_1764455), _1764451), _1764457)))))], (48957 ^ _780461) ^ [_1764614, _1764616, _1764618] : [-(hAPP(hAPP(c_List_Odrop(_1764614), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1764614), _1764616), _1764618)) = _1764618)], (48959 ^ _780461) ^ [_1764657, _1764659, _1764661, _1764663] : [-(hAPP(hAPP(c_List_Odrop(_1764657), hAPP(c_Nat_OSuc, _1764659)), hAPP(hAPP(c_List_Olist_OCons(_1764657), _1764661), _1764663)) = hAPP(hAPP(c_List_Odrop(_1764657), _1764659), _1764663))], (48961 ^ _780461) ^ [_1764713, _1764715, _1764717, _1764719, _1764721] : [hAPP(hAPP(c_List_Odrop(_1764713), _1764715), _1764717) = hAPP(hAPP(c_List_Olist_OCons(_1764713), _1764719), _1764721), -(hAPP(hAPP(c_List_Onth(_1764713), _1764717), _1764715) = _1764719)], (48967 ^ _780461) ^ [_1764865, _1764867, _1764869, _1764871] : [hAPP(hAPP(c_List_Oappend(_1764865), _1764867), _1764869) = _1764871, 48970 ^ _780461 : [(48971 ^ _780461) ^ [] : [-(_1764867 = hAPP(hAPP(c_List_Otake(_1764865), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764865)), _1764867)), _1764871))], (48973 ^ _780461) ^ [] : [-(_1764869 = hAPP(hAPP(c_List_Odrop(_1764865), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764865)), _1764867)), _1764871))]]], (48975 ^ _780461) ^ [_1765044, _1765046, _1765048, _1765050] : [-(hAPP(hAPP(c_List_Oappend(_1765044), _1765046), _1765048) = _1765050), _1765046 = hAPP(hAPP(c_List_Otake(_1765044), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765044)), _1765046)), _1765050), _1765048 = hAPP(hAPP(c_List_Odrop(_1765044), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765044)), _1765046)), _1765050)], (48985 ^ _780461) ^ [_1765259, _1765261, _1765263] : [-(hAPP(hAPP(c_List_Oappend(_1765259), hAPP(hAPP(c_List_Otake(_1765259), _1765261), _1765263)), hAPP(hAPP(c_List_Odrop(_1765259), _1765261), _1765263)) = _1765263)], (48987 ^ _780461) ^ [_1765310, _1765312, _1765314, _1765316] : [-(hAPP(hAPP(c_List_Odrop(_1765310), _1765312), hAPP(hAPP(c_List_Oappend(_1765310), _1765314), _1765316)) = hAPP(hAPP(c_List_Oappend(_1765310), hAPP(hAPP(c_List_Odrop(_1765310), _1765312), _1765314)), hAPP(hAPP(c_List_Odrop(_1765310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1765312), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765310)), _1765314))), _1765316)))], (48989 ^ _780461) ^ [_1765392, _1765394, _1765396, _1765398] : [-(hAPP(hAPP(c_List_Odrop(_1765392), _1765394), hAPP(hAPP(c_List_Olist_OCons(_1765392), _1765396), _1765398)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1765392), hAPP(hAPP(c_List_Olist_OCons(_1765392), _1765396), _1765398), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1765392), tc_List_Olist(_1765392)), c_List_Odrop(_1765392)), _1765398), _1765394))], (48991 ^ _780461) ^ [_1765483, _1765485, _1765487, _1765489] : [_1765483 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1765485), _1765483), hAPP(hAPP(c_List_Olist_OCons(_1765485), _1765487), _1765489)) = hAPP(hAPP(c_List_Olist_OCons(_1765485), _1765487), _1765489))], (48997 ^ _780461) ^ [_1765606, _1765608, _1765610, _1765612] : [-(_1765606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1765608), _1765606), hAPP(hAPP(c_List_Olist_OCons(_1765608), _1765610), _1765612)) = hAPP(hAPP(c_List_Odrop(_1765608), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1765606), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1765612))], (49003 ^ _780461) ^ [_1765678, _1765680, _1765682, _1765684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1765678), _1765680)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765682)), _1765684))), -(hAPP(hAPP(c_List_Onth(_1765682), hAPP(hAPP(c_List_Odrop(_1765682), _1765678), _1765684)), _1765680) = hAPP(hAPP(c_List_Onth(_1765682), _1765684), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1765678), _1765680)))], (49009 ^ _780461) ^ [_1765879, _1765881, _1765883, _1765885, _1765887] : [hAPP(hAPP(c_List_Oappend(_1765879), _1765881), _1765883) = hAPP(hAPP(c_List_Oappend(_1765879), _1765885), _1765887), 49012 ^ _780461 : [(49013 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765879)), _1765881)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765879)), _1765885))), 49016 ^ _780461 : [(49017 ^ _780461) ^ [] : [-(_1765881 = hAPP(hAPP(c_List_Otake(_1765879), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765879)), _1765881)), _1765885))], (49019 ^ _780461) ^ [] : [-(_1765883 = hAPP(hAPP(c_List_Oappend(_1765879), hAPP(hAPP(c_List_Odrop(_1765879), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765879)), _1765881)), _1765885)), _1765887))]]], (49021 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765879)), _1765881)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765879)), _1765885)))), 49024 ^ _780461 : [(49025 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1765879), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765879)), _1765885)), _1765881) = _1765885)], (49027 ^ _780461) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1765879), hAPP(hAPP(c_List_Odrop(_1765879), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765879)), _1765885)), _1765881)), _1765883) = _1765887)]]]]], (49029 ^ _780461) ^ [_1766392, _1766394, _1766396, _1766398, _1766400] : [-(hAPP(hAPP(c_List_Oappend(_1766392), _1766394), _1766396) = hAPP(hAPP(c_List_Oappend(_1766392), _1766398), _1766400)), 49032 ^ _780461 : [(49033 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766392)), _1766394)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766392)), _1766398))))], (49035 ^ _780461) ^ [] : [_1766394 = hAPP(hAPP(c_List_Otake(_1766392), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766392)), _1766394)), _1766398), _1766396 = hAPP(hAPP(c_List_Oappend(_1766392), hAPP(hAPP(c_List_Odrop(_1766392), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766392)), _1766394)), _1766398)), _1766400)]], 49040 ^ _780461 : [(49041 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766392)), _1766394)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766392)), _1766398)))], (49043 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Otake(_1766392), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766392)), _1766398)), _1766394) = _1766398, hAPP(hAPP(c_List_Oappend(_1766392), hAPP(hAPP(c_List_Odrop(_1766392), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766392)), _1766398)), _1766394)), _1766396) = _1766400]]], (49051 ^ _780461) ^ [_1766980, _1766982, _1766984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1766980), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766982)), _1766984))), -(hAPP(hAPP(c_List_Olist_OCons(_1766982), hAPP(hAPP(c_List_Onth(_1766982), _1766984), _1766980)), hAPP(hAPP(c_List_Odrop(_1766982), hAPP(c_Nat_OSuc, _1766980)), _1766984)) = hAPP(hAPP(c_List_Odrop(_1766982), _1766980), _1766984))], (49057 ^ _780461) ^ [_1767151, _1767153, _1767155, _1767157] : [-(hAPP(c_List_Orotate1(_1767151), c_List_Olist_ONil(_1767151)) = c_List_Olist_ONil(_1767151))], (49059 ^ _780461) ^ [_1767186, _1767188, _1767190, _1767192] : [-(hAPP(c_List_Orotate1(_1767188), hAPP(hAPP(c_List_Olist_OCons(_1767188), _1767190), _1767192)) = hAPP(hAPP(c_List_Oappend(_1767188), _1767192), hAPP(hAPP(c_List_Olist_OCons(_1767188), _1767190), c_List_Olist_ONil(_1767188))))], (49061 ^ _780461) ^ [_1767263, _1767265, _1767267, _1767269] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1767263) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1767265), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1767263)), hAPP(hAPP(c_List_Olist_OCons(_1767265), _1767267), _1767269)) = hAPP(hAPP(c_List_Olist_OCons(_1767265), _1767267), _1767269))], (49067 ^ _780461) ^ [_1767398, _1767400, _1767402, _1767404] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1767398) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1767400), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1767398)), hAPP(hAPP(c_List_Olist_OCons(_1767400), _1767402), _1767404)) = hAPP(hAPP(c_List_Odrop(_1767400), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1767398)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1767404))], (49073 ^ _780461) ^ [_1767479, _1767481, _1767483, _1767485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1767479), _1767481)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767483)), _1767485))), -(hAPP(hAPP(c_List_Otake(_1767483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1767479), _1767481)), _1767485) = hAPP(hAPP(c_List_Oappend(_1767483), hAPP(hAPP(c_List_Otake(_1767483), _1767479), _1767485)), hAPP(hAPP(c_List_Otake(_1767483), _1767481), hAPP(hAPP(c_List_Odrop(_1767483), _1767479), _1767485))))], (49079 ^ _780461) ^ [_1767688, _1767690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767688)), _1767690)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1767688), _1767690) = _1767690)], (49085 ^ _780461) ^ [_1767799, _1767801, _1767803, _1767805, _1767807] : [-(hAPP(hAPP(c_List_Ozip(_1767799, _1767801), _1767803), hAPP(hAPP(c_List_Oappend(_1767801), _1767805), _1767807)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1767799, _1767801)), hAPP(hAPP(c_List_Ozip(_1767799, _1767801), hAPP(hAPP(c_List_Otake(_1767799), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767801)), _1767805)), _1767803)), _1767805)), hAPP(hAPP(c_List_Ozip(_1767799, _1767801), hAPP(hAPP(c_List_Odrop(_1767799), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767801)), _1767805)), _1767803)), _1767807)))], (49087 ^ _780461) ^ [_1767906, _1767908, _1767910, _1767912, _1767914] : [-(hAPP(hAPP(c_List_Ozip(_1767906, _1767908), hAPP(hAPP(c_List_Oappend(_1767906), _1767910), _1767912)), _1767914) = hAPP(hAPP(c_List_Oappend(tc_prod(_1767906, _1767908)), hAPP(hAPP(c_List_Ozip(_1767906, _1767908), _1767910), hAPP(hAPP(c_List_Otake(_1767908), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767906)), _1767910)), _1767914))), hAPP(hAPP(c_List_Ozip(_1767906, _1767908), _1767912), hAPP(hAPP(c_List_Odrop(_1767908), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767906)), _1767910)), _1767914))))], (49089 ^ _780461) ^ [_1768013, _1768015, _1768017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768013), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768015)), _1768017))), -(_1768017 = hAPP(hAPP(c_List_Oappend(_1768015), hAPP(hAPP(c_List_Otake(_1768015), _1768013), _1768017)), hAPP(hAPP(c_List_Olist_OCons(_1768015), hAPP(hAPP(c_List_Onth(_1768015), _1768017), _1768013)), hAPP(hAPP(c_List_Odrop(_1768015), hAPP(c_Nat_OSuc, _1768013)), _1768017))))], (49095 ^ _780461) ^ [_1768202, _1768204, _1768206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768202), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768204)), _1768206))), -(hAPP(hAPP(c_List_Oappend(_1768204), hAPP(hAPP(c_List_Otake(_1768204), _1768202), _1768206)), hAPP(hAPP(c_List_Olist_OCons(_1768204), hAPP(c_List_Ohd(_1768204), hAPP(hAPP(c_List_Odrop(_1768204), _1768202), _1768206))), c_List_Olist_ONil(_1768204))) = hAPP(hAPP(c_List_Otake(_1768204), hAPP(c_Nat_OSuc, _1768202)), _1768206))], (49101 ^ _780461) ^ [_1768404, _1768406, _1768408] : [-(_1768404 = c_List_Olist_ONil(_1768406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1768408), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768406)), _1768404))), -(hAPP(c_List_Ohd(_1768406), hAPP(hAPP(c_List_Odrop(_1768406), _1768408), _1768404)) = hAPP(hAPP(c_List_Onth(_1768406), _1768404), _1768408))], (49111 ^ _780461) ^ [_1768599, _1768601, _1768603] : [-(_1768599 = c_List_Olist_ONil(_1768601)), -(hAPP(c_List_Ohd(_1768601), hAPP(hAPP(c_List_Oappend(_1768601), _1768599), _1768603)) = hAPP(c_List_Ohd(_1768601), _1768599))], (49117 ^ _780461) ^ [_1768669, _1768671, _1768673] : [_1768669 = c_List_Olist_ONil(_1768671), -(hAPP(c_List_Ohd(_1768671), hAPP(hAPP(c_List_Oappend(_1768671), _1768669), _1768673)) = hAPP(c_List_Ohd(_1768671), _1768673))], (49123 ^ _780461) ^ [_1768782, _1768784, _1768786] : [-(_1768782 = c_List_Olist_ONil(_1768784)), -(hAPP(c_List_Ohd(_1768784), hAPP(hAPP(c_List_Oappend(_1768784), _1768782), _1768786)) = hAPP(c_List_Ohd(_1768784), _1768782))], (49129 ^ _780461) ^ [_1768842, _1768844, _1768846] : [-(hAPP(c_List_Ohd(_1768842), hAPP(hAPP(c_List_Olist_OCons(_1768842), _1768844), _1768846)) = _1768844)], (49131 ^ _780461) ^ [_1768878, _1768880, _1768882, _1768884] : [-(_1768878 = c_List_Olist_ONil(_1768880)), -(hAPP(c_List_Ohd(_1768882), hAPP(hAPP(c_List_Omap(_1768880, _1768882), _1768884), _1768878)) = hAPP(_1768884, hAPP(c_List_Ohd(_1768880), _1768878)))], (49137 ^ _780461) ^ [_1768938, _1768940] : [-(_1768938 = c_List_Olist_ONil(_1768940)), -(hBOOL(hAPP(hAPP(c_member(_1768940), hAPP(c_List_Ohd(_1768940), _1768938)), hAPP(c_List_Oset(_1768940), _1768938))))], (49143 ^ _780461) ^ [_1768989, _1768991] : [-(_1768989 = c_List_Olist_ONil(_1768991)), -(hAPP(c_List_Ohd(_1768991), _1768989) = hAPP(hAPP(c_List_Onth(_1768991), _1768989), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49149 ^ _780461) ^ [_1769036, _1769038] : [-(_1769036 = c_List_Olist_ONil(_1769038)), -(hAPP(c_List_Orotate1(_1769038), _1769036) = hAPP(hAPP(c_List_Oappend(_1769038), c_List_Otl(_1769038, _1769036)), hAPP(hAPP(c_List_Olist_OCons(_1769038), hAPP(c_List_Ohd(_1769038), _1769036)), c_List_Olist_ONil(_1769038))))], (49155 ^ _780461) ^ [_1769101, _1769103, _1769105] : [-(_1769101 = c_List_Olist_ONil(_1769103)), -(hAPP(c_List_Ohd(_1769103), hAPP(c_List_Orotate(_1769103, _1769105), _1769101)) = hAPP(hAPP(c_List_Onth(_1769103), _1769101), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1769105, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769103)), _1769101))))], (49161 ^ _780461) ^ [_1769171, _1769173, _1769175] : [-(hAPP(hAPP(c_List_Odrop(_1769171), hAPP(c_Nat_OSuc, _1769173)), _1769175) = hAPP(hAPP(c_List_Odrop(_1769171), _1769173), c_List_Otl(_1769171, _1769175)))], (49163 ^ _780461) ^ [_1769220, _1769222, _1769224] : [-(hAPP(hAPP(c_List_Odrop(_1769220), _1769222), c_List_Otl(_1769220, _1769224)) = c_List_Otl(_1769220, hAPP(hAPP(c_List_Odrop(_1769220), _1769222), _1769224)))], (49165 ^ _780461) ^ [_1769269, _1769271, _1769273] : [-(c_List_Otl(_1769269, hAPP(hAPP(c_List_Odrop(_1769269), _1769271), _1769273)) = hAPP(hAPP(c_List_Odrop(_1769269), _1769271), c_List_Otl(_1769269, _1769273)))], (49167 ^ _780461) ^ [_1769318] : [-(c_List_Otl(_1769318, c_List_Olist_ONil(_1769318)) = c_List_Olist_ONil(_1769318))], (49169 ^ _780461) ^ [_1769366, _1769368, _1769370] : [hAPP(c_List_Orotate(_1769366, _1769368), _1769370) = c_List_Olist_ONil(_1769366), -(_1769370 = c_List_Olist_ONil(_1769366))], (49175 ^ _780461) ^ [_1769461, _1769463, _1769465] : [_1769465 = c_List_Olist_ONil(_1769461), -(hAPP(c_List_Orotate(_1769461, _1769463), _1769465) = c_List_Olist_ONil(_1769461))], (49181 ^ _780461) ^ [_1769562, _1769564, _1769566] : [-(hAPP(hAPP(c_List_Otake(_1769562), _1769564), c_List_Otl(_1769562, _1769566)) = c_List_Otl(_1769562, hAPP(hAPP(c_List_Otake(_1769562), hAPP(c_Nat_OSuc, _1769564)), _1769566)))], (49183 ^ _780461) ^ [_1769614, _1769616, _1769618] : [-(hAPP(c_List_Oset(_1769614), hAPP(c_List_Orotate(_1769614, _1769616), _1769618)) = hAPP(c_List_Oset(_1769614), _1769618))], (49185 ^ _780461) ^ [_1769675, _1769677, _1769679] : [hBOOL(hAPP(c_List_Odistinct(_1769675), hAPP(c_List_Orotate(_1769675, _1769677), _1769679))), -(hBOOL(hAPP(c_List_Odistinct(_1769675), _1769679)))], (49191 ^ _780461) ^ [_1769778, _1769780, _1769782] : [hBOOL(hAPP(c_List_Odistinct(_1769778), _1769782)), -(hBOOL(hAPP(c_List_Odistinct(_1769778), hAPP(c_List_Orotate(_1769778, _1769780), _1769782))))], (49197 ^ _780461) ^ [_1769887, _1769889] : [hBOOL(hAPP(c_List_Odistinct(_1769887), _1769889)), -(hBOOL(hAPP(c_List_Odistinct(_1769887), c_List_Otl(_1769887, _1769889))))], (49203 ^ _780461) ^ [_1769986, _1769988, _1769990, _1769992] : [-(hAPP(c_List_Orotate(_1769986, _1769988), hAPP(c_List_Orotate(_1769986, _1769990), _1769992)) = hAPP(c_List_Orotate(_1769986, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1769988), _1769990)), _1769992))], (49205 ^ _780461) ^ [_1770039, _1770041, _1770043, _1770045, _1770047] : [-(hAPP(c_List_Orotate(_1770039, _1770041), hAPP(hAPP(c_List_Omap(_1770043, _1770039), _1770045), _1770047)) = hAPP(hAPP(c_List_Omap(_1770043, _1770039), _1770045), hAPP(c_List_Orotate(_1770043, _1770041), _1770047)))], (49207 ^ _780461) ^ [_1770100, _1770102, _1770104, _1770106] : [-(hAPP(hAPP(c_List_Omap(_1770100, _1770102), _1770104), c_List_Otl(_1770100, _1770106)) = c_List_Otl(_1770102, hAPP(hAPP(c_List_Omap(_1770100, _1770102), _1770104), _1770106)))], (49209 ^ _780461) ^ [_1770153, _1770155, _1770157] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770153)), hAPP(c_List_Orotate(_1770153, _1770155), _1770157)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770153)), _1770157))], (49211 ^ _780461) ^ [_1770200, _1770202, _1770204] : [-(hAPP(c_List_Orotate(_1770200, _1770202), _1770204) = hAPP(c_List_Orotate(_1770200, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1770202, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770200)), _1770204))), _1770204))], (49213 ^ _780461) ^ [_1770250, _1770252, _1770254] : [-(c_List_Otl(_1770250, hAPP(hAPP(c_List_Olist_OCons(_1770250), _1770252), _1770254)) = _1770254)], (49215 ^ _780461) ^ [_1770284, _1770286, _1770288] : [-(_1770284 = c_List_Olist_ONil(_1770286)), -(c_List_Otl(_1770286, hAPP(hAPP(c_List_Oappend(_1770286), _1770284), _1770288)) = hAPP(hAPP(c_List_Oappend(_1770286), c_List_Otl(_1770286, _1770284)), _1770288))], (49221 ^ _780461) ^ [_1770346, _1770348, _1770350] : [-(hAPP(c_List_Orotate1(_1770346), hAPP(c_List_Orotate(_1770346, _1770348), _1770350)) = hAPP(c_List_Orotate(_1770346, _1770348), hAPP(c_List_Orotate1(_1770346), _1770350)))], (49223 ^ _780461) ^ [_1770395, _1770397, _1770399] : [-(hAPP(c_List_Orotate(_1770395, hAPP(c_Nat_OSuc, _1770397)), _1770399) = hAPP(c_List_Orotate1(_1770395), hAPP(c_List_Orotate(_1770395, _1770397), _1770399)))], (49225 ^ _780461) ^ [_1770442, _1770444] : [-(c_List_Orotate(_1770442, _1770444) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1770442), tc_List_Olist(_1770442)), _1770444), c_List_Orotate1(_1770442)))], (49227 ^ _780461) ^ [_1770485, _1770487, _1770489] : [-(c_List_Otl(_1770485, hAPP(hAPP(c_List_Oappend(_1770485), _1770487), _1770489)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1770485), _1770485, c_List_Otl(_1770485, _1770489), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1770485), tc_List_Olist(_1770485)), _1770485), hAPP(hAPP(c_COMBC(tc_List_Olist(_1770485), tc_List_Olist(_1770485), tc_List_Olist(_1770485)), c_List_Oappend(_1770485)), _1770489))), _1770487))], (49229 ^ _780461) ^ [_1770567] : [-(c_List_Orotate(_1770567, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1770567)))], (49231 ^ _780461) ^ [_1770597, _1770599, _1770601] : [-(c_List_Orotate(_1770597, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1770599), _1770601)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1770597), tc_List_Olist(_1770597), tc_List_Olist(_1770597), c_List_Orotate(_1770597, _1770599)), c_List_Orotate(_1770597, _1770601)))], (49233 ^ _780461) ^ [_1770653, _1770655, _1770657] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1770653, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770655)), _1770657)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1770655, _1770653), _1770657) = _1770657)], (49239 ^ _780461) ^ [_1770766, _1770768, _1770770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770766)), _1770768)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1770766, _1770770), _1770768) = _1770768)], (49245 ^ _780461) ^ [_1770881, _1770883] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770881)), c_List_Otl(_1770881, _1770883)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770881)), _1770883)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (49247 ^ _780461) ^ [_1770929, _1770931, _1770933] : [-(c_List_Otl(_1770929, hAPP(hAPP(c_List_Otake(_1770929), _1770931), _1770933)) = hAPP(hAPP(c_List_Otake(_1770929), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1770931), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_List_Otl(_1770929, _1770933)))], (49249 ^ _780461) ^ [_1770980, _1770982, _1770984] : [-(_1770980 = c_List_Olist_ONil(_1770982)), -(hAPP(hAPP(c_List_Otake(_1770982), hAPP(c_Nat_OSuc, _1770984)), _1770980) = hAPP(hAPP(c_List_Olist_OCons(_1770982), hAPP(c_List_Ohd(_1770982), _1770980)), hAPP(hAPP(c_List_Otake(_1770982), _1770984), c_List_Otl(_1770982, _1770980))))], (49255 ^ _780461) ^ [_1771055, _1771057, _1771059] : [-(hAPP(c_List_Orotate(_1771055, _1771057), _1771059) = hAPP(hAPP(c_List_Oappend(_1771055), hAPP(hAPP(c_List_Odrop(_1771055), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1771057, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771055)), _1771059))), _1771059)), hAPP(hAPP(c_List_Otake(_1771055), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1771057, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771055)), _1771059))), _1771059)))], (49257 ^ _780461) ^ [_1771134, _1771136] : [class_Lattices_Oab__semigroup__idem__mult(_1771134), -(_1771136 = c_List_Olist_ONil(_1771134)), -(hAPP(c_Finite__Set_Ofold1(_1771134, c_Groups_Otimes__class_Otimes(_1771134)), hAPP(c_List_Oset(_1771134), _1771136)) = hAPP(c_List_Ofoldl(_1771134, _1771134, c_Groups_Otimes__class_Otimes(_1771134), hAPP(c_List_Ohd(_1771134), _1771136)), c_List_Otl(_1771134, _1771136)))], (49267 ^ _780461) ^ [_1771290, _1771292, _1771294, _1771296] : [-(c_List_Olist_Olist__size(_1771290, _1771292, hAPP(hAPP(c_List_Olist_OCons(_1771290), _1771294), _1771296)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1771292, _1771294)), c_List_Olist_Olist__size(_1771290, _1771292, _1771296))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (49269 ^ _780461) ^ [_1771350, _1771352, _1771354, _1771356, _1771358, _1771360] : [-(hAPP(c_List_Ofoldl(_1771350, _1771352, _1771354, _1771356), hAPP(hAPP(c_List_Oappend(_1771352), _1771358), _1771360)) = hAPP(c_List_Ofoldl(_1771350, _1771352, _1771354, hAPP(c_List_Ofoldl(_1771350, _1771352, _1771354, _1771356), _1771358)), _1771360))], (49271 ^ _780461) ^ [_1771415, _1771417, _1771419, _1771421, _1771423, _1771425] : [-(hAPP(c_List_Ofoldl(_1771415, _1771417, _1771419, _1771421), hAPP(hAPP(c_List_Olist_OCons(_1771417), _1771423), _1771425)) = hAPP(c_List_Ofoldl(_1771415, _1771417, _1771419, hAPP(hAPP(_1771419, _1771421), _1771423)), _1771425))], (49273 ^ _780461) ^ [_1771478, _1771480, _1771482, _1771484, _1771486] : [-(c_List_Olist_Olist__size(_1771478, _1771480, hAPP(hAPP(c_List_Omap(_1771482, _1771478), _1771484), _1771486)) = c_List_Olist_Olist__size(_1771482, hAPP(c_Fun_Ocomp(_1771478, tc_Nat_Onat, _1771482, _1771480), _1771484), _1771486))], (49275 ^ _780461) ^ [_1771534, _1771536, _1771538, _1771540, _1771542, _1771544, _1771546] : [-(hAPP(c_List_Ofoldl(_1771534, _1771536, _1771538, _1771540), hAPP(hAPP(c_List_Omap(_1771542, _1771536), _1771544), _1771546)) = hAPP(c_List_Ofoldl(_1771534, _1771542, hAPP(hAPP(c_COMBC(_1771534, tc_fun(_1771542, _1771536), tc_fun(_1771542, _1771534)), hAPP(hAPP(c_COMBB(tc_fun(_1771536, _1771534), tc_fun(tc_fun(_1771542, _1771536), tc_fun(_1771542, _1771534)), _1771534), c_COMBB(_1771536, _1771534, _1771542)), _1771538)), _1771544), _1771540), _1771546))], (49277 ^ _780461) ^ [_1771636, _1771638, _1771640] : [class_Groups_Oab__semigroup__add(_1771636), -(c_List_Ofoldr(_1771636, _1771636, c_Groups_Oplus__class_Oplus(_1771636), _1771638, _1771640) = hAPP(c_List_Ofoldl(_1771636, _1771636, c_Groups_Oplus__class_Oplus(_1771636), _1771640), _1771638))], (49283 ^ _780461) ^ [_1771749, _1771751, _1771753] : [class_Groups_Omonoid__add(_1771749), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1771749), _1771751), hAPP(c_List_Ofoldl(_1771749, _1771749, c_Groups_Oplus__class_Oplus(_1771749), c_Groups_Ozero__class_Ozero(_1771749)), _1771753)) = hAPP(c_List_Ofoldl(_1771749, _1771749, c_Groups_Oplus__class_Oplus(_1771749), _1771751), _1771753))], (49289 ^ _780461) ^ [_1771886, _1771888, _1771890, _1771892] : [class_Groups_Osemigroup__add(_1771886), -(hAPP(c_List_Ofoldl(_1771886, _1771886, c_Groups_Oplus__class_Oplus(_1771886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1771886), _1771888), _1771890)), _1771892) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1771886), _1771888), hAPP(c_List_Ofoldl(_1771886, _1771886, c_Groups_Oplus__class_Oplus(_1771886), _1771890), _1771892)))], (49295 ^ _780461) ^ [_1772037, _1772039, _1772041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1772037), _1772039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1772037), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1772039), _1772041))))], (49301 ^ _780461) ^ [_1772152, _1772154, _1772156, _1772158] : [-(hAPP(c_List_Ofoldl(_1772152, _1772154, _1772156, _1772158), c_List_Olist_ONil(_1772154)) = _1772158)], (49303 ^ _780461) ^ [_1772191] : [class_Groups_Omonoid__add(_1772191), -(c_List_Omonoid__add__class_Olistsum(_1772191) = c_List_Ofoldl(_1772191, _1772191, c_Groups_Oplus__class_Oplus(_1772191), c_Groups_Ozero__class_Ozero(_1772191)))], (49309 ^ _780461) ^ [_1772286, _1772288] : [class_Groups_Omonoid__add(_1772286), -(hAPP(c_List_Ofoldl(_1772286, _1772286, c_Groups_Oplus__class_Oplus(_1772286), c_Groups_Ozero__class_Ozero(_1772286)), _1772288) = c_List_Ofoldr(_1772286, _1772286, c_Groups_Oplus__class_Oplus(_1772286), _1772288, c_Groups_Ozero__class_Ozero(_1772286)))], (49315 ^ _780461) ^ [_1772405, _1772407, _1772409] : [class_Groups_Omonoid__add(_1772405), -(hAPP(c_List_Ofoldl(_1772405, _1772405, c_Groups_Oplus__class_Oplus(_1772405), _1772407), _1772409) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1772405), _1772407), c_List_Ofoldr(_1772405, _1772405, c_Groups_Oplus__class_Oplus(_1772405), _1772409, c_Groups_Ozero__class_Ozero(_1772405))))], (49321 ^ _780461) ^ [_1772553, _1772555] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1772553), _1772555) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 49324 ^ _780461 : [(49325 ^ _780461) ^ [] : [-(_1772553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49327 ^ _780461) ^ [_1772667] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1772667), hAPP(c_List_Oset(tc_Nat_Onat), _1772555))), -(_1772667 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49333 ^ _780461) ^ [_1772764, _1772766] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1772764), _1772766) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1772764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 49339 ^ _780461 : [(49340 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49338 ^ [_1772764, _1772766]), hAPP(c_List_Oset(tc_Nat_Onat), _1772766))))], (49342 ^ _780461) ^ [] : [49338 ^ [_1772764, _1772766] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (49346 ^ _780461) ^ [_1772990, _1772992] : [-(c_List_Olist_Olist__size(_1772990, _1772992, c_List_Olist_ONil(_1772990)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49348 ^ _780461) ^ [_1773021, _1773023, _1773025, _1773027, _1773029] : [c_Finite__Set_Ofun__left__comm__idem(_1773021, _1773023, _1773025), -(hAPP(hAPP(c_Finite__Set_Ofold(_1773021, _1773023, _1773025), _1773027), hAPP(c_List_Oset(_1773021), _1773029)) = hAPP(c_List_Ofoldl(_1773023, _1773021, hAPP(c_COMBC(_1773021, _1773023, _1773023), _1773025), _1773027), _1773029))], (49354 ^ _780461) ^ [_1773166, _1773168] : [class_Complete__Lattice_Ocomplete__lattice(_1773166), -(c_Complete__Lattice_OSup__class_OSup(_1773166, hAPP(c_List_Oset(_1773166), _1773168)) = hAPP(c_List_Ofoldl(_1773166, _1773166, c_Lattices_Osemilattice__sup__class_Osup(_1773166), c_Orderings_Obot__class_Obot(_1773166)), _1773168))], (49360 ^ _780461) ^ [_1773281, _1773283] : [class_Complete__Lattice_Ocomplete__lattice(_1773281), -(c_Complete__Lattice_OInf__class_OInf(_1773281, hAPP(c_List_Oset(_1773281), _1773283)) = hAPP(c_List_Ofoldl(_1773281, _1773281, c_Lattices_Osemilattice__inf__class_Oinf(_1773281), c_Orderings_Otop__class_Otop(_1773281)), _1773283))], (49366 ^ _780461) ^ [_1773396, _1773398, _1773400] : [class_Lattices_Olattice(_1773396), -(c_Big__Operators_Olattice__class_OSup__fin(_1773396, hAPP(c_List_Oset(_1773396), hAPP(hAPP(c_List_Olist_OCons(_1773396), _1773398), _1773400))) = hAPP(c_List_Ofoldl(_1773396, _1773396, c_Lattices_Osemilattice__sup__class_Osup(_1773396), _1773398), _1773400))], (49372 ^ _780461) ^ [_1773525, _1773527, _1773529] : [class_Lattices_Olattice(_1773525), -(c_Big__Operators_Olattice__class_OInf__fin(_1773525, hAPP(c_List_Oset(_1773525), hAPP(hAPP(c_List_Olist_OCons(_1773525), _1773527), _1773529))) = hAPP(c_List_Ofoldl(_1773525, _1773525, c_Lattices_Osemilattice__inf__class_Oinf(_1773525), _1773527), _1773529))], (49378 ^ _780461) ^ [_1773654, _1773656, _1773658] : [class_Orderings_Olinorder(_1773654), -(c_Big__Operators_Olinorder__class_OMin(_1773654, hAPP(c_List_Oset(_1773654), hAPP(hAPP(c_List_Olist_OCons(_1773654), _1773656), _1773658))) = hAPP(c_List_Ofoldl(_1773654, _1773654, c_Orderings_Oord__class_Omin(_1773654), _1773656), _1773658))], (49384 ^ _780461) ^ [_1773783, _1773785, _1773787] : [class_Orderings_Olinorder(_1773783), -(c_Big__Operators_Olinorder__class_OMax(_1773783, hAPP(c_List_Oset(_1773783), hAPP(hAPP(c_List_Olist_OCons(_1773783), _1773785), _1773787))) = hAPP(c_List_Ofoldl(_1773783, _1773783, c_Orderings_Oord__class_Omax(_1773783), _1773785), _1773787))], (49390 ^ _780461) ^ [_1773912, _1773914, _1773916] : [class_Orderings_Olinorder(_1773912), -(c_Big__Operators_Olattice_OInf__fin(_1773912, c_Orderings_Oord__class_Omin(_1773912), hAPP(c_List_Oset(_1773912), hAPP(hAPP(c_List_Olist_OCons(_1773912), _1773914), _1773916))) = hAPP(c_List_Ofoldl(_1773912, _1773912, c_Orderings_Oord__class_Omin(_1773912), _1773914), _1773916))], (49396 ^ _780461) ^ [_1774047, _1774049, _1774051] : [class_Orderings_Olinorder(_1774047), -(c_Big__Operators_Olattice_OSup__fin(_1774047, c_Orderings_Oord__class_Omax(_1774047), hAPP(c_List_Oset(_1774047), hAPP(hAPP(c_List_Olist_OCons(_1774047), _1774049), _1774051))) = hAPP(c_List_Ofoldl(_1774047, _1774047, c_Orderings_Oord__class_Omax(_1774047), _1774049), _1774051))], (49402 ^ _780461) ^ [_1774182, _1774184, _1774186, _1774188] : [class_Complete__Lattice_Ocomplete__lattice(_1774182), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1774184, _1774182), hAPP(c_List_Oset(_1774184), _1774186)), _1774188) = hAPP(c_List_Ofoldl(_1774182, _1774184, hAPP(c_COMBC(_1774184, _1774182, _1774182), hAPP(hAPP(c_COMBB(_1774182, tc_fun(_1774182, _1774182), _1774184), c_Lattices_Osemilattice__sup__class_Osup(_1774182)), _1774188)), c_Orderings_Obot__class_Obot(_1774182)), _1774186))], (49408 ^ _780461) ^ [_1774353, _1774355, _1774357, _1774359] : [class_Complete__Lattice_Ocomplete__lattice(_1774353), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1774355, _1774353), hAPP(c_List_Oset(_1774355), _1774357)), _1774359) = hAPP(c_List_Ofoldl(_1774353, _1774355, hAPP(c_COMBC(_1774355, _1774353, _1774353), hAPP(hAPP(c_COMBB(_1774353, tc_fun(_1774353, _1774353), _1774355), c_Lattices_Osemilattice__inf__class_Oinf(_1774353)), _1774359)), c_Orderings_Otop__class_Otop(_1774353)), _1774357))], (49414 ^ _780461) ^ [_1774524, _1774526, _1774528, _1774530, _1774532] : [hBOOL(hAPP(hAPP(c_member(_1774524), _1774526), hAPP(c_List_Oset(_1774524), _1774528))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774530), hAPP(_1774532, _1774526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774530), c_List_Olist_Olist__size(_1774524, _1774532, _1774528))))], (49424 ^ _780461) ^ [_1774723, _1774725, _1774727, _1774729, _1774731] : [hBOOL(hAPP(hAPP(c_member(_1774723), _1774725), hAPP(c_List_Oset(_1774723), _1774727))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1774729), hAPP(_1774731, _1774725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1774729), c_List_Olist_Olist__size(_1774723, _1774731, _1774727))))], (49434 ^ _780461) ^ [_1774922, _1774924, _1774926, _1774928, _1774930] : [-(c_Map_Omap__upds(_1774922, _1774924, _1774926, _1774928, _1774930) = hAPP(c_List_Ofoldl(tc_fun(_1774922, tc_Option_Ooption(_1774924)), tc_prod(_1774922, _1774924), hAPP(hAPP(c_COMBB(tc_fun(_1774922, tc_fun(_1774924, tc_fun(_1774922, tc_Option_Ooption(_1774924)))), tc_fun(tc_prod(_1774922, _1774924), tc_fun(_1774922, tc_Option_Ooption(_1774924))), tc_fun(_1774922, tc_Option_Ooption(_1774924))), c_Product__Type_Oprod_Oprod__case(_1774922, _1774924, tc_fun(_1774922, tc_Option_Ooption(_1774924)))), hAPP(hAPP(c_COMBC(tc_fun(_1774922, tc_Option_Ooption(_1774924)), tc_fun(_1774924, tc_Option_Ooption(_1774924)), tc_fun(_1774922, tc_fun(_1774924, tc_fun(_1774922, tc_Option_Ooption(_1774924))))), hAPP(hAPP(c_COMBB(tc_fun(_1774922, tc_fun(tc_fun(_1774924, tc_Option_Ooption(_1774924)), tc_fun(_1774924, tc_fun(_1774922, tc_Option_Ooption(_1774924))))), tc_fun(tc_fun(_1774924, tc_Option_Ooption(_1774924)), tc_fun(_1774922, tc_fun(_1774924, tc_fun(_1774922, tc_Option_Ooption(_1774924))))), tc_fun(_1774922, tc_Option_Ooption(_1774924))), c_COMBC(_1774922, tc_fun(_1774924, tc_Option_Ooption(_1774924)), tc_fun(_1774924, tc_fun(_1774922, tc_Option_Ooption(_1774924))))), hAPP(hAPP(c_COMBB(tc_fun(_1774922, tc_fun(tc_Option_Ooption(_1774924), tc_fun(_1774922, tc_Option_Ooption(_1774924)))), tc_fun(_1774922, tc_fun(tc_fun(_1774924, tc_Option_Ooption(_1774924)), tc_fun(_1774924, tc_fun(_1774922, tc_Option_Ooption(_1774924))))), tc_fun(_1774922, tc_Option_Ooption(_1774924))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1774924), tc_fun(_1774922, tc_Option_Ooption(_1774924))), tc_fun(tc_fun(_1774924, tc_Option_Ooption(_1774924)), tc_fun(_1774924, tc_fun(_1774922, tc_Option_Ooption(_1774924)))), _1774922), c_COMBB(tc_Option_Ooption(_1774924), tc_fun(_1774922, tc_Option_Ooption(_1774924)), _1774924))), c_Fun_Ofun__upd(_1774922, tc_Option_Ooption(_1774924))))), c_Option_Ooption_OSome(_1774924))), _1774926), hAPP(hAPP(c_List_Ozip(_1774922, _1774924), _1774928), _1774930)))], (49436 ^ _780461) ^ [_1775229, _1775231] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1775229), hAPP(c_List_Oset(tc_Nat_Onat), _1775231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1775229), 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)), _1775231))))], (49442 ^ _780461) ^ [_1775338, _1775340, _1775342] : [-(c_List_Olist_Olist__size(_1775338, _1775340, _1775342) = 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(_1775338, tc_Nat_Onat), _1775340), _1775342))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775338)), _1775342)))], (49444 ^ _780461) ^ [_1775394, _1775396, _1775398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1775394, _1775394), tc_HOL_Obool)), _1775396), hAPP(hAPP(c_Product__Type_OSigma(_1775394, _1775394), _1775398), hAPP(c_COMBK(tc_fun(_1775394, tc_HOL_Obool), _1775394), _1775398)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1775394), tc_List_Olist(_1775394)), tc_HOL_Obool)), c_List_Olistrel(_1775394, _1775396)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1775394), tc_List_Olist(_1775394)), c_List_Olists(_1775394, _1775398)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1775394), tc_HOL_Obool), tc_List_Olist(_1775394)), c_List_Olists(_1775394, _1775398))))))], (49450 ^ _780461) ^ [_1775639, _1775641, _1775643] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1775639)), _1775641), c_List_Olists(_1775639, c_Wellfounded_Oacc(_1775639, _1775643)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1775639)), _1775641), c_Wellfounded_Oacc(tc_List_Olist(_1775639), c_List_Olistrel1(_1775639, _1775643)))))], (49456 ^ _780461) ^ [_1775782, _1775784] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1775782)), c_List_Olist_ONil(_1775782)), c_List_Olists(_1775782, _1775784))))], (49458 ^ _780461) ^ [_1775821, _1775823, _1775825] : [c_Relation_Orefl__on(_1775821, _1775823, _1775825), -(c_Relation_Orefl__on(tc_List_Olist(_1775821), c_List_Olists(_1775821, _1775823), c_List_Olistrel(_1775821, _1775825)))], (49464 ^ _780461) ^ [_1775920, _1775922, _1775924] : [c_Equiv__Relations_Oequiv(_1775920, _1775922, _1775924), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1775920), c_List_Olists(_1775920, _1775922), c_List_Olistrel(_1775920, _1775924)))], (49470 ^ _780461) ^ [_1776019, _1776021, _1776023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1776019, tc_HOL_Obool)), _1776021), _1776023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1776019), tc_HOL_Obool)), c_List_Olists(_1776019, _1776021)), c_List_Olists(_1776019, _1776023))))], (49476 ^ _780461) ^ [_1776154] : [-(c_List_Olists(_1776154, c_Orderings_Otop__class_Otop(tc_fun(_1776154, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1776154), tc_HOL_Obool)))], (49478 ^ _780461) ^ [_1776213, _1776215, _1776217, _1776219] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776213)), hAPP(hAPP(c_List_Oappend(_1776213), _1776215), _1776217)), c_List_Olists(_1776213, _1776219))), 49481 ^ _780461 : [(49482 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776213)), _1776215), c_List_Olists(_1776213, _1776219))))], (49484 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776213)), _1776217), c_List_Olists(_1776213, _1776219))))]]], (49486 ^ _780461) ^ [_1776404, _1776406, _1776408, _1776410] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776404)), hAPP(hAPP(c_List_Oappend(_1776404), _1776406), _1776408)), c_List_Olists(_1776404, _1776410)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776404)), _1776406), c_List_Olists(_1776404, _1776410))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776404)), _1776408), c_List_Olists(_1776404, _1776410)))], (49496 ^ _780461) ^ [_1776652, _1776654, _1776656, _1776658] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776652)), hAPP(hAPP(c_List_Olist_OCons(_1776652), _1776654), _1776656)), c_List_Olists(_1776652, _1776658))), 49499 ^ _780461 : [(49500 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776652), _1776654), _1776658)))], (49502 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776652)), _1776656), c_List_Olists(_1776652, _1776658))))]]], (49504 ^ _780461) ^ [_1776833, _1776835, _1776837, _1776839] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776833)), hAPP(hAPP(c_List_Olist_OCons(_1776833), _1776835), _1776837)), c_List_Olists(_1776833, _1776839)))), hBOOL(hAPP(hAPP(c_member(_1776833), _1776835), _1776839)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1776833)), _1776837), c_List_Olists(_1776833, _1776839)))], (49524 ^ _780461) ^ [_1777295, _1777297, _1777299] : [49526 ^ _780461 : [(49527 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777295), 49525 ^ [_1777295, _1777297, _1777299]), hAPP(c_List_Oset(_1777295), _1777297))))], (49529 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1777295), 49525 ^ [_1777295, _1777297, _1777299]), _1777299))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777295)), _1777297), c_List_Olists(_1777295, _1777299))))], (49514 ^ _780461) ^ [_1777068, _1777070, _1777072] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777068)), _1777070), c_List_Olists(_1777068, _1777072))), 49517 ^ _780461 : [(49518 ^ _780461) ^ [_1777176] : [hBOOL(hAPP(hAPP(c_member(_1777068), _1777176), hAPP(c_List_Oset(_1777068), _1777070))), -(hBOOL(hAPP(hAPP(c_member(_1777068), _1777176), _1777072)))]]], (49533 ^ _780461) ^ [_1777515, _1777517] : [-(c_List_Olists(_1777515, _1777517) = hAPP(c_Set_OCollect(tc_List_Olist(_1777515)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1777515), tc_fun(_1777515, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1777515, tc_HOL_Obool), tc_fun(tc_fun(_1777515, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1777515)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1777515, tc_HOL_Obool))), c_List_Oset(_1777515))), _1777517)))], (49535 ^ _780461) ^ [_1777593] : [-(c_List_Olists(_1777593, c_Orderings_Obot__class_Obot(tc_fun(_1777593, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1777593)), c_List_Olist_ONil(_1777593)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1777593), tc_HOL_Obool))))], (49537 ^ _780461) ^ [_1777643, _1777645, _1777647] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777643)), _1777645), c_Wellfounded_Oacc(tc_List_Olist(_1777643), c_List_Olistrel1(_1777643, _1777647)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777643)), _1777645), c_List_Olists(_1777643, c_Wellfounded_Oacc(_1777643, _1777647)))))], (49543 ^ _780461) ^ [_1777786, _1777788, _1777790, _1777792] : [49544 ^ _780461 : [(49545 ^ _780461) ^ [_1777883, _1777885] : [_1777786 = hAPP(hAPP(c_List_Olist_OCons(_1777788), _1777885), _1777883)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1777788), tc_List_Olist(_1777788))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1777788), tc_List_Olist(_1777788)), _1777790), hAPP(hAPP(c_List_Oappend(_1777788), _1777790), _1777786))), c_List_Olexord(_1777788, _1777792))))], (49549 ^ _780461) ^ [_1778000, _1778002, _1778004] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1778000), tc_List_Olist(_1778000))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1778000), tc_List_Olist(_1778000)), c_List_Olist_ONil(_1778000)), _1778002)), c_List_Olexord(_1778000, _1778004))), -(_1778002 = hAPP(hAPP(c_List_Olist_OCons(_1778000), 49552 ^ [_1778000, _1778002, _1778004]), 49553 ^ [_1778000, _1778002, _1778004]))], (49557 ^ _780461) ^ [_1778183, _1778185, _1778187] : [49558 ^ _780461 : [(49559 ^ _780461) ^ [_1778272, _1778274] : [_1778185 = hAPP(hAPP(c_List_Olist_OCons(_1778183), _1778274), _1778272)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1778183), tc_List_Olist(_1778183))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1778183), tc_List_Olist(_1778183)), c_List_Olist_ONil(_1778183)), _1778185)), c_List_Olexord(_1778183, _1778187))))], (49563 ^ _780461) ^ [_1778366, _1778368, _1778370, _1778372] : [-(_1778366 = c_List_Olist_ONil(_1778368)), 49566 ^ _780461 : [(49567 ^ _780461) ^ [] : [_1778370 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778368)), _1778366)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1778368, hAPP(hAPP(c_List_Olist__update(_1778368, _1778366), _1778370), _1778372)) = _1778372)], (49573 ^ _780461) ^ [] : [-(_1778370 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1778368)), _1778366)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1778368, hAPP(hAPP(c_List_Olist__update(_1778368, _1778366), _1778370), _1778372)) = c_List_Olast(_1778368, _1778366))]]], (49579 ^ _780461) ^ [_1778656, _1778658, _1778660, _1778662, _1778664] : [class_Groups_Omonoid__add(_1778656), class_Groups_Oordered__ab__semigroup__add(_1778656), 49589 ^ _780461 : [(49590 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778658), 49588 ^ [_1778656, _1778658, _1778660, _1778662, _1778664]), hAPP(c_List_Oset(_1778658), _1778660))))], (49592 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1778656), hAPP(_1778662, 49588 ^ [_1778656, _1778658, _1778660, _1778662, _1778664])), hAPP(_1778664, 49588 ^ [_1778656, _1778658, _1778660, _1778662, _1778664])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1778656), hAPP(c_List_Omonoid__add__class_Olistsum(_1778656), hAPP(hAPP(c_List_Omap(_1778658, _1778656), _1778662), _1778660))), hAPP(c_List_Omonoid__add__class_Olistsum(_1778656), hAPP(hAPP(c_List_Omap(_1778658, _1778656), _1778664), _1778660)))))], (49596 ^ _780461) ^ [_1779092, _1779094, _1779096] : [_1779092 = c_List_Olist_ONil(_1779094), -(c_List_Olast(_1779094, hAPP(hAPP(c_List_Olist_OCons(_1779094), _1779096), _1779092)) = _1779096)], (49602 ^ _780461) ^ [_1779191, _1779193, _1779195] : [-(_1779191 = c_List_Olist_ONil(_1779193)), -(c_List_Olast(_1779193, hAPP(hAPP(c_List_Olist_OCons(_1779193), _1779195), _1779191)) = c_List_Olast(_1779193, _1779191))], (49608 ^ _780461) ^ [_1779243, _1779245, _1779247] : [-(_1779243 = c_List_Olist_ONil(_1779245)), -(c_List_Olast(_1779245, hAPP(hAPP(c_List_Olist_OCons(_1779245), _1779247), _1779243)) = c_List_Olast(_1779245, _1779243))], (49614 ^ _780461) ^ [_1779297, _1779299, _1779301] : [_1779297 = c_List_Olist_ONil(_1779299), -(c_List_Olast(_1779299, hAPP(hAPP(c_List_Olist_OCons(_1779299), _1779301), _1779297)) = _1779301)], (49620 ^ _780461) ^ [_1779414, _1779416, _1779418] : [_1779414 = c_List_Olist_ONil(_1779416), -(c_List_Olast(_1779416, hAPP(hAPP(c_List_Oappend(_1779416), _1779418), _1779414)) = c_List_Olast(_1779416, _1779418))], (49626 ^ _780461) ^ [_1779519, _1779521, _1779523] : [-(_1779519 = c_List_Olist_ONil(_1779521)), -(c_List_Olast(_1779521, hAPP(hAPP(c_List_Oappend(_1779521), _1779523), _1779519)) = c_List_Olast(_1779521, _1779519))], (49632 ^ _780461) ^ [_1779571, _1779573, _1779575] : [-(_1779571 = c_List_Olist_ONil(_1779573)), -(c_List_Olast(_1779573, hAPP(hAPP(c_List_Oappend(_1779573), _1779575), _1779571)) = c_List_Olast(_1779573, _1779571))], (49638 ^ _780461) ^ [_1779625, _1779627, _1779629] : [_1779625 = c_List_Olist_ONil(_1779627), -(c_List_Olast(_1779627, hAPP(hAPP(c_List_Oappend(_1779627), _1779629), _1779625)) = c_List_Olast(_1779627, _1779629))], (49644 ^ _780461) ^ [_1779732, _1779734, _1779736, _1779738] : [-(_1779732 = c_List_Olist_ONil(_1779734)), -(c_List_Olast(_1779736, hAPP(hAPP(c_List_Omap(_1779734, _1779736), _1779738), _1779732)) = hAPP(_1779738, c_List_Olast(_1779734, _1779732)))], (49650 ^ _780461) ^ [_1779788, _1779790] : [-(_1779788 = c_List_Olist_ONil(_1779790)), -(hBOOL(hAPP(hAPP(c_member(_1779790), c_List_Olast(_1779790, _1779788)), hAPP(c_List_Oset(_1779790), _1779788))))], (49656 ^ _780461) ^ [_1779841, _1779843, _1779845] : [-(c_List_Olast(_1779841, hAPP(hAPP(c_List_Oappend(_1779841), _1779843), hAPP(hAPP(c_List_Olist_OCons(_1779841), _1779845), c_List_Olist_ONil(_1779841)))) = _1779845)], (49658 ^ _780461) ^ [_1779889, _1779891, _1779893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1779889), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779891)), _1779893))), -(c_List_Olast(_1779891, hAPP(hAPP(c_List_Odrop(_1779891), _1779889), _1779893)) = c_List_Olast(_1779891, _1779893))], (49664 ^ _780461) ^ [_1780016, _1780018] : [-(_1780016 = c_List_Olist_ONil(_1780018)), -(c_List_Olast(_1780018, _1780016) = hAPP(hAPP(c_List_Onth(_1780018), _1780016), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780018)), _1780016)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (49670 ^ _780461) ^ [_1780077, _1780079, _1780081] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780077, _1780077)), hAPP(hAPP(c_Product__Type_OPair(_1780077, _1780077), 49671 ^ [_1780077, _1780079, _1780081]), 49671 ^ [_1780077, _1780079, _1780081])), _1780079))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1780077), tc_List_Olist(_1780077))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780077), tc_List_Olist(_1780077)), _1780081), _1780081)), c_List_Olexord(_1780077, _1780079)))], (49677 ^ _780461) ^ [_1780252, _1780254, _1780256, _1780258] : [49680 ^ _780461 : [(49681 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780252, _1780252)), hAPP(hAPP(c_Product__Type_OPair(_1780252, _1780252), 49678 ^ [_1780252, _1780254, _1780256, _1780258]), 49679 ^ [_1780252, _1780254, _1780256, _1780258])), _1780254))], (49683 ^ _780461) ^ [] : [49678 ^ [_1780252, _1780254, _1780256, _1780258] = 49679 ^ [_1780252, _1780254, _1780256, _1780258]], (49685 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780252, _1780252)), hAPP(hAPP(c_Product__Type_OPair(_1780252, _1780252), 49679 ^ [_1780252, _1780254, _1780256, _1780258]), 49678 ^ [_1780252, _1780254, _1780256, _1780258])), _1780254))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1780252), tc_List_Olist(_1780252))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780252), tc_List_Olist(_1780252)), _1780256), _1780258)), c_List_Olexord(_1780252, _1780254)))), -(_1780256 = _1780258), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1780252), tc_List_Olist(_1780252))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1780252), tc_List_Olist(_1780252)), _1780258), _1780256)), c_List_Olexord(_1780252, _1780254))))], (49697 ^ _780461) ^ [_1780817, _1780819, _1780821] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1780817)), _1780819), c_List_Olists(_1780817, _1780821))), -(_1780819 = c_List_Olist_ONil(_1780817)), 49706 ^ _780461 : [(49707 ^ _780461) ^ [] : [-(_1780819 = hAPP(hAPP(c_List_Olist_OCons(_1780817), 49704 ^ [_1780817, _1780819, _1780821]), 49705 ^ [_1780817, _1780819, _1780821]))], (49709 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780817), 49704 ^ [_1780817, _1780819, _1780821]), _1780821)))], (49711 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1780817)), 49705 ^ [_1780817, _1780819, _1780821]), c_List_Olists(_1780817, _1780821))))]]], (49713 ^ _780461) ^ [_1781100, _1781102, _1781104] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1781100)), _1781102), c_List_Olists(_1781100, _1781104)))), 49714 ^ _780461 : [(49715 ^ _780461) ^ [] : [_1781102 = c_List_Olist_ONil(_1781100)], (49717 ^ _780461) ^ [_1781228, _1781230] : [_1781102 = hAPP(hAPP(c_List_Olist_OCons(_1781100), _1781230), _1781228), hBOOL(hAPP(hAPP(c_member(_1781100), _1781230), _1781104)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1781100)), _1781228), c_List_Olists(_1781100, _1781104)))]]], (49729 ^ _780461) ^ [_1781466, _1781468, _1781470, _1781472] : [49731 ^ _780461 : [(49732 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781466), 49730 ^ [_1781466, _1781468, _1781470, _1781472]), hAPP(c_List_Oset(_1781466), _1781468))))], (49734 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1781470, 49730 ^ [_1781466, _1781468, _1781470, _1781472])), hAPP(_1781472, 49730 ^ [_1781466, _1781468, _1781470, _1781472])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1781466, _1781470, _1781468)), c_List_Olist_Olist__size(_1781466, _1781472, _1781468))))], (49738 ^ _780461) ^ [_1781716, _1781718, _1781720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1781716), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781718)), _1781720))), -(c_List_Obutlast(_1781718, hAPP(hAPP(c_List_Otake(_1781718), _1781716), _1781720)) = hAPP(hAPP(c_List_Otake(_1781718), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1781716), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1781720))], (49744 ^ _780461) ^ [_1781869, _1781871, _1781873, _1781875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1781869), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781871)), _1781873))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1781869), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781871)), _1781875))), 49754 ^ _780461 : [(49755 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49753 ^ [_1781869, _1781871, _1781873, _1781875]), _1781869)))], (49757 ^ _780461) ^ [] : [hAPP(hAPP(c_List_Onth(_1781871), _1781873), 49753 ^ [_1781869, _1781871, _1781873, _1781875]) = hAPP(hAPP(c_List_Onth(_1781871), _1781875), 49753 ^ [_1781869, _1781871, _1781873, _1781875])]], -(hAPP(hAPP(c_List_Otake(_1781871), _1781869), _1781873) = hAPP(hAPP(c_List_Otake(_1781871), _1781869), _1781875))], (49761 ^ _780461) ^ [_1782286, _1782288, _1782290, _1782292] : [-(hAPP(hAPP(c_List_Omap(_1782286, _1782288), _1782290), c_List_Obutlast(_1782286, _1782292)) = c_List_Obutlast(_1782288, hAPP(hAPP(c_List_Omap(_1782286, _1782288), _1782290), _1782292)))], (49763 ^ _780461) ^ [_1782351, _1782353, _1782355] : [_1782351 = c_List_Olist_ONil(_1782353), -(c_List_Obutlast(_1782353, hAPP(hAPP(c_List_Oappend(_1782353), _1782355), _1782351)) = c_List_Obutlast(_1782353, _1782355))], (49769 ^ _780461) ^ [_1782456, _1782458, _1782460] : [-(_1782456 = c_List_Olist_ONil(_1782458)), -(c_List_Obutlast(_1782458, hAPP(hAPP(c_List_Oappend(_1782458), _1782460), _1782456)) = hAPP(hAPP(c_List_Oappend(_1782458), _1782460), c_List_Obutlast(_1782458, _1782456)))], (49775 ^ _780461) ^ [_1782532, _1782534, _1782536] : [_1782532 = c_List_Olist_ONil(_1782534), -(c_List_Obutlast(_1782534, hAPP(hAPP(c_List_Olist_OCons(_1782534), _1782536), _1782532)) = c_List_Olist_ONil(_1782534))], (49781 ^ _780461) ^ [_1782635, _1782637, _1782639] : [-(_1782635 = c_List_Olist_ONil(_1782637)), -(c_List_Obutlast(_1782637, hAPP(hAPP(c_List_Olist_OCons(_1782637), _1782639), _1782635)) = hAPP(hAPP(c_List_Olist_OCons(_1782637), _1782639), c_List_Obutlast(_1782637, _1782635)))], (49787 ^ _780461) ^ [_1782699, _1782701, _1782703] : [hBOOL(hAPP(hAPP(c_member(_1782699), _1782701), hAPP(c_List_Oset(_1782699), c_List_Obutlast(_1782699, _1782703)))), -(hBOOL(hAPP(hAPP(c_member(_1782699), _1782701), hAPP(c_List_Oset(_1782699), _1782703))))], (49793 ^ _780461) ^ [_1782831, _1782833] : [-(_1782831 = c_List_Olist_ONil(_1782833)), hBOOL(hAPP(c_List_Odistinct(_1782833), _1782831)), -(hBOOL(hAPP(c_List_Odistinct(_1782833), c_List_Obutlast(_1782833, _1782831))))], (49803 ^ _780461) ^ [_1782982] : [-(c_List_Obutlast(_1782982, c_List_Olist_ONil(_1782982)) = c_List_Olist_ONil(_1782982))], (49805 ^ _780461) ^ [_1783012, _1783014, _1783016] : [-(c_List_Obutlast(_1783012, hAPP(hAPP(c_List_Odrop(_1783012), _1783014), _1783016)) = hAPP(hAPP(c_List_Odrop(_1783012), _1783014), c_List_Obutlast(_1783012, _1783016)))], (49807 ^ _780461) ^ [_1783061, _1783063, _1783065] : [-(hAPP(hAPP(c_List_Odrop(_1783061), _1783063), c_List_Obutlast(_1783061, _1783065)) = c_List_Obutlast(_1783061, hAPP(hAPP(c_List_Odrop(_1783061), _1783063), _1783065)))], (49809 ^ _780461) ^ [_1783110, _1783112, _1783114, _1783116] : [49810 ^ _780461 : [(49811 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1783110), _1783112), hAPP(c_List_Oset(_1783110), c_List_Obutlast(_1783110, _1783114))))], (49813 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1783110), _1783112), hAPP(c_List_Oset(_1783110), c_List_Obutlast(_1783110, _1783116))))]], -(hBOOL(hAPP(hAPP(c_member(_1783110), _1783112), hAPP(c_List_Oset(_1783110), c_List_Obutlast(_1783110, hAPP(hAPP(c_List_Oappend(_1783110), _1783114), _1783116))))))], (49817 ^ _780461) ^ [_1783335, _1783337, _1783339] : [-(c_List_Obutlast(_1783335, hAPP(hAPP(c_List_Oappend(_1783335), _1783337), hAPP(hAPP(c_List_Olist_OCons(_1783335), _1783339), c_List_Olist_ONil(_1783335)))) = _1783337)], (49819 ^ _780461) ^ [_1783383, _1783385, _1783387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1783383), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783385)), _1783387))), -(hAPP(hAPP(c_List_Otake(_1783385), _1783383), c_List_Obutlast(_1783385, _1783387)) = hAPP(hAPP(c_List_Otake(_1783385), _1783383), _1783387))], (49825 ^ _780461) ^ [_1783524, _1783526] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783524)), c_List_Obutlast(_1783524, _1783526)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783524)), _1783526)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (49827 ^ _780461) ^ [_1783572, _1783574] : [-(c_List_Obutlast(_1783572, _1783574) = hAPP(hAPP(c_List_Otake(_1783572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783572)), _1783574)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1783574))], (49829 ^ _780461) ^ [_1783636, _1783638, _1783640, _1783642] : [_1783636 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783638)), _1783640)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1783638, hAPP(hAPP(c_List_Olist__update(_1783638, _1783640), _1783636), _1783642)) = c_List_Obutlast(_1783638, _1783640))], (49835 ^ _780461) ^ [_1783767, _1783769, _1783771, _1783773] : [-(_1783767 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783769)), _1783771)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1783769, hAPP(hAPP(c_List_Olist__update(_1783769, _1783771), _1783767), _1783773)) = hAPP(hAPP(c_List_Olist__update(_1783769, c_List_Obutlast(_1783769, _1783771)), _1783767), _1783773))], (49841 ^ _780461) ^ [_1783842, _1783844] : [-(_1783842 = c_List_Olist_ONil(_1783844)), -(hAPP(hAPP(c_List_Oappend(_1783844), c_List_Obutlast(_1783844, _1783842)), hAPP(hAPP(c_List_Olist_OCons(_1783844), c_List_Olast(_1783844, _1783842)), c_List_Olist_ONil(_1783844))) = _1783842)], (49847 ^ _780461) ^ [_1783925, _1783927, _1783929, _1783931] : [hAPP(hAPP(c_List_Oappend(_1783925), _1783927), hAPP(hAPP(c_List_Olist_OCons(_1783925), _1783929), c_List_Olist_ONil(_1783925))) = _1783931, 49850 ^ _780461 : [(49851 ^ _780461) ^ [] : [_1783931 = c_List_Olist_ONil(_1783925)], (49853 ^ _780461) ^ [] : [-(c_List_Obutlast(_1783925, _1783931) = _1783927)], (49855 ^ _780461) ^ [] : [-(c_List_Olast(_1783925, _1783931) = _1783929)]]], (49857 ^ _780461) ^ [_1784114, _1784116, _1784118, _1784120] : [-(hAPP(hAPP(c_List_Oappend(_1784114), _1784116), hAPP(hAPP(c_List_Olist_OCons(_1784114), _1784118), c_List_Olist_ONil(_1784114))) = _1784120), -(_1784120 = c_List_Olist_ONil(_1784114)), c_List_Obutlast(_1784114, _1784120) = _1784116, c_List_Olast(_1784114, _1784120) = _1784118], (49871 ^ _780461) ^ [_1784364, _1784366, _1784368, _1784370] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784364)), _1784366))), c_List_Ofoldr(tc_List_Olist(_1784368), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1784368)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1784368))), _1784370, 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(_1784364)), _1784366)), c_List_Ofoldr(tc_List_Olist(_1784368), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1784368)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1784368), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1784368)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1784368)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1784368), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1784368)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1784368), tc_List_Olist(_1784368), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1784368)))), _1784370), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (49873 ^ _780461) ^ [_1784533, _1784535, _1784537, _1784539, _1784541] : [c_List_Opartition(_1784533, _1784535, _1784537) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1784533), tc_List_Olist(_1784533)), _1784539), _1784541), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1784533, tc_HOL_Obool)), hAPP(c_List_Oset(_1784533), _1784539)), hAPP(c_List_Oset(_1784533), _1784541)) = hAPP(c_List_Oset(_1784533), _1784537))], (49879 ^ _780461) ^ [_1784702, _1784704, _1784706] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784702)), hAPP(c_List_Ofilter(_1784702, _1784704), _1784706))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784702)), _1784706))))], (49881 ^ _780461) ^ [_1784754, _1784756, _1784758] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1784754, tc_HOL_Obool)), hAPP(c_List_Oset(_1784754), hAPP(c_List_Ofilter(_1784754, _1784756), _1784758))), hAPP(c_List_Oset(_1784754), _1784758))))], (49883 ^ _780461) ^ [_1784807, _1784809] : [-(hAPP(c_List_Ofilter(_1784807, _1784809), c_List_Olist_ONil(_1784807)) = c_List_Olist_ONil(_1784807))], (49895 ^ _780461) ^ [_1785065, _1785067, _1785069] : [49897 ^ _780461 : [(49898 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785065), 49896 ^ [_1785065, _1785067, _1785069]), hAPP(c_List_Oset(_1785065), _1785069))))], (49900 ^ _780461) ^ [] : [-(hBOOL(hAPP(_1785067, 49896 ^ [_1785065, _1785067, _1785069])))]], -(hAPP(c_List_Ofilter(_1785065, _1785067), _1785069) = c_List_Olist_ONil(_1785065))], (49885 ^ _780461) ^ [_1784860, _1784862, _1784864] : [hAPP(c_List_Ofilter(_1784860, _1784862), _1784864) = c_List_Olist_ONil(_1784860), 49888 ^ _780461 : [(49889 ^ _780461) ^ [_1784957] : [hBOOL(hAPP(hAPP(c_member(_1784860), _1784957), hAPP(c_List_Oset(_1784860), _1784864))), hBOOL(hAPP(_1784862, _1784957))]]], (49914 ^ _780461) ^ [_1785400, _1785402, _1785404] : [49916 ^ _780461 : [(49917 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785400), 49915 ^ [_1785400, _1785402, _1785404]), hAPP(c_List_Oset(_1785400), _1785404))))], (49919 ^ _780461) ^ [] : [hBOOL(hAPP(_1785402, 49915 ^ [_1785400, _1785402, _1785404]))]], -(hAPP(c_List_Ofilter(_1785400, _1785402), _1785404) = _1785404)], (49904 ^ _780461) ^ [_1785200, _1785202, _1785204] : [hAPP(c_List_Ofilter(_1785200, _1785202), _1785204) = _1785204, 49907 ^ _780461 : [(49908 ^ _780461) ^ [_1785291] : [hBOOL(hAPP(hAPP(c_member(_1785200), _1785291), hAPP(c_List_Oset(_1785200), _1785204))), -(hBOOL(hAPP(_1785202, _1785291)))]]], (49923 ^ _780461) ^ [_1785592, _1785594, _1785596, _1785598, _1785600, _1785602] : [class_Orderings_Olinorder(_1785592), -(hBOOL(hAPP(_1785594, _1785596))), -(hAPP(c_List_Ofilter(_1785598, _1785594), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1785598, _1785592, _1785600), _1785596), _1785602)) = hAPP(c_List_Ofilter(_1785598, _1785594), _1785602))], (49933 ^ _780461) ^ [_1785738, _1785740, _1785742] : [hBOOL(hAPP(c_List_Odistinct(_1785738), _1785740)), -(hBOOL(hAPP(c_List_Odistinct(_1785738), hAPP(c_List_Ofilter(_1785738, _1785742), _1785740))))], (49939 ^ _780461) ^ [_1785845, _1785847, _1785849, _1785851] : [-(hAPP(c_List_Ofilter(_1785845, _1785847), c_List_Oremove1(_1785845, _1785849, _1785851)) = c_List_Oremove1(_1785845, _1785849, hAPP(c_List_Ofilter(_1785845, _1785847), _1785851)))], (49941 ^ _780461) ^ [_1785890, _1785892, _1785894, _1785896] : [-(hBOOL(hAPP(_1785890, _1785892))), -(c_List_Oremove1(_1785894, _1785892, hAPP(c_List_Ofilter(_1785894, _1785890), _1785896)) = hAPP(c_List_Ofilter(_1785894, _1785890), _1785896))], (49947 ^ _780461) ^ [_1785948, _1785950, _1785952, _1785954] : [-(hAPP(c_List_Ofilter(_1785948, _1785950), hAPP(c_List_Ofilter(_1785948, _1785952), _1785954)) = hAPP(c_List_Ofilter(_1785948, hAPP(hAPP(c_COMBS(_1785948, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1785948), c_fconj), _1785952)), _1785950)), _1785954))], (49949 ^ _780461) ^ [_1786015, _1786017, _1786019] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1786015), tc_List_Olist(_1786015)), c_List_Opartition(_1786015, _1786017, _1786019)) = hAPP(c_List_Ofilter(_1786015, _1786017), _1786019))], (49951 ^ _780461) ^ [_1786062, _1786064, _1786066] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786062)), hAPP(c_List_Ofilter(_1786062, _1786064), _1786066))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786062)), hAPP(c_List_Ofilter(_1786062, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1786062), c_fNot), _1786064)), _1786066))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786062)), _1786066))], (49953 ^ _780461) ^ [_1786153, _1786155, _1786157, _1786159] : [hBOOL(hAPP(_1786153, _1786155)), -(hAPP(c_List_Ofilter(_1786157, _1786153), hAPP(hAPP(c_List_Olist_OCons(_1786157), _1786155), _1786159)) = hAPP(hAPP(c_List_Olist_OCons(_1786157), _1786155), hAPP(c_List_Ofilter(_1786157, _1786153), _1786159)))], (49959 ^ _780461) ^ [_1786288, _1786290, _1786292, _1786294] : [-(hBOOL(hAPP(_1786288, _1786290))), -(hAPP(c_List_Ofilter(_1786292, _1786288), hAPP(hAPP(c_List_Olist_OCons(_1786292), _1786290), _1786294)) = hAPP(c_List_Ofilter(_1786292, _1786288), _1786294))], (49965 ^ _780461) ^ [_1786352, _1786354, _1786356, _1786358] : [-(hAPP(c_List_Ofilter(_1786352, _1786354), hAPP(hAPP(c_List_Oappend(_1786352), _1786356), _1786358)) = hAPP(hAPP(c_List_Oappend(_1786352), hAPP(c_List_Ofilter(_1786352, _1786354), _1786356)), hAPP(c_List_Ofilter(_1786352, _1786354), _1786358)))], (49967 ^ _780461) ^ [_1786415, _1786417, _1786419, _1786421, _1786423] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786415)), hAPP(c_List_Ofilter(_1786415, _1786417), hAPP(hAPP(c_List_Omap(_1786419, _1786415), _1786421), _1786423))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786419)), hAPP(c_List_Ofilter(_1786419, hAPP(c_Fun_Ocomp(_1786415, tc_HOL_Obool, _1786419, _1786417), _1786421)), _1786423)))], (49969 ^ _780461) ^ [_1786489, _1786491, _1786493] : [-(hAPP(c_List_Oset(_1786489), hAPP(c_List_Ofilter(_1786489, _1786491), _1786493)) = hAPP(c_Set_OCollect(_1786489), hAPP(hAPP(c_COMBS(_1786489, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1786489), c_fconj), hAPP(hAPP(c_COMBC(_1786489, tc_fun(_1786489, tc_HOL_Obool), tc_HOL_Obool), c_member(_1786489)), hAPP(c_List_Oset(_1786489), _1786493)))), _1786491)))], (49971 ^ _780461) ^ [_1786572, _1786574, _1786576] : [-(c_List_Opartition(_1786572, _1786574, _1786576) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1786572), tc_List_Olist(_1786572)), hAPP(c_List_Ofilter(_1786572, _1786574), _1786576)), hAPP(c_List_Ofilter(_1786572, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1786572, c_fNot), _1786574)), _1786576)))], (49973 ^ _780461) ^ [_1786636, _1786638, _1786640, _1786642, _1786644] : [-(hAPP(c_List_Ofilter(_1786636, _1786638), hAPP(hAPP(c_List_Omap(_1786640, _1786636), _1786642), _1786644)) = hAPP(hAPP(c_List_Omap(_1786640, _1786636), _1786642), hAPP(c_List_Ofilter(_1786640, hAPP(c_Fun_Ocomp(_1786636, tc_HOL_Obool, _1786640, _1786638), _1786642)), _1786644)))], (49975 ^ _780461) ^ [_1786705, _1786707, _1786709] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1786705), tc_List_Olist(_1786705)), c_List_Opartition(_1786705, _1786707, _1786709)) = hAPP(c_List_Ofilter(_1786705, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1786705, c_fNot), _1786707)), _1786709))], (49977 ^ _780461) ^ [_1786760, _1786762, _1786764, _1786766] : [hBOOL(hAPP(hAPP(c_member(_1786760), _1786762), hAPP(c_List_Oset(_1786760), _1786764))), -(hBOOL(hAPP(_1786766, _1786762))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786760)), hAPP(c_List_Ofilter(_1786760, _1786766), _1786764))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786760)), _1786764))))], (49987 ^ _780461) ^ [_1786934, _1786936, _1786938] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1786934, tc_HOL_Obool)), hAPP(c_List_Oset(_1786934), _1786936)), hAPP(hAPP(c_Set_Oinsert(_1786934), _1786938), c_Orderings_Obot__class_Obot(tc_fun(_1786934, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1786934), hAPP(c_List_Ofilter(_1786934, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1786934), c_fNot), hAPP(hAPP(c_COMBC(_1786934, _1786934, tc_HOL_Obool), c_fequal), _1786938))), _1786936)))], (49989 ^ _780461) ^ [_1787021, _1787023, _1787025, _1787027, _1787029] : [c_List_Opartition(_1787021, _1787023, _1787025) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1787021), tc_List_Olist(_1787021)), _1787027), _1787029), 49992 ^ _780461 : [(49993 ^ _780461) ^ [_1787174] : [hBOOL(hAPP(hAPP(c_member(_1787021), _1787174), hAPP(c_List_Oset(_1787021), _1787027))), -(hBOOL(hAPP(_1787023, _1787174)))], (49999 ^ _780461) ^ [_1787283] : [hBOOL(hAPP(hAPP(c_member(_1787021), _1787283), hAPP(c_List_Oset(_1787021), _1787029))), hBOOL(hAPP(_1787023, _1787283))]]], (50005 ^ _780461) ^ [_1787403, _1787405] : [-(c_List_Opartition(_1787403, _1787405, c_List_Olist_ONil(_1787403)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1787403), tc_List_Olist(_1787403)), c_List_Olist_ONil(_1787403)), c_List_Olist_ONil(_1787403)))], (50007 ^ _780461) ^ [_1787451, _1787453, _1787455] : [hBOOL(hAPP(c_List_Odistinct(_1787451), _1787453)), -(hAPP(c_List_Ofilter(_1787451, hAPP(hAPP(c_COMBC(_1787451, tc_fun(_1787451, tc_HOL_Obool), tc_HOL_Obool), c_member(_1787451)), hAPP(c_List_Oset(_1787451), c_List_Osublist(_1787451, _1787453, _1787455)))), _1787453) = c_List_Osublist(_1787451, _1787453, _1787455))], (50013 ^ _780461) ^ [_1787606, _1787608, _1787610, _1787612] : [-(c_List_Opartition(_1787606, _1787608, hAPP(hAPP(c_List_Olist_OCons(_1787606), _1787610), _1787612)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1787606), tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1787606), tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1787606), tc_fun(tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)))), tc_fun(tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)))), tc_List_Olist(_1787606)), c_COMBS(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), tc_fun(tc_List_Olist(_1787606), tc_fun(tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)))), tc_List_Olist(_1787606)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)), tc_fun(tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), tc_List_Olist(_1787606)), hAPP(c_If(tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), hAPP(_1787608, _1787610)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1787606), tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), tc_List_Olist(_1787606)), c_Product__Type_OPair(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), hAPP(c_List_Olist_OCons(_1787606), _1787610))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1787606), tc_fun(tc_List_Olist(_1787606), tc_List_Olist(_1787606)), tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606))), tc_fun(tc_fun(tc_List_Olist(_1787606), tc_List_Olist(_1787606)), tc_fun(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)))), tc_List_Olist(_1787606)), c_COMBB(tc_List_Olist(_1787606), tc_prod(tc_List_Olist(_1787606), tc_List_Olist(_1787606)), tc_List_Olist(_1787606))), c_Product__Type_OPair(tc_List_Olist(_1787606), tc_List_Olist(_1787606)))), hAPP(c_List_Olist_OCons(_1787606), _1787610)))), c_List_Opartition(_1787606, _1787608, _1787612)))], (50015 ^ _780461) ^ [_1788025, _1788027, _1788029] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1788025)), hAPP(c_List_Ofilter(_1788025, _1788027), _1788029)) = 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(_1788025)), _1788029)))), hAPP(hAPP(c_COMBB(_1788025, tc_HOL_Obool, tc_Nat_Onat), _1788027), hAPP(c_List_Onth(_1788025), _1788029))))))], (50017 ^ _780461) ^ [_1788105, _1788107, _1788109, _1788111] : [-(c_List_Omap__filter(_1788105, _1788107, _1788109, _1788111) = hAPP(hAPP(c_List_Omap(_1788105, _1788107), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1788107), _1788107, _1788105, c_Option_Othe(_1788107)), _1788109)), hAPP(c_List_Ofilter(_1788105, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1788105), c_fNot), hAPP(hAPP(c_COMBC(_1788105, tc_Option_Ooption(_1788107), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1788107), tc_fun(tc_Option_Ooption(_1788107), tc_HOL_Obool), _1788105), c_fequal), _1788109)), c_Option_Ooption_ONone(_1788107)))), _1788111)))], (50019 ^ _780461) ^ [_1788207, _1788209] : [-(c_List_Ofoldr(tc_List_Olist(_1788207), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1788207)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1788207))), c_List_Otranspose(_1788207, _1788209), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1788207))), hAPP(c_List_Ofilter(tc_List_Olist(_1788207), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1788207)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1788207), tc_List_Olist(_1788207), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1788207)))), _1788209)))], (50021 ^ _780461) ^ [_1788304, _1788306, _1788308, _1788310, _1788312, _1788314] : [hAPP(c_Map_Omap__of(_1788304, _1788306, _1788308), _1788310) = hAPP(c_Option_Ooption_OSome(_1788306), _1788312), hBOOL(hAPP(hAPP(_1788314, _1788310), _1788312)), -(hAPP(c_Map_Omap__of(_1788304, _1788306, hAPP(c_List_Ofilter(tc_prod(_1788304, _1788306), hAPP(c_Product__Type_Oprod_Oprod__case(_1788304, _1788306, tc_HOL_Obool), _1788314)), _1788308)), _1788310) = hAPP(c_Option_Ooption_OSome(_1788306), _1788312))], (50031 ^ _780461) ^ [_1788539, _1788541, _1788543, _1788545] : [-(c_List_Otranspose(_1788539, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1788541), tc_List_Olist(_1788539)), hAPP(c_List_Omap(_1788541, _1788539), _1788543)), _1788545)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1788541), tc_List_Olist(_1788539)), hAPP(c_List_Omap(_1788541, _1788539), _1788543)), c_List_Otranspose(_1788541, _1788545)))], (50033 ^ _780461) ^ [_1788612, _1788614] : [-(c_List_Otranspose(_1788612, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1788612)), c_List_Olist_ONil(_1788612)), _1788614)) = c_List_Otranspose(_1788612, _1788614))], (50045 ^ _780461) ^ [_1788880, _1788882] : [50047 ^ _780461 : [(50048 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1788880)), 50046 ^ [_1788880, _1788882]), hAPP(c_List_Oset(tc_List_Olist(_1788880)), _1788882))))], (50050 ^ _780461) ^ [] : [50046 ^ [_1788880, _1788882] = c_List_Olist_ONil(_1788880)]], -(c_List_Otranspose(_1788880, _1788882) = c_List_Olist_ONil(tc_List_Olist(_1788880)))], (50035 ^ _780461) ^ [_1788670, _1788672] : [c_List_Otranspose(_1788670, _1788672) = c_List_Olist_ONil(tc_List_Olist(_1788670)), 50038 ^ _780461 : [(50039 ^ _780461) ^ [_1788765] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1788670)), _1788765), hAPP(c_List_Oset(tc_List_Olist(_1788670)), _1788672))), -(_1788765 = c_List_Olist_ONil(_1788670))]]], (50054 ^ _780461) ^ [_1789075, _1789077, _1789079] : [-(c_List_Omap__filter(_1789075, _1789077, _1789079, c_List_Olist_ONil(_1789075)) = c_List_Olist_ONil(_1789077))], (50056 ^ _780461) ^ [_1789111] : [-(c_List_Otranspose(_1789111, c_List_Olist_ONil(tc_List_Olist(_1789111))) = c_List_Olist_ONil(tc_List_Olist(_1789111)))], (50058 ^ _780461) ^ [_1789145, _1789147, _1789149, _1789151, _1789153] : [-(c_List_Omap__filter(_1789145, _1789147, _1789149, hAPP(hAPP(c_List_Olist_OCons(_1789145), _1789151), _1789153)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1789147), _1789147, c_List_Omap__filter(_1789145, _1789147, _1789149, _1789153), hAPP(hAPP(c_COMBC(_1789147, tc_List_Olist(_1789147), tc_List_Olist(_1789147)), c_List_Olist_OCons(_1789147)), c_List_Omap__filter(_1789145, _1789147, _1789149, _1789153))), hAPP(_1789149, _1789151)))], (50060 ^ _780461) ^ [_1789228, _1789230, _1789232, _1789234] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1789228, tc_Nat_Onat), _1789228), c_Product__Type_Ofst(_1789228, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1789228, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1789228, tc_Nat_Onat)), _1789230), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1789228, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1789228, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1789228, tc_Nat_Onat), _1789232), _1789234))) = hAPP(hAPP(c_List_Omap(tc_prod(_1789228, tc_Nat_Onat), _1789228), c_Product__Type_Ofst(_1789228, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1789228, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1789228, tc_Nat_Onat)), _1789230), c_Product__Type_Osnd(_1789228, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1789228, tc_Nat_Onat), _1789232), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1789234)))))], (50062 ^ _780461) ^ [_1789371, _1789373] : [-(c_Random_Oselect__weight(_1789371, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1789371), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1789371, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1789371, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1789371)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1789373)) = c_Random_Oselect__weight(_1789371, _1789373))], (50064 ^ _780461) ^ [_1789434, _1789436] : [-(c_Random_Opick(_1789434, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1789434), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1789434, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1789434, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1789434)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1789436)) = c_Random_Opick(_1789434, _1789436))], (50066 ^ _780461) ^ [_1789497, _1789499, _1789501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1789497), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1789499))), c_List_Otranspose(_1789499, _1789501)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1789499)), c_List_Otranspose(_1789499, _1789501)), _1789497) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1789499), _1789499), hAPP(hAPP(c_COMBC(tc_List_Olist(_1789499), tc_Nat_Onat, _1789499), c_List_Onth(_1789499)), _1789497)), hAPP(c_List_Ofilter(tc_List_Olist(_1789499), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1789499)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1789497)), c_Nat_Osize__class_Osize(tc_List_Olist(_1789499)))), _1789501)))], (50072 ^ _780461) ^ [_1789740, _1789742] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1789740))), c_List_Otranspose(_1789740, _1789742)) = c_List_Ofoldr(tc_List_Olist(_1789740), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1789740)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1789740))), _1789742, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50074 ^ _780461) ^ [_1789801, _1789803, _1789805, _1789807, _1789809] : [-(hAPP(hAPP(c_List_Omap(_1789801, _1789803), _1789805), hAPP(c_List_Ofilter(_1789801, _1789807), _1789809)) = c_List_Omap__filter(_1789801, _1789803, hAPP(hAPP(c_COMBC(_1789801, tc_Option_Ooption(_1789803), tc_Option_Ooption(_1789803)), hAPP(hAPP(c_COMBS(_1789801, tc_Option_Ooption(_1789803), tc_fun(tc_Option_Ooption(_1789803), tc_Option_Ooption(_1789803))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1789803), tc_fun(tc_Option_Ooption(_1789803), tc_Option_Ooption(_1789803))), _1789801), c_If(tc_Option_Ooption(_1789803))), _1789807)), hAPP(hAPP(c_COMBB(_1789803, tc_Option_Ooption(_1789803), _1789801), c_Option_Ooption_OSome(_1789803)), _1789805))), c_Option_Ooption_ONone(_1789803)), _1789809))], (50076 ^ _780461) ^ [_1789927, _1789929, _1789931, _1789933, _1789935] : [class_Orderings_Olinorder(_1789927), hBOOL(hAPP(hAPP(c_member(_1789929), _1789931), hAPP(c_List_Oset(_1789929), _1789933))), c_List_Olinorder__class_Osorted(_1789927, hAPP(hAPP(c_List_Omap(_1789929, _1789927), _1789935), _1789933)), hAPP(c_List_Ohd(_1789929), hAPP(c_List_Ofilter(_1789929, hAPP(hAPP(c_COMBB(_1789927, tc_HOL_Obool, _1789929), hAPP(c_fequal, hAPP(_1789935, _1789931))), _1789935)), _1789933)) = _1789931, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1789929, _1789927, _1789935), _1789931), c_List_Oremove1(_1789929, _1789931, _1789933)) = _1789933)], (50094 ^ _780461) ^ [_1790306, _1790308, _1790310] : [-(c_List_Osublist(_1790306, _1790308, _1790310) = hAPP(hAPP(c_List_Omap(tc_prod(_1790306, tc_Nat_Onat), _1790306), c_Product__Type_Ofst(_1790306, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1790306, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1790306, 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(_1790306, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1790306, tc_Nat_Onat))), _1790310)), hAPP(hAPP(c_List_Ozip(_1790306, tc_Nat_Onat), _1790308), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1790306)), _1790308))))))], (50096 ^ _780461) ^ [_1790409] : [class_Orderings_Olinorder(_1790409), -(c_List_Olinorder__class_Osorted(_1790409, c_List_Olist_ONil(_1790409)))], (50102 ^ _780461) ^ [_1790486, _1790488] : [class_Orderings_Olinorder(_1790486), -(c_List_Olinorder__class_Osorted(_1790486, hAPP(hAPP(c_List_Olist_OCons(_1790486), _1790488), c_List_Olist_ONil(_1790486))))], (50108 ^ _780461) ^ [_1790581, _1790583, _1790585] : [class_Orderings_Olinorder(_1790581), -(c_List_Olinorder__class_Osorted(_1790581, hAPP(c_List_Ofilter(_1790581, hAPP(hAPP(c_COMBC(_1790581, _1790581, tc_HOL_Obool), c_fequal), hAPP(_1790583, _1790585))), _1790585)))], (50114 ^ _780461) ^ [_1790696, _1790698, _1790700, _1790702, _1790704] : [class_Orderings_Olinorder(_1790696), -(c_List_Olinorder__class_Osorted(_1790696, hAPP(hAPP(c_List_Omap(_1790698, _1790696), _1790700), hAPP(c_List_Ofilter(_1790698, hAPP(hAPP(c_COMBC(_1790698, _1790696, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1790696, tc_fun(_1790696, tc_HOL_Obool), _1790698), c_fequal), _1790700)), hAPP(_1790702, _1790704))), _1790704))))], (50120 ^ _780461) ^ [_1790859, _1790861, _1790863, _1790865, _1790867] : [class_Orderings_Olinorder(_1790859), c_List_Olinorder__class_Osorted(_1790859, hAPP(hAPP(c_List_Omap(_1790861, _1790859), _1790863), _1790865)), -(c_List_Olinorder__class_Osorted(_1790859, hAPP(hAPP(c_List_Omap(_1790861, _1790859), _1790863), hAPP(c_List_Ofilter(_1790861, _1790867), _1790865))))], (50130 ^ _780461) ^ [_1791046, _1791048] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1791046, _1791048)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1791048), _1791046))], (50132 ^ _780461) ^ [_1791083, _1791085] : [class_Orderings_Olinorder(_1791083), -(_1791085 = c_List_Olist_ONil(_1791083)), c_List_Olinorder__class_Osorted(_1791083, _1791085), -(c_List_Olinorder__class_Osorted(_1791083, c_List_Obutlast(_1791083, _1791085)))], (50146 ^ _780461) ^ [_1791275, _1791277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1791275), _1791277)), -(c_List_Oupt(_1791275, hAPP(c_Nat_OSuc, _1791277)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1791275, _1791277)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1791277), c_List_Olist_ONil(tc_Nat_Onat))))], (50152 ^ _780461) ^ [_1791413, _1791415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1791413), _1791415)), -(c_List_Oupt(_1791413, hAPP(c_Nat_OSuc, _1791415)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1791413, _1791415)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1791415), c_List_Olist_ONil(tc_Nat_Onat))))], (50158 ^ _780461) ^ [_1791536, _1791538] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1791536), _1791538))), -(c_List_Oupt(_1791536, hAPP(c_Nat_OSuc, _1791538)) = c_List_Olist_ONil(tc_Nat_Onat))], (50164 ^ _780461) ^ [_1791585, _1791587, _1791589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1791585), _1791587)), -(c_List_Oupt(_1791585, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1791587), _1791589)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1791585, _1791587)), c_List_Oupt(_1791587, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1791587), _1791589))))], (50170 ^ _780461) ^ [_1791728, _1791730, _1791732, _1791734] : [class_Orderings_Olinorder(_1791728), 50173 ^ _780461 : [(50174 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1791728, hAPP(hAPP(c_List_Olist_OCons(_1791728), _1791730), hAPP(hAPP(c_List_Olist_OCons(_1791728), _1791732), _1791734))), 50177 ^ _780461 : [(50178 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791728), _1791730), _1791732)))], (50180 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1791728, hAPP(hAPP(c_List_Olist_OCons(_1791728), _1791732), _1791734)))]]], (50182 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1791728, hAPP(hAPP(c_List_Olist_OCons(_1791728), _1791730), hAPP(hAPP(c_List_Olist_OCons(_1791728), _1791732), _1791734)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791728), _1791730), _1791732)), c_List_Olinorder__class_Osorted(_1791728, hAPP(hAPP(c_List_Olist_OCons(_1791728), _1791732), _1791734))]]], (50192 ^ _780461) ^ [_1792114, _1792116, _1792118, _1792120] : [class_Orderings_Olinorder(_1792114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1792114), _1792116), _1792118)), c_List_Olinorder__class_Osorted(_1792114, hAPP(hAPP(c_List_Olist_OCons(_1792114), _1792118), _1792120)), -(c_List_Olinorder__class_Osorted(_1792114, hAPP(hAPP(c_List_Olist_OCons(_1792114), _1792116), hAPP(hAPP(c_List_Olist_OCons(_1792114), _1792118), _1792120))))], (50206 ^ _780461) ^ [_1792367, _1792369, _1792371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1792367), _1792369)), _1792371)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1792369), c_List_Oupt(_1792367, _1792371)) = c_List_Oupt(_1792367, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1792367), _1792369)))], (50222 ^ _780461) ^ [_1792621, _1792623] : [50223 ^ _780461 : [(50224 ^ _780461) ^ [] : [_1792623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50226 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1792623), _1792621))]], -(c_List_Oupt(_1792621, _1792623) = c_List_Olist_ONil(tc_Nat_Onat))], (50212 ^ _780461) ^ [_1792519, _1792521] : [c_List_Oupt(_1792519, _1792521) = c_List_Olist_ONil(tc_Nat_Onat), -(_1792521 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1792521), _1792519)))], (50230 ^ _780461) ^ [_1792754, _1792756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1792754), _1792756)), -(c_List_Oupt(_1792756, _1792754) = c_List_Olist_ONil(tc_Nat_Onat))], (50236 ^ _780461) ^ [_1792847, _1792849, _1792851] : [class_Orderings_Olinorder(_1792847), 50239 ^ _780461 : [(50240 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1792847, hAPP(hAPP(c_List_Olist_OCons(_1792847), _1792849), _1792851)), 50243 ^ _780461 : [(50244 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1792847, _1792851))], (50246 ^ _780461) ^ [_1793033] : [hBOOL(hAPP(hAPP(c_member(_1792847), _1793033), hAPP(c_List_Oset(_1792847), _1792851))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1792847), _1792849), _1793033)))]]], (50252 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1792847, hAPP(hAPP(c_List_Olist_OCons(_1792847), _1792849), _1792851))), c_List_Olinorder__class_Osorted(_1792847, _1792851), 50258 ^ _780461 : [(50259 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792847), 50257 ^ [_1792847, _1792849, _1792851]), hAPP(c_List_Oset(_1792847), _1792851))))], (50261 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1792847), _1792849), 50257 ^ [_1792847, _1792849, _1792851]))]]]]], (50265 ^ _780461) ^ [_1793372, _1793374, _1793376] : [class_Orderings_Olinorder(_1793372), 50268 ^ _780461 : [(50269 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1793372, hAPP(hAPP(c_List_Oappend(_1793372), _1793374), _1793376)), 50272 ^ _780461 : [(50273 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1793372, _1793374))], (50275 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1793372, _1793376))], (50277 ^ _780461) ^ [_1793608] : [hBOOL(hAPP(hAPP(c_member(_1793372), _1793608), hAPP(c_List_Oset(_1793372), _1793374))), 50280 ^ _780461 : [(50281 ^ _780461) ^ [_1793718] : [hBOOL(hAPP(hAPP(c_member(_1793372), _1793718), hAPP(c_List_Oset(_1793372), _1793376))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793372), _1793608), _1793718)))]]]]], (50287 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1793372, hAPP(hAPP(c_List_Oappend(_1793372), _1793374), _1793376))), c_List_Olinorder__class_Osorted(_1793372, _1793374), c_List_Olinorder__class_Osorted(_1793372, _1793376), 50297 ^ _780461 : [(50298 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1793372), 50296 ^ [_1793372, _1793374, _1793376]), hAPP(c_List_Oset(_1793372), _1793374))))], (50301 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1793372), 50299 ^ [_1793372, _1793374, _1793376]), hAPP(c_List_Oset(_1793372), _1793376))))], (50303 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793372), 50296 ^ [_1793372, _1793374, _1793376]), 50299 ^ [_1793372, _1793374, _1793376]))]]]]], (50307 ^ _780461) ^ [_1794241, _1794243, _1794245, _1794247] : [c_List_Oupt(_1794241, _1794243) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1794245), _1794247), 50310 ^ _780461 : [(50311 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1794241), _1794243)))], (50313 ^ _780461) ^ [] : [-(_1794241 = _1794245)], (50315 ^ _780461) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794241), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1794243) = _1794247)]]], (50317 ^ _780461) ^ [_1794414, _1794416, _1794418, _1794420] : [-(c_List_Oupt(_1794414, _1794416) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1794418), _1794420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1794414), _1794416)), _1794414 = _1794418, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794414), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1794416) = _1794420], (50331 ^ _780461) ^ [_1794664, _1794666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794664)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794666))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794664), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794666)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794664)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794664)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794666))))], (50337 ^ _780461) ^ [_1794817, _1794819] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794817)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794819)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794817), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1794819)) = c_List_Olist_ONil(tc_Nat_Onat))], (50343 ^ _780461) ^ [_1794875, _1794877, _1794879] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1794875), c_List_Oupt(_1794877, _1794879)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1794877), _1794875), _1794879))], (50345 ^ _780461) ^ [_1794920, _1794922, _1794924] : [class_Orderings_Olinorder(_1794920), c_List_Olinorder__class_Osorted(_1794920, _1794922), -(c_List_Olinorder__class_Osorted(_1794920, hAPP(hAPP(c_List_Odrop(_1794920), _1794924), _1794922)))], (50355 ^ _780461) ^ [_1795067, _1795069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1795067), _1795069)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1795067, _1795069)) = _1795067)], (50361 ^ _780461) ^ [_1795166] : [-(c_List_Oupt(_1795166, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (50363 ^ _780461) ^ [_1795192] : [class_Orderings_Olinorder(_1795192), -(c_List_Olinorder__class_Osorted(_1795192, c_List_Olist_ONil(_1795192)))], (50369 ^ _780461) ^ [_1795269, _1795271, _1795273] : [class_Orderings_Olinorder(_1795269), c_List_Olinorder__class_Osorted(_1795269, _1795271), -(c_List_Olinorder__class_Osorted(_1795269, hAPP(hAPP(c_List_Otake(_1795269), _1795273), _1795271)))], (50379 ^ _780461) ^ [_1795416, _1795418] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1795416, _1795418)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1795416), _1795418))], (50381 ^ _780461) ^ [_1795453, _1795455] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1795453), _1795455) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1795453, _1795455)))], (50383 ^ _780461) ^ [_1795490, _1795492, _1795494] : [class_Orderings_Olinorder(_1795490), c_List_Olinorder__class_Osorted(_1795490, _1795492), hBOOL(hAPP(c_List_Odistinct(_1795490), _1795492)), c_List_Olinorder__class_Osorted(_1795490, _1795494), hBOOL(hAPP(c_List_Odistinct(_1795490), _1795494)), hAPP(c_List_Oset(_1795490), _1795492) = hAPP(c_List_Oset(_1795490), _1795494), -(_1795492 = _1795494)], (50409 ^ _780461) ^ [_1795873, _1795875, _1795877] : [class_Orderings_Olinorder(_1795873), 50412 ^ _780461 : [(50413 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1795873, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1795873, _1795873, c_COMBI(_1795873)), _1795875), _1795877)), -(c_List_Olinorder__class_Osorted(_1795873, _1795877))], (50419 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1795873, _1795877), -(c_List_Olinorder__class_Osorted(_1795873, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1795873, _1795873, c_COMBI(_1795873)), _1795875), _1795877)))]]], (50425 ^ _780461) ^ [_1796120, _1796122] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1796120, _1796122))))], (50427 ^ _780461) ^ [_1796150, _1796152, _1796154] : [class_Orderings_Olinorder(_1796150), c_List_Olinorder__class_Osorted(_1796150, _1796152), -(c_List_Olinorder__class_Osorted(_1796150, c_List_Oremove1(_1796150, _1796154, _1796152)))], (50437 ^ _780461) ^ [_1796289, _1796291] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1796289, _1796291)))], (50439 ^ _780461) ^ [_1796317, _1796319] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1796317, _1796319)))], (50441 ^ _780461) ^ [_1796345, _1796347] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1796345), _1796347)) = c_List_Oupt(_1796345, _1796347))], (50443 ^ _780461) ^ [_1796382, _1796384, _1796386] : [class_Orderings_Olinorder(_1796382), c_List_Olinorder__class_Osorted(_1796382, _1796384), -(c_List_Olinorder__class_Osorted(_1796382, c_List_Olinorder__class_Oinsort__insert__key(_1796382, _1796382, c_COMBI(_1796382), _1796386, _1796384)))], (50453 ^ _780461) ^ [_1796529, _1796531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796529), _1796531)), -(c_List_Oupt(_1796529, _1796531) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1796529), c_List_Oupt(hAPP(c_Nat_OSuc, _1796529), _1796531)))], (50459 ^ _780461) ^ [_1796655, _1796657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796655), _1796657)), -(c_List_Oupt(_1796655, _1796657) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1796655), c_List_Oupt(hAPP(c_Nat_OSuc, _1796655), _1796657)))], (50465 ^ _780461) ^ [_1796766, _1796768] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796766), _1796768))), -(c_List_Oupt(_1796766, _1796768) = c_List_Olist_ONil(tc_Nat_Onat))], (50471 ^ _780461) ^ [_1796812, _1796814] : [class_Orderings_Olinorder(_1796812), c_List_Olinorder__class_Osorted(_1796812, _1796814), -(c_List_Olinorder__class_Osorted(_1796812, c_List_Otl(_1796812, _1796814)))], (50481 ^ _780461) ^ [_1796945, _1796947, _1796949, _1796951, _1796953] : [class_Orderings_Olinorder(_1796945), 50484 ^ _780461 : [(50485 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1796945, hAPP(hAPP(c_List_Omap(_1796947, _1796945), _1796949), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1796947, _1796945, _1796949), _1796951), _1796953))), -(c_List_Olinorder__class_Osorted(_1796945, hAPP(hAPP(c_List_Omap(_1796947, _1796945), _1796949), _1796953)))], (50491 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1796945, hAPP(hAPP(c_List_Omap(_1796947, _1796945), _1796949), _1796953)), -(c_List_Olinorder__class_Osorted(_1796945, hAPP(hAPP(c_List_Omap(_1796947, _1796945), _1796949), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1796947, _1796945, _1796949), _1796951), _1796953))))]]], (50497 ^ _780461) ^ [_1797252, _1797254, _1797256, _1797258, _1797260] : [class_Orderings_Olinorder(_1797252), c_List_Olinorder__class_Osorted(_1797252, hAPP(hAPP(c_List_Omap(_1797254, _1797252), _1797256), _1797258)), -(c_List_Olinorder__class_Osorted(_1797252, hAPP(hAPP(c_List_Omap(_1797254, _1797252), _1797256), c_List_Oremove1(_1797254, _1797260, _1797258))))], (50507 ^ _780461) ^ [_1797435, _1797437, _1797439, _1797441, _1797443] : [class_Orderings_Olinorder(_1797435), c_List_Olinorder__class_Osorted(_1797435, hAPP(hAPP(c_List_Omap(_1797437, _1797435), _1797439), _1797441)), -(c_List_Olinorder__class_Osorted(_1797435, hAPP(hAPP(c_List_Omap(_1797437, _1797435), _1797439), c_List_Olinorder__class_Oinsort__insert__key(_1797437, _1797435, _1797439, _1797443, _1797441))))], (50517 ^ _780461) ^ [_1797622, _1797624] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1797622, _1797624)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1797622), hAPP(c_Nat_OSuc, _1797624)))], (50519 ^ _780461) ^ [_1797662, _1797664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1797662), _1797664)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1797662, _1797664)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1797664), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (50525 ^ _780461) ^ [_1797773, _1797775, _1797777, _1797779, _1797781, _1797783] : [class_Orderings_Olinorder(_1797773), c_List_Olinorder__class_Osorted(_1797773, hAPP(hAPP(c_List_Omap(_1797775, _1797773), _1797777), _1797779)), hBOOL(hAPP(_1797781, _1797783)), -(hAPP(c_List_Ofilter(_1797775, _1797781), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1797775, _1797773, _1797777), _1797783), _1797779)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1797775, _1797773, _1797777), _1797783), hAPP(c_List_Ofilter(_1797775, _1797781), _1797779)))], (50539 ^ _780461) ^ [_1798062, _1798064] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1798062), hAPP(c_List_Onth(_1798062), _1798064)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1798062)), _1798064))) = _1798064)], (50541 ^ _780461) ^ [_1798111, _1798113] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1798111, _1798113) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1798111, hAPP(c_Nat_OSuc, _1798113))))], (50543 ^ _780461) ^ [_1798149] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1798149) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1798149)))], (50545 ^ _780461) ^ [_1798181, _1798183, _1798185, _1798187] : [class_Groups_Ocomm__monoid__add(_1798181), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1798181), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1798181), _1798183), c_List_Oupt(_1798185, _1798187))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1798181), _1798183), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1798185, _1798187))))], (50551 ^ _780461) ^ [_1798324, _1798326, _1798328, _1798330] : [class_Groups_Ocomm__monoid__add(_1798324), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1798324), _1798326), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1798328, _1798330))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1798324), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1798324), _1798326), c_List_Oupt(_1798328, _1798330))))], (50557 ^ _780461) ^ [_1798467, _1798469, _1798471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1798467), _1798469)), _1798471)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1798467, _1798471)), _1798469) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1798467), _1798469))], (50563 ^ _780461) ^ [_1798598, _1798600] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1798598, _1798600) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1798598), hAPP(c_Nat_OSuc, _1798600))))], (50565 ^ _780461) ^ [_1798639, _1798641, _1798643] : [class_Orderings_Olinorder(_1798639), 50568 ^ _780461 : [(50569 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1798639, hAPP(hAPP(c_List_Olist_OCons(_1798639), _1798641), _1798643)), 50572 ^ _780461 : [(50579 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1798639, _1798643))], (50573 ^ _780461) ^ [_1798807] : [hBOOL(hAPP(hAPP(c_member(_1798639), _1798807), hAPP(c_List_Oset(_1798639), _1798643))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798639), _1798641), _1798807)))]]], (50581 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1798639, hAPP(hAPP(c_List_Olist_OCons(_1798639), _1798641), _1798643))), 50585 ^ _780461 : [(50586 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798639), 50584 ^ [_1798639, _1798641, _1798643]), hAPP(c_List_Oset(_1798639), _1798643))))], (50588 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1798639), _1798641), 50584 ^ [_1798639, _1798641, _1798643]))]], c_List_Olinorder__class_Osorted(_1798639, _1798643)]]], (50594 ^ _780461) ^ [_1799165, _1799167] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1799165, _1799167) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1799165), _1799167)))], (50596 ^ _780461) ^ [_1799203, _1799205, _1799207, _1799209, _1799211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1799203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1799205), _1799207))), -(hAPP(hAPP(c_List_Onth(_1799209), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1799209), _1799211), c_List_Oupt(_1799207, _1799205))), _1799203) = hAPP(_1799211, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1799207), _1799203)))], (50602 ^ _780461) ^ [_1799366, _1799368] : [class_Orderings_Olinorder(_1799366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1799366), _1799368)), 50609 ^ _780461 : [(50610 ^ _780461) ^ [] : [-(hAPP(c_List_Oset(_1799366), c_List_Olinorder__class_Osorted__list__of__set(_1799366, _1799368)) = _1799368)], (50612 ^ _780461) ^ [] : [-(c_List_Olinorder__class_Osorted(_1799366, c_List_Olinorder__class_Osorted__list__of__set(_1799366, _1799368)))], (50614 ^ _780461) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1799366), c_List_Olinorder__class_Osorted__list__of__set(_1799366, _1799368))))]]], (50616 ^ _780461) ^ [_1799587] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1799587) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1799587))))], (50618 ^ _780461) ^ [_1799622, _1799624, _1799626] : [class_Orderings_Olinorder(_1799622), hBOOL(hAPP(hAPP(c_member(_1799622), _1799624), hAPP(c_List_Oset(_1799622), _1799626))), c_List_Olinorder__class_Osorted(_1799622, _1799626), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1799622, _1799622, c_COMBI(_1799622)), _1799624), c_List_Oremove1(_1799622, _1799624, _1799626)) = _1799626)], (50632 ^ _780461) ^ [_1799863, _1799865, _1799867, _1799869] : [class_Orderings_Olinorder(_1799863), c_List_Olinorder__class_Osorted(_1799863, _1799865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1799867), _1799869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1799869), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799863)), _1799865))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1799863), hAPP(hAPP(c_List_Onth(_1799863), _1799865), _1799867)), hAPP(hAPP(c_List_Onth(_1799863), _1799865), _1799869))))], (50650 ^ _780461) ^ [_1800190, _1800192] : [class_Orderings_Olinorder(_1800190), 50653 ^ _780461 : [(50668 ^ _780461) ^ [] : [50670 ^ _780461 : [(50671 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50669 ^ [_1800190, _1800192]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800190)), _1800192))))], (50674 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50672 ^ [_1800190, _1800192]), 50669 ^ [_1800190, _1800192])))], (50676 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1800190), hAPP(hAPP(c_List_Onth(_1800190), _1800192), 50672 ^ [_1800190, _1800192])), hAPP(hAPP(c_List_Onth(_1800190), _1800192), 50669 ^ [_1800190, _1800192])))]], -(c_List_Olinorder__class_Osorted(_1800190, _1800192))], (50654 ^ _780461) ^ [] : [c_List_Olinorder__class_Osorted(_1800190, _1800192), 50657 ^ _780461 : [(50658 ^ _780461) ^ [_1800361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1800361), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1800190)), _1800192))), 50661 ^ _780461 : [(50662 ^ _780461) ^ [_1800478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1800478), _1800361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1800190), hAPP(hAPP(c_List_Onth(_1800190), _1800192), _1800478)), hAPP(hAPP(c_List_Onth(_1800190), _1800192), _1800361))))]]]]]]], (50680 ^ _780461) ^ [_1800914, _1800916, _1800918, _1800920, _1800922] : [class_Orderings_Olinorder(_1800914), c_Fun_Oinj__on(_1800916, _1800914, _1800918, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1800916, tc_HOL_Obool)), hAPP(c_List_Oset(_1800916), _1800920)), hAPP(c_List_Oset(_1800916), _1800922))), c_List_Olinorder__class_Osorted(_1800914, hAPP(hAPP(c_List_Omap(_1800916, _1800914), _1800918), _1800920)), hBOOL(hAPP(c_List_Odistinct(_1800914), hAPP(hAPP(c_List_Omap(_1800916, _1800914), _1800918), _1800920))), c_List_Olinorder__class_Osorted(_1800914, hAPP(hAPP(c_List_Omap(_1800916, _1800914), _1800918), _1800922)), hBOOL(hAPP(c_List_Odistinct(_1800914), hAPP(hAPP(c_List_Omap(_1800916, _1800914), _1800918), _1800922))), hAPP(c_List_Oset(_1800916), _1800920) = hAPP(c_List_Oset(_1800916), _1800922), -(_1800920 = _1800922)], (50710 ^ _780461) ^ [_1801497, _1801499, _1801501, _1801503] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1801497, tc_Nat_Onat), _1801497), c_Product__Type_Ofst(_1801497, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1801497, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1801497, 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(_1801497, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1801497, tc_Nat_Onat))), _1801499)), hAPP(hAPP(c_List_Ozip(_1801497, tc_Nat_Onat), _1801501), c_List_Oupt(_1801503, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1801503), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801497)), _1801501)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1801497, tc_Nat_Onat), _1801497), c_Product__Type_Ofst(_1801497, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1801497, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1801497, 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(_1801497, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1801497, 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(_1801497, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1801497, tc_Nat_Onat))), _1801503))), _1801499)), hAPP(hAPP(c_List_Ozip(_1801497, tc_Nat_Onat), _1801501), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801497)), _1801501))))))], (50712 ^ _780461) ^ [_1801702, _1801704, _1801706] : [50713 ^ _780461 : [(50714 ^ _780461) ^ [] : [-(_1801702 = c_List_Olist_ONil(tc_List_Olist(_1801704)))], (50716 ^ _780461) ^ [] : [_1801706 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 50720 ^ _780461 : [(50721 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50719 ^ [_1801702, _1801704, _1801706]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1801704))), _1801702))))], (50723 ^ _780461) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801704)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1801704)), _1801702), 50719 ^ [_1801702, _1801704, _1801706])) = _1801706]], -(c_List_Otranspose(_1801704, _1801702) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1801704)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1801704)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1801704), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1801704)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1801704)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1801704), hAPP(hAPP(c_COMBB(tc_List_Olist(_1801704), tc_fun(tc_Nat_Onat, _1801704), tc_Nat_Onat), c_List_Onth(_1801704)), hAPP(c_List_Onth(tc_List_Olist(_1801704)), _1801702))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1801704))), _1801702)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1801706)))], (50727 ^ _780461) ^ [_1802212, _1802214] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1802212)), c_List_Otranspose__rel(_1802212)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1802212)), c_List_Olist_ONil(_1802212)), _1802214))), -(c_List_Otranspose(_1802212, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1802212)), c_List_Olist_ONil(_1802212)), _1802214)) = c_List_Otranspose(_1802212, _1802214))], (50733 ^ _780461) ^ [_1802371] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1802371)), c_List_Otranspose__rel(_1802371)), c_List_Olist_ONil(tc_List_Olist(_1802371)))), -(c_List_Otranspose(_1802371, c_List_Olist_ONil(tc_List_Olist(_1802371))) = c_List_Olist_ONil(tc_List_Olist(_1802371)))], (50739 ^ _780461) ^ [_1802498, _1802500, _1802502] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1802498), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1802498))), _1802500))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1802502), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1802498))), _1802500))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1802498), _1802498), hAPP(hAPP(c_COMBC(tc_List_Olist(_1802498), tc_Nat_Onat, _1802498), c_List_Onth(_1802498)), _1802502)), hAPP(c_List_Ofilter(tc_List_Olist(_1802498), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1802498)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1802502)), c_Nat_Osize__class_Osize(tc_List_Olist(_1802498)))), c_List_Otranspose(_1802498, _1802500))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1802498)), _1802500), _1802502))], (50749 ^ _780461) ^ [_1802825, _1802827] : [-(c_List_Oconcat(_1802825, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1802825), tc_List_Olist(_1802825)), c_List_Olist_Olist__case(tc_List_Olist(_1802825), _1802825, c_List_Olist_ONil(_1802825), hAPP(hAPP(c_COMBB(tc_List_Olist(_1802825), tc_fun(tc_List_Olist(_1802825), tc_List_Olist(_1802825)), _1802825), c_COMBK(tc_List_Olist(_1802825), tc_List_Olist(_1802825))), hAPP(hAPP(c_COMBC(_1802825, tc_List_Olist(_1802825), tc_List_Olist(_1802825)), c_List_Olist_OCons(_1802825)), c_List_Olist_ONil(_1802825))))), _1802827)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1802825), _1802825), c_List_Ohd(_1802825)), hAPP(c_List_Ofilter(tc_List_Olist(_1802825), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1802825)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1802825), tc_List_Olist(_1802825), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1802825)))), _1802827)))], (50751 ^ _780461) ^ [_1802968, _1802970] : [-(c_Fun_Oinj__on(tc_List_Olist(_1802968), tc_List_Olist(_1802968), c_List_Orev(_1802968), _1802970))], (50753 ^ _780461) ^ [_1803001, _1803003, _1803005] : [-(hAPP(c_List_Ofilter(_1803001, _1803003), c_List_Oconcat(_1803001, _1803005)) = c_List_Oconcat(_1803001, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1803001), tc_List_Olist(_1803001)), c_List_Ofilter(_1803001, _1803003)), _1803005)))], (50755 ^ _780461) ^ [_1803056, _1803058] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1803056)), c_List_Oconcat(_1803056, _1803058)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1803056), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1803056))), _1803058)))], (50757 ^ _780461) ^ [_1803130, _1803132, _1803134, _1803136] : [hAPP(c_List_Orev(_1803130), _1803132) = hAPP(hAPP(c_List_Olist_OCons(_1803130), _1803134), _1803136), -(_1803132 = hAPP(hAPP(c_List_Oappend(_1803130), hAPP(c_List_Orev(_1803130), _1803136)), hAPP(hAPP(c_List_Olist_OCons(_1803130), _1803134), c_List_Olist_ONil(_1803130))))], (50763 ^ _780461) ^ [_1803279, _1803281, _1803283, _1803285] : [_1803281 = hAPP(hAPP(c_List_Oappend(_1803279), hAPP(c_List_Orev(_1803279), _1803285)), hAPP(hAPP(c_List_Olist_OCons(_1803279), _1803283), c_List_Olist_ONil(_1803279))), -(hAPP(c_List_Orev(_1803279), _1803281) = hAPP(hAPP(c_List_Olist_OCons(_1803279), _1803283), _1803285))], (50769 ^ _780461) ^ [_1803434, _1803436, _1803438] : [-(hAPP(c_List_Orev(_1803434), hAPP(hAPP(c_List_Olist_OCons(_1803434), _1803436), _1803438)) = hAPP(hAPP(c_List_Oappend(_1803434), hAPP(c_List_Orev(_1803434), _1803438)), hAPP(hAPP(c_List_Olist_OCons(_1803434), _1803436), c_List_Olist_ONil(_1803434))))], (50771 ^ _780461) ^ [_1803497] : [-(hAPP(c_List_Orev(_1803497), c_List_Olist_ONil(_1803497)) = c_List_Olist_ONil(_1803497))], (50773 ^ _780461) ^ [_1803529] : [-(c_List_Oconcat(_1803529, c_List_Olist_ONil(tc_List_Olist(_1803529))) = c_List_Olist_ONil(_1803529))], (50775 ^ _780461) ^ [_1803576, _1803578] : [c_List_Olist_ONil(_1803576) = hAPP(c_List_Orev(_1803576), _1803578), -(_1803578 = c_List_Olist_ONil(_1803576))], (50781 ^ _780461) ^ [_1803667, _1803669] : [_1803669 = c_List_Olist_ONil(_1803667), -(c_List_Olist_ONil(_1803667) = hAPP(c_List_Orev(_1803667), _1803669))], (50787 ^ _780461) ^ [_1803779, _1803781] : [hAPP(c_List_Orev(_1803779), _1803781) = c_List_Olist_ONil(_1803779), -(_1803781 = c_List_Olist_ONil(_1803779))], (50793 ^ _780461) ^ [_1803870, _1803872] : [_1803872 = c_List_Olist_ONil(_1803870), -(hAPP(c_List_Orev(_1803870), _1803872) = c_List_Olist_ONil(_1803870))], (50809 ^ _780461) ^ [_1804188, _1804190] : [50811 ^ _780461 : [(50812 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1804188)), 50810 ^ [_1804188, _1804190]), hAPP(c_List_Oset(tc_List_Olist(_1804188)), _1804190))))], (50814 ^ _780461) ^ [] : [50810 ^ [_1804188, _1804190] = c_List_Olist_ONil(_1804188)]], -(c_List_Olist_ONil(_1804188) = c_List_Oconcat(_1804188, _1804190))], (50799 ^ _780461) ^ [_1803982, _1803984] : [c_List_Olist_ONil(_1803982) = c_List_Oconcat(_1803982, _1803984), 50802 ^ _780461 : [(50803 ^ _780461) ^ [_1804073] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1803982)), _1804073), hAPP(c_List_Oset(tc_List_Olist(_1803982)), _1803984))), -(_1804073 = c_List_Olist_ONil(_1803982))]]], (50828 ^ _780461) ^ [_1804600, _1804602] : [50830 ^ _780461 : [(50831 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1804600)), 50829 ^ [_1804600, _1804602]), hAPP(c_List_Oset(tc_List_Olist(_1804600)), _1804602))))], (50833 ^ _780461) ^ [] : [50829 ^ [_1804600, _1804602] = c_List_Olist_ONil(_1804600)]], -(c_List_Oconcat(_1804600, _1804602) = c_List_Olist_ONil(_1804600))], (50818 ^ _780461) ^ [_1804394, _1804396] : [c_List_Oconcat(_1804394, _1804396) = c_List_Olist_ONil(_1804394), 50821 ^ _780461 : [(50822 ^ _780461) ^ [_1804485] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1804394)), _1804485), hAPP(c_List_Oset(tc_List_Olist(_1804394)), _1804396))), -(_1804485 = c_List_Olist_ONil(_1804394))]]], (50837 ^ _780461) ^ [_1804809, _1804811, _1804813] : [hAPP(c_List_Orev(_1804809), _1804811) = hAPP(hAPP(c_List_Olist_OCons(_1804809), _1804813), c_List_Olist_ONil(_1804809)), -(_1804811 = hAPP(hAPP(c_List_Olist_OCons(_1804809), _1804813), c_List_Olist_ONil(_1804809)))], (50843 ^ _780461) ^ [_1804934, _1804936, _1804938] : [_1804936 = hAPP(hAPP(c_List_Olist_OCons(_1804934), _1804938), c_List_Olist_ONil(_1804934)), -(hAPP(c_List_Orev(_1804934), _1804936) = hAPP(hAPP(c_List_Olist_OCons(_1804934), _1804938), c_List_Olist_ONil(_1804934)))], (50849 ^ _780461) ^ [_1805083, _1805085, _1805087] : [hAPP(hAPP(c_List_Olist_OCons(_1805083), _1805085), c_List_Olist_ONil(_1805083)) = hAPP(c_List_Orev(_1805083), _1805087), -(_1805087 = hAPP(hAPP(c_List_Olist_OCons(_1805083), _1805085), c_List_Olist_ONil(_1805083)))], (50855 ^ _780461) ^ [_1805208, _1805210, _1805212] : [_1805212 = hAPP(hAPP(c_List_Olist_OCons(_1805208), _1805210), c_List_Olist_ONil(_1805208)), -(hAPP(hAPP(c_List_Olist_OCons(_1805208), _1805210), c_List_Olist_ONil(_1805208)) = hAPP(c_List_Orev(_1805208), _1805212))], (50861 ^ _780461) ^ [_1805339, _1805341, _1805343] : [-(c_List_Oconcat(_1805339, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1805339)), _1805341), _1805343)) = hAPP(hAPP(c_List_Oappend(_1805339), _1805341), c_List_Oconcat(_1805339, _1805343)))], (50863 ^ _780461) ^ [_1805390, _1805392] : [-(hAPP(c_List_Orev(_1805390), c_List_Oconcat(_1805390, _1805392)) = c_List_Oconcat(_1805390, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1805390), tc_List_Olist(_1805390)), c_List_Orev(_1805390)), hAPP(c_List_Orev(tc_List_Olist(_1805390)), _1805392))))], (50865 ^ _780461) ^ [_1805448, _1805450, _1805452, _1805454] : [-(hAPP(c_List_Orev(_1805448), hAPP(hAPP(c_List_Omap(_1805450, _1805448), _1805452), _1805454)) = hAPP(hAPP(c_List_Omap(_1805450, _1805448), _1805452), hAPP(c_List_Orev(_1805450), _1805454)))], (50867 ^ _780461) ^ [_1805505, _1805507, _1805509, _1805511] : [-(hAPP(hAPP(c_List_Omap(_1805505, _1805507), _1805509), c_List_Oconcat(_1805505, _1805511)) = c_List_Oconcat(_1805507, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1805505), tc_List_Olist(_1805507)), hAPP(c_List_Omap(_1805505, _1805507), _1805509)), _1805511)))], (50869 ^ _780461) ^ [_1805568, _1805570] : [-(hAPP(c_List_Orev(_1805568), _1805570) = hAPP(c_List_Ofoldl(tc_List_Olist(_1805568), _1805568, hAPP(c_COMBC(_1805568, tc_List_Olist(_1805568), tc_List_Olist(_1805568)), c_List_Olist_OCons(_1805568)), c_List_Olist_ONil(_1805568)), _1805570))], (50871 ^ _780461) ^ [_1805623, _1805625] : [-(c_List_Oconcat(_1805623, _1805625) = hAPP(c_List_Ofoldl(tc_List_Olist(_1805623), tc_List_Olist(_1805623), c_List_Oappend(_1805623), c_List_Olist_ONil(_1805623)), _1805625))], (50873 ^ _780461) ^ [_1805667, _1805669, _1805671] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1805667), tc_List_Olist(_1805667), c_List_Oappend(_1805667), _1805669), _1805671) = hAPP(hAPP(c_List_Oappend(_1805667), _1805669), c_List_Oconcat(_1805667, _1805671)))], (50875 ^ _780461) ^ [_1805719, _1805721, _1805723] : [-(hAPP(c_List_Orev(_1805719), hAPP(hAPP(c_List_Oappend(_1805719), _1805721), _1805723)) = hAPP(hAPP(c_List_Oappend(_1805719), hAPP(c_List_Orev(_1805719), _1805723)), hAPP(c_List_Orev(_1805719), _1805721)))], (50877 ^ _780461) ^ [_1805777, _1805779, _1805781] : [-(c_List_Oconcat(_1805777, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1805777)), _1805779), _1805781)) = hAPP(hAPP(c_List_Oappend(_1805777), c_List_Oconcat(_1805777, _1805779)), c_List_Oconcat(_1805777, _1805781)))], (50879 ^ _780461) ^ [_1805846, _1805848] : [hBOOL(hAPP(c_List_Odistinct(_1805846), hAPP(c_List_Orev(_1805846), _1805848))), -(hBOOL(hAPP(c_List_Odistinct(_1805846), _1805848)))], (50885 ^ _780461) ^ [_1805945, _1805947] : [hBOOL(hAPP(c_List_Odistinct(_1805945), _1805947)), -(hBOOL(hAPP(c_List_Odistinct(_1805945), hAPP(c_List_Orev(_1805945), _1805947))))], (50891 ^ _780461) ^ [_1806050, _1806052] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806050)), hAPP(c_List_Orev(_1806050), _1806052)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806050)), _1806052))], (50893 ^ _780461) ^ [_1806094, _1806096] : [class_Groups_Ocomm__monoid__add(_1806094), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1806094), hAPP(c_List_Orev(_1806094), _1806096)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1806094), _1806096))], (50899 ^ _780461) ^ [_1806217, _1806219, _1806221] : [hAPP(c_List_Orev(_1806217), _1806219) = hAPP(c_List_Orev(_1806217), _1806221), -(_1806219 = _1806221)], (50905 ^ _780461) ^ [_1806312, _1806314, _1806316] : [_1806314 = _1806316, -(hAPP(c_List_Orev(_1806312), _1806314) = hAPP(c_List_Orev(_1806312), _1806316))], (50911 ^ _780461) ^ [_1806431, _1806433, _1806435] : [hAPP(c_List_Orev(_1806431), _1806433) = _1806435, -(_1806433 = hAPP(c_List_Orev(_1806431), _1806435))], (50917 ^ _780461) ^ [_1806526, _1806528, _1806530] : [_1806528 = hAPP(c_List_Orev(_1806526), _1806530), -(hAPP(c_List_Orev(_1806526), _1806528) = _1806530)], (50923 ^ _780461) ^ [_1806627, _1806629] : [-(hAPP(c_List_Orev(_1806627), hAPP(c_List_Orev(_1806627), _1806629)) = _1806629)], (50925 ^ _780461) ^ [_1806662, _1806664, _1806666, _1806668, _1806670] : [-(c_List_Ofoldr(_1806662, _1806664, _1806666, _1806668, _1806670) = hAPP(c_List_Ofoldl(_1806664, _1806662, hAPP(c_COMBC(_1806662, _1806664, _1806664), _1806666), _1806670), hAPP(c_List_Orev(_1806662), _1806668)))], (50927 ^ _780461) ^ [_1806719, _1806721, _1806723, _1806725, _1806727] : [-(hAPP(c_List_Ofoldl(_1806719, _1806721, _1806723, _1806725), _1806727) = c_List_Ofoldr(_1806721, _1806719, hAPP(c_COMBC(_1806719, _1806721, _1806719), _1806723), hAPP(c_List_Orev(_1806721), _1806727), _1806725))], (50929 ^ _780461) ^ [_1806776, _1806778] : [-(hAPP(c_List_Oset(_1806776), c_List_Oconcat(_1806776, _1806778)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1806776), tc_fun(_1806776, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1806776)), _1806778)), c_List_Oset(_1806776)))], (50931 ^ _780461) ^ [_1806832, _1806834] : [-(hAPP(c_List_Oset(_1806832), hAPP(c_List_Orev(_1806832), _1806834)) = hAPP(c_List_Oset(_1806832), _1806834))], (50933 ^ _780461) ^ [_1806872, _1806874, _1806876, _1806878] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806872)), _1806874) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1806876)), _1806878), -(hAPP(hAPP(c_List_Ozip(_1806872, _1806876), hAPP(c_List_Orev(_1806872), _1806874)), hAPP(c_List_Orev(_1806876), _1806878)) = hAPP(c_List_Orev(tc_prod(_1806872, _1806876)), hAPP(hAPP(c_List_Ozip(_1806872, _1806876), _1806874), _1806878)))], (50939 ^ _780461) ^ [_1807053, _1807055, _1807057] : [-(hAPP(c_List_Orev(_1807053), hAPP(c_List_Ofilter(_1807053, _1807055), _1807057)) = hAPP(c_List_Ofilter(_1807053, _1807055), hAPP(c_List_Orev(_1807053), _1807057)))], (50941 ^ _780461) ^ [_1807098, _1807100] : [-(_1807098 = c_List_Olist_ONil(_1807100)), -(c_List_Olast(_1807100, hAPP(c_List_Orev(_1807100), _1807098)) = hAPP(c_List_Ohd(_1807100), _1807098))], (50947 ^ _780461) ^ [_1807145, _1807147] : [-(_1807145 = c_List_Olist_ONil(_1807147)), -(hAPP(c_List_Ohd(_1807147), hAPP(c_List_Orev(_1807147), _1807145)) = c_List_Olast(_1807147, _1807145))], (50953 ^ _780461) ^ [_1807196, _1807198] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1807196), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1807196))), c_List_Otranspose(_1807196, _1807198)))))], (50955 ^ _780461) ^ [_1807242, _1807244, _1807246] : [-(hAPP(c_List_Orev(_1807242), hAPP(hAPP(c_List_Otake(_1807242), _1807244), _1807246)) = hAPP(hAPP(c_List_Odrop(_1807242), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807242)), _1807246)), _1807244)), hAPP(c_List_Orev(_1807242), _1807246)))], (50957 ^ _780461) ^ [_1807308, _1807310, _1807312] : [-(hAPP(c_List_Orev(_1807308), hAPP(hAPP(c_List_Odrop(_1807308), _1807310), _1807312)) = hAPP(hAPP(c_List_Otake(_1807308), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807308)), _1807312)), _1807310)), hAPP(c_List_Orev(_1807308), _1807312)))], (50959 ^ _780461) ^ [_1807374, _1807376, _1807378] : [-(hAPP(c_List_Orotate(_1807374, _1807376), hAPP(c_List_Orev(_1807374), _1807378)) = hAPP(c_List_Orev(_1807374), hAPP(c_List_Orotate(_1807374, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807374)), _1807378)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1807376, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807374)), _1807378)))), _1807378)))], (50961 ^ _780461) ^ [_1807447, _1807449, _1807451, _1807453] : [-(c_List_Otranspose(_1807447, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1807447)), hAPP(hAPP(c_List_Olist_OCons(_1807447), _1807449), _1807451)), _1807453)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1807447)), hAPP(hAPP(c_List_Olist_OCons(_1807447), _1807449), c_List_Oconcat(_1807447, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1807447), tc_List_Olist(_1807447)), c_List_Olist_Olist__case(tc_List_Olist(_1807447), _1807447, c_List_Olist_ONil(_1807447), hAPP(hAPP(c_COMBB(tc_List_Olist(_1807447), tc_fun(tc_List_Olist(_1807447), tc_List_Olist(_1807447)), _1807447), c_COMBK(tc_List_Olist(_1807447), tc_List_Olist(_1807447))), hAPP(hAPP(c_COMBC(_1807447, tc_List_Olist(_1807447), tc_List_Olist(_1807447)), c_List_Olist_OCons(_1807447)), c_List_Olist_ONil(_1807447))))), _1807453)))), c_List_Otranspose(_1807447, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1807447)), _1807451), c_List_Oconcat(tc_List_Olist(_1807447), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1807447), tc_List_Olist(tc_List_Olist(_1807447))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1807447)), _1807447, c_List_Olist_ONil(tc_List_Olist(_1807447)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1807447), tc_List_Olist(tc_List_Olist(_1807447))), _1807447), hAPP(hAPP(c_COMBC(tc_List_Olist(_1807447), tc_List_Olist(tc_List_Olist(_1807447)), tc_List_Olist(tc_List_Olist(_1807447))), c_List_Olist_OCons(tc_List_Olist(_1807447))), c_List_Olist_ONil(tc_List_Olist(_1807447)))))), _1807453))))))], (50963 ^ _780461) ^ [_1807673, _1807675, _1807677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1807673), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807675)), _1807677))), -(hAPP(hAPP(c_List_Onth(_1807675), hAPP(c_List_Orev(_1807675), _1807677)), _1807673) = hAPP(hAPP(c_List_Onth(_1807675), _1807677), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1807675)), _1807677)), hAPP(c_Nat_OSuc, _1807673))))], (50969 ^ _780461) ^ [_1807850, _1807852, _1807854] : [c_List_Oconcat(_1807850, _1807852) = c_List_Oconcat(_1807850, _1807854), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1807850))), _1807852) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1807850))), _1807854), 50979 ^ _780461 : [(50980 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1807850), tc_List_Olist(_1807850))), 50978 ^ [_1807850, _1807852, _1807854]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1807850), tc_List_Olist(_1807850))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1807850), tc_List_Olist(_1807850)), _1807852), _1807854)))))], (50982 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1807850), tc_List_Olist(_1807850), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1807850), tc_fun(tc_List_Olist(_1807850), tc_Nat_Onat), tc_fun(tc_List_Olist(_1807850), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1807850), tc_Nat_Onat), tc_fun(tc_List_Olist(_1807850), tc_HOL_Obool)), tc_List_Olist(_1807850)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1807850))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1807850)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1807850))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1807850)))), 50978 ^ [_1807850, _1807852, _1807854]))]], -(_1807852 = _1807854)], (50986 ^ _780461) ^ [_1808491, _1808493, _1808495] : [50988 ^ _780461 : [(50989 ^ _780461) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1808491), tc_List_Olist(_1808491))), 50987 ^ [_1808491, _1808493, _1808495]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1808491), tc_List_Olist(_1808491))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1808491), tc_List_Olist(_1808491)), _1808493), _1808495)))))], (50991 ^ _780461) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1808491), tc_List_Olist(_1808491), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1808491), tc_fun(tc_List_Olist(_1808491), tc_Nat_Onat), tc_fun(tc_List_Olist(_1808491), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1808491), tc_Nat_Onat), tc_fun(tc_List_Olist(_1808491), tc_HOL_Obool)), tc_List_Olist(_1808491)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1808491))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1808491)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1808491))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1808491)))), 50987 ^ [_1808491, _1808493, _1808495]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1808491))), _1808493) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1808491))), _1808495), 50996 ^ _780461 : [(50997 ^ _780461) ^ [] : [c_List_Oconcat(_1808491, _1808493) = c_List_Oconcat(_1808491, _1808495), -(_1808493 = _1808495)], (51003 ^ _780461) ^ [] : [_1808493 = _1808495, -(c_List_Oconcat(_1808491, _1808493) = c_List_Oconcat(_1808491, _1808495))]]], (51009 ^ _780461) ^ [_1809218, _1809220, _1809222, _1809224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1809218), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1809220)), _1809222))), -(hAPP(c_List_Orev(_1809220), hAPP(hAPP(c_List_Olist__update(_1809220, _1809222), _1809218), _1809224)) = hAPP(hAPP(c_List_Olist__update(_1809220, hAPP(c_List_Orev(_1809220), _1809222)), 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(_1809220)), _1809222)), _1809218)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1809224))], (51015 ^ _780461) ^ [_1809417, _1809419, _1809421, _1809423] : [-(c_List_Oconcat(_1809417, hAPP(hAPP(c_List_Omap(_1809419, tc_List_Olist(_1809417)), hAPP(hAPP(c_COMBC(_1809419, tc_List_Olist(_1809417), tc_List_Olist(_1809417)), hAPP(hAPP(c_COMBB(_1809417, tc_fun(tc_List_Olist(_1809417), tc_List_Olist(_1809417)), _1809419), c_List_Olist_OCons(_1809417)), _1809421)), c_List_Olist_ONil(_1809417))), _1809423)) = hAPP(hAPP(c_List_Omap(_1809419, _1809417), _1809421), _1809423))], (51017 ^ _780461) ^ [_1809504, _1809506, _1809508, _1809510] : [class_Orderings_Olinorder(_1809504), c_List_Olinorder__class_Osorted(_1809504, hAPP(c_List_Orev(_1809504), _1809506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1809508), _1809510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1809510), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1809504)), _1809506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1809504), hAPP(hAPP(c_List_Onth(_1809504), _1809506), _1809510)), hAPP(hAPP(c_List_Onth(_1809504), _1809506), _1809508))))], (51035 ^ _780461) ^ [_1809841, _1809843, _1809845] : [class_Orderings_Olinorder(_1809841), c_List_Olinorder__class_Osorted(_1809841, hAPP(c_List_Orev(_1809841), _1809843)), 51042 ^ _780461 : [(51043 ^ _780461) ^ [] : [_1809843 = c_List_Olist_ONil(_1809841), -(c_List_Ofoldr(_1809841, _1809841, c_Orderings_Oord__class_Omax(_1809841), _1809843, _1809845) = _1809845)], (51049 ^ _780461) ^ [] : [-(_1809843 = c_List_Olist_ONil(_1809841)), -(c_List_Ofoldr(_1809841, _1809841, c_Orderings_Oord__class_Omax(_1809841), _1809843, _1809845) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1809841), hAPP(hAPP(c_List_Onth(_1809841), _1809843), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1809845))]]], (51055 ^ _780461) ^ [_1810155, _1810157, _1810159, _1810161] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1810155)), c_List_Otranspose__rel(_1810155)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1810155)), hAPP(hAPP(c_List_Olist_OCons(_1810155), _1810157), _1810159)), _1810161))), -(c_List_Otranspose(_1810155, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1810155)), hAPP(hAPP(c_List_Olist_OCons(_1810155), _1810157), _1810159)), _1810161)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1810155)), hAPP(hAPP(c_List_Olist_OCons(_1810155), _1810157), c_List_Oconcat(_1810155, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1810155), tc_List_Olist(_1810155)), c_List_Olist_Olist__case(tc_List_Olist(_1810155), _1810155, c_List_Olist_ONil(_1810155), hAPP(hAPP(c_COMBB(tc_List_Olist(_1810155), tc_fun(tc_List_Olist(_1810155), tc_List_Olist(_1810155)), _1810155), c_COMBK(tc_List_Olist(_1810155), tc_List_Olist(_1810155))), hAPP(hAPP(c_COMBC(_1810155, tc_List_Olist(_1810155), tc_List_Olist(_1810155)), c_List_Olist_OCons(_1810155)), c_List_Olist_ONil(_1810155))))), _1810161)))), c_List_Otranspose(_1810155, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1810155)), _1810159), c_List_Oconcat(tc_List_Olist(_1810155), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1810155), tc_List_Olist(tc_List_Olist(_1810155))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1810155)), _1810155, c_List_Olist_ONil(tc_List_Olist(_1810155)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1810155), tc_List_Olist(tc_List_Olist(_1810155))), _1810155), hAPP(hAPP(c_COMBC(tc_List_Olist(_1810155), tc_List_Olist(tc_List_Olist(_1810155)), tc_List_Olist(tc_List_Olist(_1810155))), c_List_Olist_OCons(tc_List_Olist(_1810155))), c_List_Olist_ONil(tc_List_Olist(_1810155)))))), _1810161))))))], (51061 ^ _780461) ^ [_1810688, _1810690] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1810688), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1810688))), _1810690))), 51064 ^ _780461 : [(51065 ^ _780461) ^ [] : [_1810690 = c_List_Olist_ONil(tc_List_Olist(_1810688)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1810688))), c_List_Otranspose(_1810688, _1810690)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51071 ^ _780461) ^ [] : [-(_1810690 = c_List_Olist_ONil(tc_List_Olist(_1810688))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1810688))), c_List_Otranspose(_1810688, _1810690)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1810688)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1810688)), _1810690), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (51077 ^ _780461) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (51079 ^ _780461) ^ [_1811016, _1811018] : [class_Lattices_Obounded__lattice(_1811016), -(class_Lattices_Obounded__lattice(tc_fun(_1811018, _1811016)))], (51085 ^ _780461) ^ [_1811095, _1811097] : [class_Complete__Lattice_Ocomplete__lattice(_1811095), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1811097, _1811095)))], (51091 ^ _780461) ^ [_1811174, _1811176] : [class_Lattices_Obounded__lattice(_1811174), -(class_Lattices_Obounded__lattice__top(tc_fun(_1811176, _1811174)))], (51097 ^ _780461) ^ [_1811253, _1811255] : [class_Lattices_Obounded__lattice(_1811253), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1811255, _1811253)))], (51103 ^ _780461) ^ [_1811332, _1811334] : [class_Lattices_Olattice(_1811332), -(class_Lattices_Osemilattice__sup(tc_fun(_1811334, _1811332)))], (51109 ^ _780461) ^ [_1811411, _1811413] : [class_Lattices_Olattice(_1811411), -(class_Lattices_Osemilattice__inf(tc_fun(_1811413, _1811411)))], (51115 ^ _780461) ^ [_1811490, _1811492] : [class_Lattices_Odistrib__lattice(_1811490), -(class_Lattices_Odistrib__lattice(tc_fun(_1811492, _1811490)))], (51121 ^ _780461) ^ [_1811569, _1811571] : [class_Lattices_Oboolean__algebra(_1811569), -(class_Lattices_Oboolean__algebra(tc_fun(_1811571, _1811569)))], (51127 ^ _780461) ^ [_1811648, _1811650] : [class_Orderings_Opreorder(_1811648), -(class_Orderings_Opreorder(tc_fun(_1811650, _1811648)))], (51133 ^ _780461) ^ [_1811727, _1811729] : [-(class_Finite__Set_Ofinite(tc_fun(_1811727, _1811729))), class_Finite__Set_Ofinite(_1811727), class_Finite__Set_Ofinite(_1811729)], (51143 ^ _780461) ^ [_1811856, _1811858] : [class_Lattices_Olattice(_1811856), -(class_Lattices_Olattice(tc_fun(_1811858, _1811856)))], (51149 ^ _780461) ^ [_1811935, _1811937] : [class_Orderings_Oorder(_1811935), -(class_Orderings_Oorder(tc_fun(_1811937, _1811935)))], (51155 ^ _780461) ^ [_1812014, _1812016] : [class_Orderings_Otop(_1812014), -(class_Orderings_Otop(tc_fun(_1812016, _1812014)))], (51161 ^ _780461) ^ [_1812093, _1812095] : [class_Orderings_Oord(_1812093), -(class_Orderings_Oord(tc_fun(_1812095, _1812093)))], (51167 ^ _780461) ^ [_1812172, _1812174] : [class_Orderings_Obot(_1812172), -(class_Orderings_Obot(tc_fun(_1812174, _1812172)))], (51173 ^ _780461) ^ [_1812251, _1812253] : [class_Groups_Ouminus(_1812251), -(class_Groups_Ouminus(tc_fun(_1812253, _1812251)))], (51179 ^ _780461) ^ [_1812330, _1812332] : [class_Groups_Ominus(_1812330), -(class_Groups_Ominus(tc_fun(_1812332, _1812330)))], (51185 ^ _780461) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (51187 ^ _780461) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (51189 ^ _780461) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (51191 ^ _780461) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (51193 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (51195 ^ _780461) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (51197 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (51199 ^ _780461) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (51201 ^ _780461) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (51203 ^ _780461) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (51205 ^ _780461) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (51207 ^ _780461) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (51209 ^ _780461) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (51211 ^ _780461) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (51213 ^ _780461) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (51215 ^ _780461) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (51217 ^ _780461) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (51219 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (51221 ^ _780461) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (51223 ^ _780461) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (51225 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (51227 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (51229 ^ _780461) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (51231 ^ _780461) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (51233 ^ _780461) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (51235 ^ _780461) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (51237 ^ _780461) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (51239 ^ _780461) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (51241 ^ _780461) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (51243 ^ _780461) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (51245 ^ _780461) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (51247 ^ _780461) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (51249 ^ _780461) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (51251 ^ _780461) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (51253 ^ _780461) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (51255 ^ _780461) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (51257 ^ _780461) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (51259 ^ _780461) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (51261 ^ _780461) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (51263 ^ _780461) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (51265 ^ _780461) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (51267 ^ _780461) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (51269 ^ _780461) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (51271 ^ _780461) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (51273 ^ _780461) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (51275 ^ _780461) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (51277 ^ _780461) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (51279 ^ _780461) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (51281 ^ _780461) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (51283 ^ _780461) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (51285 ^ _780461) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (51287 ^ _780461) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (51289 ^ _780461) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (51291 ^ _780461) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (51293 ^ _780461) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (51295 ^ _780461) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (51297 ^ _780461) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (51299 ^ _780461) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (51301 ^ _780461) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (51303 ^ _780461) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (51305 ^ _780461) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (51307 ^ _780461) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (51309 ^ _780461) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (51311 ^ _780461) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (51313 ^ _780461) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (51315 ^ _780461) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (51317 ^ _780461) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (51319 ^ _780461) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (51321 ^ _780461) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (51323 ^ _780461) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (51325 ^ _780461) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (51327 ^ _780461) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (51329 ^ _780461) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (51331 ^ _780461) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (51333 ^ _780461) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (51335 ^ _780461) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (51337 ^ _780461) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (51339 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (51341 ^ _780461) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (51343 ^ _780461) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (51345 ^ _780461) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (51347 ^ _780461) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (51349 ^ _780461) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (51351 ^ _780461) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (51353 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (51355 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (51357 ^ _780461) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (51359 ^ _780461) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (51361 ^ _780461) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (51363 ^ _780461) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (51365 ^ _780461) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (51367 ^ _780461) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (51369 ^ _780461) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (51371 ^ _780461) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (51373 ^ _780461) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (51375 ^ _780461) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (51377 ^ _780461) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (51379 ^ _780461) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (51381 ^ _780461) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (51383 ^ _780461) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (51385 ^ _780461) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (51387 ^ _780461) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (51389 ^ _780461) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (51391 ^ _780461) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (51393 ^ _780461) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (51395 ^ _780461) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (51397 ^ _780461) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (51399 ^ _780461) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (51401 ^ _780461) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (51403 ^ _780461) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (51405 ^ _780461) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (51407 ^ _780461) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (51409 ^ _780461) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (51411 ^ _780461) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (51413 ^ _780461) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (51415 ^ _780461) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (51417 ^ _780461) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (51419 ^ _780461) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (51421 ^ _780461) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (51423 ^ _780461) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (51425 ^ _780461) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (51427 ^ _780461) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (51429 ^ _780461) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (51431 ^ _780461) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (51433 ^ _780461) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (51435 ^ _780461) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (51437 ^ _780461) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (51439 ^ _780461) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (51441 ^ _780461) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (51443 ^ _780461) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (51445 ^ _780461) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (51447 ^ _780461) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (51449 ^ _780461) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (51451 ^ _780461) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (51453 ^ _780461) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (51455 ^ _780461) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (51457 ^ _780461) ^ [_1814857, _1814859] : [-(class_Finite__Set_Ofinite(tc_sum(_1814857, _1814859))), class_Finite__Set_Ofinite(_1814857), class_Finite__Set_Ofinite(_1814859)], (51467 ^ _780461) ^ [_1814986] : [class_Finite__Set_Ofinite(_1814986), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1814986)))], (51473 ^ _780461) ^ [_1815061, _1815063] : [-(class_Finite__Set_Ofinite(tc_prod(_1815061, _1815063))), class_Finite__Set_Ofinite(_1815061), class_Finite__Set_Ofinite(_1815063)], (51483 ^ _780461) ^ [_1815190, _1815192] : [-(class_Smallcheck_Osmall(tc_prod(_1815190, _1815192))), class_Smallcheck_Osmall(_1815190), class_Smallcheck_Osmall(_1815192)], (51493 ^ _780461) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (51495 ^ _780461) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (51497 ^ _780461) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51499 ^ _780461) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (51501 ^ _780461) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (51503 ^ _780461) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51505 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (51507 ^ _780461) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51509 ^ _780461) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (51511 ^ _780461) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51513 ^ _780461) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (51515 ^ _780461) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (51517 ^ _780461) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51519 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (51521 ^ _780461) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (51523 ^ _780461) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (51525 ^ _780461) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (51527 ^ _780461) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51529 ^ _780461) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (51531 ^ _780461) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (51533 ^ _780461) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (51535 ^ _780461) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (51537 ^ _780461) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (51539 ^ _780461) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (51541 ^ _780461) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (51543 ^ _780461) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (51545 ^ _780461) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (51547 ^ _780461) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (51549 ^ _780461) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (51551 ^ _780461) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (51553 ^ _780461) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (51555 ^ _780461) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (51557 ^ _780461) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (51559 ^ _780461) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (51561 ^ _780461) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (51563 ^ _780461) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (51565 ^ _780461) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (51567 ^ _780461) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (51569 ^ _780461) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (51571 ^ _780461) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (51573 ^ _780461) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (51575 ^ _780461) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (51577 ^ _780461) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (51579 ^ _780461) ^ [_1816093, _1816095] : [-(hAPP(c_COMBI(_1816093), _1816095) = _1816095)], (51581 ^ _780461) ^ [_1816123, _1816125, _1816127, _1816129] : [-(hAPP(hAPP(c_COMBK(_1816123, _1816125), _1816127), _1816129) = _1816127)], (51583 ^ _780461) ^ [_1816161, _1816163, _1816165, _1816167, _1816169, _1816171] : [-(hAPP(hAPP(hAPP(c_COMBB(_1816161, _1816163, _1816165), _1816167), _1816169), _1816171) = hAPP(_1816167, hAPP(_1816169, _1816171)))], (51585 ^ _780461) ^ [_1816213, _1816215, _1816217, _1816219, _1816221, _1816223] : [-(hAPP(hAPP(hAPP(c_COMBC(_1816213, _1816215, _1816217), _1816219), _1816221), _1816223) = hAPP(hAPP(_1816219, _1816223), _1816221))], (51587 ^ _780461) ^ [_1816265, _1816267, _1816269, _1816271, _1816273, _1816275] : [-(hAPP(hAPP(hAPP(c_COMBS(_1816265, _1816267, _1816269), _1816271), _1816273), _1816275) = hAPP(hAPP(_1816271, _1816275), hAPP(_1816273, _1816275)))], (51589 ^ _780461) ^ [_1816320, _1816322] : [hBOOL(hAPP(hAPP(c_fequal, _1816320), _1816322)), -(_1816320 = _1816322)], (51595 ^ _780461) ^ [_1816409, _1816411] : [_1816409 = _1816411, -(hBOOL(hAPP(hAPP(c_fequal, _1816409), _1816411)))], (51601 ^ _780461) ^ [] : [hBOOL(c_fFalse)], (51603 ^ _780461) ^ [] : [-(hBOOL(c_fTrue))], (51605 ^ _780461) ^ [_1816540] : [hBOOL(hAPP(c_fNot, _1816540)), hBOOL(_1816540)], (51611 ^ _780461) ^ [_1816616] : [-(hBOOL(_1816616)), -(hBOOL(hAPP(c_fNot, _1816616)))], (51617 ^ _780461) ^ [_1816651, _1816653] : [hBOOL(_1816651), hBOOL(_1816653), -(hBOOL(hAPP(hAPP(c_fconj, _1816651), _1816653)))], (51627 ^ _780461) ^ [_1816790, _1816792] : [hBOOL(hAPP(hAPP(c_fconj, _1816790), _1816792)), -(hBOOL(_1816790))], (51633 ^ _780461) ^ [_1816877, _1816879] : [hBOOL(hAPP(hAPP(c_fconj, _1816877), _1816879)), -(hBOOL(_1816879))], (51639 ^ _780461) ^ [_1816964, _1816966] : [hBOOL(_1816964), -(hBOOL(hAPP(hAPP(c_fdisj, _1816964), _1816966)))], (51645 ^ _780461) ^ [_1817051, _1817053] : [hBOOL(_1817051), -(hBOOL(hAPP(hAPP(c_fdisj, _1817053), _1817051)))], (51651 ^ _780461) ^ [_1817138, _1817140] : [hBOOL(hAPP(hAPP(c_fdisj, _1817138), _1817140)), -(hBOOL(_1817138)), -(hBOOL(_1817140))], (51661 ^ _780461) ^ [_1817232, _1817234] : [-(hBOOL(_1817232)), -(hBOOL(hAPP(hAPP(c_fimplies, _1817232), _1817234)))], (51667 ^ _780461) ^ [_1817272, _1817274] : [hBOOL(_1817272), -(hBOOL(hAPP(hAPP(c_fimplies, _1817274), _1817272)))], (51683 ^ _780461) ^ [_1817494] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)), _1817494), v_G)), -(c_Hoare__Mirabelle_Otriple__valid(t_a, v_n, _1817494))], (51673 ^ _780461) ^ [_1817359, _1817361] : [hBOOL(hAPP(hAPP(c_fimplies, _1817359), _1817361)), hBOOL(_1817359), -(hBOOL(_1817361))]], input).
% 106.20/102.98  ncf('1',plain,[v_P(51688 ^ [], 51692 ^ [])],start(51696 ^ 0)).
% 106.20/102.98  ncf('1.1',plain,[-(v_P(51688 ^ [], 51692 ^ [])), v_P(51688 ^ [], 51689 ^ []), 51688 ^ [] = 51688 ^ [], 51689 ^ [] = 51692 ^ []],extension(1832 ^ 1,bind([[_806250, _806252, _806254, _806256], [51692 ^ [], 51689 ^ [], 51688 ^ [], 51688 ^ []]]))).
% 106.20/102.98  ncf('1.1.1',plain,[-(v_P(51688 ^ [], 51689 ^ []))],extension(51691 ^ 2)).
% 106.20/102.98  ncf('1.1.2',plain,[-(51688 ^ [] = 51688 ^ [])],extension(2 ^ 2,bind([[_780491], [51688 ^ []]]))).
% 106.20/102.98  ncf('1.1.3',plain,[-(51689 ^ [] = 51692 ^ []), 51692 ^ [] = 51689 ^ []],extension(4 ^ 2,bind([[_780514, _780516], [51689 ^ [], 51692 ^ []]]))).
% 106.20/102.98  ncf('1.1.3.1',plain,[-(51692 ^ [] = 51689 ^ []), c_Natural_Oevaln(c_Com_Ocom_OSKIP, 51689 ^ [], v_n, 51692 ^ [])],extension(5687 ^ 3,bind([[_871097, _871099, _871101], [51689 ^ [], v_n, 51692 ^ []]]))).
% 106.20/102.98  ncf('1.1.3.1.1',plain,[-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, 51689 ^ [], v_n, 51692 ^ []))],extension(51694 ^ 4)).
% 106.20/102.98  %-----------------------------------------------------
% 106.20/102.98  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------